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philosophy
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Two sorts of philosophical therapy Ordinary language philosophy, social criticism and the Frankfurt school
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Why is it said that the first generation of the Frankfurt School has practised a sort of a sort of ‘linguistic turn’ and ‘non-quietistic’ philosophical therapy？
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1.Freyenhagen on the 'Linguistic Turn' in Horkheimer and Adorno | Freyenhagen makes his claims regarding a 'linguistic turn' in FGFS in the context of the 'Classic Objection' to FGFS theory: Habermas's suggestion, that what Adorno and his generation were doing was 'self-undermining' because, 'by engaging in a (purportedly) totalizing critique of modern reason, it makes itself impossible. | For Freyenhagen, The Eclipse of Reason by Horkheimer refers to the eclipse of non-instrumental, 'objective' reason, which is supposed to be somehow a property of the world, by its 'subjective' double. The realm of 'objective reason' would be Horkheimer's term for things like facts about the human species – what determines, ultimately, what it would be for us to live well (or badly). Objection reason–or at any rate, certain of its claims – has been forgotten, and this has allowed the subjective reason of individual thinking subjects to run rampant – with increasingly disastrous results. Here is where the 'linguistic turn' comes in. | Freyenhagen opts to read Horkheimer's remarks about language and objective reason through the prism of the later Wittgenstein. Wittgenstein bears strong affinities with the Aristotelian Adorno and the FGFS linguistic turn. For Freyenhagen, the idea is that by reading Eclipse of Reason through Wittgenstein, we can arrive at a position whereby 'as inseparable from the human life form, language contains traces of "the structure of the reality" of this life form, and thus, of (at least part of) objective reason'.This is how the FGFS intend to accomplish their critique of (subjective) reason: by mining language, as a specifically human practice, for the fragments of objective, human rationality inevitably sedimented in it. | 2.Marcuse contra analytic philosophy | The general thrust of Marcuse's critique is that analytic philosophy is 'positive', where thought proper ought to be 'negative'. Marcuse believes that philosophy ought to be able to engage in the emancipatory critique of society and culture as it presently exists. Analytic philosophy, by contrast, seeks to purge thought of any of the resources that we need in order for this critique to take place. | According to Marcuse, analytic philosophy works against the real ends of philosophical thought in two related ways. The first is that it insists on sticking to the analysis of 'ordinary language'. This obsession with 'ordinary discourse' is 'the token of a false concreteness', and it mutilates life as lived rather than confining philosophical inquiry to the stuff of 'real life'. The second is its commitment to 'philosophy as therapy'which tends to a certain quietism that is distinctively Wittgensteinian. As Marcuse has it, by focussing their efforts on exorcising philosophical thought as such, analytic philosophy ends up 'creat[ing] more illusory problems than it has destroyed'. All 'therapeutic philosophy' amounts to, in the end, is a repression. | 3.In Marcuse's account, 'good' forms of ordinary language philosophy, and 'good' forms of philosophy as therapy | Marcuse implicitly distinguishes between "good" and "bad" forms of ordinary language philosophy, as well as between "good" and "bad" forms of philosophy understood as therapy. Marcuse indicates that he believes that language has some sort of rationality other than the public, surface-level one 'hidden' inside it. By analysing language, then, we can figure out some deep truth about the world in which it has been uttered, or written. The 'good' sort of ordinary language philosophy consists in the attempt to do just this. | For Marcuse, the patron saint of the 'good' sort of ordinary language philosophy is Karl Kraus, and what is important is that Kraus shows 'how an "internal" examination of speech and writing, of punctuation, even of typographical errors can reveal a whole moral or political system'. | What Kraus teaches us is that we can only properly understand 'ordinary' discourse, 'ordinary' life if we assume something like an 'extra-linguistic' perspective. Ordinary language philosophy therefore must reside in the realm of the political, of the moral – or at the very least the aesthetic. | Conclusion:'The real universe of ordinary language', Marcuse proclaims, 'is the struggle for existence'. The 'good' sort of ordinary language philosophy is able to show up, to cast judgement on. | 4. Philosophical therapy from the standpoint of redemption | Marcuse's identification of a way in which philosophy as therapy might be made to serve the interests of emancipatory critique: we ought to 'clarify' concepts by showing how their subjective meaning, how they appear from the perspective of 'subjective reason', fails to match up with how things 'objectively' are. | For Marcuse, such 'emancipatory' clarification 'may well fulfil a therapeutic function, and if philosophy would become therapeutic, it would really come into its own'. | Conclusion 1: Marcuse's criticisms of Wittgenstein's version of 'philosophical therapy', are really just directed at his choice of patient. The 'good' sort of philosophical therapy in fact aims at essentially the same thing as the 'bad' version did: it seeks to get reality in view. | The'philosophical therapy' that Adorno is pursuing in Minima Moralia is not only aimed at the clarification of what is 'really' there. Rather, it aims at just what Marcuse tells us the true therapist should: to clarify what is really there, in order to be able to grasp how it might otherwise be. | Conclusion 2: Adorno, and other FGFS thinkers, were, at least at times, engaged in the therapeutic analysis of 'ordinary' language and experience, clarifying the true meaning and significance of our everyday experience of the world in light of some 'objective reason' that is itself linguistic in nature, grounded in some notion of the human species analogous to that which Wittgenstein names with the idea of the human 'form of life'.
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1.Does the answer involve Fabian Freyenhagen’s interpretation of Horkheimer’s views through the lens of Wittgenstein? | 2.Does the answer include Fabian Freyenhagen’s view that the first generation of the Frankfurt School should be understood as part of the linguistic turn? | 3.Does the answer include Herbert Marcuse’s critique of analytic philosophy? | 4.Does the answer include Herbert Marcuse’s view on the ‘good’ forms of ordinary language philosophy and ‘good’ forms of philosophy understood as therapy? | 5.Does the answer include the comments of Karl Kraus by Benjamin, Adorno, and Marcuse? | 6.Does the answer include Marcuse’s view on how “philosophy as therapy” can be made to serve the interests of emancipatory critique? | 7.Does the answer include the view that the first generation of the Frankfurt School have practised a form of ‘non-quietistic’ philosophical therapy?
| 7
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1.In Fabian Freyenhagen 2023 study, he argues that there is a sort of ‘linguistic turn’ in First-Generation Frankfurt School, and here comes the affinities between the FGFS, and later Wittgenstein. But Fabian Freyenhagen does not consider the third major theorist associated with First-Generation Frankfurt School: Herbert Marcuse. 2.Tom Whyman argues that it is Herbert Marcuse’s attack on the analytic tradition in fact points the way forward – to seeing how both the analysis of ‘ordinary language’, and the associated ideal of ‘philosophical therapy’, can in fact be directed towards the emancipatory purpose insisted on by the Frankfurt School. Marcuse’s models of ‘good’ ordinary language philosophy and philosophical therapy can be used to illuminate what Adorno was doing in Minima Moralia. The overall effect is both to deepen, and to reinforce, what Freyenhagen claims about the FGFS ‘linguistic turn’.
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1.linguistic turn:a major shift in philosophy and the humanities during the 20th century, in which language became the central focus of analysis for understanding human thought, knowledge, and social life.Originated with philosophers such as Ludwig Wittgenstein, Gottlob Frege, and Ferdinand de Saussure.2.ordinary language philosophy:A school of thought in 20th-century analytic philosophy that holds that many traditional philosophical problems arise from misunderstandings of the ordinary use of language, and that close attention to how words are used in everyday contexts can clarify or eliminate these problems.Developed primarily by Ludwig Wittgenstein (later work), J.L. Austin, and Gilbert Ryle.3.quietistic philosophical therapy:A form of philosophical approach that aims not to produce new theories or systems, but to dissolve philosophical problems by clarifying the misuse of language and concepts—ultimately leading to a cessation of philosophical inquiry rather than its continuation.Rooted in Wittgenstein’s later work.4.non-quietistic’ philosophical therapy:A form of philosophical practice that, while still seeing philosophy as therapeutic—focused on clarifying conceptual or linguistic confusion—does not aim to bring philosophical inquiry to an end, but rather sees it as a continuous, critical, and active process.Inspired by Wittgenstein’s therapeutic methods, but diverges from quietism by rejecting the idea that philosophy should end in silence or rest.
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1.Elaborating on, and reinforcing, Freyenhagen’s claim that there is a fundamental affinity between FGFS and later Wittgenstein, and the FGFS through can be read through Wittgenstein. | 2.Attributing to the First-Generation Frankfurt School a method analogous to that of the later Wittgenstein, as well as the likes of Ryle and Austin, to claim the linguistic turn of FGFS. | 3.Reviewing the major theorist associated with FGFS, Marcuse’s criticisms of Wittgenstein and other analytic philosophers, and lauding of Kraus, to claim that the first generation of the Frankfurt School has practised a sort ofnon-quietistic’ philosophical therapy.
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2
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philosophy
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Once more, without feeling
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Why both welfare subjectivity and autonomy can confer moral status, and what's the relationship between them?
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1.Point out the key issue | Are there metaphysically and/or nomologically possible beings who fall outside the scope of the morality of humanity and are protected only by the morality of respect – individuals whose autonomy merits respect but who are not welfare subjects? If so, what does this imply about the relationship between moral standing and consciousness? | 2.The collection of conditions that to be jointly sufficient for an agent to be autonomous. | 2.1 What is the conception of 'autonomy'? | The term 'autonomy' be used here to denote a psychological capacity for self-government in virtue of which an individual can be credited as the author of her own thoughts and actions. | 2.2 What conditions would suffice to make the individual, like “Artemis”, autonomous? | First, she is in a position to determine her behaviour based on rational reflection. Rational reflection involves forming normative and/or evaluative judgements that can guide behaviour. Second, an autonomous individual may be required to be substantively rational to the point of being at least moderately reasons-responsive. Third, autonomy is a property that does not supervene on an individual's current state of mind and instead requires the absence of certain forms of manipulation in her past. Artemis has the right kind of history. | 3.Being a welfare subject is not necessary to satisfy those conditions | 3.1 A capacity for affective states is necessary for welfare subjectivity | (1) What is the conception of 'affective state' | Affective states are a class of psychological states of which emotions are the paradigm instance. Other commonly recognized affective states include moods and valent bodily sensations, like itches and pains. Affective states are defined at least in part by their degree of positive or negative valence and their constituent level of arousal. | (2) A very wide range of theories of welfare tell us affective states are necessary for the ability to accrue welfare goods | The hedonism,happiness, desire-fulfilment theory,Value-fulfilment theories, objective list theories all support that a capacity for affective states is necessary for the ability to accrue welfare goods. | (3)The general reason why a theory of welfare ought to impose a capacity for affective experience as a necessary condition for accruing welfare goods | There is a popular idea that what is good for someone has got to resonate with them and cannot simply leave them cold. | (4)Opposing Dorsey's denial that "valuing" possesses an essential affective dimension. | In Dorsey's example of Sant valuing living in a small town, Stan's belief about the prudential value for him of small-town living is simply in error. Small-town life just does not resonate with him. | Conclusion: A capacity for affective states is necessary for accruing welfare goods (and bads). | 3.2 A capacity for affective states is unnecessary for autonomy | (1)The hypothesis that autonomous agents need not have affective states ought to be acceptable in principle to actual Humeans | Humean theory of motivation might reject that the conditions sufficient to make a person autonomous do not entail a capacity for affective states: Humeans believe that any motivating reason consists of a desire and an appropriately related means-end belief. Not every kind of state we call a 'desire' can serve as a motivating reason when paired with a corresponding means-end belief. | We can render the hypothesis that some possible motivating reasons have evaluative beliefs as constituents consistent with the core of the Humean theory of motivation via the claim that it is possible for one and the same token mental state to be both a desire and an evaluative belief, and so to play the role of a desire in constituting some possible agent's motivating reason. | Conclusion: The hypothesis that autonomous agents need not have affective states ought to be acceptable in principle to actual Humeans. | (2)The hypothesis that autonomous agents need not have affective states is not incompatible with non-cognitivist and purely cognitivist views. | For non-cognitivism, normative or evaluative judgements are not robustly representational states. When it comes to giving a positive characterization of normative or evaluative judgements, it may be thought that non-cognitivists are committed to analysing them as affective states. But “non-cognitive” need not mean “affective”. | According to pure cognitivism, emotions just are normative and/or evaluative judgements. So it may be thought to follow from pure cognitivism that Artemis must be able to exhibit emotions, since emotions are nothing over and above normative or evaluative judgements of a certain kind. But pure cognitivism is not the view that all normative or evaluative judgements are emotions. | Conclusion: Philosophical positions such as the Humean theory of motivation, non-cognitivism, and pure cognitivism might lead one to reject the premise that autonomous agents need not have affective states. However, such rejections are misguided. | 3.3 The objective welfare goods cannot refute the hypothesis that a capacity for affective states is necessary for accruing welfare goods (and bads). | (1) Three putative welfare goods: nature fulfilment, knowledge and autonomy. | (2) nature fulfilment means the development and exercise of those capacities central to an individual's nature. But not every property that serves to characterize an individual's essence is a plausible candidate for the kind of property whose full development is a welfare good. | (3) knowledge. Knowledge requires belief. | (4) autonomy. Some authors who assert that autonomy is a welfare good seem to have in mind a different conception of autonomy – one involving a suitably high degree of independence of mind, for example. | Conclusion: Three putative welfare goods cannot refute the hypothesis that a capacity for affective states is necessary for accruing welfare goods (and bads). | | Conclusion: A capacity for affective states is necessary for welfare subjectivity. A capacity for affective states is unnecessary for autonomy. | | 4.Moral Standing Without Welfare Subjectivity | 4.1 The Argument from Humanity | At least some of the obligations we owe to our fellow human beings do not seem to be grounded in concern for their welfare. Instead, they seem to be grounded in respect for their autonomy and their status as separate, self-governing agents with their own lives to lead. | 4.2 The Argument from Vulcanity | Chalmers' poses about the ethics of killing Vulcans: Chalmers appeals to the possibility of Vulcans in arguing against the view that affective consciousness or sentience is necessary for moral standing. | Vulcans are autonomous beings who are not welfare subjects, the intuition that killing Vulcans is wrong suggests that welfare subjectivity is also unnecessary for someone's autonomy to merit respect. | | Conclusion: Welfare subjectivity is also unnecessary for someone's autonomy to merit respect. | | 5.The relationship between autonomy and phenomenal consciousness | 5.1 Autonomy without consciousness | The view that autonomy confers moral standing only in the presence of consciousness resembles a form of prejudice against the unconscious. | 5.2 Appealing to Reductive Theories of Consciousness | A posteriori physicalism, the view that the mental reduces without remainder to the physical based on identity statements that are not knowable a priori, may suggest a necessary connection between autonomy and phenomenal consciousness. | global workspace theories and higher order theories are most likely to vindicate this approach, but are both hardly immune to doubt. | The overall approach — namely, accepting a posteriori physicalism — is itself open to doubt. | 5.3 Linking Consciousness and Autonomy Without Reductionism | An argument that links consciousness and rationality may provide a way to link consciousness and autonomy without presupposing a reductive theory of consciousness. Multiple arguments for that claim can be made. | A bottom-up approach that directly interrogates the different sources of knowledge and their relationship to phenomenal consciousness may also link consciousness and autonomy without reductionism. | The conclusion that justified perceptual belief requires phenomenal consciousness in and of itself gets us a big part of the way to the conclusion that all autonomous agents must exhibit phenomenal consciousness. | Conclusion: There is a way of linking consciousness and autonomy that doesn't presuppose a reductive theory of consciousness. | | Conclusion: Autonomy entails phenomenal consciousness. | | 6.Conclusion | Conclusion1: Both welfare subjectivity and autonomy are able to confer moral status, and that autonomy does not entail welfare subjectivity. | Conclusion2: Autonomy entails phenomenal consciousness.2
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1.Does the answer discuss what conditions would suffice to make the individual autonomous? | 2.Does the answer include the view that a capacity for affective states is necessary for welfare subjectivity? | 3.Does the answer include the view that a capacity for affective states is unnecessary for autonomy? | 4.Does the answer discuss the relationship between autonomy and phenomenal consciousness? | 5.Does the answer include the view that autonomy entails phenomenal consciousness?
| 5
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1. there is a debate about whether the capacity for phenomenal consciousness is necessary for having moral understanding. 2.there is a debate about whether being a welfare subject is sufficient and necessary for moral standing. 3. The distinction between two dimensions of morality, the morality of respect and the morality of humanity, calls for the reinterpretation the relationship between moral standing and consciousness. |
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1.moral standing/moral status:The status of an entity that makes it morally considerable, meaning its interests or well-being must be taken into account in moral decision-making.An entity has moral standing if and only if it is the kind of being to whom moral obligations can be owed, or whose interests make a moral difference in how others ought to act.2.welfare subjectivity:the capacity of an entity to have a welfare—that is, to be the subject of experiences, conditions, or states that can affect its well-being positively or negatively.3.autonomy:A psychological capacity for self-government in virtue of which an individual can be credited as the author of her own thoughts and actions, but which is vulnerable (at least in beings like us) to subversion by internal impediments like addiction, mania, and the like.4.phenomenal consciousness:The property of mental states that have qualitative, experiential character—often described as “what it is like” to undergo them.5.affective states:a class of psychological states of which emotions are the paradigm instance. Other commonly recognized affective states include moods and valent bodily sensations, like itches and pains. I assume that affective states are defined at least in part by their degree of positive or negative valence and their constituent level of arousal | .
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1.By pointing out that a very wide range of theories of welfare all indicate that affective states are necessary for the ability to accrue welfare goods, and challenging the objective welfare goods that have no necessary connection with affect, to claim that a capacity for affect is necessary for accruing welfare goods.2. Refutes the view that a capacity to be benefited or harmed is necessary for moral standing by presenting an argument by analogy based on widely shared assumptions about what we owe to other human beings and a more direct argument that appeals to intuitions about the ethics of killing agents like Artemis. 3.dvocats that there is some necessary connection between phenomenal consciousness and autonomy, by reviewing global workspace theories and higher-order theories. | |
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3
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philosophy
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Patchwork ethnography
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How patchwork ethnography, as a methodology, enables ethnographers conduct fieldwork amid intersecting personal and professional responsibilities, and unlocks anthropology’s potential to further expand what theory means and who can be considered a theorist?
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Patchwork ethnography | 1.Patchwork ethnography | Background: Researchers today face multiple demands on their time, demanding a rethinking of fieldwork as a process that entails spending a year or longer in a faraway place. | Patchwork enthnography ia s solution: Patchwork enthnography calls for a "seam-full" engagement with knowledge production, that is, an engagement that foregrounds the seams in our work, the moves of contextualization/decontextualization, the indeterminacies between "data" and daily life, the movement between field site(s) and home, and the various editorial decisions ethnographers make as they refine their stories. | 2.Patchwork ethnography builds on a tradition in anthropology that has persistently questioned the discipline's truisms. | Patchwork ethnography challenges assumptions about the fixity of "the field" ; separations between "field" and "home"; the difficult negotiations of the anthropologist as insider/outsider; the gendered (masculinist) assumptions of the always available and up-for-anything fieldworker; and the presumption that the ethnographer can or even should be a detached observer. | Patchwork ethnography upends another truism of anthropological research to highlight that some of the justifications for our research design might be based not on the research topic or subjects, but on the personal circumstances of intersecting responsibilities and choices, as well as on the structural conditions of academic labor. | Danilyn Rutherford pointed that if we distinguish "objects of observation" (the field site) from "objects of study" (the research questions), researchers might be able to redesign their fieldwork around the same world phenomenon but in a different, more accessible locale under the pandemic. | Some patchwork ethnographers question the separation of "field" from "home" by positing that switching from one to the other might be a difference in attention and not physical location. | 3.Feminist and queer methodologies support patchwork enthnography | Feminist and queer methodologies question why ethnographic research and "domestic labor" are separated in actual fieldwork experiences. | Sara Ahmed points to the misguided assumption that knowledge production happens demarcated from personal lives and domestic spheres. | Chika and Gökçe's parallel experiences of the erasures of the home-field continuum allow us to perceive how difficult it was to maintain that home and field division, yet how unthinkable it had been for us to write or theorize in ways that brought the two together. | Feminist scholarship reveals the closet the fact that researchers adapt fieldwork methods around the responsibilities, commitments, and expectations that come from who we are in the world. | Conclusion: Feminist and queer methodologies support patchwork enthnography, and patchwork enthnography is a call for being honest about how the personal and the professional, the "domestic" and the academic, intersect and inform each other in all knowledge production. | 4.The fact that the enthnographer is a relational subject supports patchwork enthnography | Anthropologist' scholarly endeavors are always a product of relations and dialogues with others. | Indigenous anthropologists have shown, the impossibility of separating personal and professional relations enables radical reformulations of anthropological theorizing, wherein Indigenous theories provincialize Euro-American thought. | Conclusion: Embracing the entanglements of personal and professional relations that come from who we are in the world can profoundly change what anthropological theory means, and this aligns with the call for patchwork ethnography. | 5.The structural constraints in the neoliberal university calls for patchwork enthnography | Anthropologists and other researchers have begun to highlight the hardships of current academic labor conditions. First, scholars have problematized the neoliberalization of universities in the US, Europe, and elsewhere, in which the precaritization of academic work, the quantitative monitoring of research performance, and rising overwork under austerity measures are pushing researchers into impossible situations, rendering long stretches of fieldwork unfeasible. Second, anthropologists have recently begun to publish accounts of fieldwork that recognize the embodied aspects of ethnography, which often excludes many people from practicing it. Third, researchers have illuminated how caring responsibilities and family-career balance intersect with fieldwork and professional commitments. | Conclusion: Less-than-ideal labor conditions call for the patchwork ethnography. | | Conclusion: It is necessary to develop the concept of "patchwork ethnography" to emphasize how ethnographers carry out fieldwork while managing overlapping personal and professional responsibilities.
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1. Does the answer include perspectives discussing patchwork ethnography? | 2. Does the answer include the perspective that patchwork ethnography builds on a tradition in anthropology that has persistently questioned the discipline's truisms? | 3. Does the answer include the perspective that feminist and queer methodologies challenge the separation of domestic labor and fieldwork? | 4. Does the answer include the perspective that patchwork ethnography is a result of less-than-ideal labor conditions?
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1.Neoliberal university labor conditions, expectations of work-life balance, environmental concerns, and feminist and decolonial critiques have demanded a rethinking of fieldwork as a process that entails spending a year or longer in a faraway place. | 2.Many ethnographers have already been recombining “home” and “field” for a long time. But these innovations have remained black boxed. | 3.Anthropologists have challenged various things, including assumptions about the fixity of “the field”;separations between “field” and “home”; the difficult negotiations of the anthropologist as insider/outsider ; the gendered (masculinist) assumptions of the always available and up-foranything fieldworker ; and the presumption that the ethnographer can or even should be a detached observer. | 4.Critical conversations on methodology have interrogated the assumption that long-term continuous fieldwork is necessary or appropriate for all projects.
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1.Patchwork ethnography: A methodological approach in anthropology and related disciplines that adapts traditional ethnographic fieldwork to the realities of contemporary academic and personal life. It involves conducting short-term, multi-sited, or intermittent field visits that are "patched together" over time, rather than relying on a single, extended period of immersion in the field. 2. Feminist and queer methodologies: Research approaches that critically engage with issues of gender, sexuality, and power to challenge dominant norms and inequalities in knowledge production. 3.Field methdology:The systematic approaches and techniques used by researchers—especially in disciplines like anthropology, sociology, and human geography—to collect data through direct engagement with people, places, and social practices in their natural settings.
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1.Review the tradition in anthropology that has persistently questioned the discipline’s truisms, and interrogate the assumption that long-term continuous fieldwork is necessary or appropriate for all projects. 2.Questions the assumption of a separation between ethnographic research and 'domestic labor' by drawing on feminist and queer methodologies. 3.Advocates to embrace the entanglements of personal and professional relations that come from who we are in the world by emphasizing enthnographer is a relational subject, and its scholarly endeavors a product of relations and dialogues with others.
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4
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philosophy
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Pig-feast democracy | Direct local elections and the making of a plural political order in West Papua
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How the convergence of pig feasts and electoral politics constitutes a new institutional framework and a condition of plural political order in Indonesia-occupied West Papua?
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1.The historical overview and political context of West Papua's plural political order | Indonesian central government devised a new policy forthe region, granting special autonomy status to West Papuain 2001. | The elections are the only democratic platform that the central gov-ernment recognizes: First, the special autonomy on West Papua excluded armed groups and civil society groups, so it lacks political legitimacy among much of Papuan society. Second, the specialautonomy laws do not establish local political parties. Third, the special autonomy status does not entail recognition of Papuans'fundamental rights, such as freedom of speech and assembly,or their rights to self-determination. | Special autonomy and direct local elections has shifted the locus of political strength from thecoast to the Central Highlands, where 60 percent of Indigenous Papuans live. The highland politicians are well situated to reap the benefits of thedemocratic system, thanks to their demographic and organizational advantages. | Lukas Enembe rose as one of the most emblematic models ofthe new type of Papuan leadership. The most decisive factor in his rise lies in his skillin accumulating resources and mobilizing a new ideology of Papuan power through, among other ways, pig feasts. | 2.The birth of new pig feasts | Several characteristics of the old pig feasts persist, yet their transformationis marked most explicitly by several phenomena. First, as in other Melanesian societies, the traditional pig feasts, withtheir associated sacred character, are not held as often or atthe same scale. Second, the decline of pig feasts is followed by therise of bakar batu or barapen, which translated by the author as a "new pigfeast." A clear distinction is made between the two, especiallyregarding their sacred character and location within the sphere of ceremonial exchange. | 3.Pig feasts during the elections | The resurgence of pig feasts as a distinctive Papuan mode of political ordering began in 2013, when Lukas Enembe and Klemen Tinal ran with the support of a coalition of five political parties. | The regulatory framework creates a significant barrier for independent candidates and forces all candidates to run with political parties' machines instead. Because the special autonomy law has yet to pass a provision for local political parties, Papuan candidates are forced to approach national or Jakarta-based political parties and request their support. | Papuan candidates deal with this system in two ways. First, money politics. Second, during the gubernatorial elections, the candidates organize pig feasts for their voters, especially the Papuan ones. The decision to contribute pigs or cash to certain candidates is determined, for instance, by "whether the candidates or their families havehelped paying bride wealth, fines, or compensations in thepast, or whether they helped mediate a conflict, that sort ofthings." | The campaign teams of candidate will undertake an expansive ceremonial cycle that takes place within and beyond one's related partners, and that determines one's victory. And this achievement is usually shown in the second phase of the cycle, which takes public form as the feast itself. | The organization of pig feasts is an indicator whether the candidate can mobilize constituents to his or her favor. | Conclusion: Electoral politics has become a privileged site for the reemergence of pig feasts. Conversely, through their role in electoral politics, pig feasts in West Papua have become a politically charged site of competitive exchange. Highlanders have also treated elections as a war and that pig feasts help build alliances, especially amongthe Indigenous groups. | 4.Electoral democracy in a plural political order | In the West Papuan case, both electoral politics and pig feasts operate as a procedure to mobilize power—although with different degrees of institutionalization and formalization. | Two kinds of political order: Scholars of politics have theorized political order as a stateof being. It is a quality of stability and lack of violence in a community's political life. One strand argues "order is afunction of state capacity and their formal institutions" . The nonstatist approach to order, on the other hand, considers community capacity and informal institutions in maintaining order. | The conception of plural political order contends that various forms of political institutionalization and values can coexist, and that liberal democracy is not the pinnacle ofpolitical order. | Political order in West Papua is a kind of plural political order. It reflects different bases of democratic politics. On the one hand, electoral politics reflects the moral and political claim of the modern nation-state and its postauthoritarian ideology. On the other hand, the pig feasts function as anonstate form of political ordering, one that draws its authority from the notion of tradition. Both are an experiment in exercising political authorities enabled by the democratic transition. | | Conclusion: Pigfeasts are used to incorporate foreign elements, either moneyor the electoral system, into the indigenous cycle of ceremonial exchange. As a political form, pig feasts and other Papuan traditions have becomean important political order that competes for legitimacy in thefractured landscape of state-citizen relations in the region.
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1. Does the answer discuss the special autonomy status of West Papua? | 2. Does the answer discuss the emergence of new pig feasts in West Papua? | 3. Does the answer include content about the operation of pig feasts during elections in West Papua? | 4. Does the answer include content about the plural political order in West Papua? | 5. Does the answer discuss West Papua’s electoral politics and pig feasts within the framework of the plural political order?
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1.Pig feasts reemerged in 2013 in West Papua as a distinctive means of Papuan political ordering. | 2.West Papua was granted special autonomy status by the Indonesian government in 2001 in response to longstanding Papuan demands for greater political self-determination. | 3.Three pillars of West Papua’s governance: (1) the Papuan People’s Assembly (Majelis Rakyat Papua, hereafter MRP), (2) the Papuan People Representative Board (Dewan Perwakilan Rakyat Papua, hereafter Parliament), and (3) the governor and vice governor. | 4.The autonomy policy in West Papua makes the electionsto be the only democratic platform that the central government recognizes. |
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1.pig feast: A ceremonial event in which pigs are slaughtered, cooked, and shared among a community to mark important social, cultural, or political occasions. Common in many Indigenous societies, especially in Melanesia and Papua, pig feasts function as systems of reciprocity, alliance-building, status display, and social cohesion, often reinforcing kinship and political relationships.2.plural political order: The multiple modes of understanding and organizing power that coexist under one social field. it entails different claims about the meaning, values, and procedures of democratic politics, even though they both rely on the notion of popular sovereignty. 3.Democracy: A system of government in which power is vested in the people, who exercise that power directly or through elected representatives. It is characterized by "free and fair elections", "majority rule with respect for minority rights", "the rule of law", and "protection of civil liberties" .4.direct local elections: A form of democratic electoral process in which residents of a specific locality (such as a district, municipality, or province) vote directly to elect their local government officials—such as mayors, governors, or regional legislators—rather than having them appointed by higher levels of government or indirectly chosen by elected representatives.
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1.Conducting fieldwork in the Central Highlands as well as in the coastal cities of Nabire (Central Papua Province) and Jayapura (Papua Province) to gather empirical data.2.Adopting the theoretical perspective of plural political orders, and moving beyond the analysis of existing institutional forms, with a focus on the possibility of constructing new institutional frameworks both within and beyond electoral politics, to explore the theoretical and empirical significance of democracy. | |
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5
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philosophy
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Moral Understanding Between You and Me
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Why shared moral understanding is important?
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1.give an account of what it takes for you and me to share moral understanding | 1.1 what it takes to have moral understanding | Understanding is a positive epistemic status that is graded along both objective and subjective dimensions. On the objective side of things, I understand something only if my conception of it is accurate. On the subjective side of things, I understand something only if I conceive of it in a way that makes sense to me. | You can know more than you understand. In the case of Immoral Debt, whereas Maya may understand why Madagascar’s external debt ought to have been abolished, Jared does not. His belief that the debt ought to have been abolished is not based in his own appreciation of the reasons that make it so. He doesn’t understand himself why that moral proposition is true. | Conclusion: Moral understanding is an epistemic achievement about moral matters. When you have moral understanding, you are getting things right: you represent moral reality in an accurate way. But in addition to this, you also represent that part of moral reality in a way that makes sense to you: your moral beliefs are themselves based directly in the reasons that make those beliefs true. | 1.2 Moral understanding that is shared between you and me | When you and I share moral understanding, not only do we have moral understanding in common, but the very fact of our having moral understanding in common is itself out in the open, in a shared space between you and me. We together acknowledge that we understand things the same way and in so doing we jointly commit to this way of understanding things. | The notion of a shared space: In the example, a hot day, from Charles Taylor, the sort of public space that communication makes possible is that it creates a “common vantage point from which we survey the world together”. When you and I share moral understanding, we survey moral considerations from such a common vantage point. | The basic idea is that sharing moral understanding is structurally like sharing the experience of a hot day, with two small differences. One is that understanding is itself a committal attitude. The other is that what enters a shared space between us when we share moral understanding is usually more complex. | 2.Within the central moral practices of interpersonal justification, we owe it to others to aim at sharing moral understanding with them. | one way to get at the nature of interpersonal justification is to ask ourselves what it aims at. That is, what is the constitutive aim of justifying your action to another person? | There are two complementary ways of thinking about constitutive aims. One is in terms of success conditions. If C is what it takes for some activity A to be successful, then C is the constitutive aim of A. The second way of thinking about constitutive aims is in terms of what it takes for an agent to count as performing the activity at all. | Delivery Model of interpersonal justification points that to justify your action to someone is just to give them the reasons why your action is right. | The Delivery Model runs into two major problems. First, the Delivery Model is unable to account for the fact that the duty to justify myself to you is specifically mine to carry out. Second, in the Delivery Model, it does not matter how you respond—whether you accept or reject the reasons I have provided, whether you call into question my way of describing the situation, whether you draw my attention to considerations you think I have overlooked, and so on. | Limitations of the Delivery Model: first, Delivery Model fails to account for the fact that the practice of interpersonal justification aims at a kind of uptake on the part of the addressee. Second, the Delivery Model is unable to make sense of why we engage in the practice of justifying ourselves to others, since it does not matter how you respond. | Our account of interpersonal justification, that is, should explain the personal character of the duty to justify ourselves to others, as well as the importance of the response of the agent to whom such a justification is addressed. | The constitutive aim of interpersonal justification is shared moral understanding, which can be called Shared Understanding Model. When I am justifying myself to you, what I am doing is trying to bring it about that you understand my reasons for acting as I did, and thereby why I was justified in acting as I did. On this picture, interpersonal justification overlaps with the process of making oneself understood. I put my reasons out in the open, the reasons I take to justify my action, in the hope that you will understand me as having acted reasonably, or on good grounds. In so doing, I aim for us to understand the reasons for which I acted in the same light, as reasons justifying what I did. | The Shared Understanding Model provides a unified explanation of our two desiderata. First, it can explain the observation that, when I owe you a justification for my action, that duty is specifically mine to carry out. Second, the view can also accommodate the observation that uptake matters to interpersonal justification—that whether I am successful in justifying myself to you depends on how you respond. | The Moral address view, as another alternative, points that the aim of interpersonal justification remains to deliver or provide a justification, with the caveat that this information. But it neglects the uptake at which interpersonal justification aims. | The Knowledge view, as another alternative, pointing that knowledge is the aim of interpersonal justification, avoids the problem of indifference. But it runs into a different problem: asking you to take my word for it that I was justified in acting as I did is something altogether very different from trying to justify my action to you. Knowledge can always be acquired on the basis of someone else’s authority, but trying to secure agreement by appeal to authority is antithetical to the practice of interpersonal justification. In justifying my action, I don’t appeal to my authority. I appeal to your judgment. | Conclusion: The constitutive aim of interpersonal justification is shared moral understanding. When explicating interpersonal justification, the Shared Understanding Model outperforms the Delivery Model, the Moral Address View, and the knowledge view. | 3.An apology should aim to reflect a shared moral understanding of the wrong done to its recipient. | Feeling Bad Model of apology: It says that a good apology is one that communicates that I feel (sufficiently) bad about what I did, where the nature of the bad feeling—guilt, remorse, contriteness—is whatever feeling is either constituted by or appropriate in light of the judgment that I did something wrong. | Limitations of the Feeling Bad Model: First, it makes it too easy to delegate the duty to apologize to third parties. Second, there is more to apologizing than merely expressing a sufficient amount of bad feeling. I am not off the hook when I unwittingly express feelings of remorse. | Moral address view: It suggests that the duty to apologize is a duty to respond to a | second-personal demand. It is thus a clear improvement on the Feeling Bad Model since it adequately explains the personal character of the duty to apologize. But it fails to account for the importance of the apologizee’s perspective on the wrong at issue. | Shared Understanding Condition on apology: It suggests that an apology should aim to reflect a shared moral understanding of the wrong done to its recipient. It built up from more elementary ones. First, in apologizing to you, I need to understand what I did wrong. Second, I need to understand what I did wrong in relation to you, from your perspective: I need to recognize the appropriateness of your reasons for resenting23 or otherwise objecting to what I did. Third, that very recognition of your reasons needs to be addressed to you: I need to acknowledge, to you, that your reasons for objecting to what I did are my reasons too. | The Advantages of the Shared Understanding Model: It provides a unified explanation of these two central features of apology. What explains why I must apologize myself, as well as why your perspective on the wrong matters, is one and the same fact: that an apology should try to bring about moral understanding that is shared between us. | Conclusion: When we owe an apology, what we owe is an apology that reflects a shared moral understanding of the wrong done to its recipient. | 5.Reasoning with the Unreasonable | A worry about the shared understanding: How could I be under a moral obligation even to try to bring it about that I share moral understanding with another person, when I know that my attempt to do so is all but certainly doomed to end in failure? It seems there is no duty to try to reach a shared moral understanding. | Two general observations about the view to meet the challenge: First, the duty to justify ourselves to others, or to apologize, is a directed duty: it is the logical flipside of another person’s claim or right against me that I act in a certain way. Second, The right to a justification or an apology is really a cluster of rights is to say that it includes rights to the performance of separate actions. | Conclusion: The duty to justify ourselves to others, or to apologize, is best construed as a cluster of duties, to which a cluster of claim-rights corresponds. Central among these rights is a right that those who owe us a justification or an apology try to reach a shared moral understanding with us. When a claim-holder is sufficiently unreasonable, however, they may thereby forfeit their claim that others try to reach a shared moral understanding with them, even if they retain the more minimal claim to be given a justification or offered an apology. | | Conclusion: We sometimes owe it to others to try to share moral understanding with them, the first based on the nature of interpersonal justification, the second on the norms of apology. Moral understanding that is shared with another person is important.
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1.Does the answer include content related to sharing moral understanding? | 2.Does the answer include the view that the constitutive aim of interpersonal justification is shared moral understanding? | 3.Does the answer include content on shared understanding in the context of interpersonal justification? | 4.Does the answer include the view that an apology should aim to reflect a shared moral understanding of the wrong done to its recipient? | 5.Does the answer include content on the Shared Understanding Condition of apology?
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1.Much attention has been paid to moral understanding as an individual achievement, when a single agent gains insight into distinctly moral matters. But the importance of moral understanding cannot be fully explained by merely focusing on individuals’ moral understanding. | 2.When considering the constitutive aim of justifying one’s action to another person, a common perspective, referred to as the Delivery Model, posits that justifying an action involves simply providing reasons to demonstrate its correctness. However, this model has several limitations. | 3.Apologies are part of the basic fabric of interpersonal morality. The common explanation of apology, such as the Feeling Bad Model and the Moral Address View, has its limitations.
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1.moral understanding:The capacity to grasp the moral significance of actions, principles, or situations. It involves not only knowing moral facts or rules but also appreciating the reasons behind them, recognizing the perspectives and experiences of others, and being able to make sense of moral demands in context. 2.shared moral understanding:A mutual recognition and agreement between individuals regarding the moral significance of a situation, action, or principle. It involves not merely knowledge of each other's moral views, but a joint appreciation of why certain actions are right or wrong, grounded in common values or reasoning. This understanding forms the basis for practices such as interpersonal justification, moral accountability, and genuine apology.3.Delivery Model:A model of moral communication in which moral understanding is treated as a one-sided transfer of moral knowledge or judgment from one agent to another. This model conceptualizes moral interaction as the transmission of a moral claim or evaluation, without necessarily involving mutual recognition, dialogue, or shared interpretation. 4.moral address view:A perspective in moral philosophy that conceives moral claims, judgments, or practices as forms of address directed toward others. According to this view, moral interactions are inherently relational and communicative, involving a speaker and a respondent. The act of addressing another morally presupposes their moral agency, capacity for understanding, and potential responsiveness.5.Feeling Bad Model:A model of moral apology or moral response that centers on the expression of guilt, remorse, or feeling bad as the defining feature of a moral agent’s acknowledgment of wrongdoing. According to this model, what makes an apology morally adequate is primarily the offender's internal emotional state, particularly their sincere regret or sorrow.
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1.giving an account of what it takes for you and me to share moral understanding.2.Through comparison of the Delivery Model, the moral address view, and shared moral understanding, the constitutive aim of interpersonal justification is clarified as shared moral understanding.3.Critiquing the Feeling Bad Model reveals that an apology should aim to reflect a shared moral understanding of the wrong it seeks to address.
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6
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philosophy
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We Cease to be Mere Fragments: Justice, Alienation, | Liberalism and Socialism
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What is the relation between liberalism and socialism?
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1.Point out the key issue | Two perspectives on the relationship between liberalism and socialism: First, Someone view the two stand in fundamental opposition to each other, and the prospects for their reconciliation seem remote. Second, there exist a more eirenic perspective on the relationship between these two traditions, with more reconciliatory views seeing broad agreement between liberals and socialists on many central normative values. | Key issue: What is the fundamental relationship between liberalism and socialism? | 2.Rawls's response to Marx's critique of liberal conceptions of individual rights | 2.1 Rawls's response to Marx's critique of the atomistic and egoistic conception of society implicated by the traditional liberal 'rights of man' | Rawls responded to Marx's famous argument that the 'rights of man'—Marx follows the Declaration of the Rights of Man and of the Citizen in speaking of rights to 'equality, liberty, security, property'—presuppose an atomistic view of human relations that is antithetical to true freedom and meaningful community. | The atomistic individualism is certainly not the view held by Rawls. For Rawls, the rights and liberties protected by his first principle of justice are not those of competitive, antagonistic and egoistic property-owners, brought warily and uneasily into social contact, but the rights of free and equal citizens who are participating in the shared project of realising and sustaining a cooperative social system. | Rawls does not treat the right to private property in productive assets as a fundamental right. Rawls's line of response to Marx here suggests that on Rawls's view any version of liberalism which ruled out a socialist system of economic organisation would by virtue of that feature show itself to be defective. | Conclusion: Rawls does not say that Marx's criticisms of the atomistic and egoistic conception of society implicated by the traditional liberal 'rights of man'are without foundation. | 2.2 Rawls's response to Marx's critique of formal nature of the 'rights of the citizen'. | In 'On the Jewish Question' Marx distinguishes the 'rights of man' from the 'rights of the citizen', understood as rights to political participation (e.g., the right to vote and hold political office). As Rawls rightly says, Marx's attitude to these two varieties of rights diverge in important ways. While Marx recognises the value of the 'rights of the citizen', he thinks that under liberalism these rights are 'merely formal' in the sense that although they are held by all citizens equally, the rights are not enjoyed by all citizens equally on account of the deep inequalities of power and wealth under which these rights are exercised. | Rawls responds not by offering a general defence of the adequacy of liberal political rights, but by pointing to a special feature of his own particular conception of justice. It is a distinctive feature of Rawls's approach to the basic liberties that he defends not only a formal set of personal and political liberties, but that he further argues for the necessity of the protection of the fair value of the political liberties (FVPL). | Conclusion: Rawls's argument that Marx's critique of formal nature of the 'rights of the citizen' does not hit home against his own version of liberalism tacitly accepts that it does strike its target with regard to many other forms of liberalism, as it condemns all those forms within which adequate protections for (something at least close to) FVPL have not been put in place. | 3.Rawls's response to Marx's critique of capitalism in terms of the problem of alienated labour | Marx's objection to liberalism is that, by defending some form of capitalism, liberals effectively allow workers to lead lives of alienated toil, depriving them of the good of self-realisation in work. | Rawls maintained an acute awareness of both the value and significance of work (as a source of meaning and a basis for citizens' self-respect) and of its possible dangers and pathologies (as when its effects can become 'narrowing and demeaning'). | Rawls's writings suggest two distinct lines of response to Marx's challenge. The first points to the way that the concern with alienation in work can be mitigated through the operation of Rawls's principles of justice, in particular FEO and the Difference Principle. The second line of response gives a reference to the discussion of the idea that what Rawls calls the Aristotelian Principle 'holds for institutional forms as well as for any other human activity'. The Aristotelian Principle is the idea that 'other things equal, human beings enjoy the exercise of their realized capacities (their innate or trained abilities), and this enjoyment increases the more the capacity is realized, or the greater its complexity.' | Conclusion: Rawls's response to the alienation objection turns not on defending liberalism or capitalism per se, but showing how only a seriously egalitarian liberal regime could successfully escape Marx's criticisms. Rawls's response to Marx is tacitly critical of existing capitalist societies, which manifestly fail to live up to the egalitarian commitments embodied in justice as fairness. | 4.Rawls's criticisms of Marx's view of justice under communism | 4.1 Rawls's criticisms of Marx's commitment to a principle of self-ownership that precludes the redistribution of income and wealth. | Rawls's criticism is that Marx would reject redistributive principles, such as FEO and the Difference Principle, that Rawls takes to be necessary for 'maintaining background justice over time'. | But Rawls's claim that a principle of self-ownership is honoured in a future communist society is mistaken. Marx's vision of the development of communism is far from a society in which self-owning workers each receive the undiluted proceeds of their labour (as Rawls's interpretation seems to suggest), but rather a society in which communism develops over time through the collective development of a range of shared institutions that cater to the needs of all citizens. | Marx argues that the Contribution Principle represents a significant improvement on distribution under capitalism, where some people who do not work get rich from the labour of others. But this does not rule out the possibility that Marx might find the Difference Principle acceptable for the lower phase of communism. | Conclusion:if we limit ourselves to the somewhat non-ideal circumstances of the lower phase of communism, where moderate scarcity and a capitalist mentality prevail, Marx and Rawls's views about justice are not that far apart. | 4.2 Rawls's criticisms of Marx's commitment to a 'technological fix' that creates limitless abundance and so transcends the circumstances of justice. | On Rawls's reading, Marx's account of the higher phase of communism is a society 'beyond justice in the sense that the circumstances that give rise to the problem of distributive justice are surpassed'. | Rawls suggests that, even if under the imagined future conditions of communist superabundance, the 'evanescence of justice' should then be seen not as a pure state of liberation, but as a regrettable loss of something of great value. | However, it is likely that Rawls and Cohen misunderstand the ways in which Marx sees communist society as moving beyond 'the narrow horizon of bourgeois right' as Marx puts it in 'The Critique of the Gotha Programme', understanding this in excessively technological terms. | The transformation that Marx looked for under the higher phase of communism relied to a greater extent than Rawls appreciated on a transformation of the soul rather than a transformation of the conditions of production. Rawls and Marx would be at one in thinking that a central element of a good society is a commitment to the needs of one's fellows. | Conclusion: Rawls's deep philosophical antipathy to countenancing the evanescence of justice therefore should not have led him here to accentuate his differences from Marx; on the contrary, their views are closer together here than Rawls imagined. | | Conclusion: Marx's critique of capitalism can be endorsed by Rawls, and Rawls's own highly egalitarian liberalism plausibly evades most Marxian worries about liberal political positions. In parallel to how things stand between Rawls and Marx, so too things stand with egalitarian liberalism and socialism: neither deeply opposed nor seamlessly reconciled, but two sibling political traditions that share more than they realise, not least their shared tendency to overestimate their distance from one another.
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1. Does the answer include content on Rawls's response to Marx's critique of the atomistic and egoistic conception of society? | 2. Does the answer include content on Rawls's response to Marx's critique of the formal nature of the 'rights of the citizen'? | 3. Does the answer include content on Rawls's response to Marx's critique of alienated labour? | 4. Does the answer include content on Rawls's criticisms of Marx's commitment to a principle of self-ownership? | 5. Does the answer include content on Rawls's criticisms of Marx's commitment to a 'technological fix' transcending the circumstances of justice? | 6. Does the answer discuss the relationship between liberalism and socialism?
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1.Partisans of two political traditions, liberalism and socialism often often see one another as ideological opponents. | 2.There is a more eirenic perspective on the relationship between liberalism and socialism, with more reconciliatory views seeing broad agreement between liberals and socialists on many central normative values.
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1.Liberalism: A political and moral philosophy based on principles of individual liberty, equality before the law, and the protection of fundamental rights. It emphasizes the importance of limited government, rule of law, free markets, and the promotion of political and civil freedoms, such as freedom of speech, religion, and association. | 2.Socialism: A political and economic ideology that advocates for the collective or social ownership and democratic control of the means of production and distribution of goods. It emphasizes reducing economic inequalities by promoting social welfare, equitable distribution of resources, and workers’ participation in decision-making processes. | 3.Justice: A moral principle that individuals are to be treated according to what is due to them—whether in terms of rights, deserts, needs, or equality. It involves questions of fairness, legitimacy, and reciprocity, and is central to ethical, political, and legal theory. | 4.Alienation: The experience or condition in which a person becomes disconnected or estranged from aspects of their human nature, their work, their community, or the products of their labor. It involves a sense of powerlessness, meaninglessness, isolation, or loss of agency in relation to oneself or the surrounding social and material world.
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1.Examining Rawls’s response to Marx’s critique of liberal conceptions of individual rights, as articulated in Marx’s ‘On the Jewish Question.2.Examining Rawls’s response to Marx’s critique of capitalism concerning the problem of alienated labour, as articulated in the Economic and Philosophical Manuscripts.3.Reviewing Rawls’s criticisms of Marx’s view of justice under communism.
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7
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philosophy
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Ideology and suffering What is realistic about critical theory
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How to understand the radical realists' attempt to develop an empirically grounded ideology critique that eschews moral premises, in light of the connection between radical realism and the Frankfurt School, particularly Theodor W. Adorno?
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1.Elements of ideological flaws and the Marxist affinities with radical realism | Realists focus on practices of self-justification; that is, moments in which might makes right. When a regime resorts to overt coercion to bend the will of its subjects, ideologies have not fulfilled their function – their power lies in being a covert kind of influence, difficult to see. | The most radical members see good reasons to find ideal theories of justice ideologically suspicious. Their scepticism rooted, at least to some extent, in the being/consciousness doctrine of historical materialism. | Conclusion: Realists draw inspiration from Marx and critical theory, which is why they tend to endorse, roughly speaking, a conception of ideologically distorted beliefs, attitudes and desires as shaped and formed by powerful interests within contexts of inequality. | 2.Strategies for debunking ideologies without appealing to moral norms | Radical realists should be keen to avoid what Williams described as a 'vulgar Marxism' that rejects all moral ideas as unworldly prejudices. | Radical realists should want to say something more moderate, namely that moral theories that abstract from political facts risk being prejudice-ridden. | Feasibility can be fetishised, as radical realists could argue by drawing on Adorno. Conceptions of usefulness and comprehensibility will bear the stamp of the powers that be and might thus be delusional themselves, especially since we tend to have a poor grasp of when it is really impossible to do things differently. | For radical realists, critique of such ideological claims about necessity and nature can be powerful. It historicises concepts and ideas that claim to be universal. | Conclusion: It's a powerful strategy to criticize such ideological claims about necessity and nature. | 3.Doubts as to whether a critique of ideologies should elide moral reflection | An evident way to debunk legitimation stories without resorting to moral principles is to show that they contradict empirical facts. radical realists wish to reject the epistemic warrant of beliefs in light of the reasons to mistrust the circumstances under which they arose. They rely upon an epistemological theory of reliable verification: A belief is epistemically suspect if it depends on premises that originate from the same source by which it is supposed to be justified. | A particularly promising form of critique assesses the function of beliefs, appeals to concepts and institutions that justify and sustain a political and economic order. | In such cases, however, it becomes difficult to grasp in what sense critique can or should remain outside of the moral realm to address the cui bono question: Who benefits from certain beliefs being firmly held, and what are the implications of exposing this? | Critical Theory Test by Williams: The critical question is counterfactual: If the disadvantaged were to come to know 'properly' why they really hold a belief, 'would they give it up?'One begins with particular convictions and imagines reflective questions the disadvantaged might pose. A person following these reflective steps would realise they are in a precarious position to judge whether their trust in the official stories is justified. And practical consequences follow from such a process of enlightenment. | Conclusion: There are multiple ways in which schemes of political self-justification can be evaluated without rooting criticism in a moral normativity. | 4.Limits of ideology critique of radical realists | Realists claim they can achieve similar objectives as morality-based ideological critiques without the 'risks and complications introduced by moral premises'. But avoiding moral premises entails risks and complications of its own. It can give rise to an undialectical mode of thinking that dreams of closing off entire realms of reflection while maintaining a posture of value neutrality. | Raise three challenges to radical realists via Adorno: First, Realists do not say that the relativity of judgments to constellations of power is problematic in a moral sense. But mere mistrust of the content of beliefs and the purposes of practices, given that they are a product of motivated reasoning is not enough to discredit them. Second, Realists, given their desire for moral abstinence, might fail to account for the normative presuppositions that explain their critical attitude towards the effects of power. Third, knowledge about the true origin of beliefs as well as the pliable nature of the order of things is not only difficult to gain and appreciate; it would also not suffice to liberate us from illusions since ideologies serve multifarious deep-seated needs and desires. There is reason to question the explanatory power of the radical realist ideology critique and the extent to which it can serve as an 'instrument for agents'. | Revisiting Adorno's reflections on the elements of fascist propaganda: The function of fascist propaganda is a kind of wish-fulfillment or gratification. This distortive communication is amplified by forms of moralisation that organise the world along simple dichotomies of black and white, good and evil. Radical realists will have difficulty comprehensively criticising this kind of abuse, because it requires reflection on those moments of inversion in which the cruel comes to be seen as just, and anti-democratic wishes are cloaked as democratic. | Conclusion: The ideology critique of radical realists, which bypasses morality, has notable limitations. | 5. Ideology critique should reclaim moral concepts from their distortions | Moral anti-moralism: it holds that illusions of individual responsibility and equality of opportunity hide the oppressive and alienating aspects of capitalism, which allows misery to persist amid overflowing richness. | Adorno found talk of responsibility ideologically suspicious. It distracts from how individuals are constituted and constrained by market pressures and social coercion, hiding the fact that most kinds of economic difference arise from factors beyond their control. | Adorno's ideology critique is driven by the moral belief that all senseless suffering should be abolished, grounded in an empirical observation that should make us not feel at home in this world: The forces of production and our technological capabilities are developed to such an extent that it is materially possible that no one would have to go hungry anymore or be homeless. Still, millions live in misery, which creates a strong apologetic necessity to justify suffering that could be prevented. | Realists would be right to ask for justifications for the reflective standing of those able to discern abuses of moral concepts and lend a voice to suffering. Yet they would also have to concede the limits of their approach and acknowledge that there are kinds of radical criticism that only an experience-led, moral Ideologiekritik can make, even if that introduces complications. | Conclusion: Only on the basis of a moral anti-moralism can we detect how ideological distortions turn ideas of the good and just into a 'cover of evil'. | | Conclusion: Bringing early critical theory into a long-overdue conversation with the realist movement in political philosophy is productive. Unlike radical realists, however, Adorno thought that a crucial task of critical theory is to reveal how concepts such as freedom, responsibility and democracy can become apologetic instruments for the unacceptable. The latter requires a dialectical critique that rescues morality from moralism, which disguises the cruel as just and diverts our attention away from the real causes of suffering and pain.
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1. Does the answer include content on the elements of ideological flaws and the Marxist affinities with radical realism? | 2. Does the answer include content on strategies for debunking ideologies without appealing to moral norms? | 3. Does the answer discuss whether a critique of ideologies should elide moral reflection? | 4. Does the answer include perspectives on the limits of ideology critique of radical realists? | 5. Does the answer include the view that ideology critique should reclaim moral concepts from their distortions?
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1.Radical realism, as an influential variation of realism in political theory, seeks to expose the tainted origins and problematic functions of beliefs in the justifiability of existing practices and hierarchies by epistemic ideology critique rather than moral concepts such as justice or rights. | 2.Raymond Geuss and Bernard Williams emphasised that can epistemic ideology critique certainly be effective critical reflections. | 3.There are some scholars who suggest that the realist movement could contribute to ‘reinvigorating’ the first generation of the Frankfurt School, or at least be brought into a fruitful conversation with it.
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1.ideology critique:A form of philosophical and socio-political analysis aimed at uncovering how dominant belief systems—ideologies—function to sustain power relations, obscure social contradictions, and produce forms of false consciousness. It seeks not merely to describe ideas but to expose their historical, material, and political functions, thereby enabling emancipatory insight and action. | 2.radical realism:A philosophical position that affirms the existence of a mind-independent reality while emphasizing that our access to this reality is always mediated by historically and socially situated perspectives. It is “radical” in its insistence that critical inquiry must confront the deep, often hidden, structures of the real—especially those that are obscured by ideology, power, or dominant discourse. | 3.moralism:The philosophical stance or attitude characterized by the excessive or inappropriate application of moral principles, often involving the imposition of moral judgments without adequate attention to context, consequences, or the complexity of political and social realities. It tends to reduce complex phenomena to matters of individual virtue or vice.
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1.Examining the affinities between radical realism and the Frankfurt School, especially the work of Theodor W. Adorno. 2.Discussing some further strategies for debunking ideologies without appealing to moral norms, namely by drawing on the reliabilist approach to epistemology and addressing the problem of motivated reasoning.3.Questioning the desirability of eliding moral ideas in the critique of ideologies by highlighting tensions within the arguments of radical realists and refer to central claims from the early Frankfurt School.
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8
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philosophy
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Women who pay their own brideprice: reimagining provider masculinity through Uganda's thriving wedding industry
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How does the emergence of women who pay their own brideprice has invited a broad reimagining of the gendered economic ideologies that tether men to money under the rubric of provider masculinity in Uganda?
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1.Ugandan wedding and marriage traditions are changing | The government's stance on women's and LGBT rights is that they are foreign, brought to Uganda by Westerners to destroy African Christian values. | Uganda's contemporary legal framework for marriage is a colonial leftover, enshrined in the 1904 Marriage Act, which recognizes customary as well as religious ceremonies and civil unions. | Brideprice especially has become a flashpoint in the debates of marriage in Uganda. | 2.Ugandan's growing opulence of contemporary weddings | Grooms of the past proved their worth to their in-laws by showing humility, meaning avoiding eye contact and never speaking directly to their future kin. Now, grooms show their worth by 'splashing money', even if they can only temporarily rent the vehicles, stereo systems, and refrigerators they present as the wedding prestation. | Setting an official 'price' for marriage payments allowed missionaries and state officials seeking to settle legal disputes or convert followers to determine who was married to whom, and when the marriage began. More recently, Ugandan government officials have tried to regulate wedding expenditures by setting the nominal 'price' of a marriage exchange. | Conclusion: Ugandan's contemporary weddings are becoming increasingly luxurious. | 3.Reality television and the wedding industry boom | The 'lavish' commercialization of weddings Ugandans complained of in the 2010s is tied to the explosive growth of the country's wedding industry. The wedding industry boomed following economic liberalization, and its continued growth is fuelled by pop-cultural media, which serves both as a key authority on wedding trends and a key source of blame for their growing opulence. | Properly documenting one's wedding is one of the event's most significant costs. Tailored specifically for each couple, the production and public circulation of wedding media reflect both conventions and reimaginations of love, romance, and the material conditions of marriage. Couples have also been paying to have their ceremonies professionally filmed and televised since the mid-2000s on shows such as Okwanjula n'embaga (Introduction and wedding) and My perfect wedding. | As those wedded and waiting to wed surmise, as images of extravagant wedding spending circulate on reality television, so too do the costs of weddings increase, creating a seeming spiral of increasing demand for ever more sumptuous weddings. | Conclusion: Reality television and the booming wedding industry have increased wedding expenses. | 4.Women making marriage payments | Women raise money for weddings in several ways: through their social networks, through their parents' social networks, and from their own salaries. In each instance, women must mobilize culturally resonant forms of respectable femininity to garner financial contributions to their weddings. | Wedding fundraising typically takes place through a series of 'wedding meetings' held by the bride's family, the groom's family, and the couple themselves. That future brides and grooms hold wedding meetings together demonstrates women's key role in raising funds and couples' ability to work together as a team, to save money, and to marshal social capital into material support. | Young women also draw on their parents' social networks to raise money. In central Uganda, raising money from family friends requires young Baganda women to demonstrate they are 'well behaved', meaning raised or 'groomed'to show respect to their elders. | Some women pay the costs of their ceremonies outright, effectively sponsoring their grooms, but the practice is only discussed obliquely, in whispers, and about other people. | Women explained that paying your own brideprice to materialize a groom's masculinity was, in fact, how a bride demonstrated her value – her 'price', in a way. | Conclusion: By 2015 women paying their own brideprice was a public secret, it unsettle provider masculinity's central tenet: that men provide the money. | 5.Entrepreneurial men and wedding work | To make one's wedding extravagant, one hires top-rated wedding vendors, many of whom are university-educated young men otherwise excluded from Uganda's dismal labour economy and thus peers of the brides who employ them. | Educated young women appear to have far more access to expendable resources in the form of salaries, both than in the past and when compared with their male peers. In a context of widespread unemployment, the wedding industry provides educated men with opportunities to start businesses and earn incomes. | Beyond wages, wedding industry jobs facilitate a sense of entrepreneurial self-actualization, what Shipley calls an 'embodied poetics for business success'. As an industry, weddings provide space and time for men to cultivate aspirational fantasies towards what many consider the future for economic growth in Uganda: entrepreneurialism. | Wedding work helps men perform and feel the potential to become economically successful – and in some instances this self-fashioning also allows them to provide for their families. | Conclusion: Women who pay their own brideprice also help actualize provider masculinity among other men. | 6.Reimagining provider masculinity | That weddings generate discursive space for reflection on changing gendered norms. educated young men and women in Kampala are well aware of how concepts such as 'culture' and 'tradition' get deployed in these public debates, and the way they describe their relationship to gendered economic traditions involving brideprice ceremonies indicates these traditions are changing all the same. | Conclusion: Wedding rituals and the broader conversations they inspire provide time and space for challenging, satirizing, and tolerating transformations in the relationship between gender, money, and marriage. | | Conclusion: In Uganda, opulent weddings requiring women to help pay their own brideprice. While doing so, women are also maintaining partner's masculinity which presents economic and emotional burdens for women. Weddings, with their nostalgic invocations of gendered economic traditions, inspire thinking otherwise about what the future may hold.
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1. Does the answer include content about Ugandan weddings becoming increasingly extravagant? | 2. Does the answer discuss the phenomenon of Ugandan women paying their own bride price? | 3. Does the answer include the view that Ugandan women paying their own bride price unsettles the central tenet of provider masculinity? | 4. Does the answer include the view that Ugandan women who pay their own bride price also help actualize provider masculinity among other men through the wedding industry? | 5. Does the answer include the view that Ugandan weddings generate a discursive space for reflection on changing gendered norms? | 6. Does the answer include the view that weddings inspire thinking otherwise about what the future may hold?
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1.The trappings of wedding ceremonies become ever more sumptuous across sub-Saharan Africa, and the inability to afford marriage | payments has left young men ‘stuck in the compound’. | 2.Ugandan women are reported to benefit from ever-increasing economic opportunity, which leads the fact that young men unable to afford their weddings and young women out-earning their male peers. | 3.A curious phenomenon has emerged: "women who pay their own brideprice", which refers to a range of economic practices undertaken by brides against the conventional, if aspirational, notion that men should pay for the events enitrely.
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1.provider masculinity:A culturally specific ideal of masculinity in which a man's identity, status, and moral worth are closely tied to his ability to financially support his family or dependents. | 2.brideprice:A cultural practice in which the groom or his family gives wealth or goods to the bride's family as part of the marriage arrangement.
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1.Examining transformations in Ugandan wedding practices, with a focus on revisiting the normative as a potent site for observing gendered social change.2.Focusing on bridewealth practices and the phenomenon of women paying their own bridewealth in the context of Uganda’s shifting economic landscape, with particular attention to the relationship between money and intimacy, and to the transformation of gendered economic arrangements.
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9
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philosophy
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The platformization of the public sphere and its challenge to democracy
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How does the market entry of platforms influence the public sphere, and how can this impact be addressed？
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1. Demands on and functions of the public sphere as a societal mediation system | The conception of public sphere: The term public sphere describes (a) the social sphere where people exchange their opinions, discuss, and deliberate on public topics and (b) the process of public deliberation which leads to the formation of a public opinion. It is an important prerequisite of democracies as it enables people to observe the opinion building on political and societal topics, and therefore allows an introspective view on society. The public sphere is to be understood as a system of social mediation – an important function in today's democracies. | Theories of the public sphere can be assigned to three different paradigms. First, in the liberal paradigm, the public sphere serves as a representative sounding board for all issues and opinions on political topics. Second, in the deliberative paradigm, the power of the better argument is considered essential. The goal is to find a rationally based social consensus. Third, the participatory paradigm demands that everyone should be involved in public decision-making processes and all opinions should be considered. Everyone should be able to take part and have access without discrimination. | The functions of public sphere: It integrates different topics and opinions, legitimizes political decisions by informing citizens about facts and debates (transparency) and thus provides a prerequisite for participation. In addition, it enables public deliberation and participation in discussions. With these capacities, the public sphere contributes significantly to social orientation. | 2. Traditional media's services to society | Traditional media, which have institutionalized journalism, play an essential role in societal mediation processes: they disseminate information, ensure public communication, and still play a key role in the creation of public spheres. They are regarded as a key player for vital (mediatized) public spheres and the tenor of their reporting (= published opinion) is equated to public opinion. | However, criticism of the media and journalism has increased during the past years: Journalistic media are defamed as Lügenpresse. Journalists are accused of a biased selectivity. Economization and an increasing media concentration have had consequences for spatial and social diversity in the media, too. Therefore, trust in media fluctuates. | Journalism has fulfilled the demands of both the liberal and the deliberative paradigms with its selection and presentation of news. But these achievements are not sufficient regarding the participatory paradigm as this paradigm postulates a broader access to public communication in order to involve as many people as possible in decision-making processes. In contrast, social media offer easily accessible alternative channels to discuss all topics publicly. | 2.1 The significance of mass media for public communication in a changing society | Mass media are among society's intermediaries, as are political parties, associations, trade unions and social clubs. Historically, media were linked to the intermediaries: parties, trade unions or churches each had their own media to reach their members but also a general public. Traditional media such as the press, radio and television were the most important intermediaries – until the establishment of the internet and communication platforms. | Nowadays, new political interest groups bypass traditional media by using social media because they are able to gain access to the public sphere without the obstacles journalism has posed before. | 2.2 The structure of journalism and its contribution to society | Journalistic programs of media organizations are determined by the owners of newspapers or the socially relevant groups in the case of public broadcasters. Together they form the journalistic supply structure and formats. Over time, there has been a shift from a journalism which focused on individual political interests, where journalists oftentimes were also members of parliament, towards an understanding of journalism as a 'non-biased' service. | Driven by the success of platforms, traditional media offer more content on various different channels, which was only possible through an increase in content production. Journalistic workplaces which were formerly a place of political debate, are increasingly transforming into coordination centres for procurement, control of production, and distribution of content. The automatization of these processes which is based on algorithms supersedes former journalistic activities. Commercial pressures gain importance. | The demands on journalism have increased significantly in this process. Corresponding models are being discussed for functions of journalism: for example, 'participatory journalism', 'data journalism', and 'civic or citizen journalism'. | | Conclusion: A whole sector as well as a profession of journalism are in a state of upheaval, in a fundamental transformation process – outcome unknown. It is no longer enough to select issues and to publish articles or features with a strong emphasis on elites' and experts' opinions. Journalism must cope with new expectations. | | 3. The consequences of platformization | 3.1 Media and journalism's adaption to platform logic | Digital platforms are new intermediaries: Digital platforms are new intermediaries that constitute, coordinate and control markets by offering a wide variety of services such as the exchange of goods, the provision and exchange of information, and the facilitation of communication, in public and in private. They do not provide information services themselves but enable others to place information on the platform and communicate with each other. | Digital platforms with their new business models where users benefit from 'free' access by paying for the services with their data, have a major impact on traditiona media. Now users can access information for free which makes news consumption on the internet attractive. And because there is an increasing amount of information available free of charge, people are less willing to pay for traditional news media. Advertisers are able to target their customers more efficiently via platforms. These processes have led to a funding crisis for journalism. | Platforms are changing the norms and rules of journalism. Media and journalism had | to adapt to the multiple new distribution channels all of which have their own logic. Traditional media have become 'platform complements'. | 3.2 Increasing tabloidization and emotionalization throughout the public sphere | The new forms of provision, distribution and use of journalistic content have a variety of effects on how traditional media outlets produce content. In traditional media, content's relevance was determined by its social or political scope. That has changed. Relevance on social media is related to clicks, views, likes and shares. The orientation towards an attention-seeking economy is increasing. Content is adapted accordingly. Ever more topics need to be covered and distributed. Successful social media posts trigger attention and excitement. Traditional media, now seeking success on platforms imitate this kind of content. The social media logic is rubbing off on journalism: journalistic news contributions have been found to be increasingly emotionalized and personalized. | 3.3 Audience fragmentation and news avoidance | Traditional media are losing their audience. In the 2020 Reuters Institute's survey, among 18 to 24 year olds only 16% accessed traditional media via their own channels, the most common gateway to news was social media. | Another more recent development, which is worse, is the fact that people choose to ration or limit their exposure to news. | | Conclusion: Platforms are new institutions in the intermediary system. With the increasing dominance of platforms for public communication, they establish new norms and rules in the intermediary system. Platforms have a different business model than traditional media, but their market entry has structural and procedural effects on traditional media, journalism, and the public sphere. | | 4. The transformation of the intermediary system | Political journalism is losing resources as well as relevance. The financial crisis of traditional media has negative effects on the profession and the profession's performance. | Platforms influence the way users select information. It remains to be seen whether journalism as a service will survive in other organizational contexts than publishing houses or with other financing models than by subscriptions or donations. | The decontextualization of content, topics, and issues, in addition to the change of how people use media services could trigger social problems: The highly individualized media repertoires might lead to separate user communities, even sub-publics. | 5.Concluding remarks on the current debate and legal regulation | The influence of platforms on the intermediary system needs to be discussed from the perspective of public sphere and democracy theories. Because of platforms, the public sphere is becoming more diverse in terms of space and time. More people gain access, and more topics are being discussed. The universal access changes the constitution of the public sphere, it is getting more dynamic. However, due to these dynamics, the vast number of participants, the diversity of perspectives, views and interpretations as well as instant reactions, the aggregation of the underlying communication towards a public opinion is difficult. The public sphere loses its power to stabilize society and to integrate and it is becoming increasingly difficult to transform deliberative processes into political ones. | | Conclusion: The market entry of platforms has had structural as well as procedural consequences for the public sphere and political communication: Platforms have facilitated the access to the public sphere (input) and have also partially democratized it. However, processing topics (throughput) has become unclear and messy due to the sheer volume of topics which are now discussed in public simultaneously, and aggregation has become demanding as there are no institutionalized actors taking care of the process. The institutionalization process of platforms requires new policies. A fundamental debate about the future constitution of society as well as the development of a 'new public media system' needs to be held.
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1. Does the answer include the content of the demands on and functions of the public sphere as a societal mediation system? | 2. Does the answer include the content of the structure of journalism and its contribution to society? | 3. Does the answer discuss the consequences of platformization? | 4. Does the answer include the content of the transformation of the intermediary system? | 5. Does the answer discuss how to address the influence of platforms on the intermediary system from the perspective of public sphere and democracy theories?
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1.The public sphere has changed due to advancing social differentiation, accelerating | digitalization processes and the institutionalization of digital platforms. Information | provided on digital platforms permeates the public sphere according to the platforms’ algorithms which are based on the rules and norms of global private-sector companies. This has triggered a severe transformation of the public sphere. | 2.Younger users obtain information about current topics via platforms. This has consequences for media and journalism: They have lost reach and revenue in the advertising and the (paying) audience markets. | 3.Social media introduce new techno-commercial mechanisms in public communication. A whole sector as well as a profession are in a state of upheaval, in a fundamental transformation process — outcome unknown.
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1.Public sphere: A concept in social and political theory, primarily associated with the work of Jürgen Habermas, referring to a space where individuals come together to freely discuss and debate societal issues, share ideas, and form public opinion through rational-critical discourse. It serves as a societal mediation system, independent of the state and market, where citizens engage in communicative action to influence political and social outcomes, fostering democracy and civic participation. | 2.Journalism: The practice of gathering, verifying, analyzing, and disseminating information about current events, issues, and trends to inform the public. It involves producing news and stories through various media—such as newspapers, television, radio, and digital platforms—with the aim of providing accurate, timely, and objective accounts that contribute to public knowledge and discourse. | 3.Intermediary system: It refers to a set of institutions, processes, or platforms that facilitate communication, interaction, or exchange between different parties in society, such as individuals, organizations, or the state. It acts as a mediator, enabling the flow of information, resources, or influence within the public sphere or other social structures.
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1.Examing the influence of platforms from the perspective of public sphere and democracy theories. | 2.Reviewing the transformation of the intermediary system and the consequences of platformization
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10
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philosophy
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Anthropology, Development, and Beyond | For More Conversations with Economists and Other Scholars
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What is the relationship between anthropology and economy in the field of development studies and what it should be in face of the grave problems today?
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1.The field of development studies exemplifies the changes of economic anthropology and the relationship between economy and anthropology | In a special issue about the relations between anthropology and economics, it is mandatory to mention economic anthropology as a disciplinary niche that has represented anthropologists' visions on economic issues. | From the 1960s to the mid-1980s, Marxism as an influential theory and a common ground facilitated crossfertilizations among anthropologists, economists, historians, and geographers. | As Marxism has declined after the end of the Cold War, many of the issues discussed by economic anthropologists slowly retreated to the back of practitioners' minds or became a part of research areas identified by distinct labels and engagements with topics such as development, globalization, infrastructure, financialization, climate change, and the Anthropocene. | It is possible to find subjects dear to economic anthropology in different areas of contemporary research, but this does not mean that it currently exists in a rebranded fashion. First, economic anthropology has kept its own heuristic space. Second, the insertion in a new field of inquiry calls for new research, interlocutions, recalibrations, or creations of concepts and interpretations, and it generates genuine and original knowledge and theories. | The field of development studies allows to refer to scholarly, professional, and political relations and subjects of common interest of economists and anthropologists. | Conclusion: The field of development studies exemplifies the changes of economic anthropology and the relationship between economy and anthropology. | 2.Review the involvement of anthropologists in development since the 1940s. | Since the 1940s, development has been a discourse specialized on issues of global wealth or poverty and inequalities and on defining models and actions to solve the problems of so-called underdeveloped countries, developing countries, or emerging | economies. Economists' prominence is especially visible in places such as the World Bank (WB), the global governance institution once thought to be the mecca of development, and where they also have interacted with development anthropologists who entered this scenario as specialists on local, "backward," "exotic," "poor," and "Third World" peoples. | The involvement of anthropologists in development may be subdivided into two trends: development anthropology and the anthropology of development. Development anthropology is mainly concerned with the impacts of development on local people. The anthropology of development is mostly dedicated to a critique of "development" as a Western discourse. The study of what was called "development projects" and development agencies or agents is included in this last area of anthropological concerns. | In the 1970s the academic production on development started to blossom. By studying the impact of development projects based on comparisons of different local responses, anthropologists tried to find constant structures that would allow them to predict individual and group behavior in a vein similar to economists, whose professional practices often involve risk analysis and how to avoid contingencies. At the same time, anthropologists became hire options for multilateral and national bureaucracies and civil society agencies related to the development industry. But Whether or not the practice of "development anthropologists" had positive effects on the institutions they have worked for and on the lives of local populations is a hot issue among anthropologists that resonates with debates related to the applied or academic divide in the discipline. | In the 1990s, there is a postdevelopment critique. According to Escobar (2005), the main point of the postdevelopment debate was not to propose another version of development but to answer the question of "why, by means of which historical processes and with what consequences, Asia, Africa and Latin America were 'thought' as the 'Third World' by development discourses and practices" . One important research effort within the interdisciplinary and diverse field of postdevelopment was the study of development in concrete settings, its agents, agencies, and processes. | Conclusion: The roles anthropologists play in the field of development studies are changing. | 3.The Development Field in the Wider Juncture in the Late 1980s and 1990s | The 1990s was a particularly important decade for the involvement of anthropologists in global development policies, a professional environment usually hegemonized by economists. | Macro political, economic, and sociological dynamics that affected the world system by the end of the 1980s and beginning of the 1990s: The bipolar world of the Cold War was finished, opening a period of crisis of socialist utopian discourses and projects. This gap was filled by other utopian discourses that had been gaining momentum since the 1970s and reached their climax in 1988 and 1992. The early 1990s was a propitious juncture for a series of experiments under the banner of the newly accepted global consensus: sustainable development. | The impact of sustainable development was particularly felt in the global development agencies and in the aid industry. The window was open for a greater participation of anthropologists in these processes within multilateral agencies, state organizations, and NGOs. But development is a power field in which anthropologists and economists converge and diverge. It is made up of several social, ethnic, political, technical, professional, organizational, financial, state, and private agencies and agents. | The development field has spurred the mingling of economists and anthropologists in working environments. Their relationships are dependent on the institution's hierarchy and internal politics and not on some supposed ontological superiority of one discipline over the other. Moreover, The impact of wider political, ideological, and utopian discourses on the development field cannot be underestimated and | may open avenues of cooperation and conflict between anthropologists and economists. Generally speaking, Anthropologists will usually emphasize the value of diversity, cultural relativist approaches (such as different conceptions of nature and the good life), and the empowerment of local people. Economists will usually emphasize the value of models, numbers, rational choices, and market forces as modes of solving development problems. | 4.Changes in Academia and in the World System | The high time of development anthropology and anthropology of development is behind us, some of the subjects encompassed by the development debate of the 1990s and early 2000s are currently part of other domains of academic and public interest such as the growing field of interactions and exchanges among different epistemic communities called Anthropocene. | Limits of Anthropocene: The larger discursive and institutional field in which the Anthropocene locates itself is made up by agencies and agents that are not as identifiable as those of the development field. Moreover, in certain interpretations of the Anthropocene, there is a tendency to think that subjects of complex political fields can hardly be distinguished and that the establishment of powerful collective counterhegemonic subjects is no longer possible. Such visions obliterate the mapping of the power field now in action and make it harder to establish political priorities for scholars and citizens. | The relationship between Anthropocene and sustainable development: Anthropocene as a discourse shares similarities with sustainable development. It makes up a field of contentions where different political forces may meet, oppose, or ally themselves. There are some notable differences though. Sustainable development is a utopia, whereas the Anthropocene is a dystopia. And more importantly, sustainable development, as an heir to the many meanings and adjectives associated with "development," generated its own organizational and political field, institutional and otherwise, that, despite its normalization, has also been useful for the promotion of the notion and political field of the Anthropocene itself. | Issue for future: How each of these discursive fields, with their agents and agencies, may establish productive and virtuous exchanges between them and with other sets of progressive discourses capable of constructing new formulations to win the hearts and minds of the many millions of people who know there cannot be a future without environmental and social justice. | New challenges: The world system has changed since the 1990s, especially after the end of the Cold War, the development power field has also changed in the past two decades. The most notorious novelty is the role of China in international development. | 5.Anthropologists and Economists Are a Diverse Group of Professionals Facing New Interdisciplinary Challenges | "Heterodox economists," who are mostly oriented by political economy or Marxist theories and not by the prevailing neoclassical economics school, are aware that historical, sociological, cultural, racial, gender, and environmental dynamics are not "externalities" that may be ignored. | Anthropologists and economists make up a diverse group of professionals. Their approximations and detachments are based on both disciplinary and political visions. The kinds of specific disciplinary education and worldviews embedded in economics and anthropology are not enough to explain all divergences and convergences in the relationships between these professionals. | Conclusion: Ultimately, what is at stake when economists/anthropologists discuss development is how wealth is produced and partaken and how it affects the human | and nonhuman worlds, currently, these questions come together with major challenges. it is time for anthropologists to critically and more consistently engage with notions and problems concerning humankind. And the expectation of a generalized catastrophe caused by global warming calls for the integration of diverse cultural, political, and scientific standpoints beyond the realms of economics and anthropology.
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1. Does the answer include the perspective that the field of development studies exemplifies the changes in economic anthropology and the relationship between economy and anthropology? | 2. Does the answer review the involvement of anthropologists in development since the 1940s? | 3. Does the answer discuss the development field in the wider juncture in the late 1980s and 1990s? | 4. Does the answer discuss how anthropologists and economists should act in response to new interdisciplinary challenges? | 5. Does the answer discuss the content of changes in academia and in the world system?
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1.The world system has changed since the 1990s, when the tremendous power of social and environmental destruction deployed by triumphant neoliberal capitalist globalization became the norm. The West no longer controls the development discourse as completely as it used to. | 2.Heterodox economists are aware that historical, sociological, cultural, racial, gender, and environmental dynamics are not “externalities” that may be ignored, and anthropologists and economists make up a diverse group of professionals. | 3.How wealth is produced and partaken and how it affects the human and nonhuman worlds, which is what at stake when economists/anthropologists discuss development, currently come together with major challenges, such as the increased importance of conservative and ultraconservative politics, new imperialist wars, and climate change.
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1.development:A multidimensional process involving economic growth, social progress, and improvement in the quality of life of a population. It is understood as a complex, context-dependent transformation of societies aiming at reducing poverty, inequality, and vulnerability while expanding opportunities and freedoms for all individuals. | 2.development anthropology:A subfield of anthropology that studies the social, cultural, political, and economic dimensions of development processes and projects. It seek to understand the impacts of development from the perspectives of the people involved, aiming to improve development practices by promoting culturally sensitive, participatory, and sustainable approaches. 3.anthropology of development:A specialized area within anthropology that critically analyzes the concepts, practices, and impacts of development as a global phenomenon. It examines power dynamics, inequalities, and the unintended consequences of development, often questioning dominant development paradigms and advocating for more inclusive, locally grounded approaches. 4.Anthropocene: A proposed geological epoch that marks the period during which human activity has become the dominant influence on the Earth’s climate, ecosystems, and geology. It signifies a new era where humans significantly alter natural processes, leading to large-scale environmental changes such as climate change, biodiversity loss, pollution, and landscape transformation. | 5.Capitalocene: A critical term used to describe the current historical epoch, emphasizing that the environmental crises we face are primarily driven by the capitalist mode of production rather than humanity as a whole. It highlights how capitalism’s focus on endless economic growth, exploitation of labor, and natural resources leads to systemic environmental degradation and social inequalities.
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1.Review the involvement of anthropologists in development since the 1940s.2.Review the development field in the wider juncture in the late 1980s and 1990s, and discuss the relationship between anthropology and economy in the field of development studies.3.Disscuss the Anthropocene/Capitalocene debates under the context of current major challenges , and advocate new interdisciplinary exchanges.
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11
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Computer Science
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A Lower Bound for Light Spanners in General Graphs
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Determine the optimal lightness of spanners in graphs, specifically focusing on the dependence on the parameter \eps.
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Introduction | | Spanners are fundamental graph sparsifiers with applications in networking, chip design, flow algorithms, and more. | | Theorem 1 | For all positive integers n, k, every n-node graph has a (2k − 1)-spanner with O(n^(1+1/k)) edges. | | Conjecture 2 (Girth Conjecture) | There exists a family of n-node graphs with Ω(n^(1+1/k)) edges and girth greater than 2k. The girth of a graph is the smallest number of edges in any of its cycles. | | If any edge (u, v) is removed from such a graph, there is no alternate u–v path of length ≤ 2k − 1, otherwise a short cycle would exist. Therefore, such a graph has no (2k − 1)-spanner other than itself, giving a matching lower bound to Theorem 1. The conjecture is confirmed for k in {1, 2, 3, 5, Ω(log n)}, but proving or refuting it for other k is an open problem. | | Theorem 3 | For all positive integers n, k, and all ε > 0, every n-node graph G has a (1 + ε)(2k − 1)-spanner H with lightness | ℓ(H | G) ≤ O(ε^(-1) · n^(1/k)). | | Currently, little is known about lower bounds for lightness. A girth conjecture graph implies a lower bound of Ω(n^(1/k)) for (2k − 1)-spanners, but this does not use edge weights. No known lower bounds leverage weighted edges, so it is conceivable that no ε-dependence is needed and that sparsity and lightness bounds match. | | The main result shows that ε-dependence in lightness bounds is indeed necessary. | | Theorem 4 (Main Result) | Let k ≥ 2 be constant and assume the girth conjecture with parameter k − 1. There exists a family of n-node weighted graphs G where, for ε := Θ(n^(−1/(2k−1))), any spanner H with stretch (1 + ε)(2k − 1) has | ℓ(H | G) ≥ Ω(ε^(−1/k) · n^(1/k)). | | Thus, ε-dependence is necessary in general. This lower bound also extends to mildly super-constant k with extra technical work. | | Corollary 5 | For any n and constant k ≥ 2, assuming the girth conjecture with parameter k − 1, there exists an n-node weighted graph G where any (2k − 1)-spanner H has | ℓ(H | G) ≥ Ω(n^(k / (1 + k(2k − 1)))). | | ⸻ | | Relationship to the Weighted Girth Conjecture | | Definition 3 (Weighted Girth) | For a cycle C in a weighted graph G = (V, E, w), its normalized weight is | w*(C) := w(C) / max_{e∈C} w(e). | | The weighted girth of G is the minimum w*(C) over all cycles C in G. | | Theorem 6 | For all t ≥ 1, every graph has a t-spanner with weighted girth > t + 1. Moreover, any graph with weighted girth > t + 1 has no nontrivial t-spanner. | | Thus, the question of lightness for t-spanners is equivalent to the maximum possible lightness over all graphs of weighted girth > t + 1. This reframing is used in our lower bound construction: we aim to construct a graph H with weighted girth > (1 + ε)·2k and | ℓ(H) ≥ Ω(ε^(−1/k) · n^(1/k)). | | Conjecture 7 (Weighted Girth Conjecture) | For all n, g, there exists an unweighted n-node graph that maximizes lightness among all graphs with weighted girth exactly g. | | Our new lower bound does not refute this conjecture but does refute certain stronger variants, which may guide future attacks on the problem. | | Corollary 8 (Refutation of “Strong” Weighted Girth Conjectures) | The conjecture is false if we instead consider maximum lightness over graphs with weighted girth strictly larger than g, or allow g to be non-integral. | | Example: For g = 4, the densest unweighted girth-4 graph has Θ(n^2) edges, while girth > 4 graphs have Θ(n^(3/2)) edges. Our lower bound gives graphs with weighted girth > 4 and lightness Θ(n^(2/3)), exceeding the latter bound but not the former. This pattern holds for any even g ≥ 4. | | ⸻ | | Limitations to Further Progress | | The ε-dependence in our lower bound is far from the current upper bound’s dependence. Improving it for all ε or matching the upper bound’s ε-dependence is difficult because our bound relies on the girth conjecture with parameter k − 1. Either improvement would imply the girth conjecture for parameter k. | | Theorem 9 (Technical Limitations) | If Theorem 4 could be improved as follows— | • Holds for all 0 < ε < 1, or | • Has ε^(−1) dependence instead of ε^(−1/k) in the lower bound— | then the girth conjecture would be true for all constant k. | | Given the longstanding difficulty of the girth conjecture, these barriers are significant. | | ⸻ | | Lower Bound for Light Spanners | | Structure of Girth Conjecture Graphs | | Lemma 10 | If the girth conjecture holds for k, it can be satisfied by graphs that are: | 1. Bipartite | 2. Approximately regular (all degrees Θ(d) for some d) | 3. Have at most O(n^((k+2c−1)/k)) cycles of length (2k + 2c) containing any given edge. | | The proof constructs such graphs from arbitrary girth-conjecture graphs while preserving edge count and girth properties. | | ⸻ | | Lower Bound Construction | • Let G be an n-node graph satisfying the girth conjecture with parameter k − 1 and Lemma 10’s properties. | • Let C be a cycle on N = 4k ε^(−1) n nodes with all edges weight 1 (the spanning cycle, SC). | • Partition C into alternating clusters (k ε^(−1) nodes) and spacers (3k ε^(−1) nodes), n of each. | • Map each node v in G to a cluster X_v in C. | • For each edge (u, v) in G, add one edge of weight ε^(−1) between random nodes in X_u and X_v. | • Delete all non-SC edges in cycles X with normalized weight ≤ (1 + ε)(2k). | | Let H be the final graph. | | ⸻ | | Cycle Analysis | | Lemma 12 | If ε < 1/2, any cycle in H′ (before deletions) with normalized weight ≤ 2k(1 + ε) contains between 2k and 2k(1 + ε) non-SC edges. | | Lemma 13 | For c ≥ 0, the probability that a (2k + 2c)-cycle in G maps to a cycle in H′ with normalized weight ≤ (1 + ε)2k is at most Θ(ε)^(2k+2c) / (2k + 2c)!. | | Lemma 14 | If ε ≤ O(k · n^(−(k−1)(2^(k+2)^c + 2c))) with a small enough constant, then for each non-SC edge e, the expected number of small-normalized-weight cycles in H′ containing e is ≤ 4^c / 4. | | ⸻ | | Proof Wrap-up | | Choosing ε according to Lemma 14 and bounding c via Lemma 12 ensures that each edge survives the final deletion step with constant probability, meeting Lemma 11’s conditions and completing the proof of Theorem 4. | | For constant k, this simplifies to ε = Θ(k · N^(−2k / (2k² − k))) and | ℓ(H) = Ω_k(N^(1/k) · ε^(−1/k)). | | ⸻ | | Proof of Technical Lower Bound | | Let γ(n, 2k) be the maximum number of edges in an n-node graph with girth > 2k. The girth conjecture for k states: | γ(n, 2k) ≥ Ω(n^(1+1/k)). | | Theorem 15 | For all n, k, ε > 0, every n-node graph has a (1 + ε)(2k − 1)-spanner with | ℓ(H | G) ≤ O(ε^(−1) · γ(n, 2k)). | | Proof of Theorem 9 | Using Theorem 4 (conditional on k − 1) and induction on k, improving Theorem 4 to hold for all ε or with ε^(−1) dependence would imply γ(n, 2k) ≥ Ω(n^(1+1/k)), proving the girth conjecture for k. This shows the inherent difficulty in further improving the bound.
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1. Correctly define the free energy function related to factor graphs.
2. Correctly understand and apply the lemma stating that any graph satisfying the girth conjecture can be transformed into a bipartite, approximately regular graph in which every edge participates in at most O(n^((k+2c−1)/k)) cycles of length (2k+2c).
3. Correctly state and prove the main lower bound theorem showing that for constant k and ε := Θ(n^(−1/(2k−1))), any spanner with stretch (1 + ε)(2k − 1) must have lightness at least Ω(ε^(−1/k) · n^(1/k)), thereby establishing the necessity of ε-dependence.
4. Correctly understand and apply the theorem stating that every graph admits a t-spanner of weighted girth greater than t + 1, and that any graph with weighted girth greater than t + 1 has no nontrivial t-spanner, thus linking the light spanner problem to the weighted girth conjecture.
5. Correctly state and prove the technical limitations theorem showing that if the lower bound in Theorem 4 could be improved either to hold for all 0 < ε < 1 or to achieve ε^(−1) dependence, then the girth conjecture would follow for all constant k.
6. Correctly explain the necessity of ε-dependence in lightness bounds, and analyze how the new results improve upon previous lower bounds.
| 6
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#### Definitions and Key Concepts | | - **Spanners**: Given an input graph \( G \), a \( k \)-spanner is a subgraph \( H \) such that the distance between any two nodes \( s \) and \( t \) in \( H \) is at most \( k \) times the distance between \( s \) and \( t \) in \( G \). Formally, \( \dist_H(s, t) \le k \cdot \dist_G(s, t) \) for all nodes \( s, t \). | | - **Sparsity**: The size of a spanner \( H \) is often measured by its sparsity, which is the number of edges \( |E(H)| \). The goal is to minimize this number while maintaining the desired stretch \( k \). | | - **Lightness**: Another way to measure the size of a spanner is by its total edge weight \( w(H) \). Since the weight of a spanner can be unbounded, it is normalized by the weight of a minimum spanning tree (MST) of the input graph \( G \). The lightness of a spanner \( H \) is defined as: | \[ | \ell(H \mid G) := \frac{w(H)}{w(\mst(G))}. | \]
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## Weighted Girth | | **Definition (Weighted Girth)** | | For a cycle \( C \) in a weighted graph \( G = (V, E, w) \), its normalized weight is the quantity | \[ | w^*(C) := \frac{w(C)}{\max_{e \in C} w(e)}. | \] | The weighted girth of \( G \) is the minimum value of \( w^*(C) \) over all cycles \( C \) in \( G \).
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## Girth Conjecture Graphs | | Start with a girth conjecture graph \( G \) with parameter \( k - 1 \), ensuring it is bipartite, approximately regular, and has a bounded number of cycles. | | ## Spanning Cycle (SC) | | Construct a large cycle \( C \) with \( N = 4k\epsilon^{-1}n \) nodes, partitioned into clusters and spacers. | | ## Mapping Nodes to Clusters | | Map nodes of \( G \) to clusters of \( C \), adding high-weight edges between clusters corresponding to edges in \( G \). | | ## Random Edges and Cycle Removal | | Add random edges between clusters and remove cycles with normalized weight below a threshold to ensure the resulting graph \( H \) has the desired weighted girth.
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12
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Computer Science
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Tight Streaming Lower Bounds for Deterministic Approximate Counting
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What is the streaming complexity of the k-counter approximate counting problem, please provide a lower bound.
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Streaming Complexity of the k-Counter Approximate Counting Problem | | Computation Model: Read-once Branching Programs (ROBP) | | A read-once branching program over a finite alphabet Σ of length n consists of n+1 layers of vertices | V₀, V₁, …, Vₙ, with edges between consecutive layers labeled by distinct symbols from Σ. | • The program starts at a single vertex in V₀. | • On input x ∈ Σⁿ, the label of each symbol determines the edge taken at each step. | • Vertices in the last layer Vₙ are labeled with outputs, and the output of the program is the label of the vertex reached. | • The width is the maximum number of vertices in any layer. | • Every vertex must be reachable from some input. | | ⸻ | | Problem Definition: Approximate Counting | | {0,1}-Approximate Counting | | For n ≥ 1 and error bound Δ ≥ 0, the problem ApproxCount[n, Δ] takes input x ∈ {0,1}ⁿ and outputs a value Ŝ such that | |Ŝ − ∑ᵢ xᵢ| ≤ Δ. | | k-Counter Approximate Counting | | For integers k ≥ 2, n ≥ 1, and Δ ≥ 0, the problem ApproxCountₖ-counter[n, Δ] takes input x ∈ [k]ⁿ and outputs a k-tuple (Ŝ₁, …, Ŝₖ) such that for all j ∈ [k]: | |Ŝⱼ − #{i : xᵢ = j}| ≤ Δ. | | k-Parallel Approximate Counting | | For integers k ≥ 1, n ≥ 1, and Δ ≥ 0, the problem ApproxCountₖ-parallel[n, Δ] takes input x ∈ ({0,1}ᵏ)ⁿ and outputs (Ŝ₁, …, Ŝₖ) such that for all j ∈ [k]: | |Ŝⱼ − #{i : (xᵢ)ⱼ = 1}| ≤ Δ. | | ⸻ | | Lower Bound for k-Counter Approximate Counting | | Theorem 1 (k-Counter Lower Bound) | Let k ≥ 2, n ≥ 1, w ≥ 1, and 0 ≤ Δ ≤ n / (2(k−1)). Suppose there exists a length-n, width-w ROBP P over [k] computing ApproxCountₖ-counter[n, Δ]. | Let m be the largest integer with m ≤ n−1 and C(m+k−1, k−1) ≤ w. Then: | | C(m, k) + (n − m − 1)·w ≥ n − 2(k−1)Δ + k / (k−1). | | This bound shows that for small error Δ, the width w must be large, scaling polynomially with n for fixed k. | | ⸻ | | Corollaries | 1. Large Error Regime | If Δ = 3(kⁿ − 1), then | w ≥ Ω((n/k)^(k−1)). | 2. Width–Error Tradeoff | For 0 ≤ Δ ≤ n / (2(k−1)): | Δ ≥ n / (2(k−1)) − (√(k!)) / (2(k−1)) · √(n / w). | 3. Small Error Regime | If 1 ≤ Δ ≤ n / (10(k−1)) and n ≥ 10k: | w ≥ C(n + k − 1 − 2(kᵏ − 1)Δ, k − 1) − O(√(nΔ), k − 1). | | ⸻ | | Lower Bound for k-Parallel Approximate Counting | | Theorem 2 | For k ≥ 1, n ≥ 3k, and Δ = n/3, if a length-n, width-w ROBP P over ({0,1}ᵏ) computes ApproxCountₖ-parallel[n, Δ], then: | w ≥ n^(Ω(k)). | | This shows exponential (in k) width requirement in the parallel setting, even for constant-factor errors. | | ⸻ | | Intuition Behind the Proof | | The proof framework uses: | • Rectangle labeling: Assigns to each vertex in the ROBP a hyper-rectangle in ℕᵏ⁻¹ (or ℕᵏ in the parallel case) describing possible counts for each symbol up to that point. | • Potential function: Measures how much “uncertainty” remains in the count at each layer. | • Growth Lemma: Shows that potential grows by at least a certain amount each layer, unless width is large enough to track many distinct states. | • Final Bound: Relates the maximum possible potential at the last layer (bounded by Δ) to the accumulated growth, yielding a lower bound on w. | | ⸻ | | Final takeaway: | In the streaming model with width-limited ROBPs (equivalent to space-limited streaming algorithms), the k-counter approximate counting problem requires polynomial width (space) for small error, and even super-polynomial width in the k-parallel setting. Theorem 1 provides a general quantitative tradeoff between width, error Δ, and problem parameters.
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1. Verify that the Read-Once Branching Program (ROBP) model is explicitly chosen as the computation framework for analyzing streaming complexity.
2. Confirm that the key components of the ROBP model are clearly described, including the finite alphabet, layered graph structure, start state, transition rules, and the definition of width.
3. Check that the proof introduces **interval labeling** for the {0,1}-approximate counting case and **rectangle labeling** for the general k-counter case, which characterize the range of possible counts at each vertex.
4. Ensure that a potential function is formally defined to measure the accumulated uncertainty in ROBP states as inputs are processed.
5. Confirm that the properties of the potential function are rigorously analyzed, including its guaranteed growth when the ROBP width is small and its boundedness under approximate counting constraints.
6. Verify that the base case k=2 ({0,1}-approximate counting) is analyzed in detail, establishing that any ROBP computing ApproxCount[n, Δ] with Δ = n/10 requires width Ω(n).
7. Check that the analysis is generalized from the k=2 case to the general k-counter case via rectangle labeling and multidimensional potential functions, yielding polynomial width lower bounds.
8. Confirm that the main conclusion is clearly stated: computing k-counter approximate counting in the streaming model requires Ω(k log(n/k)) bits of space, and equivalently, width Ω((n/k)^(k−1)) in the ROBP model for error Δ = n/(3(k−1)).
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- In computer science, the streaming model is a computational model for processing large-scale data, where data arrives as a stream and algorithms need to process the data with limited storage space. In the context of streaming, exact counting of the frequency of each element may require substantial storage space, making the study of approximate counting problems of great significance. Approximate counting problems allow the algorithm to output an approximate frequency value as long as the error between this value and the true frequency is within a certain range. | - The k - counter approximate counting problem is a classic problem in streaming. Given an input string of length n, where each character of the string is from a character set of size k, the goal is to approximate the frequency of each character in the string, with the requirement that the error between the approximate frequency and the true frequency for each character does not exceed a given threshold. For example, when k = 2, the problem is equivalent to estimating the frequency of 1 (i.e., the Hamming weight) in a 01 - string. This kind of problem appears as a basic module in many complex algorithms, so studying its complexity is a fundamental question in theoretical computer science. | - In the streaming model, for the k - counter approximate counting problem, the best-known lower bound before was trivial, i.e., using O(klogn) bits of space to exactly count the frequency of each character. However, in the regime where n is much larger than k, it was previously unclear whether less space could be used to output an approximation of the frequency. In addition, for some other problems related to approximate counting, such as the heavy hitters problem and the quantile sketch problem, there are also similar issues of storage space complexity. For example, the Misra - Gries algorithm is a well - known algorithm for solving the heavy hitters problem. It uses O(k(log(n/k)+log(U/k))) bits of space in the streaming model to output the heavy hitters and their frequency estimates, but it was previously unknown whether the space complexity of this algorithm was already optimal.
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## 1. {0, 1}-Approximate Counting | For any integer n ≥ 1 and real number ∆ ≥ 0, define the problem ApproxCount[n, ∆] as follows: on any input x ∈ {0, 1}^n, a valid output of x is a real number ̂S such that | ̂S − ∑_{i=1}^n x_i | ≤ ∆. | | ## 2. k-counter Approximate Counting | For any integers k ≥ 2, n ≥ 1, and real number ∆ ≥ 0, define the problem ApproxCountk-counter[n, ∆] as follows: on any input x ∈ [k]^n, a valid output of x is a k-tuple of real numbers ( ̂S_1, · · · , ̂S_k ) such that | ̂S_j − #{i ∈ [n] : x_i = j} | ≤ ∆ for all j ∈ [k]. | | ## 3. Rectangle Labeling of the k - counter Case | For a length - n ROBP P over alphabet [k] that attempts to compute ApproxCountk - counter[n, ∆], label each vertex v ∈ Vt (0 ≤ t ≤ n) with a (k - 1) - dimensional rectangle R(v). R(v) is defined as [a1, b1] × · · · × [ak−1, bk−1], where for each j ∈ [k - 1], aj, bj are the minimal and maximal elements in {c ∈ N: ∃(x1, · · · , xt) ∈ [k]t such that (x1, · · · , xt) reaches v in P and #{i ∈ [t]: xi = j} = c}. For each 0 ≤ t ≤ n, let Rt := {R(v): v ∈ Vt} be the collection of all rectangle labels in layer Vt. | | ## 4. Potential Function | Consider a length - n ROBP P over alphabet [k] that attempts to compute ApproxCountk - counter[n, ∆]. For each 0 ≤ t ≤ n, define Tt,k := {(x1, · · · , xk−1) ∈ Nk−1: x1 + · · · + xk−1 ≤ t}, which is the set of possible numbers of 1’s, 2’s, · · · , (k - 1)’s in the first t input words. Then, for each 0 ≤ t ≤ n and (x1, · · · , xk−1) ∈ Tt,k, define φt(x1, · · · , xk−1) := maxR=[a1,b1]×···×[ak−1,bk−1]: R∈Rt, (x1,··· ,xk−1)∈R{min{b1 + · · · + bk−1, t} - x1 - · · · - xk−1}. Furthermore, for each 0 ≤ t ≤ n, define the total potential of layer Vt as Φt := ∑(x1,··· ,xk−1)∈Tt,kφt(x1, · · · , xk−1). | | ## 5. Rectangle Labeling of the k - parallel Case | For a length - n ROBP P over alphabet {0, 1}k that attempts to compute ApproxCountk - parallel[n, ∆], label each vertex v ∈ Vt (0 ≤ t ≤ n) with a k - dimensional rectangle R(v). R(v) is defined as [a1, b1] × · · · × [ak, bk], where for each j ∈ [k], aj, bj are the minimal and maximal elements in {c ∈ N: ∃(x1, · · · , xt) ∈ {0, 1}k^t, (x1, · · · , xt) reaches v and #{i ∈ [t]: (xi)j = 1} = c}. For each 0 ≤ t ≤ n, let Rt := {R(v): v ∈ Vt} be the collection of all rectangle labels in layer Vt.
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# Methodology | | The methodology employed to establish tight streaming lower bounds for deterministic approximate counting involves the following steps: | | 1. **Model Selection**: Utilize the read-once branching program (ROBP) model to represent streaming algorithms. In this model, a streaming algorithm is depicted as a layered multigraph where vertices correspond to memory states, and edges labeled with input symbols dictate transitions between states. | | | 2. **Interval and Rectangle Labeling**: For the k=2 case, label vertices in the ROBP with intervals representing possible counts of a particular symbol. Generalize this approach to higher dimensions using rectangle labeling for the k-counter case, where vertices are labeled with multidimensional rectangles representing possible counts of each symbol. | | 3. **Potential Function Analysis**: Define a potential function based on the interval or rectangle labels. This function quantifies the growth of uncertainty in the counts as the ROBP processes the input, with its growth rate tied to the width of the ROBP (corresponding to the space used by the streaming algorithm). | | 4.**Proof Strategy**: Demonstrate that if the space (or width) is too small, the potential function grows excessively, contradicting the requirement that the final approximation must stay within specified error bounds. This contradiction establishes the lower bound on the space required. | | | 5. **Implications**: Apply the results to derive lower bounds for related streaming problems, such as heavy hitters and quantile sketch, by showing that solutions to these problems can be used to approximate counts, thereby inheriting the lower bounds established for approximate counting. | | 6.**Algorithm Development**: Devise non-trivial algorithms for approximate counting that nearly match the lower bounds. These algorithms demonstrate the tightness of the results and the difficulty of improving upon them.
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13
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Computer Science
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A Refutation of the Pach-Tardos Conjecture for 0-1 Matrices
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Refute the Pach-Tardos conjecture for 0-1 matrices.
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Refuting the Pach–Tardos Conjecture for 0–1 Matrices | | The Pach–Tardos conjecture predicted an upper bound on the extremal function Ex(M, n)—the maximum number of 1s in an n × n 0–1 matrix that avoids a given forbidden submatrix M. | The work here constructs explicit 0–1 matrices with far more 1s than the conjecture would allow, thereby disproving it for certain patterns. | | ⸻ | | Core Construction | | We define a base matrix A[b, m]: | • Rows: indexed by [m] × [m]^b | • Columns: indexed by [m]^b × {0,1}^b | • Entry rule: | | A((s, r), (c, i)) = 1 if r = c + s · i | 0 otherwise | | | • Arithmetic is done coordinatewise over integers, with i treated as a 0–1 indicator vector. | | Key property (Lemma 2): | Each column has on average at least m/(b+1) - 1 ones, so | ‖A[b, m]‖₁ ≥ Ω(m/b) × (#columns). | | ⸻ | | Pattern Avoidance | | The forbidden patterns of interest are: | • S₀ and S₁: small fixed 0–1 matrices that arise in the conjecture. | • Covering patterns: defined to have a “distinguished” row with 1s at the extremes, plus certain row–interval covering properties. | | Lemma 4 gives structural constraints on the positions of 1s in A[b, m], relating the order of row/column indices to coordinate differences in the [m]^b part. | | ⸻ | | Main Lower Bound Result | | Theorem 1 | For S₀ and S₁, | | Ex(S₀, n), Ex(S₁, n) ≥ n² · √(log n − O(log log n)) | | Reasoning: | 1. Show A[b, m] contains no S₀ or S₁: | • Assume S₀ is embedded in A. | • Define difference vectors x, y, z from certain column pairs. | • Lemma 4 forces their first nonzero coordinates to be incompatible with the relative order constraints implied by S₀. | • Same argument works for S₁ (swapping two rows). | 2. Set m = 2ᵇ so that A is square: n = 2^(b² + b). | 3. With b ≈ √(log n), the density gives the claimed bound. | | Thus, these matrices are both S₀- and S₁-free yet have Ω(n² √log n) ones, contradicting the conjecture. | | ⸻ | | Extension to Covering Patterns | | Theorem 2 | If M is any covering pattern (per Definition 1), then A[b, m] is M-free and | | Ex(M, n) ≥ n² · √(log n − O(log log n)) | | Proof uses the same difference–vector argument: the covering property forces a sum of certain differences to match a global difference, but Lemma 4 forbids this. | | ⸻ | | Polylogarithmic Lower Bounds for Alternating Patterns | | For alternating patterns Pₜ, modify the construction to Aₜ[b, m] by restricting to columns with exactly t ones in their {0,1}^b part and offsetting even/odd ones differently. | | Theorem 3 | For fixed t ≥ 1: | | Ex(Pₜ, n) = Ω( n · (log n / log log n)ᵗ ) | | The proof: | • Assume a Pₜ instance appears in Aₜ. | • Label rows/columns and examine the positions of first nonzero coordinates in column differences. | • Monotonicity and parity constraints force a coordinate–value conflict, so Pₜ cannot occur. | | ⸻ | | Final Implication | | By explicitly constructing large, pattern-free matrices for S₀, S₁, and more general covering patterns, we get extremal functions far above the Pach–Tardos conjecture’s prediction. This refutes the conjecture for these patterns, replacing its proposed bound with much larger, explicit lower bounds.
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1. **Correct Definition of Forbidden Patterns**
Check that forbidden patterns in 0–1 matrices are correctly defined:
- A pattern P is contained in a matrix A if A can be transformed into P by deleting rows/columns and flipping some 1s to 0s.
- Extremal function Ex(P, n) is defined as the maximum number of 1s in an n×n matrix avoiding P.
- The connection to bipartite graphs (rows/columns correspond to bipartition, order matters) is clearly stated.
2. **Accurate Definition of Matrix Construction**
Verify the construction of the base matrices A[b, m] and their variant At[b, m]:
- Rows indexed by [m] × [m]^b, columns by [m]^b × {0,1}^b (or restricted to Hamming weight t for At).
- Entry rule: A((s,r),(c,i)) = 1 if r = c + s·i (for A[b,m]); for At[b,m], offsets split into even/odd coordinates, using s and (m+1−s).
- Ensure lexicographic ordering and coordinate-wise arithmetic are correctly specified.
3. **Valid Introduction of Alternating Coordinate Offsets**
Confirm that in the At[b,m] construction, introducing alternating offsets (i_even, i_odd) is valid and necessary:
- i_even contains the 2nd, 4th, … 1s of i; i_odd contains the 1st, 3rd, … 1s.
- Offsets s and m+1−s are applied accordingly.
- This modification ensures Pt-free property (alternating patterns cannot appear).
4. **Exact Statement and Proof of Lemma 2**
Verify Lemma 2: For the base construction A[b, m], the number of ones satisfies
\[
\|A[b,m]\|_1 \;\ge\; 2^b m^b \cdot (m/(b+1) - 1),
\]
i.e. each column contains on average at least m/(b+1) − 1 ones, so the matrix has Ω(m/b) times as many ones as columns. Confirm proof reasoning is correct (expectation over columns, non-overflow condition).
5. **Proper Definition of Covering Patterns**
Ensure Definition 1 is correct:
- A covering pattern has a distinguished row with 1s in the first and last columns.
- Other rows with ≥2 ones satisfy interval covering constraints relative to the distinguished row.
- The union of these row intervals covers the whole column range.
6. **Valid Proof of Theorem 2.1**
Confirm Theorem 2.1: For any covering pattern M, the constructed A[b, m] avoids M (M-free), and
\[
Ex(M, n) \;\ge\; n^2 \cdot \sqrt{\log n - O(\log \log n)}.
\]
Proof uses Lemma 4 and contradiction with interval covering property.
7. **Exact Statement and Proof of Theorem 2.3**
Verify Theorem 2.3: For any fixed t ≥ 1, alternating pattern Pt has extremal function
\[
Ex(P_t, n) = \Omega\big( n \cdot ( \tfrac{\log n}{\log \log n} )^t \big).
\]
Confirm that At[b,m] is Pt-free, and density argument yields the bound.
8. **Correct Definition of Landmark Columns and Signatures**
Ensure that landmark columns (F, L, a_j, b_j) are defined correctly as structural markers in each row, and that signatures (sig0, sig1, sig2) are constructed to encode distances and relative positions of landmarks.
9. **Valid Proof of Lemma 6**
Confirm Lemma 6: If an entry A(r, c*) = 1 is not the last 1 of its sig0-type, then at least one of inequalities (I.1)–(I.t) holds (relating distances between landmarks and ζ). Proof checks intervals, applies log-binned comparisons, and establishes inequality bounds.
10. **Valid Proof of Theorem 3.1**
Verify Theorem 3.1: For t ≥ 2, the extremal function of alternating patterns satisfies
\[
Ex(P_t, n) = O\big( n \cdot ( \tfrac{\log n}{\log \log n} )^t \big).
\]
Confirm that the 4-step marking process (using sig0, sig1, sig2) eliminates all unmarked 1s unless a Pt instance exists, bounding the number of 1s in Pt-free matrices.
| 10
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## Forbidden 0--1 Matrix Theory | - **Origins and Applications**: The theory of forbidden 0--1 matrices emerged in the late 1980s, applied to problems in discrete and computational geometry by Mitchell, Pach and Sharir, and Füredi. It generalizes Davenport-Schinzel theory and Turán theory to ordered bipartite graphs, influencing areas like computational geometry, data structure analysis, and the development of the graph parameter "twin width". | - **Definitions**: A matrix $A \in \{0,1\}^{n \times m}$ contains a pattern $P \in \{0,1\}^{k \times l}$ if $P$ can be obtained from $A$ by removing rows/columns and flipping 1s to 0s. If not, $A$ is $P$-free. The extremal function $\text{Ex}(P, n, m)$ is the maximum weight (number of 1s) of a $P$-free matrix in $\{0,1\}^{n \times m}$, with $\text{Ex}(P, n) = \text{Ex}(P, n, n)$. $P$ can be seen as the adjacency matrix of an ordered bipartite graph. Turán's extremal function $\text{ExT}(H, n)$ is the maximum number of edges in an $n$-vertex graph without $H$ as a subgraph. | | ## Pattern Classification | - **Turán's Extremal Function Classification**: Forbidden subgraphs are classified based on Turán's extremal function: | - Non-bipartite $H$: $\text{ExT}(H, n) = \Theta(n^2)$. | - Bipartite $H$ with a cycle: $\text{ExT}(H, n) = \Omega(n^{1+c_1})$ and $O(n^{1+c_2})$ for $0 < c_1 < c_2 < 1$. | - Acyclic (forest) $H$: $\text{ExT}(H, n) = \Theta(n)$. | - **0--1 Matrix Patterns**: Füredi and Hajnal noted $\text{Ex}(P, n) = \Omega(\text{ExT}(G(P), 2n))$ and found examples where $\text{Ex}(P, n) = \omega(\text{ExT}(G(P), 2n))$, such as $P_1$ and $Q_3$, which are acyclic matrices but have $\text{Ex}(P_1, n) = \Theta(n \log n)$ and $\text{Ex}(Q_3, n) = \Theta(n \alpha(n))$. | | ## Füredi-Hajnal and Pach-Tardos Conjectures | - **Füredi-Hajnal Conjectures**: | - **Permutation Matrix Conjecture (conj:FH-perm)**: If $P$ is a permutation matrix, then $\text{Ex}(P, n) = O(\text{ExT}(G(P), n)) = O(n)$. | - **Logarithmic Factor Conjecture (conj:FH-logn)**: For any $P$, $\text{Ex}(P, n) = O(\text{ExT}(G(P), n) \cdot \log n)$. | - **Acyclic Pattern Conjecture (conj:FH-acyclic)**: For any acyclic $P$, $\text{Ex}(P, n) = O(\text{ExT}(G(P), n) \cdot \log n) = O(n \log n)$. | - **Pach-Tardos Conjecture (conj:PachTardos)**: For an acyclic 0--1 pattern $P$: | - **Weak Version**: $\text{Ex}(P, n) = O(n \log^{C_P} n)$ for some constant $C_P$. | - **Strong Version**: $\text{Ex}(P, n) = O(n \log^{\|P\|_1 - 3} n)$.
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## Covering Pattern | A pattern \( M \in \{0,1\}^{\alpha \times \beta} \) with rows indexed by \( 0 \leq i < \alpha \) and columns by \( 0 \leq j < \beta \). There exists a distinguished row \( k^* \) such that: | 1. \( M(k^*, 0) = M(k^*, \beta - 1) = 1 \). | 2. Let \( J \) be the set of row indices (excluding \( k^* \)) with at least two 1s. \( J \) contains at most one element \( j_0 < k^* \). For any \( j \in J \) where \( j > k^* \), some column contains two 1s in rows \([k^*, j]\). | 3. For \( l \in J \), define \( \text{first}(l) \) and \( \text{last}(l) \) as the column indices of the first and last 1s in row \( l \). The real intervals \([\text{first}(l), \text{last}(l)]\) cover the entire range \([0, \beta - 1]\). | | ## Landmark Columns | For a 1 in matrix \( A \) at position \( (r, c) \): | - **F** and **L**: The first and last 1s in row \( r \) following column \( c \). | - **a_j** and **b_j**: Consecutive 1s in row \( r \) such that \( F \leq a_j < b_j \leq a_{j+1} \) and \( b_j - a_j \) is maximized. | | ## Signatures | For a 1 in matrix \( A \) at position \( (r, c) \) that is not one of the last two 1s in its row: | - **sig0(r, c)**: A vector \( \left( \left\lfloor \log_\zeta (F - c) \right\rfloor, \left\lfloor \log_\zeta (b_1 - a_1) \right\rfloor, \ldots, \left\lfloor \log_\zeta (b_{t-1} - a_{t-1}) \right\rfloor \right) \). | - **sig1(r, c)**: A vector \( \left( \left\lfloor \log_{1+\epsilon} (a_1 - c) \right\rfloor, \ldots, \left\lfloor \log_{1+\epsilon} (a_{t-1} - c) \right\rfloor \right) \) and the relative positions of \( \left\lfloor \log_{1+\epsilon} (b_j - c) \right\rfloor \) to the vector elements. | - **sig2(r, c)**: A vector \( \left( \left\lfloor \log_{1+\epsilon} (b_1 - c) \right\rfloor, \ldots, \left\lfloor \log_{1+\epsilon} (b_{t-1} - c) \right\rfloor \right) \), the relative positions of \( \left\lfloor \log_{1+\epsilon} (a_j - c) \right\rfloor \) to the vector elements, and a vector \( \left( \min \left\{ \frac{a_2 - b_1}{(b_1 - c)/2}, 3t \right\}, \ldots, \min \left\{ \frac{L - b_{t-1}}{(b_{t-1} - c)/2}, 3t \right\} \right) \).
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## 1. Matrix Construction | - **Construct Special Matrices**：Define a new class of 0-1 matrices \( A[b, m] \) with rows indexed by \([m] \times [m]^b\) and columns by \([m]^b \times \{0, 1\}^b\). Fill the elements with \( A((s, r), (c, i)) = 1 \) if \( r = c + s \cdot i \). | - **Introduce Alternating Coordinate Offsets**：Based on \( A[b, m] \), construct \( A_t[b, m] \) matrices by restricting columns (e.g., to those with weight \( t \)). | | ## 2. Refuting the Conjecture | - **Construct Counterexample Matrices**：Using the constructed \( A[b, m] \) matrices, demonstrate that for two weight-6 patterns \( S_0 \) and \( S_1 \), their extremal functions have a lower bound of \( n2^{\Omega(\sqrt{\log n})} \). | - **Expand the Scope of Counterexamples**：Further prove that all patterns in the covering pattern class have similar lower bounds. This extends the counterexamples from \( S_0 \) and \( S_1 \) to a broader covering pattern category. | | ## 3. Alternating Pattern Class Analysis | - **Lower Bound Proof**：Using the constructed \( A_t[b, m] \) matrices, show that the extremal function of the alternating pattern class \( P_t \) has a lower bound of \( \Omega(n(\log n / \log \log n)^t) \). | - **Upper Bound Proof**：Through an analysis and marking process, demonstrate that the extremal function of the alternating pattern class \( P_t \) has an upper bound of \( O(n(\log n / \log \log n)^t) \).
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14
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Computer Science
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Universal Perfect Samplers for Incremental Streams
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How can we develop exact G-sampling algorithms for functions G in the specific class G (including p-th moments and logarithmic functions) when the vector x is presented as an incremental stream of positive updates, aiming to achieve exact sampling with limited memory and potentially supporting sampling a sequence of k indices with or without replacement?
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Exact G-sampling from positive-update streams | | Goal. Given a vector x ∈ Rⁿ₊ arriving as an incremental stream of positive updates (v, Δ), sample indices exactly with probability proportional to G(x(v)), for any G in the class | G(z) = c·1[z>0] + γ₀ z + ∫₀^∞ (1 − e^{−rz}) ν(dr) | (where c, γ₀ ≥ 0 and ν is a Lévy measure). This class includes z^p (p∈(0,1]), 1−e^{−τz}, and log(1+z). We also want limited memory and the ability to output k indices with or without replacement. | | Below is a clean recipe that achieves truly perfect sampling (zero error probability) with small space. | | ⸻ | | Key tool: Lévy-induced level functions | | For any G ∈ G, there exists a deterministic level function ℓ_G(a, b) such that: | • If Y ~ Exp(λ) and U ~ Uniform(0,1), then ℓ_G(Y, U) ~ Exp(G(λ)). | • ℓ_G is monotone increasing in both a and b. | | Interpretation: ℓ_G converts standard exponentials into exponentials whose rate is G(·). This is the engine behind exact sampling. | | ⸻ | | One-sample, O(1) state: Generic G-Sampler | | Maintain just a pair (v*, h*), initialized as (⊥, +∞). Use a pairwise-independent hash H : [n] → [0,1]. | | On update (v, Δ): | 1. Draw fresh Y ~ Exp(1). | 2. Compute h = ℓ_G(Y/Δ, H(v)). | 3. If h < h*, set (v*, h*) ← (v, h). | | Guarantee. At all times, P[v* = v] = G(x(v)) / G(∑_u x(u)). | Intuition: per index v, the minimum over its updates, | | h_v = min_i ℓ_G( (Y_i)/Δ_i , H(v) ) ~ Exp(G(x(v))) | | and the global min over v is an exponential race with total rate G(∑ x); the winner is sampled with exact G-weights. | | Space. Two words (plus the hash seed). | | ⸻ | | Many G’s, one pass, small space: ParetoSampler | | We can be universal over the whole class G by storing only the Pareto frontier of points | | (a_i, b_i, v_i) = (Y_i/Δ_i, H(v_i), v_i) | | ordered by (a, b). | | Update: insert (Y/Δ, H(v), v) and keep only the frontier. | Query(G): return the v attached to the frontier point that minimizes ℓ_G(a, b). | | Guarantee. For any G ∈ G, the returned v is an exact G-sample. | Space. Frontier size is O(log n) w.h.p., so space is O(log n) words after poly(n) updates. | | ⸻ | | k samples without replacement | | We need the k smallest keys among { h_v ~ Exp(G(x(v))) }. | | Streaming algorithm (heap of size k): | • For each update (v, Δ), compute h_candidate = ℓ_G(Y/Δ, H(v)) as before. | • Maintain, per index v, the current best key h_v = min of its candidates. | • Maintain a max-heap of the global k smallest distinct h_v. Replace the heap top if a new h_v beats it. | • At any time, output the heap’s k indices: this is the exact k-sample without replacement under G-weights (the order in the heap is the correct exponential-race order). | | Space. O(k) keys plus bookkeeping; in practice O(k + log n) words. | | (Why correct?) Independent exponentials with rates G(x(v)) order the indices exactly as sampling without replacement with those weights. | | ⸻ | | k samples with replacement | | Two standard exact options: | 1. Independent rounds. Repeat the one-sample algorithm k times using independent hash “salts” H₁, …, H_k (or disjoint RNG streams). Each round returns an exact G-weighted draw; duplicates can occur. | • Space: O(k) (one (v*, h*) per round) or O(k log n) if using the Pareto frontier per round. | 2. Poisson clocks (exponential races). For each v, generate an infinite sequence of i.i.d. keys { h_v^(j) ~ Exp(G(x(v))) } using independent salts; merge globally and take the first k arrivals with replacement. Streaming-wise, maintain the current k smallest among all generated keys. | • Space: O(k) keys; cost is extra randomness per additional arrival. | | Both methods give exact G-weighted sampling with replacement. | | ⸻ | | Instantiations for common G | | You get explicit ℓ_G and drop them straight into the update rules: | • p-th moments (G(z) = z^p, 0 < p ≤ 1). Use the subordinator for a stable law; this yields a closed-form ℓ_G. The special case p=1/2 gives the neat update: | | h = sqrt(2Y/Δ) · erf⁻¹(H(v)) | | (the F_{1/2} sampler). This produces exact p-weighted samples. | | • Poisson weight (G(z) = 1 − e^{−τz}): corresponds to a Poisson process; ℓ_G is a simple transform of Y/Δ and H(v). | • Logarithmic weight (G(z) = log(1+z)): corresponds to a Gamma subordinator; again ℓ_G is explicit via its CDF inversion. | | Because the class G matches Laplace exponents of non-negative Lévy processes, deriving ℓ_G is systematic: find the subordinator for G, define | ℓ_G(a, b) = inf{ t : P(X_t ≥ a) ≥ b }, or directly invert the map (Y, U) ↦ ℓ_G(Y, U) so that its output is Exp(G(·)). | | ⸻ | | Memory, updates, and guarantees | • Updates: Each stream update touches constant state: draw one exponential, one hash, one ℓ_G, and maybe a heap replace. | • Space: | • 1 sample → 2 words. | • Universal over G → O(log n) words w.h.p. (Pareto frontier). | • k without replacement → O(k) words; with replacement via independent rounds → O(k) as well. | • Correctness: All samplers are exact (no approximation, no failure prob): (ε, η, δ) = (0, 0, 0). | | ⸻ | | TL;DR (what to implement) | • Pick your G and its ℓ_G. | • For each (v, Δ): | • draw Y ~ Exp(1), compute h = ℓ_G(Y/Δ, H(v)), | • update (v*, h*) (one sample), the Pareto frontier (universal), or the top-k heap (k-sampling). | • Query at any time to return an exact G-weighted sample (or k of them).
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1. **Correctly Define the Function Class G**
Ensure that the function class G is defined as
\[
G(z) = c·1[z>0] + γ_0 z + \int_0^\infty (1 - e^{-rz}) \, \nu(dr),
\]
where c, γ₀ ≥ 0 and ν is a non-negative Lévy measure with ∫ min(r,1)ν(dr) < ∞.
Verify its interpretation as the class of Laplace exponents of non-negative one-dimensional Lévy processes, and confirm that it includes examples such as \(G(z) = z^p\) (p ∈ (0,1]), \(G(z) = 1 - e^{−τz}\), and \(G(z) = \log(1+z)\).
2. **Correctly Explain the Properties of Non-negative Lévy Processes**
Review the definition of non-negative Lévy processes (stationary and independent increments, stochastic continuity, non-negativity) and explain how the Lévy–Khintchine theorem establishes a one-to-one correspondence between any \(G ∈ G\) and a subordinator process with parameters (c, γ₀, ν).
3. **Correctly Interpret the Lévy-induced Level Function ℓG**
Verify the definition
\[
ℓ_G(a, b) = \inf\{t : P(X_t ≥ a) ≥ b\},
\]
where \(X_t\) is the Lévy process associated with G.
Confirm that ℓG is monotone increasing in both arguments and that applying ℓG to exponential/Uniform random variables transforms Exp(λ) into Exp(G(λ)), which is the key to perfect sampling.
4. **Correctly Describe the Function and Storage Efficiency of the General G-Sampler**
State that the generic G-Sampler (Algorithm 1) maintains only a pair (v*, h*) in memory, i.e. 2 words, and guarantees that at all times \(P[v* = v] = G(x(v))/G(x)\).
5. **Correctly Explain the Update Process of the General G-Sampler**
Detail that for each update (v, Δ), the sampler:
- draws Y ~ Exp(1),
- computes h = ℓG(Y/Δ, H(v)),
- updates (v*, h*) if h is smaller.
Verify that per-index minima h_v follow Exp(G(x(v))) and the global winner follows the exponential race with rate G(x).
6. **Correctly State the Storage Efficiency and Sampling Performance of ParetoSampler**
Confirm that ParetoSampler keeps only the Pareto frontier of tuples (Y/Δ, H(v), v). Its expected size is < ln n+1 and O(log n) with high probability, so total space is O(log n) words, while still allowing exact sampling for any G at query time.
7. **Correctly Interpret the Pareto Frontier Maintenance Mechanism of ParetoSampler**
Ensure that each update inserts (Y/Δ, H(v), v) and prunes dominated points. At query time, given any G, the chosen index is the one attached to the frontier point with minimal ℓG(a, b).
8. **Correctly Present and Prove Lemma 1 (Level Function Lemma)**
State: For any G ∈ G, there exists ℓG such that
- **2D-monotonicity**: if a ≤ a′ and b ≤ b′ then ℓG(a, b) ≤ ℓG(a′, b′),
- **G-transformation**: if Y ~ Exp(λ) and U ~ Uniform(0,1), then ℓG(Y, U) ~ Exp(G(λ)).
Proof relies on the Lévy–Khintchine representation, showing that the distribution of ℓG(Y, U) matches Exp(G(λ)).
9. **Correctly Present and Prove Theorems 1 and 2 (Correctness of Samplers)**
- **Theorem 1 (G-Sampler)**: The generic sampler always stores a pair (v*, h*) such that h* ~ Exp(G(x)) and P[v* = v] = G(x(v))/G(x), hence it is a truly perfect sampler.
- **Theorem 2 (ParetoSampler)**: ParetoSampler uses O(log n) space (w.h.p.) and for any G ∈ G produces exact samples with the same distribution as G-Sampler.
Proofs use Lemma 1 and exponential race arguments.
10. **Correctly Derive the Expressions for ℓG for Specific Functions G**
Show explicit forms:
- \(G(z) = 1[z>0]\): ℓG(a, b) = −log(1−b) (F₀ sampler).
- \(G(z) = z\): ℓG(a, b) = a (F₁ sampler).
- \(G(z) = √z\): ℓG(a, b) = √(2a) · erf⁻¹(b) (F1/2 sampler).
- \(G(z) = 1−e^{−τz}\): ℓG found by solving Poisson tail equations.
- \(G(z) = log(1+z)\): ℓG found as solution of Gamma CDF equations.
11. **Correctly Present the Method for Sampling Without Replacement and Provide Theoretical Guarantees**
State that the (G, k)-Sampler-WOR algorithm maintains the k smallest keys {(v, h)} under ℓG.
**Theorem 4**: Its output distribution satisfies
\[
P((v_1,…,v_k)) = \prod_{i=1}^k \frac{G(x(v_i))}{G(x) - \sum_{j<i} G(x(v_j))},
\]
exactly matching sampling k indices without replacement. Space usage is 2k words for (G,k)-Sampler-WOR or O(k log n) for k-ParetoSampler-WOR.
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- The G-sampling problem involves a function G: R+ → R+. For a vector x ∈ R+n, the G-moment is defined as G(x) = ∑v∈[n]G(x(v)). The goal of G-sampling is to select an index v* ∈ [n] such that pr(v* = v) = G(x(v))/G(x). | | - Approximate G-samplers may introduce multiplicative and additive errors in the probability, and can have a non-trivial probability of failure. | | - The class of functions G includes Laplace exponents of non-negative, one-dimensional Lévy processes. It encompasses several well-studied classes such as pth moments G(z) = z^p for p ∈ [0, 1], logarithms G(z) = log(1 + z), and Cohen and Geri's soft concave sublinear functions used to approximate concave sublinear functions like cap statistics. | | - For G-sampling from incremental streams, Min-sketch and reservoir sampling can be used for F₀ and F₁ frequency moments.
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### Definition 1 (Approximate/Perfect/Truly Perfect G-samplers) | Let \( G : \mathbb{R}_+ \to \mathbb{R}_+ \) be a function. An approximate G-sampler with parameters \( (\epsilon, \eta, \delta) \) is a sketch of \( \mathbf{x} \) that can produce an index \( v^* \in [n] \cup \{\perp\} \) such that \( \Pr(v^* = \perp) \leq \delta \) (where \( v^* = \perp \) indicates failure) and | \[ | \Pr(v^* = v \mid v^* \neq \perp) \in (1 \pm \epsilon)\frac{G(\mathbf{x}(v))}{G(\mathbf{x})} \pm \eta. | \] | If \( (\epsilon, \eta) = (0, 1/\text{poly}(n)) \), the sampler is said to be perfect. If \( (\epsilon, \eta) = (0, 0) \), it is truly perfect. | | ### Definition 2 (Non-negative Lévy processes) | A random process \( X = (X_t)_{t \geq 0} \) is a non-negative Lévy process if it satisfies: | 1. **Non-negativity**: \( X_t \in \mathbb{R}_+ \cup \{\infty\} \) for all \( t \in \mathbb{R}_+ \). | 2. **Stationary Increments**: \( X_{t+s} - X_t \sim X_s \) for all \( t, s \in \mathbb{R}_+ \). | 3. **Independent Increments**: For any \( 0 \leq t_1 < t_2 < \ldots < t_k \), \( X_{t_1}, X_{t_2} - X_{t_1}, \ldots, X_{t_k} - X_{t_{k-1}} \) are mutually independent. | 4. **Stochastic Continuity**: \( X_0 = 0 \) almost surely and \( \lim_{t \searrow 0} \Pr(X_t > \epsilon) = 0 \) for any \( \epsilon > 0 \). | | ### Definition 3 (Lévy-induced level function) | Let \( G \in \mathcal{G} \) and \( X = (X_t)_{t \geq 0} \) be the corresponding non-negative Lévy process. The induced level function \( \ell_G : (0, \infty) \times (0, 1) \to \mathbb{R}_+ \) is defined, for \( a \in (0, \infty) \) and \( b \in (0, 1) \), as | \[ | \ell_G(a, b) = \inf\{ t \mid \Pr(X_t \geq a) \geq b \}. | \]
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## Leveraging Lévy Process Properties | | Since the function class G corresponds to non-negative Lévy processes, examining the properties of Lévy processes and related functions offers a novel perspective and theoretical foundation for constructing samplers. The Lévy-Khintchine representation theorem is especially useful as it links function G with non-negative Lévy processes, enabling the definition of the Lévy-induced level function ℓG, which is crucial for perfect sampling. | | ## Design of the General G-Sampler | | A general G-sampler has been developed, utilizing only 2 words of memory and capable of always returning an index v∗ according to the precise probability distribution of G(x(v))/G(x). | | ### Update Process | | When handling each update operation (v,∆), a new exponentially distributed random variable Y is generated. Based on the current update's increment ∆ and the level function ℓG of function G, a new value h is computed. If this h is less than the currently stored minimum h∗, the stored index and corresponding h value are updated. | | ## Design of ParetoSampler | | ParetoSampler employs O(logn) words of memory (with high probability) and can generate exact G samples for any given G∈G at query time. | | ### Maintenance of the Pareto Frontier | | During each update, tuples related to the update are generated, and the minimal Pareto frontier of these tuples is maintained. When sampling is required, the corresponding tuple is selected from the Pareto frontier based on the given G to determine the sampled index.
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15
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Computer Science
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Quasi-Monte Carlo Beyond Hardy-Krause
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How to develop a numerical integration method that combines the advantages of Monte Carlo and quasi-Monte Carlo methods to achieve smaller errors, higher flexibility, better performance, and more efficient computation?
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Build a “best-of-both-worlds” integrator in 5 steps | | Here’s how to actually develop a method that keeps Monte-Carlo’s flexibility and unbiasedness but beats MC error (and even the classic QMC Koksma–Hlawka bound) whenever the integrand allows it. | | 1) Replace Hardy–Krause by a smoothed-out variation | | Define a new variation of f:[0,1]^d\to\mathbb{R} from its Fourier coefficients \hat f(k), k\in\mathbb{Z}^d: | \sigma_{\text{SO}}(f)^2 \ := \ \sum_{k\neq 0} |\hat f(k)|^2 \prod_{j=1}^d \max(1, |k_j|). | This “smoothed-out variation” sits between MC variance and HK variation: | \sigma(f) \ \le\ \sigma_{\text{SO}}(f)\ \le\ \sigma_{\text{HK}}(f)\quad\text{and}\quad | \sigma_{\text{SO}}(f)^2 \le \sigma(f)\,\sigma_{\text{HK}}(f). | Intuition: it penalizes high frequencies less than \sigma_{\text{HK}}, so it gives tighter—and often much tighter—QMC-style error control. | | 2) Generate points by Subgaussian Transference (MC → low-discrepancy) | | Goal: keep MC’s unbiased sampling, but sculpt the samples to have low (dyadic) discrepancy. | • Start with n_0=n^2 i.i.d. uniform points in [0,1]^d. | • Pick a dyadic scale h=\Theta(\log(dn)) and apply a random shift of the dyadic grid (wrap around on the cube). | • Iterative halving (T = \log_2 n rounds): | For current set A_t, | 1. For each point z_j\in A_t, build a sparse incidence vector to all dyadic boxes up to level h (plus one coordinate to enforce balance). | 2. Run a fast online subgaussian vector-balancing routine (e.g., Self-Balancing Walk) to color points x_j\in\{\pm1\} with: | \left\|\sum_{j\le t} x_j\,v_j\right\|_2\ \text{is subgaussian (polylog bounds).} | 3. Keep the “−1” half as A_{t+1} (balanced split). | • Return A_T with exactly n points; estimate \int f by the average over A_T. | | This procedure is randomized (so unbiased) yet enforces low discrepancy on all dyadic boxes with high probability. | | 3) What you get—formal error guarantees | | All expectations below are over the algorithm’s randomness. | • Unbiased: \mathbb{E}[\text{err}(A_T,f)] = 0. | • MC-level safety: | \mathbb{E}[\text{err}(A_T,f)^2] \;\le\; e^{O(d)}\ \frac{\sigma(f)^2}{n} | (so you don’t do worse than standard MC up to a modest e^{O(d)} factor). | • QMC-style bound (with HK): | |\text{err}(A_T,f)| \;\le\; e^{O(d)}\ \frac{\sigma_{\text{HK}}(f)}{n} w.h.p. | • Stronger, beyond HK (key win): | \mathbb{E}[\text{err}(A_T,f)^2] \;\le\; e^{O(d)}\ \frac{\sigma_{\text{SO}}(f)^2}{n^2}. | Typical error is therefore e^{O(d)}\,\sigma_{\text{SO}}(f)/n, which can be much smaller than the HK/Koksma rate. | • Best-of-both-worlds (automatic adaptivity): for any decomposition f=g+h, | \mathbb{E}[\text{err}(A_T,f)^2]\ \le\ e^{O(d)}\bigg(\sigma(g)^2 \;+\; \frac{\sigma_{\text{SO}}(h)^2}{n^2}\bigg). | Taking g=f,h=0 recovers MC; taking g=0,h=f gives the \sigma_{\text{SO}} rate. The algorithm adapts to whichever is better. | | 4) Why it works (one-line sketch) | | Using the Hlawka–Zaremba identity, the integration error is an inner product of the set’s continuous discrepancy with mixed derivatives of f. The coloring step makes the dyadic discrepancy subgaussian across all scales, and a random shift plus a Fourier argument converts that discrepancy control into the \sigma_{\text{SO}}-driven variance bound above. | | 5) Practical notes (efficiency, flexibility, performance) | • Computation: Each balancing call is near-linear in input sparsity; overall runtime is near-linear in the total nonzeros of the incidence vectors across the T=O(\log n) rounds. The Self-Balancing Walk is online and very fast in practice. | • Memory: Works with sparse dyadic incidences; no heavy lattices or digital nets to build. | • Flexibility: Still pure-random sampling at the start ⇒ unbiased estimates, natural error bars, easy parallelism, black-box f. | • Performance: On smooth/structured integrands, the \sigma_{\text{SO}} bound yields smaller errors than both plain MC and classic QMC at the same n; on rough/noisy f, you automatically fall back to MC-like performance. | | ⸻ | | Minimal pseudocode | | Input: target n, dimension d | n0 ← n^2 | A0 ← n0 i.i.d. uniform points in [0,1]^d | h ← Θ(log(d n)); pick random shift s ∈ [0,1)^d and shift dyadic grid | | for t = 0 .. log2 n − 1: | build sparse incidence vectors v_j for each z_j ∈ A_t (to dyadic boxes up to level h) | x ← SelfBalancingWalk({v_j}) # x_j ∈ {+1,−1}, balanced, subgaussian discrepancy | A_{t+1} ← { z_j ∈ A_t : x_j = −1 } | | Return A_T; estimate I ≈ (1/|A_T|) ∑_{z∈A_T} f(z) | | | ⸻ | | Bottom line | | Do this (Subgaussian Transference with \sigma_{\text{SO}}): you keep MC’s simplicity and unbiasedness, you inherit QMC’s low-discrepancy power, and you provably achieve smaller typical errors—often O(\sigma_{\text{SO}}(f)/n)—with high flexibility and efficient computation.
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1. **Clearly define Monte Carlo (MC) and Quasi-Monte Carlo (QMC) methods**
- MC: Uses i.i.d. uniform random points; unbiased; error ≈ σ(f)/√n.
- QMC: Uses structured low-discrepancy point sets; error bounded by Koksma–Hlawka inequality; can achieve O(σ_HK(f)/n).
- Define geometric discrepancy notions (continuous discrepancy, star discrepancy, etc.).
2. **Thoroughly explain the Koksma–Hlawka inequality**
- State the ℓ² version:
\[
|err(A,f)| \le D^*_2(A) \cdot \sigma_{HK}(f)/n,
\]
where D^*_2 is the ℓ²-discrepancy and σ_HK is Hardy–Krause variation.
- Explain sharpness: for any point set, there exist functions achieving equality.
- Discuss limitations: σ_HK(f) can be much larger than σ(f), so QMC may perform worse than MC for oscillatory functions.
3. **Propose and describe the SubgTransference algorithm**
- Start with n² random samples.
- Iteratively split sets using a subgaussian vector-balancing routine (BalSubgDisc / Self-Balancing Walk).
- After T = log n rounds, obtain n points with low discrepancy and preserved randomness.
- Runtime Õ(n²), i.e. amortized Õ(1) per sample.
4. **Introduce the new variation measure σ_SO(f)**
- Defined via Fourier coefficients:
\[
\sigma_{SO}(f)^2 := \sum_{k \neq 0} |\hat f(k)|^2 \prod_{j=1}^d \max(1,|k_j|).
\]
- Prove inequalities: σ(f) ≤ σ_SO(f) ≤ σ_HK(f), and σ_SO(f)² ≤ σ(f)·σ_HK(f).
- Intuition: penalizes high frequencies less heavily than σ_HK.
5. **Present and prove Theorem 1.1 (Beyond Hardy–Krause)**
- **Theorem 1.1**: For any f, the integration error using points AT from SubgTransference satisfies
\[
\mathbb{E}[err(AT,f)^2] \le Õ_d(1)\cdot \frac{\sigma_{SO}(f)^2}{n^2}.
\]
- Thus, the typical error is Õ_d(σ_SO(f)/n), improving on the Koksma–Hlawka bound.
6. **Present and prove Theorem 1.4 (Best of MC and Hardy–Krause)**
- **Theorem 1.4**: For any f, unbiasedness holds: E[err(AT,f)] = 0, and
\[
\mathbb{E}[err(AT,f)^2] \le Õ_d(1) \cdot \min_{f=g+h} \left( \frac{\sigma(g)^2}{n} + \frac{V_{HK}(h)^2}{n^2} \right).
\]
- Interpretation: algorithm automatically adapts to whichever bound (MC or HK-based QMC) is tighter.
7. **Present and prove Theorem 1.5 (Best of MC and σ_SO)**
- **Theorem 1.5**: For any f, unbiasedness holds, and
\[
\mathbb{E}[err(AT,f)^2] \le Õ_d(1) \cdot \min_{f=g+h} \left( \frac{\sigma(g)^2}{n} + \frac{\sigma_{SO}(h)^2}{n^2} \right).
\]
- This bound is strictly stronger than Theorem 1.4, and shows adaptivity between MC error and the new σ_SO-driven QMC error.
8. **Analyze runtime of SubgTransference**
- Each level processes O(n²) sparse vectors; total runtime Õ(n²).
- Amortized per output sample: Õ(1).
- Explain why this is near-linear in total nonzeros of incidence vectors.
9. **Derive the Hlawka–Zaremba formula for d=1 and apply it**
- In 1D:
\[
err(A,f) = \int_0^1 D(x) f'(x)\, dx,
\]
where D(x) is discrepancy of [0,x].
- Use this to motivate cancellations exploited by σ_SO.
10. **Summarize Appendix proofs and technical details**
- Appendix B: step-by-step derivation of Hlawka–Zaremba in 1D via integration by parts.
- Appendix C: counterexamples showing prefix-interval discrepancy fails to be subgaussian.
- Appendix D: details on the structured decomposition matrix Ph.
11. **Compare σ_SO with σ and σ_HK**
- Show hierarchy: σ(f) ≤ σ_SO(f) ≤ σ_HK(f).
- σ_SO smooths high frequencies, yielding better bounds for oscillatory functions (e.g., f(x)=sin(kx): MC error ~ 1/√n, QMC error ~ k/n, σ_SO-based error ~ √k/n).
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# Background | | Numerical integration is a crucial technique in science and engineering for solving definite integrals of functions, especially when exact computation is infeasible due to the complexity of the function or when the function can only be accessed via evaluations. | | ## Monte Carlo (MC) Methods | | ### Basic Principle | MC methods estimate integrals by averaging function values at randomly sampled points. For example, to compute the integral of a function \(f(x)\) over the interval \([0,1]\), we generate \(n\) independent uniformly random samples \(x_1, x_2, \ldots, x_n\) and use the sample mean \(\frac{1}{n}\sum_{i=1}^n f(x_i)\) as an estimate of the integral. | | ### Error Analysis | The standard error of MC methods is \(O\left(\frac{\sigma(f)}{\sqrt{n}}\right)\), where \(\sigma(f)\) is the standard deviation of \(f\). To achieve an accuracy of \(\epsilon\), the required number of samples is approximately \(n \approx \frac{\sigma(f)^2}{\epsilon^2}\). This indicates that MC methods have a slow convergence rate but remain effective and easy to implement for high-dimensional integration problems. | | ## Quasi-Monte Carlo (QMC) Methods | | ### Basic Principle | QMC methods use deterministic low-discrepancy point sets instead of random samples for numerical integration. These low-discrepancy sequences, such as van der Corput, Halton, and Sobol sequences, are designed to be more evenly distributed in the integration domain, potentially leading to more accurate integral estimates. | | ### Koksma-Hlawka Inequality | The Koksma-Hlawka inequality provides the theoretical foundation for error analysis in QMC methods. It states that the error is bounded by the product of the discrepancy of the point set and the Hardy-Krause variation of the function. Specifically, the error bound can be expressed as \(O\left(\frac{\sigma_{\text{HK}}(f)}{n} \times D^*(X)\right)\), where \(\sigma_{\text{HK}}(f)\) is the Hardy-Krause variation of \(f\) and \(D^*(X)\) is the star discrepancy of the point set \(X\). Under ideal conditions, low-discrepancy point sets have a discrepancy that grows slowly with the number of samples \(n\), allowing QMC methods to achieve a convergence rate of \(O\left(\frac{1}{n}\right)\) for moderate dimensions.
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## Smoothed-out Variation | The smoothed-out variation, denoted as σSO(f), is defined as: | | σSO(f)^2 := \sum_{k \in \mathbb{Z}^d \setminus \{0\}} \|\hat{f}(k)\|^2 \cdot \sum_{j \in [d]} \max(1, |k_j|) | | where \(\hat{f}(k)\) are the Fourier coefficients of the function \(f\).
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1. **Combining Classical Transference Principle in Geometric Discrepancy with Recent Algorithmic Advances in Combinatorial Discrepancy** | - Leverage the transference principle to apply low-discrepancy colorings from combinatorial discrepancy to geometric discrepancy, while maintaining subgaussian properties | | 2. **Exploiting Subgaussianity and Structural Properties** | - Combine the subgaussian properties of low-combinatorial-discrepancy colorings with the combinatorial structures from the transference principle. This creates specific cancellation effects in the exact expression for numerical integration error, leading to the improved variation measure σSO(f).
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Computer Science
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Tight Bounds and Phase Transitions for Incremental and Dynamic Retrieval
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Determining the optimal redundancy $R$ for retrieval data structures in the incremental and dynamic settings when the universe size is polynomial, i.e., $|\mathcal{U}| = \poly(n)$.
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| Answer (direct) | | For a polynomial universe |\mathcal U|=\mathrm{poly}(n), the optimal redundancy R:=S-nv for retrieval data structures is: | • Incremental setting (insert-only): | R_{\text{inc}}=\Theta\!\Big(n\;+\;n\cdot\max\{0,\;\log(\tfrac{\log n}{v})\}\Big). | Equivalently: | • If v\ge c\log n (for a constant c>0), then R_{\text{inc}}=\Theta(n). | • If v=\log n/\log\log n, then R_{\text{inc}}=\Theta(n\log\log\log n). | • If v=\log^{0.99}n, then R_{\text{inc}}=\Theta(n\log\log n). | These bounds are tight: there is an incremental structure with | S\le nv+O(n)+O\!\left(n\log\!\left(\tfrac{\log n}{v}\right)\right) | and a matching lower bound | S\ge nv+\Omega(n)+\Omega\!\left(n\log\!\left(\tfrac{\log n}{v}\right)\right) | \quad (\text{for }|\mathcal U|\ge n^3), | giving the phase transition around v\asymp \log n. Timewise, the construction achieves O(1) queries/updates and O(1) amortized expected insertions. | • Dynamic setting (insertions & deletions): | R_{\text{dyn}}=\Theta(n\log\log n). | Specifically, any dynamic retrieval DS needs | S\ge nv+\Omega(n\log\log n)\quad (|\mathcal U|\ge n^3), | and this is achievable up to constants via succinct dynamic hashing (e.g., using the provided dynamic table with parameter t=2, yielding | S\le nv+O(n\log\log n) and O(1) expected update/query time). | | So, the answer your draft conveyed is right on the incremental side (tight upper+lower) and gives the correct dynamic lower bound; to be fully complete, make explicit that the dynamic upper bound S\le nv+O(n\log\log n) is attainable, hence R_{\text{dyn}}=\Theta(n\log\log n).
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1. Setup
- States |U| = poly(n).
- Defines redundancy R := S - nv.
2. Incremental formula
- Gives R_inc = Θ(n + n * max{0, log(log n / v)}).
- Mentions phase transition at v ≍ log n.
3. Incremental cases
- v ≥ c log n ⇒ R_inc = Θ(n).
- v = log n / log log n ⇒ R_inc = Θ(n log log log n).
- v = log^0.99 n ⇒ R_inc = Θ(n log log n).
4. Incremental bounds
- Upper bound: S ≤ nv + O(n) + O(n log(log n / v)).
- Lower bound: S ≥ nv + Ω(n) + Ω(n log(log n / v)), for |U| ≥ n^3.
5. Incremental performance
- Achieves O(1) query and update.
- Achieves O(1) amortized insertion.
6. Dynamic formula
- Gives R_dyn = Θ(n log log n).
- Requires |U| ≥ n^3.
7. Dynamic bounds
- Lower bound: S ≥ nv + Ω(n log log n).
- Upper bound: S ≤ nv + O(n log log n).
8. Dynamic performance
- Achieves O(1) expected query.
- Achieves O(1) expected update.
9. Completeness
- Incremental: bounds are tight.
- Dynamic: both bounds matched, confirming Θ(n log log n).
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Retrieval data structures are designed to answer key-value queries without explicitly storing the keys, which helps save space. The problem of optimizing these data structures can be formulated in four settings: static, value-dynamic, incremental, and dynamic. Each setting offers different levels of dynamism to the user. The static setting supports only queries, the value-dynamic setting supports queries and updates, the incremental setting supports queries, updates, and insertions, and the dynamic setting supports all operations including deletions. | | Previous research has established optimal bounds for the static and value-dynamic settings. For the static setting, minimal perfect hashing can achieve a redundancy of $R = \Theta(n)$, and further improvements have shown that the optimal redundancy can be $o(n)$ with $O(1)$ query time. For the value-dynamic setting, a recent result established a tight bound of $R = \Theta(n)$. | | The incremental and dynamic settings have also been studied, with the state-of-the-art upper bound achieving a redundancy of $R = \Theta(n \log \log n)$. However, there has been an open question about whether the optimal redundancy could shrink as the value size $v$ increases, especially in the incremental setting.
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- **Retrieval Data Structure**: | - A data structure that answers key-value queries without storing keys explicitly. | - Given a set of \( n \) keys \( K \subseteq \mathcal{U} \) and a \( v \)-bit value \( f(k) \) for each key \( k \in K \), it supports queries of the form: | \[ | \texttt{Query}(k) = | \begin{cases} | f(k) & \text{if } k \in K \\ | \text{anything} & \text{otherwise} | \end{cases} | \] | | - **Four Settings**: | - **Static**: Supports only queries. | - **Value-dynamic**: Supports queries and updates. | - **Incremental**: Supports queries, updates, and insertions. | - **Dynamic**: Supports all operations including deletions. | | - **Redundancy**: | - If a solution uses space \( nv + R \), it is said to have redundancy \( R \). | - The goal is to determine the optimal redundancy \( R \) for each setting. | | - **Minimal Perfect Hashing**: | - A technique to achieve redundancy \( R = \Theta(n) \) in the static setting. | - Further improvements have shown redundancy can be \( o(n) \) with \( O(1) \) query time. | | - **Phase Transition**: | - A phenomenon where the optimal space redundancy changes significantly as the value size \( v \) approaches \( \log n \). | - In the incremental setting, redundancy decreases from \( \Theta(n \log \log n) \) to \( \Theta(n) \). | | - **Perfect Universe Reducing Hash Function**: | - A hash function \( h: [U_1] \rightarrow [U_2] \) for a hash table \( H \) on universe \( U_1 \) such that for every pair of keys \( k_1, k_2 \) in \( H \), \( h(k_1) \neq h(k_2) \).
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**Conduct a Technical Overview of the Upper Bound Results**: | - Observe that for an incremental retrieval data structure with a target space usage of \( S \) bits (\( S \geq n \cdot v \)), up to \( \ell \leq n \) key-value pairs inserted so far, it is possible to store an additional \( \leq \frac{S - \ell \cdot v}{\ell} \) bits of information per inserted key. | - Utilize these extra bits to reduce the collision rate for the earlier inserted items. As more key-value pairs are inserted, demonstrate how to implement a universe reduction technique to decrease the amount of extra information stored per key, in order to avoid exceeding the maximum space of \( S \) bits. | - Ensure that this universe reduction step, which occurs after the items have been inserted, does not introduce any new collisions. By performing this universe-reduction step \( O(\log^*(n)) \) times, gracefully adjust the collision rate over time to achieve the upper bound of space usage. | | **Achieve Efficient Time Complexity**: | - Tackle the challenge of efficiently finding a valid universe-reducing hash function over large universes by bucketing the keys and representing the universe-reducing hash function properly, employing lookup table techniques to bypass the efficiency barrier. | - Specifically, partition the fingerprint space \([n \log^2 n]\) into \( n/B \) buckets (\( B := (\log \log n)^{10} \)), and use two \( B \)-wise independent hash functions \( h_{\text{buk}}: U \rightarrow [n/B] \) and \( h_1: U \rightarrow [B \log^2 n] \) to map each key to a pair \((b, f)\), where \( b \) indicates the bucket the key belongs to, and \( f \) is the fingerprint of length \((\log B + 2 \log \log n)\) bits within that bucket. This approach reduces the fingerprint size to \((\log B + 2 \log \log n)\) bits. | - By doing so, reduce the effective size of the universes being dealt with to sub-logarithmic, thereby enabling the use of explicit lookup tables for finding valid universe reductions. | | **Address the Issue of Small Bucket Sizes**: | - When a newly inserted key is mapped to a bucket already containing \( 4B \) keys, insert the key into the collision set instead. Since each bucket is limited to at most \( 4B \) keys (fingerprints), describe the set of fingerprints in each bucket using only \( O(B \cdot t_j) \) bits, which can be encoded within \( O(1) \) words and manipulated efficiently using lookup tables.
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