Results for 'S. Barry Cooper'

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  1.  48
    The d.r.e. degrees are not dense.S. Barry Cooper, Leo Harrington, Alistair H. Lachlan, Steffen Lempp & Robert I. Soare - 1991 - Annals of Pure and Applied Logic 55 (2):125-151.
    By constructing a maximal incomplete d.r.e. degree, the nondensity of the partial order of the d.r.e. degrees is established. An easy modification yields the nondensity of the n-r.e. degrees and of the ω-r.e. degrees.
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  2.  41
    Computability Theory.S. Barry Cooper - 2003 - Chapman & Hall.
    Computability theory originated with the seminal work of Gödel, Church, Turing, Kleene and Post in the 1930s. This theory includes a wide spectrum of topics, such as the theory of reducibilities and their degree structures, computably enumerable sets and their automorphisms, and subrecursive hierarchy classifications. Recent work in computability theory has focused on Turing definability and promises to have far-reaching mathematical, scientific, and philosophical consequences. Written by a leading researcher, Computability Theory provides a concise, comprehensive, and authoritative introduction to contemporary (...)
  3.  42
    Bounding and Nonbounding Minimal Pairs in the Enumeration Degrees.S. Barry Cooper, Angsheng Li, Andrea Sorbi & Yue Yang - 2005 - Journal of Symbolic Logic 70 (3):741 - 766.
    We show that every nonzero $\Delta _{2}^{0}$ e-degree bounds a minimal pair. On the other hand, there exist $\Sigma _{2}^{0}$ e-degrees which bound no minimal pair.
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  4.  23
    Cupping and noncupping in the enumeration degrees of ∑20 sets.S. Barry Cooper, Andrea Sorbi & Xiaoding Yi - 1996 - Annals of Pure and Applied Logic 82 (3):317-342.
    We prove the following three theorems on the enumeration degrees of ∑20 sets. Theorem A: There exists a nonzero noncuppable ∑20 enumeration degree. Theorem B: Every nonzero Δ20enumeration degree is cuppable to 0′e by an incomplete total enumeration degree. Theorem C: There exists a nonzero low Δ20 enumeration degree with the anticupping property.
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  5.  8
    Enumeration Reducibility Using Bounded Information: Counting Minimal Covers.S. Barry Cooper - 1987 - Mathematical Logic Quarterly 33 (6):537-560.
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  6.  23
    Enumeration Reducibility Using Bounded Information: Counting Minimal Covers.S. Barry Cooper - 1987 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 33 (6):537-560.
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  7.  50
    The density of the low2 n-r.e. degrees.S. Barry Cooper - 1991 - Archive for Mathematical Logic 31 (1):19-24.
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  8. On minimal pairs of enumeration degrees.Kevin McEvoy & S. Barry Cooper - 1985 - Journal of Symbolic Logic 50 (4):983-1001.
  9.  26
    Cupping and noncupping in the enumeration degrees of∑< sub> 2< sup> 0 sets.S. Barry Cooper, Andrea Sorbi & Xiaoding Yi - 1996 - Annals of Pure and Applied Logic 82 (3):317-342.
  10.  8
    Complementing below recursively enumerable degrees.S. Barry Cooper & Richard L. Epstein - 1987 - Annals of Pure and Applied Logic 34 (1):15-32.
  11.  14
    On a Conjecture of Kleene and Post.S. Barry Cooper - 2001 - Mathematical Logic Quarterly 47 (1):3-34.
    A proof is given that 0′ is definable in the structure of the degrees of unsolvability. This answers a long-standing question of Kleene and Post, and has a number of corollaries including the definability of the jump operator.
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  12.  28
    On the distribution of Lachlan nonsplitting bases.S. Barry Cooper, Angsheng Li & Xiaoding Yi - 2002 - Archive for Mathematical Logic 41 (5):455-482.
    We say that a computably enumerable (c.e.) degree b is a Lachlan nonsplitting base (LNB), if there is a computably enumerable degree a such that a > b, and for any c.e. degrees w,v ≤ a, if a ≤ w or; v or; b then either a ≤ w or; b or a ≤ v or; b. In this paper we investigate the relationship between bounding and nonbounding of Lachlan nonsplitting bases and the high /low hierarchy. We prove that there (...)
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  13.  24
    Properly Σ2 minimal degrees and 0″ complementation.S. Barry Cooper, Andrew E. M. Lewis & Yue Yang - 2005 - Mathematical Logic Quarterly 51 (3):274-276.
    We show that there exists a properly Σ2 minimal degree b, and moreover that b can be chosen to join with 0′ to 0″ – so that b is a 0″ complement for every degree a such that 0′ ≤ a < 0″.
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  14.  15
    Extending and interpreting Post’s programme.S. Barry Cooper - 2010 - Annals of Pure and Applied Logic 161 (6):775-788.
    Computability theory concerns information with a causal–typically algorithmic–structure. As such, it provides a schematic analysis of many naturally occurring situations. Emil Post was the first to focus on the close relationship between information, coded as real numbers, and its algorithmic infrastructure. Having characterised the close connection between the quantifier type of a real and the Turing jump operation, he looked for more subtle ways in which information entails a particular causal context. Specifically, he wanted to find simple relations on reals (...)
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  15.  42
    The machine as data: a computational view of emergence and definability.S. Barry Cooper - 2015 - Synthese 192 (7):1955-1988.
    Turing’s paper on computable numbers has played its role in underpinning different perspectives on the world of information. On the one hand, it encourages a digital ontology, with a perceived flatness of computational structure comprehensively hosting causality at the physical level and beyond. On the other, it can give an insight into the way in which higher order information arises and leads to loss of computational control—while demonstrating how the control can be re-established, in special circumstances, via suitable type reductions. (...)
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  16.  13
    Corrigendum to “The d.r.e. degrees are not dense” [Ann. Pure Appl. Logic 55 (1991) 125–151].S. Barry Cooper, Leo Harrington, Alistair H. Lachlan, Steffen Lempp & Robert I. Soare - 2017 - Annals of Pure and Applied Logic 168 (12):2164-2165.
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  17.  8
    Strong Minimal Covers for Recursively Enumerable Degrees.S. Barry Cooper - 1996 - Mathematical Logic Quarterly 42 (1):191-196.
    We prove that there exists a nonzero recursively enumerable Turing degree possessing a strong minimal cover.
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  18.  71
    On Lachlan’s major sub-degree problem.S. Barry Cooper & Angsheng Li - 2008 - Archive for Mathematical Logic 47 (4):341-434.
    The Major Sub-degree Problem of A. H. Lachlan (first posed in 1967) has become a long-standing open question concerning the structure of the computably enumerable (c.e.) degrees. Its solution has important implications for Turing definability and for the ongoing programme of fully characterising the theory of the c.e. Turing degrees. A c.e. degree a is a major subdegree of a c.e. degree b > a if for any c.e. degree x, ${{\bf 0' = b \lor x}}$ if and only if (...)
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  19.  9
    Preface.S. Barry Cooper, Herman Geuvers, Anand Pillay & Jouko Väänänen - 2008 - Annals of Pure and Applied Logic 156 (1):1-2.
  20.  92
    Splitting and nonsplitting II: A low {\sb 2$} C.E. degree about which ${\bf 0}'$ is not splittable.S. Barry Cooper & Angsheng Li - 2002 - Journal of Symbolic Logic 67 (4):1391-1430.
    It is shown that there exists a low2 Harrington non-splitting base-that is, a low2 computably enumerable (c.e.) degree a such that for any c.e. degrees x, y, if $0' = x \vee y$ , then either $0' = x \vee a$ or $0' = y \vee a$ . Contrary to prior expectations, the standard Harrington non-splitting construction is incompatible with the $low_{2}-ness$ requirements to be satisfied, and the proof given involves new techniques with potentially wider application.
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  21.  11
    Bounding and nonbounding minimal pairs in the enumeration degrees.S. Barry Cooper, Angsheng Li, Andrea Sorbi & Yue Yang - 2005 - Journal of Symbolic Logic 70 (3):741-766.
    We show that every nonzero Δ20, e-degree bounds a minimal pair. On the other hand, there exist Σ20, e-degrees which bound no minimal pair.
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  22. How the World Computes.S. Barry Cooper (ed.) - 2012
     
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  23. Sets and Proofs.S. Barry Cooper & John K. Truss - 2001 - Studia Logica 69 (3):446-448.
  24.  19
    Turing Centenary Conference: How the World Computes.S. Barry Cooper, Anuj Dawar, Martin Hyland & Benedikt Löwe - 2014 - Annals of Pure and Applied Logic 165 (9):1353-1354.
  25.  15
    The discontinuity of splitting in the recursively enumerable degrees.S. Barry Cooper & Xiaoding Yi - 1995 - Archive for Mathematical Logic 34 (4):247-256.
    In this paper we examine a class of pairs of recursively enumerable degrees, which is related to the Slaman-Soare Phenomenon.
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  26.  13
    What Makes A Computation Unconventional?S. Barry Cooper - 2013 - In Gordana Dodig-Crnkovic Raffaela Giovagnoli (ed.), Computing Nature. pp. 255--269.
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  27.  34
    How Enumeration Reducibility Yields Extended Harrington Non-Splitting.Mariya I. Soskova & S. Barry Cooper - 2008 - Journal of Symbolic Logic 73 (2):634 - 655.
  28. There is No Low Maximal D.C.E. Degree.Marat Arslanov, S. Barry Cooper & Angsheng Li - 2000 - Mathematical Logic Quarterly 46 (3):409-416.
    We show that for any computably enumerable set A and any equation image set L, if L is low and equation image, then there is a c.e. splitting equation image such that equation image. In Particular, if L is low and n-c.e., then equation image is n-c.e. and hence there is no low maximal n-c.e. degree.
     
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  29.  25
    There is no low maximal d. c. e. degree– Corrigendum.Marat Arslanov, S. Barry Cooper & Angsheng Li - 2004 - Mathematical Logic Quarterly 50 (6):628-636.
    We give a corrected proof of an extension of the Robinson Splitting Theorem for the d. c. e. degrees.
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  30.  6
    Preface.Samuel R. Buss, S. Barry Cooper, Benedikt Löwe & Andrea Sorbi - 2009 - Annals of Pure and Applied Logic 160 (3):229-230.
  31.  27
    Noncappable enumeration degrees below 0'e. [REVIEW]S. Barry Cooper & Andrea Sorbi - 1996 - Journal of Symbolic Logic 61 (4):1347 - 1363.
    We prove that there exists a noncappable enumeration degree strictly below 0' e.
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  32.  23
    Automorphisms of η-like computable linear orderings and Kierstead's conjecture.Charles M. Harris, Kyung Il Lee & S. Barry Cooper - 2016 - Mathematical Logic Quarterly 62 (6):481-506.
    We develop an approach to the longstanding conjecture of Kierstead concerning the character of strongly nontrivial automorphisms of computable linear orderings. Our main result is that for any η-like computable linear ordering, such that has no interval of order type η, and such that the order type of is determined by a -limitwise monotonic maximal block function, there exists computable such that has no nontrivial automorphism.
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  33.  4
    Eric Voegelin's Analysis of the Deformation of Consciousness in Voltaire.Barry Cooper - 1996 - Lumen: Selected Proceedings From the Canadian Society for Eighteenth-Century Studies 15:37.
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  34.  16
    The historian's craft.Barry Cooper - 1994 - History of European Ideas 18 (3):453-455.
    *Introduction by Joseph R. Strayer\n(ix-x) Not that Bloch was the greatest French historian of his generation, though he would certainly rank high in any list. Not even that he was the most widely read—others excelled in that art of combining exact knowledge with readability which has distinguished French scholarship for many years. Others have talked about the narrowness of purely political history, the evils of excessive specialization, and the unreality of the conventional periodization of history—without ever leaving their own limited (...)
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  35.  5
    Hegelian Elements in Merleau-Ponty’s La Structure du Comportement.Barry Cooper - 1975 - International Philosophical Quarterly 15 (4):411-423.
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  36.  4
    Voegelin Recollected: Conversations on a Life.Barry Cooper & Jodi Bruhn (eds.) - 2007 - University of Missouri.
    Although his contributions to philosophy are revered and his writings have been collected, Eric Voegelin’s persona will inevitably fade with the memories of those who knew him. This book preserves the human element of Voegelin by capturing those valuable personal recollections. Barry Cooper and Jodi Bruhn conducted intensive interviews with Voegelin’s wife, his closest friends, and his first-generation students—many of whom have since passed on—in order to bring to print everything important about his life and personality. American scholars (...)
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  37.  22
    Eric Voegelin and the foundations of modern political science.Barry Cooper - 1999 - Columbia: University of Missouri Press. Edited by Eric Voegelin.
    This important new work is a major analysis of the foundation of Eric Voegelin's political science.
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  38. Finding Our Way through Phenotypes.Andrew R. Deans, Suzanna E. Lewis, Eva Huala, Salvatore S. Anzaldo, Michael Ashburner, James P. Balhoff, David C. Blackburn, Judith A. Blake, J. Gordon Burleigh, Bruno Chanet, Laurel D. Cooper, Mélanie Courtot, Sándor Csösz, Hong Cui, Barry Smith & Others - 2015 - PLoS Biol 13 (1):e1002033.
    Despite a large and multifaceted effort to understand the vast landscape of phenotypic data, their current form inhibits productive data analysis. The lack of a community-wide, consensus-based, human- and machine-interpretable language for describing phenotypes and their genomic and environmental contexts is perhaps the most pressing scientific bottleneck to integration across many key fields in biology, including genomics, systems biology, development, medicine, evolution, ecology, and systematics. Here we survey the current phenomics landscape, including data resources and handling, and the progress that (...)
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  39.  4
    Consciousness and politics: from analysis to meditation in the late work of Eric Voegelin.Barry Cooper - 2015 - South Bend, Indiana: St. Augustine's Press.
    Consciousness and Politics begins with an analysis of the problem of the historicity of truth as it was formulated shortly before Voegelin abandoned his eight-volume History of Political Ideas. The analysis then follows a more or less chronological path, discussing the arguments developed in The New Science of Politics, Voegelin's most famous book, the differentiation of consciousness and the problems of myth and nature as presented in the early volumes of Order and History. Starting in the 1960s, Voegelin began a (...)
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  40.  7
    On the Form of the American Mind (Cw1).Eric Voegelin, Jurgen Gebhardt, Barry Cooper & Ruth Hein (eds.) - 1989 - University of Missouri.
    In 1924, not quite two years after receiving his doctorate from the University of Vienna, Eric Voegelin was named a Laura Spelman Rockefeller Memorial Fellow and thus given the opportunity to pursue postdoctoral studies in the United States. For the next twenty-four months, Voegelin worked with some of the most creative scholars in America and at several of the country's great universities, an experience that undoubtedly influenced his scholarly and personal perspectives throughout his life. A more immediate result was the (...)
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  41.  6
    Faith and Political Philosophy: The Correspondence Between Leo Strauss and Eric Voegelin, 1934-1964.Peter Christopher Emberley & Barry Cooper (eds.) - 1993 - Pennsylvania State University Press.
    Leo Strauss and Eric Voegelin were political theorists of the first rank whose impact on the study of political science in North America has been profound. A study of their writings is one of the most expeditious ways to explore the core of political science; comparing and contrasting the positions both theorists have taken in assessing that core provides a comprehensive appreciation of the main options of the Western tradition. In fifty-three recently discovered letters, Strauss and Voegelin explore the nature (...)
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  42.  8
    Faith and Political Philosophy: The Correspondence Between Leo Strauss and Eric Voegelin, 1934-1964.Peter Christopher Emberley & Barry Cooper (eds.) - 1993 - University of Missouri.
    _Faith and Political Philosophy_ consists of fifty-three letters between Leo Strauss and Eric Voegelin, two of the most important political theorists of the twentieth century. In this correspondence, Strauss and Voegelin explore the nature of their similarities and differences, offering insightful observations about one another's work, about the state of the discipline, and about the influences working on them. The letters shed light on many assumptions made in their published writings, often with an openness that removes all vestiges of uncertainty.
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  43.  3
    On the Form of the American Mind.Jurgen Gebhardt & Barry Cooper (eds.) - 1995 - University of Missouri.
    In 1924, not quite two years after receiving his doctorate from the University of Vienna, Eric Voegelin was named a Laura Spelman Rockefeller Memorial Fellow and thus given the opportunity to pursue postdoctoral studies in the United States. For the next twenty-four months, Voegelin worked with some of the most creative scholars in America and at several of the country's great universities, an experience that undoubtedly influenced his scholarly and personal perspectives throughout his life. A more immediate result was the (...)
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  44.  3
    Philosophy, Literature, and Politics: Essays Honoring Ellis Sandoz.Charles R. Embry & Barry Cooper (eds.) - 2005 - University of Missouri.
    The essays in this collection honor Professor Ellis Sandoz, Hermann Moyse Jr. Distinguished Professor of Political Science, Louisiana State University, and founding director of the Eric Voegelin Institute for American Renaissance Studies, an institute located at Louisiana State University and devoted to research and publication in the fields of political philosophy, constitutional law, and Voegelin studies. Without the tireless leadership—both academic and economic—of Ellis Sandoz, who was one of Eric Voegelin’s early students and his first American doctoral candidate at the (...)
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  45.  9
    Developing an Ethics Education Framework for Accounting.Steven Dellaportas, Beverley Jackling, Philomena Leung & Barry J. Cooper - 2011 - Journal of Business Ethics Education 8 (1):63-82.
    The purpose of this paper is to propose a framework of ethics education that promotes the structured learning of ethics in the accounting discipline. The Ethics Education Framework (EEF) is based on three key inter-related components that includes: Rest’s (1986) Four-Component Model of ethical decision-making and behaviour; the key cognitive and behavioural objectives of ethics education; and the discrete and pervasive approaches to delivering content. The EEF providesuniversity students and professional accountants a structure to learn to identify, analyse, and resolve (...)
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  46.  30
    10.5840/jbee2011816.Steven Dellaportas, Beverley Jackling, Philomena Leung & Barry J. Cooper - 2000 - Journal of Business Ethics Education 1 (1):63-82.
    The purpose of this paper is to propose a framework of ethics education that promotes the structured learning of ethics in the accounting discipline. The Ethics Education Framework is based on three key inter-related components that includes: Rest’s Four-Component Model of ethical decision-making and behaviour; the key cognitive and behavioural objectives of ethics education; and the discrete and pervasive approaches to delivering content. The EEF providesuniversity students and professional accountants a structure to learn to identify, analyse, and resolve ethical issues (...)
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  47.  16
    Ontogeny of prosocial behavior across diverse societies.Bailey R. House, Joan B. Silk, Joseph Henrich, H. Clark Barrett, Brooke A. Scelza, Adam H. Boyette, Barry S. Hewlett, Richard McElreath & Stephen Laurence - 2013 - Proceedings of the National Academy of Sciences of the United States of America 110 (36):14586-14591.
    Humans are an exceptionally cooperative species, but there is substantial variation in the extent of cooperation across societies. Understanding the sources of this variability may provide insights about the forces that sustain cooperation. We examined the ontogeny of prosocial behavior by studying 326 children 3–14 y of age and 120 adults from six societies (age distributions varied across societies). These six societies span a wide range of extant human variation in culture, geography, and subsistence strategies, including foragers, herders, horticulturalists, and (...)
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  48.  22
    Against Individualism: A Confucian Rethinking of the Foundations of Morality, Politics, Family, and Religion. [REVIEW]Barry Allen - 2015 - Review of Metaphysics 69 (2):409-410.
    This work by an accomplished and respected comparative philosopher criticizes the Western ideology of individualism from the perspective of a Confucian morality of the family. Individualism is a name for the Enlightenment era ideology of the autonomous individual. The philosophical pillars of this ideology are Locke and especially Kant, and it runs through practically all modern moral philosophy. It is the moral psychology of classical liberalism, no less than of its libertarian and communitarian critics. They are different politically, but ontologically (...)
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  49.  97
    David Hume as a Social Theorist.Brian Barry - 2010 - Utilitas 22 (4):369-392.
    This article examines Russell Hardin's interpretation of Hume's argument that great social order depends on coordination convention. The main argument shows that despite an apparent move in that direction Hume's main argument is that justice and the other convention-based virtues rest on a cooperative convention which solves a prisoner's dilemma problem and that states are required when a society exceeds some small size because only states can solve the large number prisoner's dilemma problems that constitute the 'problem of social order'. (...)
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  50.  8
    The Environment in Question: Ethics and Global Issues.David E. Cooper & Joy Palmer (eds.) - 1992 - Taylor & Francis US.
    By addressing specific global problems and placing them within an ethical context, "The Environment in Question" provides the reader with both a theoretical and practical understanding of environmental issues. The contributors are internationally known figures drawn from the various disciplines which bear upon these issues, such as geography, psychology, social policy, and philosophy. The contributions range from those tackling individual concrete issues (such as nuclear waste and the threat to the rain forest) to those addressing matters of policy, principle and (...)
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