The Experts below are selected from a list of 318 Experts worldwide ranked by ideXlab platform
Rudolf Hilfer - One of the best experts on this subject based on the ideXlab platform.
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Classification Theory FOR PHASE TRANSITIONS
International Journal of Modern Physics B, 1993Co-Authors: Rudolf HilferAbstract:A refined Classification Theory for phase transitions in thermodynamics and statistical mechanics in terms of their orders is introduced and analyzed. The refined thermodynamic Classification is based on two independent generalizations of Ehrenfests traditional Classification scheme. The statistical mechanical Classification Theory is based on generalized limit theorems for sums of random variables from probability Theory and the newly defined block ensemble limit. The block ensemble limit combines thermodynamic and scaling limits and is similar to the finite size scaling limit. The statistical Classification scheme allows for the first time a derivation of finite size scaling without renormalization group methods. The Classification distinguishes two fundamentally different types of phase transitions. Phase transitions of order λ>1 correspond to well known equilibrium phase transitions, while phase transitions with order λ
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Classification Theory for anequilibrium phase transitions.
Physical review. E Statistical physics plasmas fluids and related interdisciplinary topics, 1993Co-Authors: Rudolf HilferAbstract:The paper introduces a Classification of phase transitions in which each transition is characterized through its generalized order and a slowly varying function. This characterization is shown to be applicable in statistical mechanics as well as in thermodynamics albeit for different mathematical reasons. By introducing the block ensemble limit the statistical Classification is based on the Theory of stable laws from probability Theory. The block ensemble limit combines scaling limit and thermodynamic limit. The thermodynamic Classification on the other hand is based on generalizing Ehrenfest's traditional Classification scheme. Both schemes imply the validity of scaling at phase transitions without the need to invoke renormalizaton-group arguments
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SCALING Theory AND THE Classification OF PHASE TRANSITIONS
Modern Physics Letters B, 1992Co-Authors: Rudolf HilferAbstract:The recent Classification Theory for phase transitions (R. Hilfer, Physica Scripta 44, 321 (1991)) and its relation with the foundations of statistical physics is reviewed. First it is outlined how Ehrenfests Classification scheme can be generalized into a general thermodynamic Classification Theory for phase transitions. The Classification Theory implies scaling and multiscaling thereby eliminating the need to postulate the scaling hypothesis as a fourth law of thermodynamics. The new Classification has also led to the discovery and distinction of nonequilibrium transitions within equilibrium statistical physics. Nonequilibrium phase transitions are distinguished from equilibrium transitions by orders less than unity and by the fact that equilibrium thermodynamics and statistical mechanics become inapplicable at the critical point. The latter fact requires a change in the Gibbs assumption underlying the canonical and grandcanonical ensembles in order to recover the thermodynamic description in the critical limit.
F. Campana - One of the best experts on this subject based on the ideXlab platform.
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Orbifolds, special varieties and Classification Theory
Annales de l’institut Fourier, 2004Co-Authors: F. CampanaAbstract:Le present article decrit a l'aide de fibrations fonctorielles intrinseques, la structure geometrique (et conjecturalement la pseudometrique de Kobayashi ainsi que l'arithmetique dans le cas projectif) des varietes Kahleriennes compactes. Les varietes speciales sont tout d'abord definies comme etant les varietes Kahleriennes compactes ne possedant pas d'application meromorphe surjective sur une orbifolde de type general, la structure d'orbifolde de la base provenant du diviseur des fibres multiples. On montre que les varietes Kahleriennes compactes qui sont, soit rationnellement connexes, soit a dimension de Kodaira nulle sont speciales. Nous construisons ensuite fonctoriellement, pour toute telle variete X, l' unique fibration c X : X → C(X) (le coeur de X) dont les fibres sont speciales et dont la base orbifolde est soit de type general, soit un point (ce dernier cas se produisant si et seulement si X est speciale). Le coeur de X est ensuite canoniquement decompose comme une tour de fibrations a fibres soit κ-rationnellement engendrees (une version faible de la connexite rationnelle), soit a dimension de Kodaira nulle. En particulier, les varietes speciales sont donc de telles tours de fibrations. L'ingredient technique essentiel des demonstrations est une version orbifolde de la conjecture C n,m d'Iitaka, etablie lorsque la base orbifolde est de type general. Le coeur de X permet de donner une description qualitative conjecturale tres simple de la pseudometrique de Kobayashi de X et de la distribution de ses points K-rationnels (si X est projective, definie sur le corps K de type fini sur Q), description se reduisant a celle de Lang lorsque X est de type general.
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Special Varieties and Classification Theory
Annales de l'Institut Fourier, 2004Co-Authors: F. CampanaAbstract:A new class of compact Kähler manifolds, called special, is defined, which are the ones having no surjective meromorphic map to an orbifold of general type. The special manifolds are in many respect higher-dimensional generalisations of rational and elliptic curves. For example, we show that being rationally connected or having vanishing Kodaira dimension implies being special. Moreover, for any compact Kähler $X$ we define a fibration $c_X:X\to C(X)$, which we call its core, such that the general fibres of $c_X$ are special, and every special subvariety of $X$ containing a general point of $X$ is contained in the corresponding fibre of $c_X$. We then conjecture and prove in low dimensions and some cases that: 1) Special manifolds have an almost abelian fundamental group. 2) Special manifolds are exactly the ones having a vanishing Kobayashi pseudometric. 3) The core is a fibration of general type, which means that so is its base $C(X)$,when equipped with its orbifold structure coming from the multiple fibres of $c_X$. 4) The Kobayashi pseudometric of $X$ is obtained as the pull-back of the orbifold Kobayashi pseudo-metric on $C(X)$, which is a metric outside some proper algebraic subset. 5) If $X$ is projective,defined over some finitely generated (over $\Bbb Q$) subfield $K$ of the complex number field, the set of $K$-rational points of $X$ is mapped by the core into a proper algebraic subset of $C(X)$. These two last conjectures are the natural generalisations to arbitrary $X$ of Lang's conjectures formulated when $X$ is of general type.
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Orbifolds, special varieties and Classification Theory: an appendix
Annales de l’institut Fourier, 2004Co-Authors: F. CampanaAbstract:Pour toute variete compacte Kahlerienne X et pour toute relation d'equivalence engendree par une relation binaire symetrique de graphe analytique et compact dans X x X, l'existence d'un quotient meromorphe est connue par Inv. Math. 63 (1981). Nous donnons ici une preuve simplifiee et detaillee de l'existence de ce quotient, en suivant l'approche de cet article. Ces quotients sont utilises dans une des deux constructions du coeur de Xdans le precedent article de ce fascicule, et aussi dans l'etude de nombreux autres problemes.
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Special Varieties and Classification Theory: An Overview
Acta Applicandae Mathematicae, 2003Co-Authors: F. CampanaAbstract:Lang's conjectures link the geometric, hyperbolic, and arithmetic properties of projective complex varieties of general type. We propose here an extension of these conjectures to arbitrary projective varieties X. This extension rests on the notion of ‘special’ variety. This class contains manifolds either rationally connected or with vanishing Kodaira dimension. We further construct for any X its ‘core’, which is a fibration c X : X→C(X) with general fibre special and orbifold base of general type. This fibration seems to permit us to decompose X according to the dichotomy ‘special’ vs ‘general type’, and not only leads to the above-mentioned extension of Lang's conjectures but also to a simple global view of Classification Theory.
Joseph T. Tennis - One of the best experts on this subject based on the ideXlab platform.
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Four Orders of Classification Theory and Their Implications
Cataloging & Classification Quarterly, 2018Co-Authors: Joseph T. TennisAbstract:This article provides an interpretation of the structure of Classification Theory literature, from the late 19th Century to the present, by dividing it into four orders, and then describes the rela...
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words and emotional work Classification Theory s constructs useful for the analysis of social media data in terms of gender race and sexuality
Social Science Research Network, 2017Co-Authors: Joseph T. TennisAbstract:Presents constructs from Classification Theory and relates them to the study of hashtags and other forms of tags in social media data. Argues these constructs are useful to the study of the intersectionality of race, gender, and sexuality. Closes with an introduction to an historical case study from Amazon.com.
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Foundational, First-Order, and Second-Order Classification Theory
KNOWLEDGE ORGANIZATION, 2015Co-Authors: Joseph T. TennisAbstract:Both basic and applied research on the construction, implementation, maintenance, and evaluation of Classification schemes is called Classification Theory. If we employ Ritzer's metatheoretical method of analysis on the over one-hundred year-old body of literature, we can see categories of Theory emerge. This paper looks at one particular part of knowledge organization work, namely Classification Theory, and asks 1) what are the contours of this intellectual space, and, 2) what have we produced in the theoretical reflection on constructing, implementing, and evaluating Classification schemes? The preliminary findings from this work are that Classification Theory can be separated into three kinds: foundational Classification Theory, first-order Classification Theory, and second-order Classification Theory, each with its own concerns and objects of study.
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Ranganathan's layers of Classification Theory and the FASDA model of Classification
NASKO, 2011Co-Authors: Joseph T. TennisAbstract:Describes four waves of Ranganathan’s dynamic Theory of Classification. Outlines components that distinguish each wave, and porposes ways in which this understanding can inform systems design in the contemporary environment, particularly with regard to interoperability and scheme versioning. Ends with an appeal to better understanding the relationship between structure and semantics in faceted Classification schemes and similar indexing languages.
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Experientialist Epistemology and Classification Theory: Embodied and Dimensional Classification
Knowledge Organization, 2005Co-Authors: Joseph T. TennisAbstract:What theoretical framework can help in building, maintaining and evaluating networked knowledge organization resources? Specifically, what theoretical framework makes sense of the semantic prowess of ontologies and peer-to-peer sys- tems, and by extension aids in their building, maintenance, and evaluation? I posit that a theoretical work that weds both for- mal and associative (structural and interpretive) aspects of knowledge organization systems provides that framework. Here I lay out the terms and the intellectual constructs that serve as the foundation for investigative work into experientialist classifi- cation Theory, a theoretical framework of embodied, infrastructural, and reified knowledge organization. I build on the inter- pretive work of scholars in information studies, cognitive semantics, sociology, and science studies. With the terms and the framework in place, I then outline Classification Theory 鈂s critiques of classificato ry structures. In order to address these cri- tiques with an experientialist approach an experientialist semantics is offered as a design commitment for an example: metadata in peer-to-peer network knowledge organization structures.
Carey E. Priebe - One of the best experts on this subject based on the ideXlab platform.
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Shuffled Graph Classification: Theory and Connectome Applications
Journal of Classification, 2015Co-Authors: Joshua T. Vogelstein, Carey E. PriebeAbstract:We develop a formalism to address statistical pattern recognition of graph valued data. Of particular interest is the case of all graphs having the same number of uniquely labeled vertices. When the vertex labels are latent, such graphs are called shuffled graphs. Our formalism provides insight to trivially answer a number of open statistical questions including: (i) under what conditions does shuffling the vertices degrade Classification performance and (ii) do universally consistent graph classifiers exist? The answers to these questions lead to practical heuristic algorithms with state-of-the-art finite sample performance, in agreement with our theoretical asymptotics. Applying these methods to classify sex and autism in two different human connectome Classification tasks yields successful Classification results in both applications.
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Shuffled Graph Classification: Theory and Connectome Applications
arXiv: Quantitative Methods, 2011Co-Authors: Joshua T. Vogelstein, Carey E. PriebeAbstract:We develop a formalism to address statistical pattern recognition of graph valued data. Of particular interest is the case of all graphs having the same number of uniquely labeled vertices. When the vertex labels are latent, such graphs are called shuffled graphs. Our formalism provides insight to trivially answer a number of open statistical questions including: (i) under what conditions does shuffling the vertices degrade Classification performance and (ii) do universally consistent graph classifiers exist? The answers to these questions lead to practical heuristic algorithms with state-of-the-art finite sample performance, in agreement with our theoretical asymptotics.
Roberto M. Cesar - One of the best experts on this subject based on the ideXlab platform.
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Shape Analysis and Classification: Theory and Practice - Shape Analysis and Classification: Theory and Practice
2010Co-Authors: Luciano Da Fontoura Costa, Roberto M. CesarAbstract:From the Publisher: Advances in shape analysis impact a wide range of disciplines, from mathematics and engineering to medicine, archeology, and art. Anyone just entering the field, however, may find the few existing books on shape analysis too specific or advanced, and for researchers interested in the specific problem of shape recognition and characterization, traditional books on computer vision are too general.Shape Analysis and Classification: Theory and Practice offers an integrated and conceptual introduction to this dynamic field and its myriad applications. Beginning with the basic mathematical concepts, it deals with shape analysis, from image capture to pattern Classification, and presents many of the most advanced and powerful techniques used in practice. The authors explore the relevant aspects of both shape characterization and recognition, and give special attention to practical issues, such as guidelines for implementation, validation, and assessment.Shape Analysis and Classification provides a rich resource for the computational characterization and Classification of general shapes, from characters to biological entities. Both beginning and advanced researchers can directly use its state-of-the-art concepts and techniques to solve their own problems involving the characterization and Classification of visual shapes.
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shape analysis and Classification Theory and practice
2000Co-Authors: Luciano Da Fontoura Costa, Roberto M. CesarAbstract:From the Publisher: Advances in shape analysis impact a wide range of disciplines, from mathematics and engineering to medicine, archeology, and art. Anyone just entering the field, however, may find the few existing books on shape analysis too specific or advanced, and for researchers interested in the specific problem of shape recognition and characterization, traditional books on computer vision are too general.Shape Analysis and Classification: Theory and Practice offers an integrated and conceptual introduction to this dynamic field and its myriad applications. Beginning with the basic mathematical concepts, it deals with shape analysis, from image capture to pattern Classification, and presents many of the most advanced and powerful techniques used in practice. The authors explore the relevant aspects of both shape characterization and recognition, and give special attention to practical issues, such as guidelines for implementation, validation, and assessment.Shape Analysis and Classification provides a rich resource for the computational characterization and Classification of general shapes, from characters to biological entities. Both beginning and advanced researchers can directly use its state-of-the-art concepts and techniques to solve their own problems involving the characterization and Classification of visual shapes.
