1,720,974 research outputs found
Tropical limit and a micro-macro correspondence in statistical physics
No full textTropical mathematics is used to establish a correspondence between certain microscopic and macroscopic objects in statistical models. Tropical algebra gives a common framework for macrosystems (subsets) and their elementary constituents (elements) that is well-behaved with respect to composition. This kind of connection is studied with maps that preserve a monoid structure. The approach highlights an underlying order relation that is explored through the concepts of filter and ideal. Particular attention is paid to asymmetry and duality between max- and min-criteria. Physical implementations are presented through simple examples in thermodynamics and non-equilibrium physics. The phenomenon of ultrametricity, the notion of tropical equilibrium and the role of ground energy in non-equilibrium models are discussed. Tropical symmetry, i.e. idempotence, is investigated
Complexity reduction for sign configurations through the KP II equation and its information-theoretic aspects
No full textWe provide a combinatorial setting to explore the information content associated with the fulfillment of the Kadomtsev-Petviashvili (KP) II equation. We start from a special family of solutions of KP II, namely, tau-functions of Wronskian type. A solution in this class can be expressed as a sum of exponentials, and we look at combinations of signs (signatures) for the nonvanishing terms in this sum. We prove a characterization of the signatures that return another solution of the KP II equation: they can be represented as choices of signs for columns and rows of a coefficient matrix, so we recover a function satisfying the whole KP hierarchy from this single constraint. The redundancy of this representation for different choices of the initial solution is investigated. Enumerative, information-theoretic, and geometric aspects of this construction are discussed
Zeros and amoebas of partition functions
No full textSingular sectors sing (loci of zeros) for real-valued non-positively defined partition functions of n variables are studied. It is shown that sing have a stratified structure where each stratum is a set of certain hypersurfaces in n. The concept of statistical amoeba is introduced and the properties of a family of statistical amoebas are studied. The relation with algebraic amoebas is discussed. Tropical limits of statistical amoebas are considered too. Applications of the concept of statistical amoeba to the analysis of singular sectors for integrable equations and properties of macroscopic systems with multiple equilibria, including frustrated systems, are discussed
Tropical limit in statistical physics
No full textTropical limit for macroscopic systems in equilibrium defined as the formal limit of Boltzmann cosntant tends to infinity is discussed
Geometry of basic statistical physics mapping
No full textThe geometry of hypersurfaces defined by the relation which generalizes the classical formula for free energy in terms of microstates is studied. The induced metric, the Riemann curvature tensor, the Gauss-Kronecker curvature and its associated entropy are calculated. A special class of ideal statistical hypersurfaces is analyzed in detail. Non-ideal hypersurfaces and singularities similar to those of the phase transitions are considered. The tropical limit of the statistical hypersurfaces and the double scaling tropical limit are discussed too
Streaming generalized cross entropy
No full textWe propose a new method to combine adaptive processes with a class of entropy estimators for the case of streams of data. Starting from a first estimation obtained from a batch of initial data, model parameters are estimated at each step by combining the prior knowledge with the new observation (or a block of observations). This allows to extend the maximum entropy technique to a dynamical setting, also distinguishing between entropic contributions of the signal and the error. Furthermore, it provides a suitable approximation of standard GME problems when the exacted solutions are hard to evaluate. We test this method by performing numerical simulations at various sample sizes and batch dimensions. Moreover, we extend this analysis exploring intermediate cases between streaming GCE and standard GCE, i.e., considering blocks of observations of different sizes to update the estimates, and incorporating collinearity effects as well. The role of time in the balance between entropic contributions of signal and errors is further explored considering a variation of the Streaming GCE algorithm, namely Weighted Streaming GCE. Finally, we discuss the results: In particular, we highlight the main characteristics of this method, the range of application, and future perspectives
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
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