1,008 research outputs found
Integrable mappings and polynomial growth
We describe birational representations of discrete groups generated by
involutions, having their origin in the theory of exactly solvable
vertex-models in lattice statistical mechanics. These involutions correspond
respectively to two kinds of transformations on matrices: the
inversion of the matrix and an (involutive) permutation of the
entries of the matrix. We concentrate on the case where these permutations are
elementary transpositions of two entries. In this case the birational
transformations fall into six different classes. For each class we analyze the
factorization properties of the iteration of these transformations. These
factorization properties enable to define some canonical homogeneous
polynomials associated with these factorization properties. Some mappings yield
a polynomial growth of the complexity of the iterations. For three classes the
successive iterates, for , actually lie on elliptic curves. This analysis
also provides examples of integrable mappings in arbitrary dimension, even
infinite. Moreover, for two classes, the homogeneous polynomials are shown to
satisfy non trivial non-linear recurrences. The relations between
factorizations of the iterations, the existence of recurrences on one or
several variables, as well as the integrability of the mappings are analyzed.Comment: 45 page
Littératures francophones et formation des enseignants de FLE
Alors qu’en France les littératures francophones sont marginalisées dans les programmes des licences et masters de lettres, elles apparaissent régulièrement dans les cours des «parcours» ou «mention» FLE de licence, tout comme dans ceux des masters de didactique du FLE. Nous nous interrogeons ici, en prenant appui sur une enquête par questionnaire menée auprès d\u27étudiants de master FLE, sur les raisons de cette présence des littératures francophones dans ces cours, qui pourrait sembler de prime abord inattendue, mais renvoie de fait à l’attention qui leur est portée depuis une quinzaine d’années dans le domaine de la didactique du FLE. Quelle place tiennent-elles dans les formations ? Quels objectifs leur sont assignés ? Que connaissent ces futurs enseignants de FLE de ces littératures ? Quel rôle pensent-ils qu’elles puissent tenir dans leur pratique future
Holonomic functions of several complex variables and singularities of anisotropic Ising n-fold integrals
Lattice statistical mechanics, often provides a natural (holonomic) framework
to perform singularity analysis with several complex variables that would, in a
general mathematical framework, be too complex, or could not be defined.
Considering several Picard-Fuchs systems of two-variables "above" Calabi-Yau
ODEs, associated with double hypergeometric series, we show that holonomic
functions are actually a good framework for actually finding the singular
manifolds. We, then, analyse the singular algebraic varieties of the n-fold
integrals , corresponding to the decomposition of the magnetic
susceptibility of the anisotropic square Ising model. We revisit a set of
Nickelian singularities that turns out to be a two-parameter family of elliptic
curves. We then find a first set of non-Nickelian singularities for and , that also turns out to be rational or ellipic
curves. We underline the fact that these singular curves depend on the
anisotropy of the Ising model. We address, from a birational viewpoint, the
emergence of families of elliptic curves, and of Calabi-Yau manifolds on such
problems. We discuss the accumulation of these singular curves for the
non-holonomic anisotropic full susceptibility.Comment: 36 page
A Fast and Efficient Incremental Approach toward Dynamic Community Detection
Community detection is a discovery tool used by network scientists to analyze
the structure of real-world networks. It seeks to identify natural divisions
that may exist in the input networks that partition the vertices into coherent
modules (or communities). While this problem space is rich with efficient
algorithms and software, most of this literature caters to the static use-case
where the underlying network does not change. However, many emerging real-world
use-cases give rise to a need to incorporate dynamic graphs as inputs.
In this paper, we present a fast and efficient incremental approach toward
dynamic community detection. The key contribution is a generic technique called
, which examines the most recent batch of changes made to an
input graph and selects a subset of vertices to reevaluate for potential
community (re)assignment. This technique can be incorporated into any of the
community detection methods that use modularity as its objective function for
clustering. For demonstration purposes, we incorporated the technique into two
well-known community detection tools. Our experiments demonstrate that our new
incremental approach is able to generate performance speedups without
compromising on the output quality (despite its heuristic nature). For
instance, on a real-world network with 63M temporal edges (over 12 time steps),
our approach was able to complete in 1056 seconds, yielding a 3x speedup over a
baseline implementation. In addition to demonstrating the performance benefits,
we also show how to use our approach to delineate appropriate intervals of
temporal resolutions at which to analyze an input network
Detectives in the managerial iron cage? Evidence from English police investigation units
Cet article questionne les relations entre réformes néo-managériales, organisations policières et dynamiques professionnelles dans les services d’investigation de deux polices britanniques. Prenant pour point de départ les réformes néo-managériales qu’ont connues les polices depuis le début des années 1990, il montre qu’à partir d’un suivi de l’activité plus détaillé et resserré temporellement et d’une accountability chiffrée, on assiste à une plus forte intégration organisationnelle, redéfinissant les conditions d’exercice de l’activité professionnelle. Ces réformes donnent lieu à des jugements contradictoires : certains considèrent les objectifs chiffrés, le suivi plus précis et automatisé comme bénéfiques, là où d’autres y voient des contraintes affectant négativement leur activité professionnelle. Malgré sa rigidité, ce régime de performance autorise tout de même des réappropriations qui peuvent s’opérer selon trois logiques : spécialisation, aménagement de la temporalité et usages différents des indicateurs chiffrés dans la gestion des équipes.This article questions the relationship between neo-managerial reforms, professional police and professional dynamics in investigatory police units of two British forces. Based on the analysis of neo-managerial reforms that have impacted upon the British police since the 90’s, it shows a stronger organisational integration based on a more detailed and tightened monitoring of activity and an internal accountability focused on numerical targets which redefine the conditions of professional activity. These reforms are the object of contradictory judgments: some officers consider that numerical targets, automatized monitoring and increased control are beneficial to police activity, whilst others see them as unnecessary constraints with perverse effects. Despite its ap–parent rigidity, this performance regime still allows professional adaptations that can operate within three logics: specialisation, management of temporality and different uses of quantitative indicators in team management
Location of the Multicritical Point for the Ising Spin Glass on the Triangular and Hexagonal Lattices
A conjecture is given for the exact location of the multicritical point in
the phase diagram of the +/- J Ising model on the triangular lattice. The
result p_c=0.8358058 agrees well with a recent numerical estimate. From this
value, it is possible to derive a comparable conjecture for the exact location
of the multicritical point for the hexagonal lattice, p_c=0.9327041, again in
excellent agreement with a numerical study. The method is a variant of duality
transformation to relate the triangular lattice directly with its dual
triangular lattice without recourse to the hexagonal lattice, in conjunction
with the replica method.Comment: 9 pages, 1 figure; Minor corrections in notatio
On the complexity of some birational transformations
Using three different approaches, we analyze the complexity of various
birational maps constructed from simple operations (inversions) on square
matrices of arbitrary size. The first approach consists in the study of the
images of lines, and relies mainly on univariate polynomial algebra, the second
approach is a singularity analysis, and the third method is more numerical,
using integer arithmetics. Each method has its own domain of application, but
they give corroborating results, and lead us to a conjecture on the complexity
of a class of maps constructed from matrix inversions
Strong disorder fixed points in the two-dimensional random-bond Ising model
The random-bond Ising model on the square lattice has several disordered
critical points, depending on the probability distribution of the bonds. There
are a finite-temperature multicritical point, called Nishimori point, and a
zero-temperature fixed point, for both a binary distribution where the coupling
constants take the values +/- J and a Gaussian disorder distribution. Inclusion
of dilution in the +/- J distribution (J=0 for some bonds) gives rise to
another zero-temperature fixed point which can be identified with percolation
in the non-frustrated case (J >= 0). We study these fixed points using
numerical (transfer matrix) methods. We determine the location, critical
exponents, and central charge of the different fixed points and study the
spin-spin correlation functions. Our main findings are the following: (1) We
confirm that the Nishimori point is universal with respect to the type of
disorder, i.e. we obtain the same central charge and critical exponents for the
+/- J and Gaussian distributions of disorder. (2) The Nishimori point, the
zero-temperature fixed point for the +/- J and Gaussian distributions of
disorder, and the percolation point in the diluted case all belong to mutually
distinct universality classes. (3) The paramagnetic phase is re-entrant below
the Nishimori point, i.e. the zero-temperature fixed points are not located
exactly below the Nishimori point, neither for the +/- J distribution, nor for
the Gaussian distribution.Comment: final version to appear in JSTAT; minor change
Duality in finite-dimensional spin glasses
We present an analysis leading to a conjecture on the exact location of the
multicritical point in the phase diagram of spin glasses in finite dimensions.
The conjecture, in satisfactory agreement with a number of numerical results,
was previously derived using an ansatz emerging from duality and the replica
method. In the present paper we carefully examine the ansatz and reduce it to a
hypothesis on analyticity of a function appearing in the duality relation. Thus
the problem is now clearer than before from a mathematical point of view: The
ansatz, somewhat arbitrarily introduced previously, has now been shown to be
closely related to the analyticity of a well-defined function.Comment: 12 pages, 3 figures; A reference added; to appear in J. Stat. Phy
Notch signaling during human T cell development
Notch signaling is critical during multiple stages of T cell development in both mouse and human. Evidence has emerged in recent years that this pathway might regulate T-lineage differentiation differently between both species. Here, we review our current understanding of how Notch signaling is activated and used during human T cell development. First, we set the stage by describing the developmental steps that make up human T cell development before describing the expression profiles of Notch receptors, ligands, and target genes during this process. To delineate stage-specific roles for Notch signaling during human T cell development, we subsequently try to interpret the functional Notch studies that have been performed in light of these expression profiles and compare this to its suggested role in the mouse
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