Papers by François Bavaud
Studies in Classification, Data Analysis, and Knowledge Organization, 2015
Lecture Notes in Computer Science, 2012
Journal of Geographical Systems, 2013
In a weighted spatial network, as specified by an exchange matrix, the variances of the spatial v... more In a weighted spatial network, as specified by an exchange matrix, the variances of the spatial values are inversely proportional to the size of the regions. Spatial values are no more exchangeable under independence, thus weakening the rationale for ordinary permutation and bootstrap tests of spatial autocorrelation. We propose an alternative permutation test for spatial autocorrelation, based upon exchangeable spatial modes, constructed as linear orthogonal combinations of spatial values. The coefficients obtain as eigenvectors of the standardised exchange matrix appearing in spectral clustering, and generalise to the weighted case the concept of spatial filtering for connectivity matrices. Also, two proposals aimed at transforming an acessibility matrix into a exchange matrix with with a priori fixed margins are presented. Two examples (inter-regional migratory flows and binary adjacency networks) illustrate the formalism, rooted in the theory of spectral decomposition for reversible Markov chains.
Geographical Analysis, 2010
General properties of spatial weights models, in particular Markovian properties, are systematica... more General properties of spatial weights models, in particular Markovian properties, are systematically investigated. The role of stationary spatial distribution, interpretable as an importance-centrality or prominence index, is emphasized. Spatial interaction models, and among them the gravity model, are classified with respect to the time reversal and aggregation invariance properties obeyed by the associated spatial weights. Nine examples, involving connectivity, flows and distance decay analysis, integral geometry and Dirichlet-Voronoi tessellations illustrate the main concepts, with a particular geometrical emphasis, and show how traditional, heuristic ingredients aimed at defining spatial weights can be recovered form general models.
Transactions of the American Mathematical Society, 1992
Transactions of the American Mathematical Society, 1992
Journal of Statistical Physics, 1987
A unified treatment of viscoelasticity is developed in the framework of nonequilibrium classical ... more A unified treatment of viscoelasticity is developed in the framework of nonequilibrium classical statistical mechanics. An exact correspondence between Mori's continued-fractions formalism and theological circuits is shown.
Letters in Mathematical Physics, 1990
We study the statistical mechanical properties of a two-dimensional assembly of free particles co... more We study the statistical mechanical properties of a two-dimensional assembly of free particles coupled to a mechanical reservoir. The particles-reservoir interaction is modelised by an Hamiltonian depending on the convex hull of the particles only. We concentrate on models whose energy is the sum of an area-term, a perimeter term and possibly a term preventing the particles occupying the interior of the convex hull. The range of coupling constants insuring a thermodynamic behaviour, as well as the associated free energy per particle are exactly determined.
Journal of Statistical Physics, 1986
New expressions for the elastic moduli of a classical system are derived. They involve only the t... more New expressions for the elastic moduli of a classical system are derived. They involve only the two-point correlation function and the derivative of the onepoint correlation function, both only on the boundary of the system. These expressions, valid for any interaction derivable from a potential, are proved from a mechanical point of view by generalizing the virial theorem of Clausius, and from a statistical point of view by a direct method that constitutes an alternative to Green's dilatation method.
Journal of Statistical Physics, 1986
We consider continuous systems of particles in the framework of classical statistical mechanics a... more We consider continuous systems of particles in the framework of classical statistical mechanics and derive a general expression for the static elastic moduli tensor in terms of correlation functions. We find sufficient conditions for the vanishing of the shear modulus. Relationships between these conditions and others insuring translational or rotational invariance are discussed.
Journal of Statistical Physics, 1989
The difficulties inherent in the construction of two-dimensional pressure ensembles are discussed... more The difficulties inherent in the construction of two-dimensional pressure ensembles are discussed, and are tackled by defining an energy cost depending on the convex hull of the set of particles. An energy proportional to the area of the convex hull is not able to prevent evaporation of the system, whereas an energy proportional to the area of the circumcircle of the convex hull ensures a thermodynamic behavior. In the latter model, which turns out to be exactly solvable, various characterizations are given of the geometry of a typical state.
Reviews of Modern Physics, 1991
This article investigates in a systematic way the properties of the classical continuous mean-fie... more This article investigates in a systematic way the properties of the classical continuous mean-field theory governed by the generalized Poisson-Boltzmann-Emàen equation p,-\: A^expl-p I ndy pg)Vf x -Ð) together with the associated variational problem infol J ndx J ndy p1u-)p(l\V7-y\ +kf I ndx p¡\\np(x\. Origins of the theory are traced back. Past studies (free2ing theories, electrostatic and self-gravitating systems) are relocated in a broader framework' New results concerning the thermodynamic limit, phase transitions, metastability, and the shape of density profiles ate provided' In particular, the question of ground states (in relationship to condensation and wetting phenomena) is illustrated by numerous explicit solutions.
Communications in Mathematical Physics, 1990
We consider two-dimensional assemblies of particles governed by hamiltonians depending on the are... more We consider two-dimensional assemblies of particles governed by hamiltonians depending on the area and the perimeter of their convex hull. Provided the hamiltonian is quadratically homogeneous in the coordinates, we find an exact formula for the free energy. Phase transitions resulting from the competition between area and perimeter can easily be produced and explicitly dealt with. We illustrate those features by a simple example undergoing a second-order transition.
Journal of Statistical Physics, 1994
Three planar classical particles interact via a potential proportional to the area of the triangl... more Three planar classical particles interact via a potential proportional to the area of the triangle they form. This system is equivalent to two oscillators attached to the origin, the nearest being repelled by and the other being attracted to it (piecewise integrable Hamiltonian). Numerical simulations show two types of trajectories: those apparently escaping to infinity, and those in confined quasiperiodic orbits. Adiabatic theories lead to discrete recurrence relations and allow for the second type only. A general method allowing prediction of first return time of the slow motion as well as a short/long-period relation is presented. The issue of the possibly metastable nature of escaping trajectories is raised.
Résumé We propose context-dependant utility models, where the utility of a multiattribute potenti... more Résumé We propose context-dependant utility models, where the utility of a multiattribute potential alternative is weighted in a way depending on the multiattribute utility of the present alternative. Such models reflect principles as "satisfaction of a need makes it invisible", or "the need creates the context", as well as other possibilities. They are shown to produce intransitivites as well as context-dependant preference reversals. Relationship with Tversky's additive model as well as Fechnerian and stochastic transitive properties are investigated. A particular class of weights, called NEAR, turns out to have local optimality properties, and reproduce general features of risk attitude in human species.
Local formalism deals with weighted unoriented networks, specified by an exchange matrix, determi... more Local formalism deals with weighted unoriented networks, specified by an exchange matrix, determining the selection probabilities of pairs of vertices. It permits to define local inertia and local autocorrelation relatively to arbitrary networks. In particular, free partitioned exchanges amount in defining a categorical variable (hard membership), together with canonical spectral scores, identical to Fisher's discriminant functions. One demonstrates how to extend the construction of the latter to any unoriented network, and how to assess the similarity between canonical and original configurations, as illustrated on four datasets.
Studies in Classification, Data Analysis, and Knowledge Organization, 2000
Textual autocorrelation is a broad and pervasive concept, referring to the similarity between nea... more Textual autocorrelation is a broad and pervasive concept, referring to the similarity between nearby textual units: lexical repetitions along consecutive sentences, semantic association between neighbouring lexemes, persistence of discourse types (narrative, descriptive, dialogal...) and so on. Textual autocorrelation can also be negative, as illustrated by alternating phonological or morpho-syntactic categories, or the succession of word lengths. This contribution proposes a general Markov formalism for textual navigation, and inspired by spatial statistics. The formalism can express well-known constructs in textual data analysis, such as term-document matrices, references and hyperlinks navigation, (web) information retrieval, and in particular textual autocorrelation, as measured by Moran's I relatively to the exchange matrix associated to neighbourhoods of various possible types. Four case studies (word lengths alternation, lexical repulsion, parts of speech autocorrelation,...
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Papers by François Bavaud