1,721,003 research outputs found
Equivalence of dynamics for systems with transverse constraints
No full textThis paper is concerned with the dynamics of a mechanical system subject to nonintegrable constraints. In the first part, we prove the equivalence between the classical nonholonomic equations and those derived from the nonholonomic variational formulation, proposed by Kozlov in [10–12], for a class of constrained systems with constraints transverse to a foliation. This result extends the equivalence between the two formulations, proved for holonomic constraints, to a class of linear nonintegrable ones. In the second part, we derive the nonholonomic variational reduced equations for a constrained system with symmetry and constraint transverse to a principal bundle fibration, using a reduction procedure similar to the one developed in [5]. The resulting equations are compared with the nonholonomic reduced ones through mechanical examples
Replicated point processes with application to population dynamics models
No full textIn this paper we study spatially clustered distribution of individuals using point process theory. In particular we discuss the spatially explicit neutral model of population dynamics of Shimatani (2010) which extends previous works on Malécot theory of isolation by distance. We reformulate Shimatani model of replicated Neyman-Scott process to allow for a general dispersal kernel function and we show that the random migration hypothesis can be substituted by the long dispersal distance property of the kernel. Moreover, the extended framework presented here is fit to handle spatially explicit statistical estimators of genetic variability like Moran autocorrelation index or Sørensen similarity index. We discuss the pivotal role of the choice of dispersal kernel for the above estimators in a toy model of dynamic population genetics theory
Computation of the phase fraction in a discrete model for a pseudoelastic material
No full textWe consider a discrete model of a pseudoelastic material formed by a chain of bistable elements (snap springs). This model exhibits non monotone stress-strain relation due to the non convexity of the potential energy and it can mimic the hysteretic behaviour observed under cyclic loading in a hard device. We compute all the possible equilibrium states compatible with a given total strain and we apply the Maximum Entropy Principle. Given an arbitrary hysteresis cycle, we are able to infer the evolution of the phase fraction and of the information entropy along the cycl
Isotropic submanifolds generated by the Maximum Entropy principle and Onsager reciprocity relations
No full textWe show that the Maximum Entropy Principle (MEP) (Phys. Rev. 106 (Part I and 11) (1957) 620-630; Phys. Rev. 108 (1957) 171-630), when considered as a constrained extremization problem, defines in a natural way a Morse Family and a related isotropic (Lagrangian in the finite-dimensional case) submanifold of an infinite-dimensional linear symplectic space. This geometric approach becomes useful when dealing with the MEP with nonlinear constraints and it allows to derive Onsager-like reciprocity relations as a consequence of the isotropy
Geometry and control of thermodynamic systems described by generalized exponential families
Full text linkIn this paper we investigate the geometric structure and control of exponential families depending on additional parameters, called external parameters. These generalized expo- nential families emerge naturally when one applies the maximum entropy formalism to derive the equilibrium statistical mechanics framework. We study the associated statistical model, compute the Fisher metric and introduce a natural fibration of the parameter space over the external parameter space. The Fisher Riemannian metric allows to endow this fi- bration with an Ehresmann connection and to study the geometry and control of these statistical models. As an example, we show that horizontal lift of paths in the external pa- rameter space corresponds to an isentropic evolution of the system. We apply the theory to the example of an ideal gas and an ideal gas in a rotating rigid container
Remarks on the Maximum Entropy Principle with Application to the Maximum Entropy Theory of Ecology
Full text linkIn the first part of the paper we work out the consequences of the fact that Jaynes’ Maximum Entropy Principle, when translated in mathematical terms, is a constrained extremum problem for an entropy function H ( p ) expressing the uncertainty associated with the probability distribution p. Consequently, if two observers use different independent variables p or g ( p ) , the associated entropy functions have to be defined accordingly and they are different in the general case. In the second part we apply our findings to an analysis of the foundations of the Maximum Entropy Theory of Ecology (M.E.T.E.) a purely statistical model of an ecological community. Since the theory has received considerable attention by the scientific community, we hope to give a useful contribution to the same community by showing that the procedure of application of MEP, in the light of the theory developed in the first part, suffers from some incongruences. We exhibit an alternative formulation which is free from these limitations and that gives different results
Maximum Entropy Theory of Ecology: A Reply to Harte
Full text linkIn a paper published in this journal, I addressed the following problem: under which conditions will two scientists, observing the same system and sharing the same initial information, reach the same probabilistic description upon the application of the Maximum Entropy inference principle (MaxEnt) independent of the probability distribution chosen to set up the MaxEnt procedure. This is a minimal objectivity requirement which is generally asked for scientific investigation. In the same paper, I applied the findings to a critical examination of the application of MaxEnt made in Harte’s Maximum Entropy Theory of Ecology (METE). Prof. Harte published a comment to my paper and this is my reply. For the sake of the reader who may be unaware of the content of the papers, I have tried to make this reply self-contained and to skip technical details. However, I invite the interested reader to consult the previously published papers
Book Review: Hui, C.; Richardson, D. Invading Ecological Networks; Cambridge University Press: Cambridge, UK, 2022; ISBN: 9781108778374
Full text linkThe book addresses the problem of describing the dynamics of the interaction of alien species with an ecosystem using modern network theory [...
Lagrangian Submanifolds of Symplectic Structures Induced by Divergence Functions
Full text linkDivergence functions play a relevant role in Information Geometry as they allow for the introduction of a Riemannian metric and a dual connection structure on a finite dimensional manifold of probability distributions. They also allow to define, in a canonical way, a symplectic structure on the square of the above manifold of probability distributions, a property that has received less attention in the literature until recent contributions. In this paper, we hint at a possible application: we study Lagrangian submanifolds of this symplectic structure and show that they are useful for describing the manifold of solutions of the Maximum Entropy principle
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