Related papers: A variational principle for a non-integrable model

We prove that autoparallel curves associated with a torsion-free but not necessarily metric-compatible affine connection can be derived from an action principle. We explicitly construct the action functional and show by standard variational…

A mechanism is proposed for the appearance of power law distributions in various complex systems. It is shown that in a conservative mechanical system composed of subsystems with different numbers of degrees of freedom a robust power-law…

We present an alternative nonconservative gravitational theory based on the Herglotz variational principle in a fully covariant form. The present model may be seen as an improvement of the theory proposed in Ref. [Lazo et al, Phys. Rev. D…

In this paper, we give rates of convergence in the strong invariance principle for non-adapted sequences satisfying projective criteria. The results apply to the iterates of ergodic automorphisms T of the d-dimensional torus, even in the…

We present a simple combinatorial framework for establishing approximate tensorization of variance and entropy in the setting of spin systems (a.k.a. undirected graphical models) based on balanced separators of the underlying graph. Such…

We study the variational principle over an Hilbert-Einstein like action for an extended geometry taking into account torsion and non-metricity. By extending the semi-Riemannian geometry, we obtain an effective energy-momentum tensor which…

We present a new variational principle for linking models of beams and deformable solids, providing also its mathematical analysis. Despite the apparent differences between the two types of governing equations, it will be shown that the…

In this paper we extend the standard differential geometric theory of Hamiltonian dynamics to noncommutative spaces, beginning with symplectic forms. Derivations on the algebra are used instead of vector fields, and interior products and…

We consider a Gibbs distribution over all spanning trees of an undirected, edge weighted finite graph, where, up to normalization, the probability of each tree is given by the product of its edge weights. Defining the weighted degree of a…

Here we present the entropic dynamics formalism for networks. That is, a framework for the dynamics of graphs meant to represent a network derived from the principle of maximum entropy and the rate of transition is obtained taking into…

Bayesian inference problems require sampling or approximating high-dimensional probability distributions. The focus of this paper is on the recently introduced Stein variational gradient descent methodology, a class of algorithms that rely…

A conditional independence graph is a concise representation of pairwise conditional independence among many variables. Graphical Random Forests (GRaFo) are a novel method for estimating pairwise conditional independence relationships among…

The variance of the number of particles in a set is an important quantity in understanding the statistics of non-interacting fermionic systems in low dimensions. An exact map of their ground state in a harmonic trap in one and two…

The discrete gradient structure and the positive definiteness of discrete fractional integrals or derivatives are fundamental to the numerical stability in long-time simulation of nonlinear integro-differential models. We build up a…

In this article, I give a definition of topological entropy for random dynamical systems associated to an infinite countable discrete amenable group action. I obtain a variational principle between the topological entropy and measurable…

We consider the soft-core Widom-Rowlinson model for particles with spins and holes, on a Cayley tree of order $d$ (which has $d + 1$ nearest neighbours), depending on repulsion strength $\beta$ between particles of different signs and on an…

We consider the problem of learning a graph from a finite set of noisy graph signal observations, the goal of which is to find a smooth representation of the graph signal. Such a problem is motivated by the desire to infer relational…

Methods for predicting material properties often rely on empirical models or approximations that overlook the fundamental topological nature of quantum interactions. We introduce a topological framework based on string theory and graph…

In this paper we continue the program, initiated in Ref. hep-th/0112246, to investigate an integrable noncommutative version of the sine-Gordon model. We discuss the origin of the extra constraint which the field function has to satisfy in…

This work introduces DiGress, a discrete denoising diffusion model for generating graphs with categorical node and edge attributes. Our model utilizes a discrete diffusion process that progressively edits graphs with noise, through the…