Related papers: Hierarchical Maximum Entropy via the Renormalizati…
Motion generation in cluttered, dense, and dynamic environments is a central topic in robotics, rendered as a multi-objective decision-making problem. Current approaches trade-off between safety and performance. On the one hand, reactive…
We report universal statistical properties displayed by ensembles of pure states that naturally emerge in quantum many-body systems. Specifically, two classes of state ensembles are considered: those formed by i) the temporal trajectory of…
Gaussian process regression has proven very powerful in statistics, machine learning and inverse problems. A crucial aspect of the success of this methodology, in a wide range of applications to complex and real-world problems, is…
(Neal and Hinton, 1998) recast maximum likelihood estimation of any given latent variable model as the minimization of a free energy functional $F$, and the EM algorithm as coordinate descent applied to $F$. Here, we explore alternative…
A statistical treatment of finite unbound systems in the presence of collective motions is presented and applied to a classical Lennard-Jones Hamiltonian, numerically simulated through molecular dynamics. In the ideal gas limit, the flow…
We establish an exact equivalence between the Functional Renormalization Group (FRG) and the Ricci flow modified by a potential-driven diffeomorphism. By reformulating the Polchinski exact renormalization group equation into an…
In this article the problem of reconstructing the pattern of connection between agents from partial empirical data in a macro-economic model is addressed, given a set of behavioral equations. This systemic point of view puts the focus on…
The maximum entropy principle from statistical mechanics states that a closed system attains an equilibrium distribution that maximizes its entropy. We first show that for graphs with fixed number of edges one can define a stochastic edge…
Large-$N$ renormalization group equations for one- and two-matrix models are derived. The exact renormalization group equation involving infinitely many induced interactions can be rewritten in a form that has a finite number of coupling…
We define the class of multivariate group entropies as a novel set of information - theoretical measures, which extends significantly the family of group entropies. We propose new examples related to the "super-exponential" universality…
Hierarchy is one of the most conspicuous features of numerous natural, technological and social systems. The underlying structures are typically complex and their most relevant organizational principle is the ordering of the ties among the…
The collection of data on populations of networks is becoming increasingly common, where each data point can be seen as a realisation of a network-valued random variable. A canonical example is that of brain networks: a typical neuroimaging…
The canonical ensemble describes an open system in equilibrium with a heat bath of fixed temperature. The probability distribution of such a system, the Boltzmann distribution, is derived from the uniform probability distribution of the…
We study the inverse problem of inferring the state of a finite-level quantum system from expected values of a fixed set of observables, by maximizing a continuous ranking function. We have proved earlier that the maximum-entropy inference…
The efficiency of a large hierarchical organisation is simulated on Barabasi-Albert networks, when each needed link leads to a loss of information. The optimum is found at a finite network size, corresponding to about five hierarchical…
Hierarchical model fitting has become commonplace for case-control studies of cognition and behaviour in mental health. However, these techniques require us to formalise assumptions about the data-generating process at the group level,…
I present an unbiased method of mapping particles to distribution functions and vice versa. This method alone defines the canonical formulation of statistical mechanics, since it can be used to derive the principle of maximum entropy in…
We uncover connections between maximum likelihood estimation in statistics and norm minimization over a group orbit in invariant theory. We focus on Gaussian transformation families, which include matrix normal models and Gaussian graphical…
The article deals with the mathematical model for media with hierarchical structure. Using the hamiltonian formalism, the dynamical system describing the state of hierarchically connected structural elements was derived. According to the…
Trophic coherence, a measure of a graph's hierarchical organisation, has been shown to be linked to a graph's structural and dynamical aspects such as cyclicity, stability and normality. Trophic levels of vertices can reveal their…