Related papers: Random geometric complexes in the thermodynamic re…
In this paper, a quantum computational framework for algebraic topology based on simplicial set theory is presented. This extends previous work, which was limited to simplicial complexes and aimed mostly to topological data analysis. The…
It has long been suggested that the mid-latitude atmospheric circulation possesses what has come to be known as `weather regimes', loosely categorised as regions of phase space with above-average density and/or extended persistence. Their…
We develop a quantum topological data analysis (QTDA) protocol based on the estimation of the density of states (DOS) of the combinatorial Laplacian. Computing topological features of graphs and simplicial complexes is crucial for analyzing…
We study perturbations of the Erdos-Renyi model for which the statistical weight of a graph depends on the abundance of certain geometrical patterns. Using the formal correspondance with an exactly solvable effective model, we show the…
We develop inductive biases for the machine learning of complex physical systems based on the port-Hamiltonian formalism. To satisfy by construction the principles of thermodynamics in the learned physics (conservation of energy,…
In this paper we show how almost cosymplectic structures are a natural framework to study thermodynamical systems. Indeed, we are able to obtain the same evolution equations obtained previously by Gay-Balmaz and Yoshimura (see Entropy,…
Large graphs are sometimes studied through their degree sequences (power law or regular graphs). We study graphs that are uniformly chosen with a given degree sequence. Under mild conditions, it is shown that sequences of such graphs have…
We present the development of the approach to thermodynamics based on measurement. First of all, we recall that considering classical thermodynamics as a theory of measurement of extensive variables one gets the description of thermodynamic…
Recently, a morphological transition in the velocity distribution of a relativistic gas has been pointed out which shows hallmarks of a critical phenomenon. Here, we provide a general framework which allows for a thermodynamic approach to…
In this paper, we study the expectation values of topological invariants of the Vietoris-Rips complex and \v{C}ech complex for a finite set of sample points on a Riemannian manifold. We show that the Betti number and Euler characteristic of…
Standard statistical mechanical or condensed matter arguments tell us that bulk properties of a physical system do not depend too much on boundary conditions. Random tilings of large regions provide counterexamples to such intuition, as…
We give a complete expansion, at any accuracy order, for the iterated convolution of a complex valued integrable sequence in one space dimension. The remainders are estimated sharply with generalized Gaussian bounds. The result applies in…
We define a dynamic model of random networks, where new vertices are connected to old ones with a probability proportional to a sublinear function of their degree. We first give a strong limit law for the empirical degree distribution, and…
We consider a finite sequence of random points in a finite domain of a finite-dimensional Euclidean space. The points are sequentially allocated in the domain according to a model of cooperative sequential adsorption. The main peculiarity…
We consider the monomer-dimer model on sequences of random graphs locally convergent to trees. We prove that the monomer density converges almost surely, in the thermodynamic limit, to an analytic function of the monomer activity. We…
Let $K$ be a finite simplicial complex. We prove that the normalized expected Betti numbers of a random subcomplex in its $d$-th barycentric subdivision $\text{Sd}^d (K)$ converge to universal limits as $d$ grows to $+ \infty$. In…
Simplicial complexes are increasingly used to understand the topology of complex systems as different as brain networks and social interactions. It is therefore of special interest to extend the study of percolation to simplicial complexes.…
This article proves the existence of a bound on the sum of local Betti numbers of a real analytic germ by a polynomial function of its multiplicity. This result can be interpreted as a localization of the classical Oleinik-Petrovsky bound…
We introduce a model for a growing random graph based on simultaneous reproduction of the vertices. The model can be thought of as a generalisation of the reproducing graphs of Southwell and Cannings and Bonato et al to allow for a random…
Recent research on the fundamentals of statistical mechanics has led to an interesting discovery [1-3]: With locally nonchaotic barriers, as Boltzmann's H-theorem is inapplicable, there exist nontrivial non-thermodynamic systems that can…