Related papers: A Correspondence Between Deep Boltzmann Machines a…
Probabilistic Boolean Networks (PBNs) have been previously proposed so as to gain insights into complex dy- namical systems. However, identification of large networks and of the underlying discrete Markov Chain which describes their…
In wireless networks, the knowledge of nodal distances is essential for several areas such as system configuration, performance analysis and protocol design. In order to evaluate distance distributions in random networks, the underlying…
Understanding the operation of biological and artificial networks remains a difficult and important challenge. To identify general principles, researchers are increasingly interested in surveying large collections of networks that are…
A framework for relativistic thermodynamics and statistical physics is built by first exploiting the symmetries between energy and momentum in the derivation of the Boltzmann distribution, then using Einstein's energy-momentum relationship…
In the present paper, we studied a Dynamic Stochastic Block Model (DSBM) under the assumptions that the connection probabilities, as functions of time, are smooth and that at most $s$ nodes can switch their class memberships between two…
A multi-relaxation-time discrete Boltzmann model (DBM) with split collision is proposed for both subsonic and supersonic compressible reacting flows, where chemical reactions take place among various components. The physical model is based…
The bulk boundary correspondence, one of the most significant features of topological matter, theoretically connects the existence of edge modes at the boundary with topological invariants of the bulk spectral bands. However, it remains…
Building on previous work on the stochastic analysis for Grassmann random variables, we introduce a forward-backward stochastic differential equation (FBSDE) which provides a stochastic quantisation of Grassmann measures. Our method is…
This paper extends the possibility to examine the underlying curvature of data through the lens of topology by using the Betti curves, tools of Persistent Homology, as key topological descriptors, building on the clique topology approach.…
The Restricted Boltzmann Machine (RBM) is one of the simplest generative neural networks capable of learning input distributions. Despite its simplicity, the analysis of its performance in learning from the training data is only well…
In this chapter we take a look at the universal approximation question for stochastic feedforward neural networks. In contrast to deterministic networks, which represent mappings from a set of inputs to a set of outputs, stochastic networks…
This work introduces a number of algebraic topology approaches, such as multicomponent persistent homology, multi-level persistent homology and electrostatic persistence for the representation, characterization, and description of small…
Understanding feature-outcome associations in high-dimensional data remains challenging when relationships vary across subpopulations, yet standard methods assuming global associations miss context-dependent patterns, reducing statistical…
In this work, we begin to investigate the possibility of training a deep neural network on the task of binary code understanding. Specifically, the network would take, as input, features derived directly from binaries and output English…
Starting from the working hypothesis that both physics and the corresponding mathematics have to be described by means of discrete concepts on the Planck scale, one of the many problems one has to face in this enterprise is to find the…
Understanding the deep representations of complex networks is an important step of building interpretable and trustworthy machine learning applications in the age of internet. Global surrogate models that approximate the predictions of a…
An adaptive modeling method (AMM) that couples a deep neural network potential and a classical force field is introduced to address the accuracy-efficiency dilemma faced by the molecular simulation community. The AMM simulated system is…
We characterise the dynamics of neuronal activity, in terms of field theory, using neural units placed on a 2D-lattice modelling the cortical surface. The electrical activity of neuronal units was analysed with the aim of deriving a neural…
This paper concerns the asymptotic ground state properties of heavy atoms in strong, homogeneous magnetic fields. In the limit when the nuclear charge Z tends to infinity with the magnetic field B satisfying B >> Z^{4/3} all the electrons…
Neural networks are high-dimensional nonlinear dynamical systems that process information through the coordinated activity of many connected units. Understanding how biological and machine-learning networks function and learn requires…