Related papers: Pattern generation problems arising in multiplicat…

We consider the problem of learning deep generative models from data. We formulate a method that generates an independent sample via a single feedforward pass through a multilayer perceptron, as in the recently proposed generative…

We develop information-theoretic measures of spatial structure and pattern in more than one dimension. As is well known, the entropy density of a two-dimensional configuration can be efficiently and accurately estimated via a converging…

In this article, we discuss a novel approach to solving number sequence problems, in which sequences of numbers following unstated rules are given, and missing terms are to be inferred. We develop a methodology of decomposing test sequences…

Present theoretical predictions for the entanglement entropy through topological defects are violated by numerical simulations. In order to resolve this, we introduce a paradigm shift in the preparation of reduced density matrices in the…

We introduce a simple lattice model in which percolation is constructed on top of critical percolation clusters, and show that it can be repeated recursively any number $n$ of generations. In two dimensions, we determine the percolation…

Percolation refers to an interesting class of problems related to the properties of disordered systems, usually formulated in terms of objects randomly placed on an underlying lattice or continuum. Despite the simplicity of the setup, most…

Begin with a set of four points in the real plane in general position. Add to this collection the intersection of all lines through pairs of these points. Iterate. Ismailescu and Radoi\v{c}i\'{c} (2003) showed that the limiting set is dense…

We propose a manifold matching approach to generative models which includes a distribution generator (or data generator) and a metric generator. In our framework, we view the real data set as some manifold embedded in a high-dimensional…

Living systems operate far from thermal equilibrium by converting the chemical potential of ATP into mechanical work to achieve growth, replication or locomotion. Given time series observations of intra-, inter- or multicellular processes,…

We propose new linear combinations of compositions of a basic second-order scheme with appropriately chosen coefficients to construct higher order numerical integrators for differential equations. They can be considered as a generalization…

This paper deals with the design of Excitation and Measurement Patterns (EMPs) for the identification of dynamical networks, when the objective is to identify only a subnetwork embedded in a larger network. Recent results have shown how to…

In this paper we deal with a network of agents seeking to solve in a distributed way Mixed-Integer Linear Programs (MILPs) with a coupling constraint (modeling a limited shared resource) and local constraints. MILPs are NP-hard problems and…

We consider the numerical irreducible decomposition of a positive dimensional solution set of a polynomial system into irreducible factors. Path tracking techniques computing loops around singularities connect points on the same irreducible…

Understanding the structural complexity and predictability of complex networks is a central challenge in network science. Although recent studies have revealed a relationship between compression-based entropy and link prediction…

The notion of metric entropy dimension is introduced to measure the complexity of entropy zero dynamical systems. For measure preserving systems, we define entropy dimension via the dimension of entropy generating sequences. This…

We consider uniform random permutations drawn from a family enumerated through generating trees. We develop a new general technique to establish a central limit theorem for the number of consecutive occurrences of a fixed pattern in such…

We consider a minimal controllability problem (MCP), which determines the minimum number of input nodes for a descriptor system to be structurally controllable. We investigate the "forbidden nodes" in descriptor systems, denoting nodes that…

The estimation of a precision matrix is a crucial problem in various research fields, particularly when working with high dimensional data. In such settings, the most common approach is to use the penalized maximum likelihood. The…

We consider a system composed of a fixed number of particles with total energy smaller or equal to some prescribed value. The particles are non-interacting, indistinguishable and distributed over fixed number of energy levels. The energy…

A matching is said to be disconnected if the saturated vertices induce a disconnected subgraph and induced if the saturated vertices induce a 1-regular graph. The disconnected and induced matching numbers are defined as the maximum…