Related papers: Skorokhod's M1 topology for distribution-valued pr…
Topology identification and inference of processes evolving over graphs arise in timely applications involving brain, transportation, financial, power, as well as social and information networks. This chapter provides an overview of graph…
We present a way of topologizing sets of Galois types over structures in abstract elementary classes with amalgamation. In the elementary case, the topologies thus produced refine the syntactic topologies familiar from first order logic. We…
We study convergence in law of partial sums of linear processes with heavy-tailed innovations. In the case of summable coefficients necessary and sufficient conditions for the finite dimensional convergence to an $\alpha$-stable L\'evy…
We investigate the advantages of machine learning techniques to recognize the dynamics of topological objects in quantum field theories. We consider the compact U(1) gauge theory in three spacetime dimensions as the simplest example of a…
Although copulas are used and defined for various infinite-dimensional objects (e.g. Gaussian processes and Markov processes), there is no prevalent notion of a copula that unifies these concepts. We propose a unified approach and define…
A new method for the statistical analysis of 3D point processes, based on the family of Minkowski functionals, is explained and applied to modelled galaxy distributions generated by a toy-model and cosmological simulations of the…
We present a novel M-theoretic approach of constructing and classifying anyonic topological phases of matter, by establishing a correspondence between (2+1)d topological field theories and non-hyperbolic 3-manifolds. In this construction,…
Directed paths have been used by several authors to describe concurrent executions of a program. Spaces of directed paths in an appropriate state space contain executions with all possible legal schedulings. It is interesting to investigate…
In this paper the sufficient conditions for convergence in Skorokhod space $D[0,1]$ of sequence of random processes with random time substitution are obtained.
For a stationary sequence that is regularly varying and associated we give conditions which guarantee that partial sums of this sequence, under normalization related to the exponent of regular variation, converge in distribution to a…
We propose a bulk topological invariant for one-dimensional Floquet systems with chiral symmetry which quantifies the particle transport on each sublattice during the evolution. This chiral flow is physically motivated, locally computable,…
Stochastic processes find applications in modelling systems in a variety of disciplines. A large number of stochastic models considered are Markovian in nature. It is often observed that higher order Markov processes can model the data…
Behaviors of many engineering systems are described by lumped parameter models that encapsulate the spatially distributed nature of the system into networks of lumped elements; the dynamics of such a network is governed by a system of…
Living systems exhibit complex yet organized behavior on multiple spatiotemporal scales. To investigate the nature of multiscale coordination in living systems, one needs a meaningful and systematic way to quantify the complex dynamics, a…
We introduce a unified sensitivity concept for shape and topological perturbations and perform the sensitivity analysis for a discretized PDE-constrained design optimization problem in two space dimensions. We assume that the design is…
We consider a generalization of the Hopfield model, where the entries of patterns are Gaussian and diluted. We focus on the high-storage regime and we investigate analytically the topological properties of the emergent network, as well as…
An analogue of the classical Mecke formula for Poisson point processes is proved for the class of space-time STIT tessellation processes. From this key identity the Markov property of a class of associated random processes is derived. This…
We study a class models of correlated random networks in which vertices are characterized by \textit{hidden variables} controlling the establishment of edges between pairs of vertices. We find analytical expressions for the main topological…
We present topological characterization of classical stochastic processes described by discrete-time Markov chains on lattices. We point out that point-gap topology of stochastic matrices entails two distinct physical consequences that…
Topological holography is a holographic principle that describes the generalized global symmetry of a local quantum system in terms of a topological order in one higher dimension. This framework separates the topological data from the local…