Related papers: Chaos representations for Marked Point Processes
The theory of ``Markov-up'' processes is being developed. This is a new class of stochastic processes with ``partial'' markovian features; it could also be called ``one-sided Markov''. Such a behavior may be found in the real world and in…
Probabilistic models learned as density estimators can be exploited in representation learning beside being toolboxes used to answer inference queries only. However, how to extract useful representations highly depends on the particular…
Given a marked renewal point process (assuming that the marks are i.i.d.) we say that an unbounded region is stable if it contains finitely many points of the point process with probability one. In this paper we provide algorithms that…
We propose an information-theoretic statistical model to describe the universal features of those chaotic scattering processes characterized by a prompt and an equilibrated component. The model, introduced in the past in nuclear physics,…
In this paper, we consider a class of inhomogeneous semi-Markov processes directly based on intensity processes for marked point processes. We show that this class satisfies the semi-Markov properties defined elsewhere in the literature. We…
Randomized measurements constitute a simple measurement primitive that exploits the information encoded in the outcome statistics of samples of local quantum measurements defined through randomly selected bases. In this work we exploit the…
We develop a class of integrals on a manifold M called exponential iterated integrals, an extension of K. T. Chen's iterated integrals. It is shown that the matrix entries of any upper triangular representation of the fundamental group of M…
Motivated by Alain-Sol Sznitman's interlacement process, we consider the set of $\{0,1\}$-valued processes which can be constructed in an analogous way, namely as a union of sets coming from a Poisson process on a collection of sets. Our…
Symbolic dynamics has proven to be an invaluable tool in analyzing the mechanisms that lead to unpredictability and random behavior in nonlinear dynamical systems. Surprisingly, a discrete partition of continuous state space can produce a…
A generic method to investigate many-body continuous-variable systems is pedagogically presented. It is based on the notion of matrix product states (so-called MPS) and the algorithms thereof. The method is quite versatile and can be…
Invariances in neural networks are useful and necessary for many tasks. However, the representation of the invariance of most neural network models has not been characterized. We propose measures to quantify the invariance of neural…
We consider a hidden Markov model, where the signal process, given by a diffusion, is only indirectly observed through some noisy measurements. The article develops a variational method for approximating the hidden states of the signal…
We prove that the Markov operator associated to an iterated function system consisting of phi-max-contractions with probabilities has a unique invariant measure whose support is the attractor of the system.
We study a simple one-dimensional quantum system on a circle with n scale free point interactions. The spectrum of this system is discrete and expressible as a solution of an explicit secular equation. However, its statistical properties…
We present a scalable Gaussian process model for identifying and characterizing smooth multidimensional changepoints, and automatically learning changes in expressive covariance structure. We use Random Kitchen Sink features to flexibly…
In this note we consider the point process of eigenvalues of the tensor product of two independent random unitary matrices of size m by m and n by n. When n becomes large, the process behaves like the superposition of m independent sine…
We give exact formulae for a wide family of complexity measures that capture the organization of hidden nonlinear processes. The spectral decomposition of operator-valued functions leads to closed-form expressions involving the full…
Fixed point iterations are known to generate chaos, for some values in their parameter range. It is an established fact that Turing Machines are fixed point iterations. However, as these Machines operate in integer space, the standard…
This paper shows a novel way of simulating a Markov process by a quantum computer. The main purpose of the paper is to show a particular application of quantum computing in the field of stochastic processes analysis. Using a Quantum…
In this paper, we study discrete spectrum of invariant measures for countable discrete amenable group actions. We show that an invariant measure has discrete spectrum if and only if it has bounded measure complexity. We also prove that,…