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For a mixed stochastic differential equation containing both Wiener process and a H\"older continuous process with exponent $\gamma>1/2$, we prove a stochastic viability theorem. As a consequence, we get a result about positivity of…
Statistical learning algorithms are finding more and more applications in science and technology. Atomic-scale modeling is no exception, with machine learning becoming commonplace as a tool to predict energy, forces and properties of…
We give a brief account of the current limitations and possibilities in the field of computational simulation of materials. We then focus on the effect that the emergence of machine learning interatomic potentials is having on the field and…
This paper reveal the selective rotation in the CNNs' forward processing. It elucidates the activation function as a discerning mechanism that unifies and quantizes the rotational aspects of the input data. Experiments show how this defined…
This paper presents a study of the properties of a matrix model that was introduced to describe transitions between all Wigner surmises of Random Matrix theory. New results include closed-form exact analytical expressions for the…
Stationarity is a very common assumption in time series analysis. A vector autoregressive process is stationary if and only if the roots of its characteristic equation lie outside the unit circle, constraining the autoregressive coefficient…
Results regarding probable bifurcations from fixed points are presented in the context of general dynamical systems (real, random matrices), time-delay dynamical systems (companion matrices), and a set of mappings known for their properties…
We study the persistence probability of a centered stationary Gaussian process on $\mathbb{Z}$ or $\mathbb{R}$, that is, its probability to remain positive for a long time. We describe the delicate interplay between this probability and the…
The potential applications of boundary functionals of random processes, such as the extreme values of these processes, the moment of first reaching a fixed level, the value of the process at the moment of reaching the level, the moment of…
We obtain complementary recurrence and transience criteria for processes $X=(X_n)_{n \ge 0}$ with values in $\mathbb R^d_+$ fulfilling a non-linear equation $X_{n+1}=MX_n+g(X_n)+ \xi_{n+1}$. Here $M$ denotes a primitive matrix having…
Forecasting time series on graphs is a fundamental problem in graph signal processing. When each entity of the network carries a vector of values for each time stamp instead of a scalar one, existing approaches resort to the use of product…
Computing the distribution of trajectories from a Gaussian Process model of a dynamical system is an important challenge in utilizing such models. Motivated by the computational cost of sampling-based approaches, we consider approximations…
In causal models, a given mechanism is assumed to be invariant to changes of other mechanisms. While this principle has been utilized for inference in settings where the causal variables are observed, theoretical insights when the variables…
This paper considers a time-varying vector error-correction model that allows for different time series behaviours (e.g., unit-root and locally stationary processes) to interact with each other to co-exist. From practical perspectives, this…
We treat the problem of characterizing in a systematic way the qualitative features of two-dimensional dynamical systems. To that end, we construct a representation of the topological features of phase portraits by means of diagrams that…
We present novel equivalences in random matrix and tensor models between complex and self-adjoint theories with nontrivial quadratic terms in the action, established through an intermediate field representation. More precisely, we show that…
Many real-world problems encountered in several disciplines deal with the modeling of time-series containing different underlying dynamical regimes, for which probabilistic approaches are very often employed. In this paper we describe…
Multivalued projections are applied to the study of weighted least squares solutions of linear relations equations (or inclusions) and some of its applications. To this end a matrix representation of multivalued projections with respect to…
Quantum transients are temporary features of matter waves before they reach a stationary regime. Transients may arise after the preparation of an unstable initial state or due to a sudden interaction or a change in the boundary conditions.…
For many stochastic processes there is an underlying coordinate space, $V$, with the process moving from point to point in $V$ or on variables (such as spin configurations) defined with respect to $V$. There is a matrix of transition…