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A commonly-used representation for motion prediction of actors is a sequence of waypoints (comprising positions and orientations) for each actor at discrete future time-points. While this approach is simple and flexible, it can exhibit…

We consider the down/up crossing property of weighted Markov branching processes. The joint probability distribution of multi crossing numbers of such processes are obtained. In particular, for Markov branching processes, the probability…

The aim of this paper is to study some continuous-time bivariate Markov processes arising from group representation theory. The first component (level) can be either discrete (quasi-birth-and-death processes) or continuous (switching…

The interest in a system often resides in the interplay among different parameters governing its evolution. It is thus often required to access many of them at once for a complete description. Assessing how quantum enhancement in such…

Motivated by the multivariate wavelet theory, and by the spectral theory of transfer operators, we construct an abstract affine structure and a multiresolution associated to a matrix-valued weight. We describe the one-to-one correspondence…

In this short paper, we propose a new multi-fractal flow model, aiming to provide a possible explanation for the crossover phenomena that appear in the estimation of Hurst exponent for network traffic. It is shown that crossover occurs if…

In this note our aim is to show a paradox in the spectral representation of stationary random processes.

In this paper, we give a AR$(1)$ type of characterization covering all multivariate strictly stationary processes indexed by the set of integers. Consequently, we derive continuous time algebraic Riccati equations for the parameter matrix…

We study the problem of learning permutation invariant representations that can capture "flexible" notions of containment. We formalize this problem via a measure theoretic definition of multisets, and obtain a theoretically-motivated…

Proper states' representations are the key to the successful dynamics modeling of chaotic systems. Inspired by recent advances of deep representations in various areas such as natural language processing and computer vision, we propose the…

In urban driving scenarios, forecasting future trajectories of surrounding vehicles is of paramount importance. While several approaches for the problem have been proposed, the best-performing ones tend to require extremely detailed input…

We develop a rigorous connection between statistical properties of an interference pattern and the coherence properties of the underlying quantum state. With explicit examples, we demonstrate that even for inaccurate reconstructions of…

We introduce a concept of a quantum wide sense stationary process taking values in a C*-algebra and expected in a sub-algebra. The power spectrum of such a process is defined, in analogy to classical theory, as a positive measure on…

The bifurcation theory of ordinary differential equations (ODEs), and its application to deterministic population models, are by now well established. In this article, we begin to develop a complementary theory for diffusion-like…

Pathwise predictability and predictors for discrete time processes are studied in deterministic setting. It is suggested to approximate convolution sums over future times by convolution sums over past time. It is shown that all band-limited…

Linear approximations to the decision boundary of a complex model have become one of the most popular tools for interpreting predictions. In this paper, we study such linear explanations produced either post-hoc by a few recent methods or…

Understanding the interaction between multiple agents is crucial for realistic vehicle trajectory prediction. Existing methods have attempted to infer the interaction from the observed past trajectories of agents using pooling, attention,…

We develop the theory of linear evolution equations associated with the adjacency matrix of a graph, focusing in particular on infinite graphs of two kinds: uniformly locally finite graphs as well as locally finite line graphs. We discuss…

This article is devoted to some time-changed stochastic models based on multivariate stable processes. The considered models have several advantages in comparison with classical time-changed Brownian motions - for instance, it turns out…

Sparse representation of structured signals requires modelling strategies that maintain specific signal properties, in addition to preserving original information content and achieving simpler signal representation. Therefore, the major…