Related papers: The Graph Structure of the Generalized Discrete Ar…
A classical problem in random number generation is the sampling of elements from a given discrete distribution. Formally, given a set of indices $S = \{1, \dots, n\}$ and sequence of weights $w_1, \dots, w_n \in \mathbb{R}^+$, the task is…
Motivated by microscopic traffic modeling, we analyze dynamical systems which have a piecewise linear concave dynamics not necessarily monotonic. We introduce a deterministic Petri net extension where edges may have negative weights. The…
Graph neural networks (GNNs) are a popular class of machine learning models whose major advantage is their ability to incorporate a sparse and discrete dependency structure between data points. Unfortunately, GNNs can only be used when such…
Random feature maps are ubiquitous in modern statistical machine learning, where they generalize random projections by means of powerful, yet often difficult to analyze nonlinear operators. In this paper, we leverage the "concentration"…
Due to the deterministic nature of chaotic systems, fluctuations in their trajectories arise solely from the choice of initial conditions. Some of these dynamical fluctuations may lead to extremely unlikely scenarios. Understanding the…
Artificial Neural Networks (ANNs), including fully-connected networks and transformers, are highly flexible and powerful function approximators, widely applied in fields like computer vision and natural language processing. However, their…
We investigate the random dynamics of rational maps on the Riemann sphere and the dynamics of semigroups of rational maps on the Riemann sphere. We show that regarding random complex dynamics of polynomials, in most cases, the chaos of the…
Time series forecasting is an extensively studied subject in statistics, economics, and computer science. Exploration of the correlation and causation among the variables in a multivariate time series shows promise in enhancing the…
We introduce a complex-plane generalization of the consecutive level-spacing distribution, used to distinguish regular from chaotic quantum spectra. Our approach features the distribution of complex-valued ratios between nearest- and…
We consider a family of singular maps as an example of a simple model of dynamical systems exhibiting the property of robust chaos on a well defined range of parameters. Critical boundaries separating the region of robust chaos from the…
Deep NLP models benefit from underlying structures in the data---e.g., parse trees---typically extracted using off-the-shelf parsers. Recent attempts to jointly learn the latent structure encounter a tradeoff: either make factorization…
Glass networks model systems of variables that interact via sharp switching. A body of theory has been developed over several decades that, in principle, allows rigorous proof of dynamical properties in high dimensions that is not normally…
We develop a percolation model for nodal domains in the eigenvectors of quantum chaotic torus maps. Our model follows directly from the assumption that the quantum maps are described by random matrix theory. Its accuracy in predicting…
The stationary distributions of sums of positions of trajectories generated by the logistic map have been found to follow a basic renormalization group (RG) structure: a nontrivial fixed-point multi-scale distribution at the period-doubling…
We study the behaviour of discrete dynamical systems generated by a continuous map $f$ of a compact real interval into itself where at randomly chosen times a function different from $f$ - so called impulse function is applied. We show that…
Deep Learning methods, specifically convolutional neural networks (CNNs), have seen a lot of success in the domain of image-based data, where the data offers a clearly structured topology in the regular lattice of pixels. This…
After investigating by examples the unusual and striking elementary properties of the Penrose tilings and the Arnold cat map, we associate a finite symbolic dynamics with finite grammar rules to each of them. Instead of studying these…
Random matrix theory has played an important role in recent work on statistical network analysis. In this paper, we review recent results on regimes of concentration of random graphs around their expectation, showing that dense graphs…
We introduce a new class of identifiable DAG models where the conditional distribution of each node given its parents belongs to a family of generalized hypergeometric distributions (GHD). A family of generalized hypergeometric…
Theoretical expressions for the distribution of the ratio of consecutive level spacings for quantum systems with transiting dynamics remain unknown. We propose a family of one-parameter distributions $P(r)\equiv P(r;\beta)$, where…