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Scattering of electromagnetic waves in billiard-like systems has become a standard experimental tool of studying properties associated with Quantum Chaos. Random Matrix Theory (RMT) describing statistics of eigenfrequencies and associated…
All intelligence is collective intelligence, in the sense that it is made of parts which must align with respect to system-level goals. Understanding the dynamics which facilitate or limit navigation of problem spaces by aligned parts thus…
This contribution describes a statistical model for decaying quantum systems (e.g. photo-dissociation or -ionization). It takes the interference between direct and indirect decay processes explicitely into account. The resulting expressions…
When randomized ensemble methods such as bagging and random forests are implemented, a basic question arises: Is the ensemble large enough? In particular, the practitioner desires a rigorous guarantee that a given ensemble will perform…
Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and structured multipliers, but adequate formal support for this…
We study the properties of elections that have a given position matrix (in such elections each candidate is ranked on each position by a number of voters specified in the matrix). We show that counting elections that generate a given…
In this article we investigate no-resonance conditions for quantum many body chaotic systems and random matrix models. No-resonance conditions are properties of the spectrum of a model, usually employed as a theoretical tool in the analysis…
We study the effects of topological (connectivity) disorder on phase transitions. We identify a broad class of random lattices whose disorder fluctuations decay much faster with increasing length scale than those of generic random systems,…
Hierarchical taxonomies are common in many contexts, and they are a very natural structure humans use to organise information. In machine learning, the family of methods that use the 'extra' information is called hierarchical…
We present an analysis of sets of matrices with rank less than or equal to a specified number $s$. We provide a simple formula for the normal cone to such sets, and use this to show that these sets are prox-regular at all points with rank…
We apply Tsallis's q-indexed nonextensive entropy to formulate a random matrix theory (RMT), which may be suitable for systems with mixed regular-chaotic dynamics. We consider the super-extensive regime of q < 1. We obtain analytical…
We derive the mean eigenvalue density for symmetric Gaussian random N x N matrices in the limit of large N, with a constraint implying that the row sum of matrix elements should vanish. The result is shown to be equivalent to a result found…
This work studies the throughput scaling laws of ad hoc wireless networks in the limit of a large number of nodes. A random connections model is assumed in which the channel connections between the nodes are drawn independently from a…
This paper examines the consensus problem on time-varying matrix-weighed undirected networks. First, we introduce the matrix-weighted integral network for the analysis of such networks. Under mild assumptions on the switching pattern of the…
A new necessary and sufficient condition for the existence of minor left prime factorizations of multivariate polynomial matrices without full row rank is presented. The key idea is to establish a relationship between a matrix and its full…
We investigate the capacity scaling of MIMO systems with the system dimensions. To that end, we quantify how the mutual information varies when the number of antennas (at either the receiver or transmitter side) is altered. For a system…
We consider a space of sparse Boolean matrices of size $n \times n$, which have finite co-rank over $GF(2)$ with high probability. In particular, the probability such a matrix has full rank, and is thus invertible, is a positive constant…
This paper considers the problem of recovery of a low-rank matrix in the situation when most of its entries are not observed and a fraction of observed entries are corrupted. The observations are noisy realizations of the sum of a low rank…
Network densification is a natural way to support dense mobile applications under stringent requirements, such as ultra-low latency, ultra-high data rate, and massive connecting devices. Severe interference in ultra-dense networks poses a…
In distributed optimization, the communication of model updates can be a performance bottleneck. Consequently, gradient compression has been proposed as a means of increasing optimization throughput. In general, due to information loss,…