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Probabilistic ideas and tools have recently begun to permeate into several fields where they had traditionally not played a major role, including fields such as numerical linear algebra and optimization. One of the key ways in which these…
We consider the problem of reconstructing a signal from multi-layered (possibly) non-linear measurements. Using non-rigorous but standard methods from statistical physics we present the Multi-Layer Approximate Message Passing (ML-AMP)…
A density matrix describes the statistical state of a quantum system. It is a powerful formalism to represent both the quantum and classical uncertainty of quantum systems and to express different statistical operations such as measurement,…
In recent years, randomized algorithms have established themselves as fundamental tools in computational linear algebra, with applications in scientific computing, machine learning, and quantum information science. Many randomized matrix…
In this paper, we derive the analytical behavior of the limiting spectral distribution of non-central covariance matrices of the "general information-plus-noise" type, as studied in [14]. Through the equation defining its Stieltjes…
Many real-world problems in machine learning, signal processing, and communications assume that an unknown vector $x$ is measured by a matrix A, resulting in a vector $y=Ax+z$, where $z$ denotes the noise; we call this a single measurement…
We present a technique for constructing suitable posterior probability distributions in situations for which the sampling distribution of the data is not known. This is very useful for modern scientific data analysis in the era of "big…
In this short note we collect together known results on the use of Random Matrix Theory in lattice statistical mechanics. The purpose here is two fold. Firstly the RMT analysis provides an intrinsic characterization of integrability, and…
This paper explores the application of large language models (LLMs) in designing strategic mechanisms -- including auctions, contracts, and games -- for specific purposes in communication networks. Traditionally, strategic mechanism design…
Over time, clinical trials have increasingly incorporated complex design and analysis elements such as interim analyses, adaptations, multiple endpoints, and sophisticated multiplicity schemes for multiple endpoints and/or treatment arms…
We review elementary properties of random matrices and discuss widely used mathematical methods for both hermitian and nonhermitian random matrix ensembles. Applications to a wide range of physics problems are summarized. This paper…
One of the biggest challenges in the field of biomedical imaging is the comprehension and the exploitation of the photon scattering through disordered media. Many studies have pursued the solution to this puzzle, achieving light-focusing…
Learning probabilistic models over strings is an important issue for many applications. Spectral methods propose elegant solutions to the problem of inferring weighted automata from finite samples of variable-length strings drawn from an…
The integration of large language models (LLMs) with external tools has significantly expanded the capabilities of AI agents. However, as the diversity of both LLMs and tools increases, selecting the optimal model-tool combination becomes a…
Large Language Models (LLMs) have emerged as powerful tools in various research domains. This article examines their potential through a literature review and firsthand experimentation. While LLMs offer benefits like cost-effectiveness and…
Results on the spectral behavior of random matrices as the dimension increases are applied to the problem of detecting the number of sources impinging on an array of sensors. A common strategy to solve this problem is to estimate the…
In complex systems, crucial parameters are often subject to unpredictable changes in time. Climate, biological evolution and networks provide numerous examples for such non-stationarities. In many cases, improved statistical models are…
This is a review of the Riemann-Hilbert approach to the large $N$ asymptotics in random matrix models and its applications. We discuss the following topics: random matrix models and orthogonal polynomials, the Riemann-Hilbert approach to…
Random networks are increasingly used to analyse complex transportation networks, such as airline routes, roads and rail networks. So far, this research has been focused on describing the properties of the networks with the help of random…
A key functionality of emerging connected autonomous systems such as smart cities, smart transportation systems, and the industrial Internet-of-Things, is the ability to process and learn from data collected at different physical locations.…