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Given a bipartite system, correlations between its subsystems can be understood as information that each one carries about the other. In order to give a model-independent description of secure information disposal, we propose the paradigm…
In a previous paper it was shown that a machine learning regression problem can be solved within the framework of random function theory, with the optimal kernel analytically derived from symmetry and indifference principles and coinciding…
We propose and analyze a protocol to study quantum information scrambling using statistical correlations between measurements, which are performed after evolving a quantum system from randomized initial states. We prove that the resulting…
We consider a Hamiltonian $H$ which is the sum of a deterministic part $H_0$ and of a random potential $V$. For finite $N \times N$ matrices, following a method introduced by Kazakov, we derive a representation of the correlation functions…
The conformational behavior of a coarse-grained finite polymer chain near an attractive spherical surface was investigated by means of multicanonical Monte Carlo computer simulations. In a detailed analysis of canonical equilibrium data…
We consider a statistical mechanical model of a generic flexible polyelectrolyte, comprised of identically charged monomers with long range electrostatic interactions, and short-range interactions quantified by a disorder field along the…
The gravitational wave sky is starting to become very crowded, with the fourth science run (O4) at LIGO expected to detect $\mathcal{O}(100)$ compact object coalescence signals. Data analysis issues start to arise as we look further…
Randomized rounding is a standard method, based on the probabilistic method, for designing combinatorial approximation algorithms. In Raghavan's seminal paper introducing the method (1988), he writes: "The time taken to solve the linear…
Large amount of multidimensional data represented by multiway arrays or tensors are prevalent in modern applications across various fields such as chemometrics, genomics, physics, psychology, and signal processing. The structural complexity…
Quantum entanglement is one of the core features of quantum theory. While it is typically revealed by measurements along carefully chosen directions, here we review different methods based on so-called random or randomized measurements.…
This paper proposes methods for likelihood-based inference in multivariate linear regressions when the correlation matrix of the responses is separable; that is, it has a Kronecker product structure, but the variances are unrestricted. The…
The increasing need for data privacy and the demand for robust machine learning models have fueled the development of synthetic data generation techniques. However, current methods often succeed in replicating simple summary statistics but…
Smoothed analysis is a framework for analyzing the complexity of an algorithm, acting as a bridge between average and worst-case behaviour. For example, Quicksort and the Simplex algorithm are widely used in practical applications, despite…
In recent years, there has been an upswing of interest in estimating information from data emerging in a lot of areas beyond communications. This paper aims at estimating the information between two random phenomena by using consolidated…
The ability to precisely quantify similarity between various entities has been a fundamental complication in various problem spaces specifically in the classification of cellular images. Contemporary similarity measures applied in the…
Quantum chaos is the study of quantum systems whose classical description is chaotic. How does chaos manifest itself in the quantum world? In this spirit, we study the dynamical generation of entanglement as a signature of chaos in a system…
A complex network is a condensed representation of the relational topological framework of a complex system. A main reason for the existence of such networks is the transmission of items through the entities of these complex systems. Here,…
We present a detailed account of a recently proposed phenomenological theory for noncatenated ring polymer melts (Phys. Rev. Lett. 106, 167802 (2011)). A basic assumption lies in the implementation of the noncatenation constraint via the…
We use Photon Correlation Imaging, a recently introduced space-resolved dynamic light scattering method, to investigate the spatial correlation of the dynamics of a variety of jammed and glassy soft materials. Strikingly, we find that in…
Alignment algorithms usually rely on simplified models of gaps for computational efficiency. Based on an isomorphism between alignments and physical helix-coil models, we show in statistical mechanics that alignments with realistic laws for…