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Kendall transformation is a conversion of an ordered feature into a vector of pairwise order relations between individual values. This way, it preserves ranking of observations and represents it in a categorical form. Such transformation…
Rigid particles pack into structures, such as sand dunes on the beach, whose overall stability is determined by the average number of contacts between particles. However, when packing spatially extended objects with flexible shapes,…
Three decades of research in communication complexity have led to the invention of a number of techniques to lower bound randomized communication complexity. The majority of these techniques involve properties of large submatrices…
We study the approximability of an existing framework for clustering edge-colored hypergraphs, which is closely related to chromatic correlation clustering and is motivated by machine learning and data mining applications where the goal is…
Extensions to various information theoretic quantities used for nonlinear time series analysis are discussed, as well as their relationship to the generalized correlation integral. It is shown that calculating redundancies from the…
This paper studies a polymer chain in the vicinity of a linear interface separating two immiscible solvents. The polymer consists of random monomer types, while the interface carries random charges. Both the monomer types and the charges…
We investigate quantum information processing and manipulations in disordered systems of ultracold atoms and trapped ions. First, we demonstrate generation of entanglement and local realization of quantum gates in a quantum spin glass…
Randomness extraction is the process of constructing a source of randomness of high quality from one or several sources of randomness of lower quality. The problem can be modeled using probability distributions and min-entropy to measure…
Coupled problems with various combinations of multiple physics, scales, and domains can be found in numerous areas of science and engineering. A key challenge in the formulation and implementation of corresponding coupled models is to…
The normalized information distance is a universal distance measure for objects of all kinds. It is based on Kolmogorov complexity and thus uncomputable, but there are ways to utilize it. First, compression algorithms can be used to…
Dynamical systems can be analyzed as computational devices capable of performing information processing. In coupled oscillators, enlarged capabilities are expected when the set of units is formed by subsets with collective behaviour within…
In this paper, we identify partial correlation information structures that allow for simpler reformulations in evaluating the maximum expected value of mixed integer linear programs with random objective coefficients. To this end, assuming…
The spatial correlations of entangled polymer dynamics are examined by molecular dynamics simulations and neutron spin-echo spectroscopy. Due to the soft nature of topological constraints, the initial spatial decays of intermediate…
A monochromatic point source, embedded in a three-dimensional disordered medium, is considered. The resulting intensity pattern exhibits a new type of long-range correlations. The range of these correlations is infinite and their magnitude,…
In this paper, we study parallel algorithms for the correlation clustering problem, where every pair of two different entities is labeled with similar or dissimilar. The goal is to partition the entities into clusters to minimize the number…
An accurate description of strong correlation is quintessential for the exploration of emerging chemical phenomena. While near-term variational quantum algorithms provide a theoretically scalable framework for quantum chemical problems, the…
Hinging on ideas from physical-layer network coding, some promising proposals of coded random access systems seek to improve system performance (while preserving low complexity) by means of packet repetitions and decoding of linear…
A new method of diagonalisation of the XY-Hamiltonian of inhomogeneous open linear chains with periodic (in space) changing Larmor frequencies and coupling constants is developed. As an example of application, multiple quantum dynamics of…
In this paper we exploit concepts of information theory to address the fundamental problem of identifying and defining the most suitable tools to extract, in a automatic and agnostic way, information from a generic string of characters. We…
We investigate topological, combinatorial, statistical, and enumeration properties of finite graphs with high Kolmogorov complexity (almost all graphs) using the novel incompressibility method. Example results are: (i) the mean and variance…