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It has been observed that the reduced density matrices of bipartite qudit pure states possess a Gram matrix structure. This observation has opened a possibility of analysing the entanglement in such systems from the purely geometrical point…
We develop fixed-point algorithms for the approximation of structured matrices with rank penalties. In particular we use these fixed-point algorithms for making approximations by sums of exponentials, or frequency estimation. For the basic…
We study the problem of approximating a matrix $\mathbf{A}$ with a matrix that has a fixed sparsity pattern (e.g., diagonal, banded, etc.), when $\mathbf{A}$ is accessed only by matrix-vector products. We describe a simple randomized…
We study the problem of matching agents who arrive at a marketplace over time and leave after d time periods. Agents can only be matched while they are present in the marketplace. Each pair of agents can yield a different match value, and…
Federated Learning (FL) is a privacy-protected machine learning paradigm that allows model to be trained directly at the edge without uploading data. One of the biggest challenges faced by FL in practical applications is the heterogeneity…
The paper describes an approach to measuring convergence of an algorithm to its result in terms of an entropy-like function of partitions of its inputs of a given length. The goal is to look at the algorithmic data processing from the…
The method of choice to study one-dimensional strongly interacting many body quantum systems is based on matrix product states and operators. Such method allows to explore the most relevant, and numerically manageable, portion of an…
In this paper, optimal convergence for an adaptive finite element algorithm for elastoplasticity is considered. To this end, the proposed adaptive algorithm is established within the abstract framework of the axioms of adaptivity [Comput.…
A significant challenge in nature-inspired algorithmics is the identification of specific characteristics of problems that make them harder (or easier) to solve using specific methods. The hope is that, by identifying these characteristics,…
The seminal work of Dwork {\em et al.} [ITCS 2012] introduced a metric-based notion of individual fairness. Given a task-specific similarity metric, their notion required that every pair of similar individuals should be treated similarly.…
We consider h-adaptive algorithms in the context of the finite element method (FEM) and the boundary element method (BEM). Under quite general assumptions on the building blocks SOLVE, ESTIMATE, MARK, and REFINE of such algorithms, we prove…
Most prior work on online matching problems has been with the flexibility of keeping some vertices unmatched. We study three related online matching problems with the constraint of matching every vertex, i.e., with no rejections. We adopt a…
Network or graph structures are ubiquitous in the study of complex systems. Often, we are interested in complexity trends of these system as it evolves under some dynamic. An example might be looking at the complexity of a food web as…
A major problem in the study of complex socioeconomic systems is represented by privacy issues$-$that can put severe limitations on the amount of accessible information, forcing to build models on the basis of incomplete knowledge. In this…
In this work, we study the numerical optimization of nearest-neighbor concurrence of bipartite one and two dimensional lattices, as well as non bipartite two dimensional lattices. These systems are described in the framework of a…
It is a hard and important problem to find the criterion of the set of positive-definite matrixes which can be written as reduced density operators of a multi-partite quantum state. This problem is closely related to the study of many-body…
We give a quantitative analysis of a theorem due to Fenghui Wang and Huanhuan Cui concerning the convergence of a multi-parametric version of the proximal point algorithm. Wang and Cui's result ensures the convergence of the algorithm to a…
We present a novel approach to performing fitness approximation in genetic algorithms (GAs) using machine-learning (ML) models, through dynamic adaptation to the evolutionary state. Maintaining a dataset of sampled individuals along with…
In this paper, we introduce a particular class of matrices. We study the concept of a matrix to be \emph{balanced}. We study some properties of this concept in the context of matrix operations. We examine the behaviour of various matrix…
While recent work has established divergence as a key framework for understanding evenness, there is currently no research exploring how the families of measures within the divergence-based framework relate to each other. This paper uses…