Related papers: Antieigenvalue Analysis, New Applications: Continu…
We study the eigenvalue problem for some special class of anti-triangular matrices. Though the eigenvalue problem is quite classical, as far as we know, almost nothing is known about properties of eigenvalues for anti-triangular matrices.…
Recent times are witnessing rapid development in machine learning algorithm systems, especially in reinforcement learning, natural language processing, computer and robot vision, image processing, speech, and emotional processing and…
In this paper we discuss recent developments in econometrics that we view as important for empirical researchers working on policy evaluation questions. We focus on three main areas, where in each case we highlight recommendations for…
This is a review paper of the role of Carleman estimates in the theory of Multidimensional Coefficient Inverse Problems since the first inception of this idea in 1981.
This is a review article for Encyclopedia of Complexity and System Science, to be published by Springer http://refworks.springer.com/complexity/. The paper reviews statistical models for money, wealth, and income distributions developed in…
This book is based on notes compiled over the many years I have been teaching the course "Applied Functional Analysis" in the first year of the Master programme at Delft University of Technology, for students with previous exposure to the…
We introduce the concept of theta-antieigenvalue and theta-antieigenvector of a bounded linear operator on complex Hilbert space. We study the relation between theta-antieigenvalue and centre of mass of a bounded linear operator and compute…
We present an implementation of E-anti-unification as defined in Heinz (1995), where tree-grammar descriptions of equivalence classes of terms are used to compute generalizations modulo equational theories. We discuss several improvements,…
In this paper, we study an adaptive finite element method for a class of a nonlinear eigenvalue problems that may be of nonconvex energy functional and consider its applications to quantum chemistry. We prove the convergence of adaptive…
This article is a brief introduction to quantum algorithms for the eigenvalue problem in quantum many-body systems. Rather than a broad survey of topics, we focus on providing a conceptual understanding of several quantum algorithms that…
Eigenvalue analysis is widely used for linear instability analysis in both external and internal aerodynamics. It typically involves finding the steady state, linearizing around it to obtain the Jacobian, and then solving for its…
This Ph.D. thesis provides a comprehensive review of the state-of-the-art in the field of Variational Quantum Algorithms and Quantum Machine Learning, including numerous original contributions. The first chapters are devoted to a brief…
Since its origin in the thermodynamics of the 19th century, the concept of entropy has also permeated other fields of physics and mathematics, such as Classical and Quantum Statistical Mechanics, Information Theory, Probability Theory,…
Econophysics has developed as a research field that applies the formalism of Statistical Mechanics and Quantum Mechanics to address Economics and Finance problems. The branch of Econophysics that applies of Quantum Theory to Economics and…
In this article we are interested for the numerical study of nonlinear eigenvalue problems. We begin with a review of theoretical results obtained by functional analysis methods, especially for the Schrodinger pencils. Some recall are given…
For this special issue, the article aims at discussing a few econophysics problems studied so far rather successfully. The following "applications" in micro-econo-physics are considered : (i) financial crashes; it is emphasized that one can…
In this review we discuss, from a unified point of view, a variety of Monte Carlo methods used to solve eigenvalue problems in statistical mechanics and quantum mechanics. Although the applications of these methods differ widely, the…
This is an extended version of my 2018 Heinemann prize lecture describing the work for which I got the prize. The citation is very broad so this describes virtually all my work prior to 1995 and some afterwards. It discusses work in…
The inverse electromagnetic scattering problem for anisotropic media in general does not have a unique solution. A possible approach to this problem is through the use of appropriate "target signatures," i.e. eigenvalues associated with the…
Classification is a machine learning method used in many practical applications: text mining, handwritten character recognition, face recognition, pattern classification, scene labeling, computer vision, natural langage processing. A…