Related papers: Trumping and Power Majorization
This paper is a brief review of recent developments in random matrix theory. Two aspects are emphasized: the underlying role of integrable systems and the occurrence of the distribution functions of random matrix theory in diverse areas of…
We summarize some of the recent developments which link certain problems in combinatorial theory related to random growth to random matrix theory.
The framework of reinforcement learning or optimal control provides a mathematical formalization of intelligent decision making that is powerful and broadly applicable. While the general form of the reinforcement learning problem enables…
The concept of typicality refers to properties holding for the "overwhelming majority" of cases and is a fundamental idea of the qualitative approach to dynamical problems. We argue that measure-theoretical typicality would be the adequate…
Entanglement is one of the most striking features of quantum mechanics, and yet it is not specifically quantum. More specific to quantum mechanics is the connection between entanglement and thermodynamics, which leads to an identification…
We discuss the problem of adding random matrices, which enable us to study Hamiltonians consisting of a deterministic term plus a random term. Using a diagrammatic approach and introducing the concept of ``gluon connectedness," we calculate…
Represented spaces form the general setting for the study of computability derived from Turing machines. As such, they are the basic entities for endeavors such as computable analysis or computable measure theory. The theory of represented…
The theory of ``Markov-up'' processes is being developed. This is a new class of stochastic processes with ``partial'' markovian features; it could also be called ``one-sided Markov''. Such a behavior may be found in the real world and in…
The aim of this paper is to study some aspects of matrix theory through Pasting and Reversing. We start giving a summary of previous results concerning to Pasting and Reversing over vectors and matrices, after we rewrite such properties of…
We study a quantum theory based on two assumptions: In the intrinsic frame of reference of an isolated, macroscopic system, (i) the system has no global motion and is not entangled with any other system, (ii) time evolution of statevectors…
A two-state master equation based decision making model has been shown to generate phase transitions, to be topologically complex and to manifest temporal complexity through an inverse power-law probability distribution function in the…
Low-rank matrix factorizations are a class of linear models widely used in various fields such as machine learning, signal processing, and data analysis. These models approximate a matrix as the product of two smaller matrices, where the…
Recent developments in mathematics have provided powerful tools for comparing the eigenvalues of matrices related to each other via a moment map. In this paper we survey some of the more concrete aspects of the approach with a particular…
We investigate the analogy between magnetism and rotation in relativistic theory. In nonrelativistic theory, the exact correspondence between magnetism and rotation is established in the presence of an external trapping potential. Based on…
The paper that is commented by Touchette contains a computational study which opens the door to a desirable generalization of the standard large deviation theory (applicable to a set of $N$ nearly independent random variables) to systems…
The Boolean matrix factorization problem consists in approximating a matrix by the Boolean product of two smaller Boolean matrices. To obtain optimal solutions when the matrices to be factorized are small, we propose SAT and MaxSAT…
In this paper we study some weak majorization properties with applications for the trees. A strongly notion of majorization is introduced and Hardy-Littlewood-Polya's inequality is generalized.
In this article, we discuss the remarkable connection between two very different fields, number theory and nuclear physics. We describe the essential aspects of these fields, the quantities studied, and how insights in one have been…
We present a novel, universal description of quantum entanglement using group theory and generalized characteristic functions. It leads to new reformulations of the separability problem, and the positivity of partial transpose (PPT)…
We introduce new entanglement monotones which generalize, to the case of many parties, those which give rise to the majorization-based partial ordering of bipartite states' entanglement. We give some examples of restrictions they impose on…