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For a multipartite system, we sort out all possible entanglements, each of which is among a set of subsystems. Each entanglement can be measured by a generalized relative entropy of entanglement, which is conserved on average under…
In this paper we derive a two-component system of nonlinear equations which model two-dimensional shallow water waves with constant vorticity. Then we prove well-posedness of this equation using a geometrical framework which allows us to…
We present a lattice Boltzmann algorithm based on an underlying free energy that allows the simulation of the dynamics of a multicomponent system with an arbitrary number of components. The thermodynamic properties, such as the chemical…
We study a few dynamical systems composed of many components whose sizes evolve according to multiplicative stochastic rules. We compare them with respect to the emergence of power laws in the size distribution of their components. We show…
There are two fair ways to distribute particles in boxes. The first way is to divide the particles equally between the boxes. The second way, which is calculated here, is to score fairly the particles between the boxes. The obtained power…
In this paper, we present a critical collection of essential mathematical tools and techniques for the analysis of Boltzmann-type kinetic equations, which in recent years have established themselves as a flexible and powerful paradigm to…
Multilevel methods are among the most efficient numerical methods for solving large-scale systems of equations that arise from discretized partial differential equations. Two-level convergence theory plays a fundamental role in the analysis…
We investigate the additivity properties for both bipartite and multipartite systems by using entropic uncertainty relations (EUR) defined in terms of the joint Shannon entropy of probabilities of local measurement outcomes. In particular,…
Problem solving (e.g., drug design, traffic engineering, software development) by task forces represents a substantial portion of the economy of developed countries. Here we use an agent-based model of cooperative problem solving systems to…
Quantifying cooperation or synergy among random variables in predicting a single target random variable is an important problem in many complex systems. We review three prior information-theoretic measures of synergy and introduce a novel…
The goal of this paper is to disentangle the roles of volume and of participation rate in the price response of the market to a sequence of transactions. To do so, we are inspired the methodology introduced in arXiv:1402.1288,…
This paper looks at a common law legal system as a learning algorithm, models specific features of legal proceedings, and asks whether this system learns efficiently. A particular feature of our model is explicitly viewing various aspects…
Symmetry is an important property of quantum mechanical systems which may dramatically influence their behavior in and out of equilibrium. In this paper, we study the effect of symmetry on tripartite entanglement properties of typical…
Based on the effective field theory philosophy, a universal form of the scaling laws could be easily derived with the scaling anomalies naturally clarified as the decoupling effects of underlying physics. In the novel framework, the…
Price of anarchy, the performance ratio, which could characterize the loss of efficiency of the distributed supply chain management compared with the integrated supply chain management is discussed by utilizing newsvendor problem in single…
Democracies employ elections at various scales to select officials at the corresponding levels of administration. The geographical distribution of political opinion, the policy issues delegated to each level, and the multilevel interactions…
A generalized two-component model with peakon solutions is proposed in this paper. It allows an arbitrary function to be involved in as well as including some existing integrable peakon equations as special reductions. The generalized…
Taylor's law (TL), a power-law relationship between the mean and variance of a quantity, has been observed across diverse scientific disciplines. Despite its ubiquity, the underlying mechanisms responsible for TL are not yet fully…
The continuous phase transition, indicated by the macroscopic order parameter and the occurrence of the spontaneous symmetry breaking, is well illustrated based on the Ginzburg-Landau's paradigm. In systems described by one order parameter,…
We study randomized variants of two classical algorithms: coordinate descent for systems of linear equations and iterated projections for systems of linear inequalities. Expanding on a recent randomized iterated projection algorithm of…