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We study a general family of facility location problems defined on planar graphs and on the 2-dimensional plane. In these problems, a subset of $k$ objects has to be selected, satisfying certain packing (disjointness) and covering…
The Kuramoto model is a paradigmatic tool for studying the dynamics of collective behavior in large ensembles of coupled dynamical systems. Over the past decade a great deal of progress has been made in analytical descriptions of the…
We address the dynamics of a bosonic system coupled to either a bosonic or a magnetic environment, and derive a set of sufficient conditions that allow one to describe the dynamics in terms of the effective interaction with a classical…
In this paper, we consider the Klein-Gordon-Schr\"{o}dinger system with the higher order Yukawa coupling in $ \mathbb{R}^{1+1} $, and prove the local and global wellposedness in $L^2\times H^{1/2}$. The method to be used is adapted from the…
The cosmological implications of introducing a variation to the fine structure `constant', \alpha are examined within the context of Loop Quantum Cosmology. The evolution of \alpha is described using the model introduced by Bekenstein,…
After briefly reviewing the relativistic approach to positioning systems based on the introduction of the emission coordinates, we show how explicit maps can be obtained between the Cartesian coordinates and the emission coordinates, for…
We study the classic $k$-median and $k$-means clustering objectives in the beyond-worst-case scenario. We consider three well-studied notions of structured data that aim at characterizing real-world inputs: Distribution Stability…
In this paper we establish a generally and globally valid coordinate system in curved space-time with the simultaneous hypersurface orthogonal to the time coordinate. The time coordinate can be preseted according to practical evolving…
A powerful approach to computing Feynman integrals or cosmological correlators is to consider them as solution to systems of differential equations. Often these can be chosen to be Gelfand-Kapranov-Zelevinsky (GKZ) systems. However, their…
One of a classical synchronization model is the Kuramoto model. We propose both first and second order Kuramoto dynamical models on graphs using discrete optimal transport dynamics. We analyze the synchronization behaviors for some examples…
Synchronisation of coupled oscillators is a ubiquitous phenomenon, occurring in topics ranging from biology and physics, to social networks and technology. A fundamental and long-time goal in the study of synchronisation has been to find…
Large scale numerical experiments are commonplace today in theoretical physics. The high performance algorithms described herein are the most compact, efficient methods known for representing and analyzing systems modeled well by sets or…
In this paper, we introduce the boundary $\mathcal{U}X$ of a coarse proximity space $(X,\mathcal{B},{\bf b}).$ This boundary is a subset of the boundary of a certain Smirnov compactification. We show that $\mathcal{U}X$ is compact and…
A recently proposed dimensional reduction approach for studying synchronization in the Kuramoto model is employed to build optimal network topologies to favor or to suppress synchronization. The approach is based in the introduction of a…
Topologically-ordered matter is a novel quantum state of matter observed only in a small number of physical systems, notably two-dimensional electron systems exhibiting fractional quantum Hall effects. It was recently proposed that a simple…
The accurate description of the interaction of a quantum system with a its environment is a challenging problem ubiquitous across all areas of physics, and lies at the foundation of quantum mechanics theory. Here we pioneer a new strategy…
We use the Koashi-Imoto decomposition of the degrees of freedom of joint system-environment initial states to investigate the reduced dynamics. We show that a subset of joint system-environment initial states guarantees completely positive…
The Kuramoto model is a classical nonlinear ODE system designed to study synchronization phenomena. Each equation represents the phase of an oscillator and the coupling between them is determined by a graph. There is an increasing interest…
The Kuramoto model is a classical mathematical model in the field of non-linear dynamical systems that describes the evolution of coupled oscillators in a network that may reach a synchronous state. The relationship between the network's…
Current GNSS systems rely on global reference frames which are fixed to the Earth (via the ground stations) so their precision and stability in time are limited by our knowledge of the Earth dynamics. These drawbacks could be avoided by…