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This paper introduces a method for predicting the likely behaviors of continuous nonlinear systems in equilibrium in which the input values can vary. The method uses a parameterized equation model and a lower bound on the input joint…
We study entropy-bounded computational geometry, that is, geometric algorithms whose running times depend on a given measure of the input entropy. Specifically, we introduce a measure that we call range-partition entropy, which unifies and…
The configuration manifold $M$ of a mechanical system consisting of two unconstrained rigid bodies in $\mathbb{R}^n$, $n\geq 1$, is a manifold with boundary (typically with singularities.) A complete description of the system requires…
The entropy region is a fundamental object in information theory. An outer bound for the entropy region is defined by a minimal set of Shannon-type inequalities called elemental inequalities also referred to as the Shannon region. This…
We study the problem of persistence of attractors with smooth boundary for a class of set-valued dynamical systems that naturally arise in the context of random and control dynamical systems, as well as in systems modeling the dynamical…
We consider the outer billiards map with contraction outside polygons. We construct a 1-parameter family of systems such that each system has an open set in which the dynamics is reduced to that of a piecewise contraction on the interval.…
We study the stability of deterministic systems given sequences of large, jump-like perturbations. Our main result is to dervie a lower bound for the probability of the system to remain in the basin, given that perturbations are rare…
We calculate the energy and the condensate fraction of a system of trapped bosons interacting via a short-range two-body potential with positive scattering length. The potential is attractive and has a two-body bound state. When the…
In this work, based on the moving-least-squares immersed boundary method, we proposed a new technique to improve the calculation of the volume force representing the body boundary. For boundary with simple geometry, we theoretically analyse…
The boundary Weyl anomalies live on a codimension-1 boundary, $\partial {\cal M}$. The entanglement entropy originates from infinite correlations on both sides of a codimension-2 surface, $\Sigma$. Motivated to have a further understanding…
Bound state and time evolution for single excitation in one dimensional XXZ spin chain within non-Markovian reservoir are studied exactly. As for bound state, a common feature is the localization of single excitation, which means the…
We evaluate masses of bottom and charmed baryons using several non-relativistic quark potentials which parameters have been adjusted to the meson spectra. Heavy Quark Symmetry leads to important simplifications of the three body problem,…
We consider interacting one-dimensional bosons in the universal low-energy regime. The interactions consist of a combination of attractive and repulsive parts that can stabilize quantum gases, droplets and liquids. In particular, we study…
This paper has been withdrawn by the author. Ferrofluids suspended in liquids and constrained in quasi-two dimensional domains were exposed to transverse magnetic fields. The points of elliptical instability of nearly circular drops were…
Random tilings are interesting as idealizations of atomistic models of quasicrystals and for their connection to problems in combinatorics and algorithms. Of particular interest is the tiling entropy density, which measures the relation of…
We study the computational problem of rigorously describing the asymptotic behaviour of topological dynamical systems up to a finite but arbitrarily small pre-specified error. More precisely, we consider the limit set of a typical orbit,…
We consider entropic uncertainty relations for outcomes of the measurements of a quantum state in 3 or more mutually unbiased bases (MUBs), chosen from the standard construction of MUBs in prime dimension. We show that, for any choice of 3…
Locomotion in the real world involves unexpected perturbations, and therefore requires strategies to maintain stability to successfully execute desired behaviours. Ensuring the safety of locomoting systems therefore necessitates a…
We present a set of new energy-stable open boundary conditions for tackling the backflow instability in simulations of outflow/open boundary problems for incompressible flows. These boundary conditions are developed through two steps: (i)…
The zero-temperature limit of the backgammon model under resetting is studied. The model is a balls-in-boxes model whose relaxation dynamics is governed by the density of boxes containing just one particle. As these boxes become rare at…