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We study approximation algorithms for satisfiable and nearly satisfiable instances of ordering constraint satisfaction problems (ordering CSPs). Ordering CSPs arise naturally in ranking and scheduling, yet their approximability remains…
Collective response dynamics of a strongly coupled system departs from the continuum phase upon transition to the quasicrystalline phase, or formation of a Wigner lattice. The wave nonlinearity leading to the modulational instability in…
Regularization methods have been recently developed to construct stable approximate solutions to classical partial differential equations considered as final value problems. In this paper, we investigate the backward parabolic problem with…
In the context of mathematical modeling, it is sometimes convenient to integrate models of different nature. These types of combinations, however, might entail difficulties even when individual models are well-understood, particularly in…
We extend the notion of numerical stability of finite difference approximations to include hyperbolic systems that are first order in time and second order in space, such as those that appear in Numerical Relativity. By analyzing the symbol…
In this paper, several numerical examples to illustrate limitations of Quasi Steady-State (QSS) model in long-term voltage stability analysis are presented. In those cases, the QSS model provided incorrect stability assessment. Causes of…
We establish local existence and a quasi-optimal error estimate for piecewise cubic minimizers to the bending energy under a discretized inextensibility constraint. In previous research a discretization is used where the inextensibility…
We study necessary and sufficient conditions for contraction and incremental stability of dynamical systems with respect to non-Euclidean norms. First, we introduce weak pairings as a framework to study contractivity with respect to…
A low-order finite element method is constructed and analysed for an incompressible non-Newtonian flow problem with power-law rheology. The method is based on a continuous piecewise linear approximation of the velocity field and piecewise…
The convergence and optimality of adaptive mixed finite element methods for the Poisson equation are established in this paper. The main difficulty for mixed finite element methods is the lack of minimization principle and thus the failure…
Preserving stability is a central problem in data-driven model order reduction of dynamical systems. For linear systems whose dynamics depend on geometric or physical parameters, multivariate rational approximation algorithms such as the…
We investigate the dynamical stability of the holographic system with two order parameters, which exhibits competition and coexistence of condensations. In the linear regime, we have developed the gauge dependent formalism to calculate the…
Optimal convergence rates of adaptive finite element methods are well understood in terms of the axioms of adaptivity. One key ingredient is the discrete reliability of a residual-based a posteriori error estimator, which controls the error…
We study the stability of quantum motion of classically regular systems in presence of small perturbations. Onthe base of a uniform semiclassical theory we derive the fidelity decay which displays a quite complexbehaviour, from Gaussian to…
In recent years, novel quantifications of measurement error in quantum mechanics have for the first time enabled precise formulations of Heisenberg's famous but often challenged measurement uncertainty relation. These relations take the…
Recent advancements in photon induced near-field electron microscopy (PINEM) enable the preparation, coherent manipulation and characterization of free-electron quantum states. The available measurement consists of electron energy…
Quantum systems in extreme conditions can exhibit universal behavior far from equilibrium associated to nonthermal fixed points with a wide range of topical applications from early-universe inflaton dynamics and heavy-ion collisions to…
To understand the empirical success of approximate MAP inference, recent work (Lang et al., 2018) has shown that some popular approximation algorithms perform very well when the input instance is stable. The simplest stability condition…
The accuracy of quasilinear theory applied to the electron bump-on-tail instability, a classic model problem, is explored with conservative high-order discontinuous Galerkin methods applied to both the quasilinear equations and to a direct…
Synchronization of fractional-order chaotic systems is a hot topic in the field of nonlinear study. The co-coupled synchronization between two fractional-order chaotic systems with different initial conditions is investigated in this paper.…