相关论文: Analytical Multi-kinks in smooth potentials

In this work we extend the range of applicability of a method recently introduced where coupled first-order nonlinear equations can be put into a linear form, and consequently be solved completely. Some general consequences of the present…

We describe some field theoretic methods for studying quantum spin systems in one dimension. These include the nonlinear sigma-model approach which is particularly useful for large values of the spin, the idea of Luttinger liquids and…

The global weak martingale solution is built through a four-level approximation scheme to stochastic compressible active liquid crystal system driven by multiplicative noise in a smooth bounded domain in $\mathbb{R}^{3}$ with large initial…

This paper presents a novel framework for high-dimensional nonlinear quantum computation that exploits tensor products of amplified vector and matrix encodings to efficiently evaluate multivariate polynomials. The approach enables the…

We show that moment inequalities in a wide variety of economic applications have a particular linear conditional structure. We use this structure to construct uniformly valid confidence sets that remain computationally tractable even in…

Analytic and optimization methods for solving inverse kinematics (IK) problems have been deeply studied throughout the history of robotics. The two strategies have complementary strengths and weaknesses, but developing a unified approach to…

We develop a linear-algebraic framework for dimensional analysis in systems with constraints, particularly when variables are numerous or related by implicit relations so that direct elimination is impractical. By expressing both…

To model combinatorial decision problems involving uncertainty and probability, we extend the stochastic constraint programming framework proposed in [Walsh, 2002] along a number of important dimensions (e.g. to multiple chance constraints…

We prove that the ground state for the Dirac equation on Minkowski space in static, smooth external potentials satisfies the Hadamard condition. We show that it follows from a condition on the support of the Fourier transform of the…

We investigate the presence of localized solutions in models described by a single real scalar field with generalized dynamics. The study offers a method to solve very intricate nonlinear ordinary differential equations, and we illustrate…

We consider the optimization of pairwise objective functions, i.e., objective functions of the form $H(\mathbf{x}) = H(x_1,\ldots,x_N) = \sum_{1\leq i<j \leq N} H_{ij}(x_i,x_j)$ for $x_i$ in some continuous state spaces $\mathcal{X}_i$.…

Quantum nonrelativistic systems with $2\times2$ matrix potentials are investigated. Physically, they simulate charged or neutral fermions with non-trivial dipole momenta, interacting with an external electric field. Assuming rotationally…

In this paper, we propose a catalog of iterative methods for solving the Split Feasibility Problem in the non-convex setting. We study four different optimization formulations of the problem, where each model has advantageous in different…

Making predictions in an unseen environment given data from multiple training environments is a challenging task. We approach this problem from an invariance perspective, focusing on binary classification to shed light on general nonlinear…

Accurate modeling of spin-orbit coupling and noncollinear magnetism requires noncollinear density functionals within the two-component generalized Kohn-Sham (GKS) framework, yet constructing and implementing noncollinear functionals remains…

We show how complexity theory can be introduced in machine learning to help bring together apparently disparate areas of current research. We show that this new approach requires less training data and is more generalizable as it shows…

This paper is concerned with a class of nonhomogeneous quasilinear elliptic system driven by the locally symmetric potential and the small continuous perturbations in the whole-space $\mathbb{R}^N$. By a variant of Clark's theorem without…

We present a preference learning framework for multiple criteria sorting. We consider sorting procedures applying an additive value model with diverse types of marginal value functions (including linear, piecewise-linear, splined, and…

Determining whether a nonlinear multi-input system is differentially flat remains challenging. One way to obtain computationally tractable sufficient conditions is to give complete characterizations of flat normal forms. We introduce a…

Discrete combinatorial optimization consists in finding the optimal configuration that minimizes a given discrete objective function. An interpretation of such a function as the energy of a classical system allows us to reduce the…