相关论文: Nonembeddability theorems via Fourier analysis

We show how to construct loss-tolerant linear steering inequalities using a generic set of von Neumann measurements that are violated by $d$-dimensional states, and that rely only upon a simple property of the set of measurements used (the…

We analyze monotone difference schemes for strongly degenerate convection-diffusion equations in one spatial dimension. These nonlinear equations are well-posed within a class of (discontinuous) entropy solutions. We prove that the L1…

The Gridding algorithm has shown great utility for reconstructing images from non-uniformly spaced samples in the Fourier domain in several imaging modalities. Due to the non-uniform spacing, some correction for the variable density of the…

Electron transport properties of few-electron open quantum dots within the spin-restricted Hartree-Fock approximation are studied. The self-consistent numerical calculations were performed for a whole device, including the semi-infinite…

We consider a surface with negative curvature in $\Bbb R^3$ which is a cubic perturbation of the saddle. For this surface, we prove a new restriction theorem, analogous to the theorem for paraboloids proved by L. Guth in 2016. This specific…

In the study of Heisenberg's error-disturbance relation, it is commonly believed that the non-unitary change of states hinders us from deducing the information encoded in original states about subsequently measured observable. However, we…

We establish the Level-1 and Level-3 Large Deviation Principles (LDPs) for invariant measures on shift spaces over finite alphabets under very general decoupling conditions for which the thermodynamic formalism does not apply. Such…

The domain-independent universal Normalized Information Distance based on Kolmogorov complexity has been (in approximate form) successfully applied to a variety of difficult clustering problems. In this paper we investigate theoretical…

Unmanned vehicle navigation concerns estimating attitude, position, and linear velocity of the vehicle the six degrees of freedom (6 DoF). It has been known that the true navigation dynamics are highly nonlinear modeled on the Lie Group of…

For $0 < \alpha \leq 1$, let $E$ be a compact subset of the $d$-dimensional moment curve in $\mathbb{R}^d$ such that $N(E,\varepsilon) \lesssim \varepsilon^{-\alpha}$ for $0 <\varepsilon <1$ where $N(E,\varepsilon)$ is the smallest number…

The construction of a solution of the perturbed KdV equation encounters obstacles to asymptotic integrability beyond the first order, when the zero-order approximation is a multiple-soliton wave. In the standard analysis, the obstacles lead…

Results are presented of a full leading-order evaluation of the shear viscosity, flavor diffusion constants, and electrical conductivity in high temperature QCD and QED. The presence of Coulomb logarithms associated with gauge interactions…

We study the estimation of the value function for continuous-time Markov diffusion processes using a single, discretely observed ergodic trajectory. Our work provides non-asymptotic statistical guarantees for the least-squares…

We consider 2D fermions on a plane with a perpendicular magnetic field, described by Landau levels. It is wellknown that, semiclassically, restriction to the lowest Landau levels (LLL) implies two constraints on a 4D phase space, that…

We make progress towards an analytical understanding of the regime of validity of perturbation theory for large scale structures and the nature of some non-perturbative corrections. We restrict ourselves to 1D gravitational collapse, for…

Spacetime nonmetricity can be studied experimentally through its couplings to fermions and photons. We use recent high-precision searches for Lorentz violation to deduce first constraints involving the 40 independent nonmetricity components…

We assess the accuracy of a recently introduced nonlinear interference model for general dual-polarization 4D formats.~ Unlike previous models for polarization-multiplexed 2D formats, an average gap from split-step Fourier simulations…

The goal of ordinal embedding is to represent items as points in a low-dimensional Euclidean space given a set of constraints in the form of distance comparisons like "item $i$ is closer to item $j$ than item $k$". Ordinal constraints like…

For multi-variable finite measure spaces, we present in this paper a new framework for non-orthogonal $L^2$ Fourier expansions. Our results hold for probability measures $\mu$ with finite support in $\mathbb{R}^d$ that satisfy a certain…

We compute the one-level density for the family of cubic Dirichlet $L$-functions when the support of the Fourier transform of a test function is in $(-1,1)$. We also establish the Ratios conjecture prediction for the one-level density for…