相关论文: Second-Order Converses via Reverse Hypercontractiv…
In this paper, we introduce and study the conformal mean curvature flow of submanifolds of higher codimension in the Euclidean space $\bbr^n$. This kind of flow is a special case of a general modified mean curvature flow which is of various…
A distributed binary hypothesis testing (HT) problem over a noisy (discrete and memoryless) channel studied previously by the authors is investigated from the perspective of the strong converse property. It was shown by Ahlswede and…
It has been shown recently that predictions from Mode-Coupling Theory for the glass transition of hard-spheres become increasingly bad when dimensionality increases, whereas replica theory predicts a correct scaling. Nevertheless if one…
In this study, we investigate the Shallow Water Equations incorporating source terms accounting for Manning friction and a non-flat bottom topology. Our primary focus is on developing and validating numerical schemes that serve a dual…
A strong converse theorem for the classical capacity of a quantum channel states that the probability of correctly decoding a classical message converges exponentially fast to zero in the limit of many channel uses if the rate of…
We derive several efficiently computable converse bounds for quantum communication over quantum channels in both the one-shot and asymptotic regime. First, we derive one-shot semidefinite programming (SDP) converse bounds on the amount of…
The problem of inferring pair-wise and higher-order interactions in complex systems involving large numbers of interacting variables, from observational data, is fundamental to many fields. Known to the statistical physics community as the…
A strong direct product theorem (SDPT) states that solving n instances of a problem requires Omega(n) times the resources for a single instance, even to achieve success probability exp(-Omega(n)). We prove that quantum communication…
Training conversational question-answering (QA) systems requires a substantial amount of in-domain data, which is often scarce in practice. A common solution to this challenge is to generate synthetic data. Traditional methods typically…
The Lie-Trotter formula, together with its higher-order generalizations, provides a direct approach to decomposing the exponential of a sum of operators. Despite significant effort, the error scaling of such product formulas remains poorly…
A general conversion strategy by involving a shifted parameter $\theta$ is proposed to construct high-order accuracy difference formulas for fractional calculus operators. By converting the second-order backward difference formula with such…
For the prescribed scalar curvature equation on $S^n$ ($n \ge 6$), we consider the situation where the number of bubbles tends to infinity in the Lyapunov-Schmidt (finite dimension) reduction method. In an outstanding paper by Wei and Yan,…
In modern communication systems such as the Internet, random losses of information can be mitigated by oversampling the source. This is equivalent to expanding the source using overcomplete systems of vectors (frames), as opposed to the…
We present a controlled rare-weak-link theory of the superfluid-to-Bose/Mott glass transition in one-dimensional disordered systems. The transition has Kosterlitz-Thouless critical properties but may occur at an arbitrary large value of the…
We extend from the hyperfinite setting to general von Neumann algebras Mosonyi and Ogawa's (2015) and Mosonyi and Hiai's (2023) results showing the operational interpretation of sandwiched relative R\'enyi entropy in the strong converse of…
Set-disjointness problems are one of the most fundamental problems in communication complexity and have been extensively studied in past decades. Given its importance, many lower bound techniques were introduced to prove communication lower…
We construct a monotone quantity for the classical obstacle problem with non-smooth obstacle, and show that the blow-ups are homogeneous functions of degree $\alpha<2$.
A unified approach to prove the converses for the quantum channel capacity theorems is presented. These converses include the strong converse theorems for classical or quantum information transfer with error exponents and novel explicit…
A classical (or quantum) superintegrable system on an n-dimensional Riemannian manifold is an integrable Hamiltonian system with potential that admits 2n-1 functionally independent constants of the motion that are polynomial in the momenta,…
Three decades of research in communication complexity have led to the invention of a number of techniques to lower bound randomized communication complexity. The majority of these techniques involve properties of large submatrices…