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量子测量,作为提取信息的基本手段,是量子信息论中一个基本而重要的概念。量子态层析是指通过对多份同一未知量子态进行量子测量,再利用测量获取的信息对量子态进行估计,以确定真实量子态的过程。如何选择量子测量以有效地获取量子态的信息是量子态层析中的一个核心问题。理想的量子测量方案中涉及的量子测量算子要尽可能少,并且在实验中要易于实现。
Fisher-consistent loss functions play a fundamental role in the construction of successful binary margin-based classifiers. In this paper we establish the Fisher-consistency condition for multicategor...
We consider the traveling wave problem for the one dimensional Keller-Segel system with a birth term of either a Fisher/KPP type or with a truncation for small population densities. We prove that ther...
We consider the Fisher-KPP equation with a nonlocal saturation effect defined through an interaction kernel φ(x) and investigate the possible differences with the standard Fisher-KPP equation. Our fir...
We consider Fisher-KPP-type reaction-diffusion equations with spatially inhomogeneous reaction rates. We show that a sufficiently strong localized inhomogeneity may prevent existence of transition-fro...
In this paper, we explain in simple PDE terms a famous result of Bramson about the logarithmic delay of the position of the solutions u(t, x) of Fisher-KPP reaction-diffusion equations in R, with resp...
We consider solutions of the KPP equation with a time-dependent diffusivity of the formσ(t/T). For an initial condition that is compactly supported, we show that when σ(s) is increasing in time the fr...
We consider the Fisher-KPP equation with a non-local interaction term. We establish a condition on the interaction that allows for existence of non-constant periodic solutions,and prove uniform upper ...
This paper concerns the semi-wavefronts (i.e. bounded solutions $u=\phi(x \nu +ct) >0,$ $ |\nu|=1, $ satisfying $\phi(-\infty)=0$) to the delayed KPP-Fisher equation $$u_t(t,x) = \Delta u(t,x) + u(t,x...
We study the Fisher-KPP equation where the Laplacian is replaced by the generator of a Feller semigroup with power decaying kernel, an important example being the fractional Laplacian. In contrast wit...
Abstract: In a classical work of the 1950's, Lee and Yang proved that for fixed nonnegative temperature, the zeros of the partition functions of a ferromagnetic Ising model always lie on the unit circ...
Abstract: The aim of this paper is to study differential and spectral properties of the infinitesimal operator of two dimensional Markov processes with diffusion and discrete components. The infinites...
Abstract: Kagan and Shepp (2005, Amer. Statist.) presented an elegant example of a mixture model for which an insufficient statistic preserves Fisher information. This note uses the regularity propert...

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