超衍射成像中 双螺旋点扩展函数的三维定位精度

开关效应和单分子定位的结合可以实现样品的超衍射分辨成像, 双螺旋点扩展函数将单分子定位纳米分辨从二维扩展到了三维.本文对双螺旋点扩展函数的三维定位精度展开了探讨.首先, 基于费希尔信息量, 计算了双螺旋点扩展函数的无偏估计, 得出其理论定位精度, 并分析了光子数、背景噪声以及有效像元尺寸大小对其定位精度的影响; 其次, 基于单分子定位实验过程中对于数据分析通常采用的高斯拟合质心定位算法, 通过误差传递函数定律求得双螺旋点扩展函数的轴向定位精度.计算机模拟结果表明, 在光子数大于1000的条件下, 高斯拟合质心定位精度和费希尔信息量理论定位精度符合较好. 本文的讨论不仅为双螺旋点扩展函数的三维定位精度提供了理论依据, 同时也可为实验提供理论指导. 关键词： 双螺旋点扩展函数 费希尔信息量 定位精度 高斯拟合     

Entropy,Fisher Information and Variance with Frost-Musulin Potenial

This study presents the Shannon and Renyi information entropy for both position and momentum space and the Fisher information for the position-dependent mass Schrödinger equation with the Frost-Musulin potential. The analysis of the quantum mechanical probability has been obtained via the Fisher information. The variance information of this potential is equally computed. This controls both the chemical properties and physical properties of some of the molecular systems. We have observed the behaviour of the Shannon entropy. Renyi entropy, Fisher information and variance with the quantum number n respectively.     

Correlated cortical populations can enhance sound localization performance

Neurons within cortical populations often evidence some degree of response correlation. Correlation has generally been regarded as detrimental to the decoding performance of a theoretical vector-averaging observer making inferences about the physical world-for example, an observer estimating the location of a sound source. However, if an alternative decoder is considered, in this case a Maximum Likelihood estimator, performance can improve when responses in the population are correlated. Improvement in sound localization performance is demonstrated analytically using Fisher information, and is also shown using Monte Carlo simulations based on recordings from single neurons in cat primary auditory cortex.     

浅海中水平线列阵深度对匹配场定位性能的影响

以浅海声传播模型为基础,通过计算机仿真观察到以下物理现象：浅海中海底水平线列阵的匹配场定位性能优于其他深度水平线列阵.利用简正波建模方法揭示了这一现象的物理机理.按照简正波理论,各号模式的形状是海水深度的函数.通过比较不同深度上各号模式幅度的变化,发现海底模式幅值接近零的模式号数明显小于其他深度.这说明海底水平线列阵可以对更多号模式进行采样,进而获得更多的目标声源信息,取得更好的匹配场定位效果. 关键词： 水平线列阵 匹配场定位 基阵深度     

Quantum confinement in an asymmetric double‐well potential through energy analysis and information entropic measure

Localization of a particle in the wells of an asymmetric double‐well (DW) potential is investigated here. Information entropy‐based uncertainty measures, such as Shannon entropy, Fisher information, Onicescu energy, etc., and phase‐space area, are utilized to explain the contrasting effect of localization‐delocalization and role of asymmetric term in such two‐well potentials. In asymmetric situation, two wells behaves like two different potentials. A general rule has been proposed for arrangement of quasi‐degenerate pairs, in terms of asymmetry parameter. Further, it enables to describe the distribution of particle in either of the deeper or shallow wells in various energy states. One finds that, all states eventually get localized to the deeper well, provided the asymmetry parameter attains certain threshold value. This generalization produces symmetric DW as a natural consequence of asymmetric DW. Eigenfunctions, eigenvalues are obtained by means of a simple, accurate variation‐induced exact diagonalization method. In brief, information measures and phase‐space analysis can provide valuable insight toward the understanding of such potentials.     

Chaos and quantum Fisher information in the quantum kicked top

Quantum Fisher information is related to the problem of parameter estimation.Recently,a criterion has been proposed for entanglement in multipartite systems based on quantum Fisher information.This paper studies the behaviours of quantum Fisher information in the quantum kicked top model,whose classical correspondence can be chaotic.It finds that,first,detected by quantum Fisher information,the quantum kicked top is entangled whether the system is in chaotic or in regular case.Secondly,the quantum Fisher information is larger in chaotic case than that in regular case,which means,the system is more sensitive in the chaotic case.     

Weighted Fisher informations, their derivation and use

Fisher information has been used to derive many laws of physics, including its differential equations. In many of these Fisher-based derivations the information in the time measurement is required to be negative. Yet by its expression in the standard derivation of the Cramer-Rao (CR) inequality, a negative Fisher seems impossible. To the contrary, we show that in fact the standard CR derivation allows the Fisher to be meaningfully regarded as either negative or positive. The mathematics allow it, and the choice to be made depends upon the physical parameter whose information level is sought. For example, the rules of special relativity require an imaginary time parameter ict, , with c the speed of light and t the time. The squared time parameter is then negative, requiring (as shown) the Fisher information to be negative as well. Further generalizations of the CR derivation are also made, which allow the estimation of general parameters using arbitrarily weighted mean-squared error criteria. The weights are found to define a family of correspondingly weighted Fisher informations. Finally, a condition is found for achieving efficient estimation in the presence of any weight function.     

Fisher Information of Wavefunctions： Classical and Quantum

A parametric quantum mechanical wavefunction naturally induces parametric probability distributions by taking absolute square, and we can consider its classical Fisher information. On the other hand, it also induces parametric rank-one projections which may be viewed as density operators, and we can talk about its quantum Fisher information. Among many versions of quantum Fisher information, there are two prominent ones. The first, defined via a quantum score function, was introduced by Helstrom in 1967 and is well known. The second, defined via the square root of the density operator, has its origin in the skew information introduced by Wigner and Yanase in 1963 and remains relatively unnoticed. This study is devoted to investigating the relationships between the classical Fisher information and these two versions of quantum Fisher information for wavefunctions. It is shown that the two versions of quantum Fisher information differ by a factor 2 and that they dominate the classical Fisher information. The non-coincidence of these two versions of quantum Fisher information may be interpreted as a manifestation of quantum discord. We further calculate the difference between the Helstrom quantum Fisher information and the classical Fisher information, and show that it is precisely the instantaneous phase fluctuation of the wavefunctions.     

Spin Squeezing and Quantum Fisher Information in Generalized Two-Axis Twisting Model

We investigated spin squeezing and quantum Fisher information in generalized two-axis twisting model; which generalizes the two-axis twisting model including a linear interaction controlled by an external field. In particular, we are interested in the dependence of spin squeezing and quantum Fisher information on the external field. By adopting frozen-spin approximation, we derive the theoretical and numerical results for spin squeezing and quantum Fisher information. Except certain special conditions, the stronger external field induces to stronger squeezing. Spin squeezing parameter and the reciprocal of the mean quantum Fisher information per particle are periodic function; but the external field has not important effect on the period.     

An energy-independent nonlocal potential model for bound and scattering states

The general expression of the nucleon-nucleus optical potential has been obtained using Watson's multiple scattering theory and Wolfenstein's parametrization of the nucleon-nucleon scattering amplitude. The resulting theoretical potential is nonlocal and consists of an energy-independent central volume plus surface real and imaginary potential and of a Thomas-like spin-orbit term. The analysis has been restricted to N = Z spherical nuclei, so that neither isospin-isospin nor spin-spin interactions have been included. The widely used Perey-Buck, Greenlees, and Watson expressions of the optical potential are easily obtained as particular cases. For practical purposes, the nonlocal potential has been parametrized in the Frahn-Lemmer form, using Woods-Saxon radial form factors, and the equivalent local potential (ELP) has been calculated by a Perey-Buck-like transformation.The ELP has a radial behavior very similar to the original nonlocal one, but the potential depths and radii are energy dependent. The six free parameters in the ELP have been adjusted to fit the available experimental data in the ?70 to + 150 MeV range of interest in nuclear reactions, namely, energies of single hole and single particle states, charge distributions, proton elastic scattering cross sections, and polarizations. The fitted potential depths show an energy dependence in remarkable agreement with the model predictions with a central nonlocality range β ? 1 F and a spin-orbit nonlocality range β₃ ? 0.8 F. The relative importance of surface and volume dependence in the real central potential in also discussed.     

Information-Efficient,Off-Center Sampling Results in Improved Precision in 3D Single-Particle Tracking Microscopy

In this work, we present a 3D single-particle tracking system that can apply tailored sampling patterns to selectively extract photons that yield the most information for particle localization. We demonstrate that off-center sampling at locations predicted by Fisher information utilizes photons most efficiently. When performing localization in a single dimension, optimized off-center sampling patterns gave doubled precision compared to uniform sampling. A ~20% increase in precision compared to uniform sampling can be achieved when a similar off-center pattern is used in 3D localization. Here, we systematically investigated the photon efficiency of different emission patterns in a diffraction-limited system and achieved higher precision than uniform sampling. The ability to maximize information from the limited number of photons demonstrated here is critical for particle tracking applications in biological samples, where photons may be limited.     

Fisher-like atomic divergences: Mathematical grounds and physical applications

Two different local divergence measures, the Fisher (FD) and the Jensen–Fisher (JFD) ones, are compared in this work by applying them to atomic one-particle densities in position and momentum spaces. They are defined in terms of the absolute and the relative Fisher information functionals. The analysis here afforded includes not only neutral atoms, but also singly-charged cations. The results are interpreted and justified according to (i) shell-filling patterns, (ii) short- and long-range behaviors of the atomic densities, and (iii) the value of the atomic ionization potential. The strengths of the FD measure, as compared to the JFD one, are emphasized.     

Fisher-Rényi entropy product and information plane

Connection between Fisher information and Rényi entropy has been established. This link allows us to define the Fisher-Rényi information plane and an entropic product in terms of these quantities. New Rényi uncertainty relations are obtained for single particle densities of many particle systems in position-momentum conjugate spaces.     

Analysis of electromagnetic pre-seismic emissions using Fisher information and Tsallis entropy

In this work, we investigate the dynamics of electromagnetic precursors, recorded prior to significant earthquakes in Greece. The analysis of these signals is performed using Fisher information, which is a powerful tool for investigating complex and non-stationary signals. Our results point to a decrease of the precursor complexity as the main tectonic event is approaching. The results are compatible to those derived using Tsallis entropy. The sensitivity of Fisher information and Tsallis entropy are compared on the basis of the features of the underlying fracture process which they reveal.     

Fisher information for spike-based population decoding

We evaluate the Fisher information of a population of model neurons that receive dynamical input and interact via spikes. With spatially independent threshold noise, the spike-based Fisher information that summarizes the information carried by individual spike timings has a particularly simple analytical form. We calculate the loss of information caused by abandoning spike timing and study the effect of synaptic connections on the Fisher information. For a simple spatiotemporal input, we derive the optimal recurrent connectivity that has a local excitation and global inhibition structure. The optimal synaptic connections depend on the spatial or temporal feature of the input that the system is designed to code.     

Logarithm Versus Square Root： Comparing Quantum Fisher Information

In classical statistics, the Fisher information is unique in the sense that it is essentially the only monotone Riemannian metric on the space of probability densities. In quantum theory, this uniqueness breaks down, and there are many natural quantum analogues of the Fisher information, among which two particular versions distinguish themselves by their intuitive and informational significance： The first has its origin in the skew information introduced by Wigner and Yanase in 1963 in the context of quantum measurement, and is defined via the square root of the density operator. The second arises from Helstrom＇s study of quantum detection in 1967, and is defined via the symmetric logarithmic derivative. The aim of this paper Js to compare these two versions of quantum Fisher information, and to establish two informational inequalities relating them.     

光与物质相互作用系统中的量子Fisher信息和自旋压缩

Fisher信息是估计理论中的重要概念,最近发现与量子信息中的纠缠判据具有密切联系.非旋波近似条件下,Dicke模型经典相空间表现为混沌动力学特征.本文详细考察了Dicke模型描述的光与物质相互作用系统中量子Fisher信息和自旋压缩动力学特性.结果表明:在短时瞬态情况下,无论初态处于规则区域还是混沌区域系统均表现为纠缠性质;但在长时稳态情况下,初态处于规则区域时系统纠缠消失,而初态处于混沌区域时系统则一直存在纠缠.通过与系统自旋压缩动力学性质相比较,发现量子Fisher信息可以更有效地刻画量子混沌.进一步考察初态处于规则和混沌区域时系统密度矩阵和纯度的动力学演化特性,发现混沌导致系统退相干现象发生,说明量子Fisher信息对混沌更敏感.     

Fluctuation of gauge field for general nonlinear Fokker-Planck equation and covariant version of Fisher information matrix

We clarify a strong link between general nonlinear Fokker-Planck equations with gauge fields associated with nonequilibrium dynamics and the Fisher information of the system. The notion of Abelian gauge theory for the non-equilibrium Fokker-Planck equation has proposed in the literature, in which the associated curvature represents internal geometry. We present the fluctuation of the gauge field can be decomposed into three parts. We further show that if we define the Fisher information matrix by using a covariant derivative then it gives correlation of the flux components but it is not gauge invariant.     

Generation of depth-perception information in stereoscopic nuclear magnetic resonance imaging by non-linear magnetic field gradients

Stereoscopic NMR images have been produced in the past. However, because of the gradients are linear, only isometric projections can be produced, i.e., they do not carry correct depth-perception information. The resulting stereoscopic image will not have correct relative sizes at different depths. This paper gives an analysis of what perception information is needed and shows that it can be produced by a non-linear magnetic field gradient. The concept is exemplified by simulations and its implementation is demonstrated successfully by experiments. The depth-encoding gradient can be generated by static steel pieces or by current loops. The procedure can be incorporated into any existing hardware and pulse sequences, and has potential application in surgery.