基于渐进添边的准循环压缩感知时延估计算法

针对时延估计问题中压缩感知类算法现有测量矩阵需要大量数据存储量的问题,提出了一种基于渐进添边的准循环压缩感知时延估计算法,实现了稀疏测量矩阵条件下接收信号时延的准确估计.该算法首先建立压缩感知与最大似然译码之间的理论桥梁,然后推导基于低密度奇偶校验码的测量矩阵的设计准则,引入渐进添边的思想构造具有准循环结构的稀疏测量矩阵,最后利用正交匹配追踪算法正确估计出时延.对本文算法的计算复杂度与测量矩阵的数据存储量进行理论分析.仿真结果表明,所提算法在测量矩阵维数相同的条件下正确重构概率高于高斯随机矩阵和随机奇偶校验测量矩阵,相比于随机奇偶校验矩阵,在数据存储量相等的条件下,以较少的计算复杂度代价得到了重构概率的较大提高.     

How does a strong magnetic field destroy localization in two-dimensional disordered systems?

Two dimensional disorder in a strong magnetic field is investigated in terms of random matrix theory and in comparison to the conventional Anderson tight-binding model. Disorder is introduced by an ensemble average over a random potential which has to be projected onto single Landau bands. This leads to a random matrix problem for single Landau levels whose special properties are examined. We describe a method which allows a proper projection of various random potentials, specified by a correlation function, onto arbitrary subspaces. The matrix elements of the Hamiltonian for single Landau bands are strongly correlated along the diagonals. The influence of such correlations on the localization properties is examined for a disk geometry. We obtain a qualitative understanding for the question raised in the title of the paper.     

Determining Transport Properties of Complex Multiterminal Systems: S‐Matrix of General Tight‐Binding Periodic Leads

Calculation of the scattering matrix (S‐matrix) of a system allows direct determination of its transport properties. Within the scattering theory, S‐matrices relate amplitudes of incoming and outgoing waves in semi‐infinite leads attached to a scattering region. Recently, an assembly method to calculate S‐matrices of arbitrary tight‐binding systems connected to atomic chains has been proposed, were the S‐matrices of subsystems are used to obtain S‐matrix of the total system. In this paper, a new efficient method to obtain S‐matrices of general periodic leads is established, which can be used in the mentioned assembly method, allowing to address coherent quantum transport of arbitrary multiterminal systems with complex geometries trough Landauer‐Büttiker formalism. In addition, a new method to determine extended‐state band structures of general infinite periodic wires is presented, which exploits properties of the S‐matrix. Finally, these methods are used to obtain band structure of graphene arm‐chair and zig‐zag nanoribbons and transmission functions in three terminal Z‐shaped graphene nanoribbon structures.     

Scaling concept applied to the defect formation caused by interactions between melittin and phosphatidylcholine (PC) model membranes

Summary A simple computer model of defection process caused by interactions between melittin and phosphatidylcholine (PC) model membrane has been proposed. It leads to a scaling formula which connects the average diameter (or linear size parameter) of the affected domain with the reciprocity of the number of such domains. Some preliminary investigations show the scaling exponent to be a small fractional number between ca. 0.3 and 0.1, depending on the number of possible infection directions and the type of lattice taken as a lipid matrix. Such small values of the scaling exponent can roughly be interpreted in terms of random tesselations on a plane (like random Voronoi networks), and the whole process displays a statistical self-similarity. The values obtained seem to be, however, small comparable to the scaling exponents characteristic for the faulting process occurring during the earthquake propagation. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

Statistical scattering theory, the supersymmetry method and universal conductance fluctuations

This paper describes a novel analytical approach to the problem of conductance fluctuations in mesoscopic systems which, in particular, gives account of the influence of the coupling to external leads. We consider the case of a linear disordered sample in the metallic regime, which is coupled to two ideally conducting external leads. Using the many-channel approximation to Landauer's formula, we relate the conductance to the total transmission probability through the sample. The microscopic Hamiltonian of the quasi-one-dimensional disordered sample is formulated in terms of a random matrix, and the elements of the associated scattering matrix which determine the transmission are constructed from statistical scattering theory. We show that in addition to the Thouless energy, E_c, and the mean level spacing, d, there exists in the theory, a third energy scale, Γ, determined by the number of channels in the leads and the strength of the coupling between disordered sample and leads. Related to Γ, is a new length scale, L₀. We find that for sample lengths L >L₀, the properties of the conductance depend only weakly on the coupling to the external leads and, for very large L, become identical with those of quasi-one-dimensional conductors in the weak localization limit. On the other hand, for L < L₀, the coupling to the leads strongly affects the behaviour of both the average and the variance of the conductance. The magnitude of L₀ is typically several magnitudes of ten times the elastic mean free path and thus comparable to the sizes of experimental devices. A further novel aspect of our work is the demonstration that the assumption of GOE statistics for the Hamiltonian is sufficient to yield universal conductance fluctuations.     

Broken time‐reversal symmetry scattering at the Anderson transition

We study numerically the statistical properties of some scattering quantities for the Power‐law Banded Random Matrix model at criticality in the absence of time‐reversal symmetry, with a small number of single‐channel leads attached to it. We focus on the average scattering matrix elements, the conductance probability distribution, and the shot noise power as a function of the effective bandwidth b of the model. We find a smooth transition from insulating‐ to metallic‐like behavior in the scattering properties of the model by increasing b. We contrast our results with existing random matrix theory predictions.     

Factorization fo random Jacobi operators and Bäcklund transformations

Summary We show that a positive definite random Jacobi operatorL over an abstract dynamical systemT: XX can be factorized asL=D ², whereD is again a random Jacobi operator but defined over a new dynamical systemS: YY which is an integral extension ofT. An isospectral random Toda deformation ofL corresponds to an isospectral random Volterra deformation ofD. The factorization leads to commuting Bäcklund transformations which can be written explicitly in terms of Titchmarsh-Weyl functions. In the periodic case, the Bäcklund transformations are time 1 maps of a Toda flow with a time dependent Hamiltonian.This article was processed by the author using the Springer-Verlag TEX EconThe macro package 1991.     

Diffusive-ballistic crossover in 1D quantum walks

We show that particle transport, as characterized by the equilibrium mean square displacement, in a uniform, quantum multibaker map, is generically ballistic in the long time limit, for any fixed value of Planck's constant. However, for fixed times, the semiclassical limit leads to diffusion. Random matrix theory provides explicit analytical predictions for the mean square displacement of a particle in the system. These results exhibit a crossover from diffusive to ballistic motion, with crossover time on the order of the inverse of Planck's constant. We expect that, for a large class of 1D quantum random walks similar to the quantum multibaker, a sufficient condition for diffusion in the semiclassical limit is classically chaotic dynamics in each cell. The systems described generalize known quantum random walks and may have applications for quantum computation.     

Quantum-statistical approach to gross properties of peripheral collisions between heavy nuclei

Non-equilibrium quantum-statistical mechanics is applied to peripheral collisions between heavy nuclei (A?40) where a large number of degrees of freedom are involved during the process. By eliminating the relative motion from the explicit consideration, the transitions between different channels are determined by a Liouville equation with timedependent coupling matrix elements. The introduction of subsets of channels (coarse graining) leads to the definition of macroscopic variables which correspond to observable quantities. The equation of motion for the macroscopic variables become irreversible by assuming the values of the coupling matrix elements to be randomly distributed. The validity and possible applications of the resulting master equations are discussed.     

Structural evaluation of polysilane-derived products: from amorphous to thermodynamically stable phases

A polysilane with a C-to-Si ratio of 6.0 was pyrolysed to produce an amorphous matrix (source powder), which was heated further to obtain different products. These polysilane-derived samples were studied using X-ray diffraction, Raman spectroscopy, solid-state magic-angle-spinning nuclear magnetic resonance and transmission electron microscopy. The source powder is a hydrogenated matrix composed of free carbon, random SiC₄ sites and trace SiCO species. Pyrolysis of the source powder leads to the nucleation and growth of SiC and progressive organization of free carbon. SiC forms at 1100°C and fast growth appears at 1700°C accompanied by obvious weight loss. SiC decomposition also occurs at high temperatures, which leads to the formation of relatively well-organized carbon. The structural evolution is discussed and compared with the literature.     

随机间距稀疏三元Toeplitz矩阵相位掩模压缩成像

压缩成像是一种基于压缩传感(CS)理论的新成像方法,其优点是可以用比传统的Nyquist采样定理所需测量数目少得多的测量值重建原稀疏或可压缩图像。在研究Bernoulli和Toeplitz测量矩阵的基础上,提出一种新的随机间距稀疏三元Toeplitz相位掩模矩阵。实验结果表明,在可压缩双透镜成像系统中,与Bernoulli和Bernoulli-Toeplitz相位掩模矩阵相比,新相位掩模矩阵的成像信噪比与之相当。但是随机独立变元个数和非零元个数显著减少,在数据存储与传输时更具优势,物理上更易实现,甚至重建时间是只有它们的21%～66%。     

Rate of Entropy Production in Stochastic Mechanical Systems

Entropy production in stochastic mechanical systems is examined here with strict bounds on its rate. Stochastic mechanical systems include pure diffusions in Euclidean space or on Lie groups, as well as systems evolving on phase space for which the fluctuation-dissipation theorem applies, i.e., return-to-equilibrium processes. Two separate ways for ensembles of such mechanical systems forced by noise to reach equilibrium are examined here. First, a restorative potential and damping can be applied, leading to a classical return-to-equilibrium process wherein energy taken out by damping can balance the energy going in from the noise. Second, the process evolves on a compact configuration space (such as random walks on spheres, torsion angles in chain molecules, and rotational Brownian motion) lead to long-time solutions that are constant over the configuration space, regardless of whether or not damping and random forcing balance. This is a kind of potential-free equilibrium distribution resulting from topological constraints. Inertial and noninertial (kinematic) systems are considered. These systems can consist of unconstrained particles or more complex systems with constraints, such as rigid-bodies or linkages. These more complicated systems evolve on Lie groups and model phenomena such as rotational Brownian motion and nonholonomic robotic systems. In all cases, it is shown that the rate of entropy production is closely related to the appropriate concept of Fisher information matrix of the probability density defined by the Fokker–Planck equation. Classical results from information theory are then repurposed to provide computable bounds on the rate of entropy production in stochastic mechanical systems.     

无序介质激光的方向效应

无序介质激光是由该介质的非周期-类结构与相匹配的泵浦光场相互作用时其整体多重散射的干涉效应产生的.因此其局域模不仅与无序介质被泵浦的功率、面积有关,而且与方向有关.本文以ZnO粉末激光为例,运用传输矩阵的方法计算模拟了其局域模谱的方向效应.     

Rheology of interfacial protein-polysaccharide composites

The aim of this paper is to check feasibility of using the maximal-entropy random walk in algorithms finding communities in complex networks. A number of such algorithms exploit an ordinary or a biased random walk for this purpose. Their key part is a (dis)similarity matrix, according to which nodes are grouped. This study en- compasses the use of a stochastic matrix of a random walk, its mean first-passage time matrix, and a matrix of weighted paths count. We briefly indicate the connection between those quantities and propose substituting the maximal-entropy random walk for the previously chosen models. This unique random walk maximises the entropy of ensembles of paths of given length and endpoints, which results in equiprobability of those paths. We compare the performance of the selected algorithms on LFR benchmark graphs. The results show that the change in performance depends very strongly on the particular algorithm, and can lead to slight improvements as well as to significant deterioration.     

Implementation of a quantum random number generator based on the optimal clustering of photocounts

To implement quantum random number generators, it is fundamentally important to have a mathematically provable and experimentally testable process of measurements of a system from which an initial random sequence is generated. This makes sure that randomness indeed has a quantum nature. A quantum random number generator has been implemented with the use of the detection of quasi-single-photon radiation by a silicon photomultiplier (SiPM) matrix, which makes it possible to reliably reach the Poisson statistics of photocounts. The choice and use of the optimal clustering of photocounts for the initial sequence of photodetection events and a method of extraction of a random sequence of 0’s and 1’s, which is polynomial in the length of the sequence, have made it possible to reach a yield rate of 64 Mbit/s of the output certainly random sequence.     

A novel formulation of Cabibbo–Kobayashi–Maskawa matrix renormalization

We present a gauge-independent quark mass counterterm for the on-shell renormalization of the Cabibbo–Kobayashi–Maskawa (CKM) matrix in the Standard Model that is directly expressed in terms of the Lorentz-invariant self-energy functions, and automatically satisfies the hermiticity constraints of the mass matrix. It is very convenient for practical applications and leads to a gauge-independent CKM counterterm matrix that preserves unitarity and satisfies other highly desirable theoretical properties, such as flavor democracy.     

An interpretation of the She-Lévêque model based on order statistics

We present an interpretation of the She-Lévêque model in fully developed turbulence based on order statistics. Turbulent behavior at large values of the Reynolds number is often studied through the scaling behavior of moments of the distribution of the velocity differences and of the energy dissipation. The present interpretation leads to a derivation of the scaling exponents ζ_p and τ_p of these moments, without any postulate about a universal relation over the fluctuation structures such as the one used by She and Lévêque. The interpretation is based on the fact that the hierarchy of fluctuation structures imposes statistical constraints, whereupon the order p itself is seen as a random variable. As proposed by She and Lévêque, the hierarchy of the structures is such that the structures of larger order affect locally lower order structures through an entrainment process. This phenomenon leads to the Fisher-Tippett law, one of three asymptotic distributions for the extreme value of a random sample as the size of the sample grows to infinity.