The anisotropic effect of hexagonal warping on the transport

In the presence of hexagonal warping (HW), the surface state of a topological insulator (TI) exhibits anisotropic Fermi surface. In this work, we study the transport properties of a TI junction, focusing on the influence of anisotropic effect of the HW on the scattering. We establish general expressions for calculating the scattering with an arbitrary angle between TI surface and the potential step, and find that the transmission probability and conductance have a strong dependence on the angle, making TI junction a promising platform for studying the geometry control of transport. Remarkably, we find that the HW can induce a triple refraction, which gives rise to an anomalous increase of the transmission probability when varying incident angle. The general expressions here for calculating the scattering can be extended to the systems with trigonally and tetragonally warped Fermi surface.     

Symbolic local information transfer

Recently, the permutation-information theoretic approach has been used in a broad range of research fields. In particular, in the study of high-dimensional dynamical systems, it has been shown that this approach can be effective in characterizing global properties, including the complexity of their spatiotemporal dynamics. Here, we show that this approach can also be applied to reveal local spatiotemporal profiles of distributed computations existing at each spatiotemporal point in the system. J. T. Lizier et al. have recently introduced the concept of local information dynamics, which consists of information storage, transfer, and modification. This concept has been intensively studied with regard to cellular automata, and has provided quantitative evidence of several characteristic behaviors observed in the system. In this paper, by focusing on the local information transfer, we demonstrate that the application of the permutation-information theoretic approach, which introduces natural symbolization methods, makes the concept easily extendible to systems that have continuous states. We propose measures called symbolic local transfer entropies, and apply these measures to two test models, the coupled map lattice (CML) system and the Bak-Sneppen model (BS-model), to show their relevance to spatiotemporal systems that have continuous states. In the CML, we demonstrate that it can be successfully used as a spatiotemporal filter to stress a coherent structure buried in the system. In particular, we show that the approach can clearly stress out defect turbulences or Brownian motion of defects from the background, which gives quantitative evidence suggesting that these moving patterns are the information transfer substrate in the spatiotemporal system. We then show that these measures reveal qualitatively different properties from the conventional approach using the sliding window method, and are also robust against external noise. In the BS-model, we demonstrate that these measures can provide novel insight to the model, featuring how symbolic local information transfer is related to the dynamical properties of the elements involved in a spatiotemporal dynamics.     

Signatures of bulk topology in the non-linear optical spectra of Dirac-Weyl materials

Graphene, topological insulators (TI) and the Weyl semimetal are shown to be well-characterized using the phenomenon of anomalous Rabi oscillation (ARO). These oscillations occur far from conventional resonance and Floquet theory shows them to be unique to these systems. Of particular interest is the bulk topological insulator (TI) where the wave-vector dependent frequency of the ARO is seen to be gapped in topologically trivial situations and gapless when there is a non-vanishing Chern number. It is shown that the Chern number may be directly inferred by performing a pump-probe experiment in the bulk without referring to surface states. A simpler alternative to the Lindblad method is invoked in order to incorporate dephasing effects that despite leading to a non-unitary time evolution of the wave-function, is nevertheless, probability conserving. The differential transmission coefficient versus the pump pulse duration (when all else is held fixed) has the form of a sinusoidal function with an amplitude that decays as a power law in the pump duration (alternatively, the “area” of the pump pulse). The exponent of this power law decay is indicative of the Chern number of the bulk in case of TI and more generally indicative of the particular member of the family of materials that may be collectively referred to as – Dirac-Weyl materials.     

Local information‐distance thermodynamics of molecular fragments

The Fisher information contained in a probability distribution is summarized. The corresponding measures of the information distance, relative to the reference probability density, are introduced and discussed. These concepts are designed as analogues of the Kullback‐Leibler directed divergence and Kullback's divergence. For these alternative measures of the missing information the equilibrium (“stockholder”) scheme of Hirshfeld, of a division of the molecular electron density into the subsystem components, is derived from the minimum principle of the local or global entropy deficiency relative to the free‐subsystem (“promolecule”) reference. The local information distance densities are used to describe instantaneous electron distributions in molecular subsystems within a thermodynamic‐like approach to the density fluctuations and irreversible processes. The key concepts of such a local irreversible “thermodynamics” are introduced. They include the corresponding local affinities (forces) and the conjugate fluxes (responses), which together determine the local entropy deficiency source. These quantities depend on the adopted measure of the information distance and selected state‐parameters. For each such representation the relevant Onsager‐type reciprocity relations can be derived, which reflect the symmetries between the linear effects of affinities on fluxes.     

Information,information gain,and efficiency of self-organizing systems close to instability points

Selforganizing systems are those which can acquire macroscopic spatial, temporal, or spatio-temporal structures without interference from the outside by mere changes of control parameters. The slaving principle which has been derived for such systems close to their instability points allows one to give the probability distribution of the total system a specific form.This in turn allows one to decompose information and information gain into a part which refers to the order parameters alone and a second part which is a sum over the information of the slaved modes averaged over the distribution of the order parameters. Close to instability points the information of the order parameters changes dramatically whereas the information of the slaved modes does not. Therefore close to these points it is sufficient to study the behavior of the order parameter information and information gain which is done explicitly for a large class of systems undergoing nonequilibrium phase transitions. It is shown how information and information gain as well as efficiency (in the sense defined in this paper) can be measured directly.     

Importance sampling for randomly excited dynamical systems

An importance sampling technique for linear and non-linear dynamical systems subjected to random excitations is presented. Applying a transformation of probability measures, controls are introduced in the system of Itô stochastic differential equations such that the sample trajectories can be influenced in a predetermined way. As is shown, there exist controls resulting in unbiased zero-variance estimators. However, these optimal controls are in general not accessible and have to be replaced by sub-optimal ones derived from an optimization procedure analogous to the first order reliability method known from time-invariant problems. The efficiency of the proposed Monte Carlo simulation technique is demonstrated by estimating first-passage probabilities of typical oscillators under external white-noise excitation.     

论动态信息理论

本文综述了作者的研究成果.近十年,作者将现有静态统计信息理论拓展至动态过程,建立了以表述动态信息演化规律的动态信息演化方程为核心的动态统计信息理论.基于服从随机性规律的动力学系统(如随机动力学系统和非平衡态统计物理系统)与遵守确定性规律的动力学系统(如电动力学系统)的态变量概率密度演化方程都可看成是其信息符号演化方程,推导出了动态信息(熵)演化方程.它们表明:对于服从随机性规律的动力学系统,动态信息密度随时间的变化率是由其在系统内部的态变量空间和传递过程的坐标空间的漂移、扩散和耗损三者引起的,而动态信息熵密度随时间的变化率则是由其在系统内部的态变量空间和传递过程的坐标空间的漂移、扩散和产生三者引起的.对于遵守确定性规律的动力学系统,动态信息(熵)演化方程与前者的相比,除动态信息(熵)密度在系统内部的态变量空间仅有漂移外,其余皆相同.信息和熵已与系统的状态和变化规律结合在一起,信息扩散和信息耗损同时存在.当空间噪声可略去时,将会出现信息波.若仅研究系统内部的信息变化,动态信息演化方程就约化为与表述上述动力学系统变化规律的动力学方程相对应的信息方程,它既可看成是表述动力学系统动态信息的演化规律,亦可看成是动力学系统的变化规律都可由信息方程表述.进而给出了漂移和扩散信息流公式、信息耗散率公式和信息熵产生率公式及动力学系统退化和进化的统一信息表述公式.得到了反映信息在传递过程中耗散特性的动态互信息公式和动态信道容量公式,它们在信道长度和信号传递速度之比趋于零的极限情况下变为现有的静态互信息公式和静态信道容量公式.所有这些新的理论公式和结果都是从动态信息演化方程统一推导出的.     

用多焦点全息透镜实现多重谱分数傅里叶变换

提出用多焦点全息透镜实现多重谱分数傅里叶变换.利用全息方法通过一次曝光制作出多焦点的全息透镜,分析了用此全息元件实现这种变换的条件,并在实验上实现了多重谱分数傅里叶变换. 实验结果表明这种变换方法简便可行,可广泛应用于多通道光学信息处理系统及多目标图像识别系统中.     

Design optimization for dynamic response of vibration mechanical system with uncertain parameters using convex model

The concept of uncertainty plays an important role in the design of practical mechanical system. The most common methods for solving uncertainty problems are to model the parameters as a random vector. A natural way to handle the randomness is to admit that a given probability density function represents the uncertainty distribution. However, the drawback of this approach is that the probability distribution is difficult to obtain. In this paper, we use the non-probabilistic convex model to deal with the uncertain parameters in which there is no need for probability density functions. Using the convex model theory, a new method to optimize the dynamic response of mechanical system with uncertain parameters is derived. Because the uncertain parameters can be selected as the optimization parameters, the present method can provide more information about the optimization results than those obtained by the deterministic optimization. The present method is implemented for a torsional vibration system. The numerical results show that the method is effective.     

Frequency response design of uncertain systems using performance indices and meta-models

Systems that are operated near their resonance frequencies experience vibrations that can lead to impaired performance, overstressing, fatigue fracture and adverse human reactions. Frequency response (FR) analysis can be invoked to mitigate the effects. When components of a system are described by random variables, modal frequencies and modal shapes, or, amplitudes and phases, are also random variables and the frequency response (FR) design of the system becomes more complex since it requires the solution of a frequency-variant probability problem. This paper presents a methodology to provide the frequency response design of uncertain systems using a transfer function approach. The methodology is found to be robust, expandable and flexible and can be applied to multi-disciplinary systems with n-dof and multiple design constraints. The novelty of the approach is the creation of a frequency-invariant probability problem through: (a) the discretization of the frequency band of interest into multiple contiguous point frequencies, (b) the introduction of new performance indices that measure the probability of success over the entire frequency band, and (c) the introduction of explicit meta-models to provide sufficiently fast probability evaluations through Monte Carlo simulation. The key to the performance indices are limit-state functions formed at all discrete, contiguous, frequencies. Each limit-state function establishes a conformance region in terms of the random design variables. The probabilities of the conformance regions are correctly combined to provide a single series-system index to be maximized by adjusting distribution parameters. The simple explicit meta-model is based on Kriging and performance measures at arbitrary design sets are efficiently calculated. Error analysis suggests ways to predict and control the errors with regards to meta-model fitting and probability calculations and so the method appears sufficiently accurate for engineering applications. The proposed methodology has applications in numerous areas such as electrical filters and structural mechanics – all with n-dof and multiple responses. The Performance indices can be evaluated at any frequency over any number of frequency ranges. A case study of a vibration absorber mechanism shows how the new methodology provides an improved and timely design with controllable accuracy when compared with previous proposals that employed modal frequencies.     

Information Geometric Theory in the Prediction of Abrupt Changes in System Dynamics

Detection and measurement of abrupt changes in a process can provide us with important tools for decision making in systems management. In particular, it can be utilised to predict the onset of a sudden event such as a rare, extreme event which causes the abrupt dynamical change in the system. Here, we investigate the prediction capability of information theory by focusing on how sensitive information-geometric theory (information length diagnostics) and entropy-based information theoretical method (information flow) are to abrupt changes. To this end, we utilise a non-autonomous Kramer equation by including a sudden perturbation to the system to mimic the onset of a sudden event and calculate time-dependent probability density functions (PDFs) and various statistical quantities with the help of numerical simulations. We show that information length diagnostics predict the onset of a sudden event better than the information flow. Furthermore, it is explicitly shown that the information flow like any other entropy-based measures has limitations in measuring perturbations which do not affect entropy.     

Ladderpath Approach: How Tinkering and Reuse Increase Complexity and Information

The notion of information and complexity are important concepts in many scientific fields such as molecular biology, evolutionary theory and exobiology. Many measures of these quantities are either difficult to compute, rely on the statistical notion of information, or can only be applied to strings. Based on assembly theory, we propose the notion of a ladderpath, which describes how an object can be decomposed into hierarchical structures using repetitive elements. From the ladderpath, two measures naturally emerge: the ladderpath-index and the order-index, which represent two axes of complexity. We show how the ladderpath approach can be applied to both strings and spatial patterns and argue that all systems that undergo evolution can be described as ladderpaths. Further, we discuss possible applications to human language and the origin of life. The ladderpath approach provides an alternative characterization of the information that is contained in a single object (or a system) and could aid in our understanding of evolving systems and the origin of life in particular.     

Control of Correlation Using Confinement in Case of Quantum System

This article investigates the behavior of a Moshinsky atom in a 1D harmonic trap. Focus is given on the theoretical foundations of confinement and its impact on the correlation between particles in the Moshinsky atom. The investigation begins by illustrating the (de)localization of the probability density function using Shannon entropy. The basics of correlation and interpretation of correlation using tools such as mutual information and statistical correlation coefficients and how these can be quantified are discussed. Then the concept of confinement is explored. The impact of interaction strength and confinement on Shannon entropy, statistical correlation coefficients, and mutual information is investigated. How interaction strength and confinement can be used to induce correlations between previously uncorrelated particles, as well as how they can be used to suppress correlations between previously correlated particles is discussed. Their implications for quantum information processing and quantum simulation are discussed. In conclusion, confinement is a powerful tool for controlling correlations in quantum systems, and its impact on correlation can be understood through theoretical models. The importance of experimental studies in this field, which provide insights into the behavior of quantum systems under confinement and pave the way for future applications in quantum technology is also emphasized.     

数字水印的鲁棒性评测模型

数字水印的鲁棒性是水印技术实用化的一个重要指标.与通过StirMark测试和各种仿真测试不同,定义互信息作为代价函数,建立水印系统鲁棒性描述和度量的一般模型.以扩频水印和量化水印为范例,推导出评测鲁棒性的互信息度量计算模型,并仿真分析了高斯噪声和JPEG压缩条件下互信息函数对鲁棒性的评估结果.实验以统计误比特率的方法计算图像DCT域中低频系数为载体的扩频水印误码率和一段音频数据三级小波细节系数为载体的量化水印误码率.互信息函数和误码率之间的匹配关系验证了互信息度量模型的有效性,互信息函数可以作为代价函数预测误码率的变化趋势. 关键词： 数字水印 鲁棒性 互信息 误码率     

Chemical reactions and fluctuations

Lattice systems with one species diffusion-reaction processes under local complete exclusion rules are studied analytically. We discuss a rigorously derived Fokker-Planck equation for a so-called pseudo-probability. This probability distribution depends on continuous variables in contrast to the original discrete master equation, and their stochastic dynamics may be interpreted as a substitute process which is completely equivalent to the original lattice dynamics. Especially, averages and correlation functions of the continuous variables are connected to corresponding lattice quantities by simple relations. Although the substitute process for diffusion-reaction systems with exclusion rules has some similarities to the well known substitute process for the same system without exclusion rules, their exist a set of remarkable differences. The given approach is not only valid for the discussed single species processes. We give sufficient arguments that arbitrary combinations of uni-molecular and bimolecular lattice reactions under complete local exclusions may be described in terms of our approach.     

Resilient mounting systems in buildings

The basic elements of resilient mounting systems are described and various measures for quantifying the effect of such systems defined. Using electrical analogue circuits, the calculation of these measures is illustrated. With special reference to resilient mounting systems in buildings, under specified assumptions, improved analogies for system elements are derived, thus arriving finally at a complete electrical analogy of a compound mounting system. Some results of computer calculations, as well as a greatly simplified method suitable for manual computation, are presented.The second section of the paper describes the application to practical problems of the approach developed in the first section.Data from present standards for maximum permissible noise and vibration levels are given in suitable form. Nomograms for calculation of the lowest eigenfrequency of concrete floor fields are also given.     

Covert non-orthogonal multiple access communication assisted by multi-antenna jamming

As the Internet of Things (IoT) becomes increasingly popular, the amount of information transmitted through the IoT network has increased significantly. Therefore, the privacy and security problem of the transmitted information has become a major area of focus. Motivated by this, this paper considers the covert communication based on non-orthogonal multiple access (NOMA), which consists of a transmitter, a legal user, a warden with power detection function and a multi-antenna jammer. To realize the covert communication between the transmitter and the legitimate user, the detection error probability of the warden is firstly derived, and then the optimal detection threshold and the minimum detection error probability (MDEP) are obtained. In addition, with the aim of designing this system, the average MDEP of the warden is calculated, and the closed form solution for the outage probability (OP) of the communication link is obtained. Then, a scheme is proposed to optimize the covertness of this system under the covertness constraint and interruption constraint, through which the maximum covert throughput of the system can be obtained. The simulated numerical results validate the theoretical analysis, and testify that: (i) the detection performance of the warden can be reduced by increasing the maximum jamming power of the jammer or reducing the transmitting power of the transmitter; (ii) by optimizing the power allocation factor, the maximum covert throughput of the system can be obtained under the premise of satisfying the covertness constraint and interruption condition; (iii) the proposed optimization scheme can enhance the covertness performance of this system.     

How fundamental is the character of thermal uncertainty relations?

We discuss here two different information measures of the Tsallis type, and their associated probability distributions, in order to repeat the Mandelbrot Cramer–Rao steps that lead to a thermal uncertainty relation for exponential distributions. We deal first with the original Tsallis measure and discuss afterwards a second entropic measure associated with the concept of escort distribution. In neither case it is possible to re-obtain a thermal uncertainty relationship. We conclude therefore that the thermal uncertainty, as derived from the Cramer–Rao inequality, cannot be as fundamental as the quantum one.     

Error Performance of Amplitude Shift Keying-Type Asymmetric Quantum Communication Systems

We propose an amplitude shift keying-type asymmetric quantum communication (AQC) system that uses an entangled state. As a first step toward development of this system, we evaluated and considered the communication performance of the proposed receiver when applied to the AQC system using a two-mode squeezed vacuum state (TSVS), the maximum quasi-Bell state, and the non-maximum quasi-Bell state, along with an asymmetric classical communication (ACC) system using the coherent state. Specifically, we derived an analytical expression for the error probability of the AQC system using the quasi-Bell state. Comparison of the error probabilities of the ACC system and the AQC systems when using the TSVS and the quasi-Bell state shows that the AQC system using the quasi-Bell state offers a clear performance advantage under specific conditions. Additionally, it was clarified that there are cases where the universal lower bound on the error probability for the AQC system was almost achieved when using the quasi-Bell state, unlike the case in which the TSVS was used.