Spin Structure of Quantum Transport Theory

Relativistic quantum transport theory is investigated in the Nambu-Jona-Lasinio model. The spin structure of the kinetic equations is systematically analyzed. The covariant transport and constraint equations are derived in a matrix form in the spin space.     

Maximum entropy approach to statistical inference for an ocean acoustic waveguide

A conditional probability distribution suitable for estimating the statistical properties of ocean seabed parameter values inferred from acoustic measurements is derived from a maximum entropy principle. The specification of the expectation value for an error function constrains the maximization of an entropy functional. This constraint determines the sensitivity factor (β) to the error function of the resulting probability distribution, which is a canonical form that provides a conservative estimate of the uncertainty of the parameter values. From the conditional distribution, marginal distributions for individual parameters can be determined from integration over the other parameters. The approach is an alternative to obtaining the posterior probability distribution without an intermediary determination of the likelihood function followed by an application of Bayes' rule. In this paper the expectation value that specifies the constraint is determined from the values of the error function for the model solutions obtained from a sparse number of data samples. The method is applied to ocean acoustic measurements taken on the New Jersey continental shelf. The marginal probability distribution for the values of the sound speed ratio at the surface of the seabed and the source levels of a towed source are examined for different geoacoustic model representations.     

Modularity functions maximization with nonnegative relaxation facilitates community detection in networks

We show here that the problem of maximizing a family of quantitative functions, encompassing both the modularity (Q-measure) and modularity density (D-measure), for community detection can be uniformly understood as a combinatoric optimization involving the trace of a matrix called modularity Laplacian. Instead of using traditional spectral relaxation, we apply additional nonnegative constraint into this graph clustering problem and design efficient algorithms to optimize the new objective. With the explicit nonnegative constraint, our solutions are very close to the ideal community indicator matrix and can directly assign nodes into communities. The near-orthogonal columns of the solution can be reformulated as the posterior probability of corresponding node belonging to each community. Therefore, the proposed method can be exploited to identify the fuzzy or overlapping communities and thus facilitates the understanding of the intrinsic structure of networks. Experimental results show that our new algorithm consistently, sometimes significantly, outperforms the traditional spectral relaxation approaches.     

Fisher information as the basis for Maxwell's equations

Maxwell's equations of classical electrodynamics may be derived on the following statistical basis. Consider a gedanken experiment whereby the mean space-time coordinate for photons in an electromagnetic field is to be determined by observation of one photon's space-time coordinate. An efficient (i.e. optimum) estimate obeys a condition of minimum Fisher information, or minimum precision, according to the second law of thermodynamics. The Fisher information I is a simple functional of the probability law governing space-time coordinates of the “particles” of the field. This probability law is modeled as the source-free Poynting energy flow density, i.e., the ordinary local intensity in the optical sense, or, the square of the four-vector potential. When the Fisher information is extremized subject to an additive constraint term in the total interaction energy, Maxwell's equations result.     

Distribution of proper delay times in quantum chaotic scattering: a crossover from ideal to weak coupling

The probability distribution of the proper delay times during scattering on a chaotic system is derived in the framework of the random matrix approach and the supersymmetry method. The result obtained is valid for an arbitrary number of scattering channels as well as arbitrary coupling to the energy continuum. The case of statistically equivalent channels is studied in detail. In particular, the semiclassical limit of an infinite number of weak channels is paid appreciable attention.     

Rigorous solution to a quantum statistical mechanical laser model

A quantum mechanical laser model with relaxation and pumping mechanisms is solved rigorously. A basic equation for the density matrix is derived by the damping theory and is transformed into a corresponding c-number equation for a (quasi-) probability density. This is done with the aid of the quantum phase space method. The probability density is expanded in terms of orthogonal polynomials. The expansion coefficients are solved to give a continued fraction. A complete solution is obtained, namely, time evolution of the probability density is determined as well as that for certain physical quantities. The solution is valid even for strong coupling between photons and atoms: it is free from restriction on system parameters. Detailed studies on dynamics are performed for typical values of the system parameters. This is a prototype of interacting quantum nonequilibrium systems. Relevance to systems other than a laser is briefly mentioned.     

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.     

气溶胶抛撒过程中首次破碎液滴的尺寸分布

对气溶胶爆炸抛撒过程中,首次破碎液滴的尺寸分布进行理论和数值研究.基于热力学第二定律的最大熵增理论,建立首次破碎过程满足的方程组约束条件,给出破碎后液滴尺寸分布的确定方法,并对Air-blast喷管实验和Samirant相关实验进行数值模拟预测,与实验数据符合较好.     

AN ALTERNATIVE APPROACH IN NUCLEAR DOUBLE BETA DECAY THEORY

A new formula as a series of commutators of two axial vector currents and the nuclear Hamiltonian H_S derived for estimating the 2β-decay nuclear matrix element without using explicitly the closure approximation. With a simple assumption of the nuclear wave function and the Hamiltonian H_S, it is shown that the leading term in 2υ-2β decay matrix element vanishes and thus the smallness of 2υ-2β decay probability seems to be understood.     

Robust matched-field processing using a coherent broadband white noise constraint processor

Adaptive matched-field processing (MFP) is not only very sensitive to mismatch, but also requires the received sound levels to exceed a threshold signal-to-noise ratio. Furthermore, acoustic sources and interferers have to move slowly enough across resolution cells so that a full rank cross-spectral density matrix can be constructed. Coherent-broadband MFP takes advantage of the temporal complexity of the signal, and therefore offers an additional gain over narrow-band processing by augmenting the dimension of the data space. However, the sensitivity to mismatch is also increased in the process, since a single constraint is usually not enough to achieve robustness and the snapshot requirement becomes even more problematic. The white noise constraint method, typically used for narrow-band processing, is applied to a previously derived broadband processor to enhance its robustness to environmental mismatch and snapshot deficiency. The broadband white noise constraint theory is presented and validated through simulation and experimental data. The dynamic range bias obtained from the snapshot-deficient processing is shown to be consistent with that previously presented in the literature for a single frequency.     

Evidence for a general template in central optimal processing for pitch of complex tones

Optimum processor theory successfully accounts for earlier pitch data by including the constraint that component tones in a complex stimulus are estimated as successive harmonics. This constraint gives the paradoxical prediction that a periodic complex tone comprising nonsuccessive harmonics cannot evoke periodicity pitch corresponding to its period. Most published data from pitch-shift experiments imply the necessity for this constraint. New periodicity pitch experiments on pitch shift and musical interval recognition were performed which prove that the theoretical constraint is not generally true. New and old data are reconciled by replacing the maximum likelihood estimation of the theory with maximum posterior probability estimation and removing the successive harmonic constraint. Periodicity pitch is estimated by optimizing the match between the aurally measured frequencies of stimulus components and a general harmonic template over some a priori expected pitch range. The new, more general, formulation reduces in many experimental situations to the successive harmonic constraint as a special case.     

An Integrable Symplectic Map of a Differential-Difference Hierarchy

By choosing a discrete matrix spectral problem, a hierarchy of integrable differential-difference equations is derived from the discrete zero curvature equation, and the Hamiltonian structures are built. Through a higher-order Bargmann symmetry constraint, the spatial part and the temporal part of the Lax pairs and adjoint Lax pairs, which we obtained are respectively nonlinearized into a new integrable symplectic map and a finite-dimensional integrable Hamiltonian system in Liouville sense.     

Macroscopic Time Evolution and MaxEnt Inference for Closed Systems with Hamiltonian Dynamics

MaxEnt inference algorithm and information theory are relevant for the time evolution of macroscopic systems considered as problem of incomplete information. Two different MaxEnt approaches are introduced in this work, both applied to prediction of time evolution for closed Hamiltonian systems. The first one is based on Liouville equation for the conditional probability distribution, introduced as a strict microscopic constraint on time evolution in phase space. The conditional probability distribution is defined for the set of microstates associated with the set of phase space paths determined by solutions of Hamilton’s equations. The MaxEnt inference algorithm with Shannon’s concept of the conditional information entropy is then applied to prediction, consistently with this strict microscopic constraint on time evolution in phase space. The second approach is based on the same concepts, with a difference that Liouville equation for the conditional probability distribution is introduced as a macroscopic constraint given by a phase space average. We consider the incomplete nature of our information about microscopic dynamics in a rational way that is consistent with Jaynes’ formulation of predictive statistical mechanics, and the concept of macroscopic reproducibility for time dependent processes. Maximization of the conditional information entropy subject to this macroscopic constraint leads to a loss of correlation between the initial phase space paths and final microstates. Information entropy is the theoretic upper bound on the conditional information entropy, with the upper bound attained only in case of the complete loss of correlation. In this alternative approach to prediction of macroscopic time evolution, maximization of the conditional information entropy is equivalent to the loss of statistical correlation, and leads to corresponding loss of information. In accordance with the original idea of Jaynes, irreversibility appears as a consequence of gradual loss of information about possible microstates of the system.     

Hénon混沌系统的自适应广义预测控制快速算法

提出了一种带有约束矩阵的Hénon 混沌系统的广义预测控制快速算法,首先用带有遗忘因子的递推最小二乘参数辨识法来逼近混沌系统,然后该算法引入了一种约束矩阵,约束矩阵的引入避免了矩阵求逆的计算,占用内存小,计算速度快,并且具有较强的跟踪给定信号和抑制系统参数摄动和随机噪声的能力.仿真结果验证了该方法的有效性. 关键词： 广义预测控制 约束矩阵 Hénon混沌系统 参数辨识     

New ways of deriving Arnowitt—Deser—Misner constraint equations in four—dimensional gravity

In this paper,the Arnowitt-Deser-Misner (ADM) constraint equations are naturally derived in two different ways.One method is to construct a one-parametric gravitational action in the Lorentzian spacetime.Hence,the oneparametric ADM constraint equations can be obtained.The other method is to apply the double complex function method to Einstein-Hilbert gravitational fields in Hamiltonian formulation,Therefore the double ADM constraint equations can be obtained,in which the well-known ADM constraint equations are included as a special case.     

Asymptotics of harmonic microwave mixing in a sinusoidal potential

Analytic asymtotic results are derived for the harmonic microwave mixing voltage due to a stochastic charged particle trapped in the potential thoughs of a sinusoidal pinning potential. The time averaged probability distribution of the corresponding Smoluchowski equation is evaluated from a matrix continued fraction. The problem can be solved by Bessel functions with a field strength matrix appearing in the order index. It is found that the harmonic mixing voltage saturates at a finite value depending only on the microwave field strengths when the potential troughs become very deep compared to thermal energy.     

Constrained adaptation for feedback cancellation in hearing aids.

In feedback cancellation in hearing aids, an adaptive filter is used to model the feedback path. The output of the adaptive filter is subtracted from the microphone signal to cancel the acoustic and mechanical feedback picked up by the microphone, thus allowing more gain in the hearing aid. In general, the feedback-cancellation filter adapts on the hearing-aid input signal, and signal cancellation and coloration artifacts can occur for a narrow-band input. In this paper, two procedures for LMS adaptation with a constraint on the magnitude of the adaptive weight vector are derived. The constraints greatly reduce the probability that the adaptive filter will cancel a narrow-band input. Simulation results are used to demonstrate the efficacy of the constrained adaptation.     

Optimal causal inference: estimating stored information and approximating causal architecture

We introduce an approach to inferring the causal architecture of stochastic dynamical systems that extends rate-distortion theory to use causal shielding--a natural principle of learning. We study two distinct cases of causal inference: optimal causal filtering and optimal causal estimation. Filtering corresponds to the ideal case in which the probability distribution of measurement sequences is known, giving a principled method to approximate a system's causal structure at a desired level of representation. We show that in the limit in which a model-complexity constraint is relaxed, filtering finds the exact causal architecture of a stochastic dynamical system, known as the causal-state partition. From this, one can estimate the amount of historical information the process stores. More generally, causal filtering finds a graded model-complexity hierarchy of approximations to the causal architecture. Abrupt changes in the hierarchy, as a function of approximation, capture distinct scales of structural organization. For nonideal cases with finite data, we show how the correct number of the underlying causal states can be found by optimal causal estimation. A previously derived model-complexity control term allows us to correct for the effect of statistical fluctuations in probability estimates and thereby avoid overfitting.     

Outer synchronization between two different fractional-order general complex dynamical networks

Outer synchronization between two different fractional-order general complex dynamical networks is investigated in this paper.Based on the stability theory of the fractional-order system,the sufficient criteria for outer synchronization are derived analytically by applying the nonlinear control and the bidirectional coupling methods.The proposed synchronization method is applicable to almost all kinds of coupled fractional-order general complex dynamical networks.Neither a symmetric nor irreducible coupling configuration matrix is required.In addition,no constraint is imposed on the inner-coupling matrix.Numerical examples are also provided to demonstrate the validity of the presented synchronization scheme.Numeric evidence shows that both the feedback strength k and the fractional order α can be chosen appropriately to adjust the synchronization effect effectively.     

Fluctuations and stability of stationary non-equilibrium systems in detailed balance

A generalized thermodynamic potential for Markoffian systems with detailed balance and far from thermal equilibrium has been derived in a previous paper. It was shown that the principle of detailed balance is equivalent to a set of conditions fulfilled by this potential (“potential conditions”). The properties of this potential allow us to extend the validity of a number of thermodynamic concepts well known for systems in or near thermal equilibrium to stationary states far from thermal equilibrium. The concept of symmetry breaking phase transitions for these systems is introduced in analogy to thermal equilibrium systems by considering the dependence of the stationary probability density of the system on a set of externally controlled parameters {λ}. A functional of the time dependent probability density of the system is defined in close analogy to the Gibb's definition of entropy. This functional has the properties of a Ljapunov functional of the governing Fokker-Planck equation showing the stability of the stationary probability density. The Langevin equations connected with the Fokker-Planck equation are considered. It is shown that, by means of the potential conditions, generalized “thermodynamic” fluxes and forces may be defined in such a way that the smoothly varying part of the Langevin equations (kinetic equations) constitutes a linear relation between fluxes and forces. The matrix of coefficients is given by the diffusion matrix of the Fokker-Planck equation. The symmetry relations which hold for this matrix due to the potential conditions then lead to the Onsager-Casimir symmetry relations extended to systems with detailed balance near stationary states far from thermal equilibrium. Finally it is shown that under certain additional assumptions the generalized thermodynamic potential may be used as a Ljapunov function of the kinetic equations.