Parallel Dynamics of Hopfield Network with Self-coupling Terms

The parallel dynamics of Hopfield network with self-coupling terms is calculated by an analytical approach with probability theory. The explicit formulas obtained for the first two steps of evolu tion of main overlap are in good agreement with computer simulations.     

Stochastic Symmetry-Breaking in a Gaussian Hopfield Model

We study a two-pattern Hopfield model with Gaussian disorder. We find that there are infinitely many pure states at low temperatures in this model, and that the metastate is supported on an infinity of symmetric pairs of pure states. The origin of this phenomenon is the random breaking of a rotation symmetry of the distribution of the disorder variables.     

Determination of Domain of Attraction by Short-Time Overlap Dynamics in Neural Networks

Since the overlap dynamics of spin-glass-like neural network is solely governed by such two parameters, the symmetry of the net's connections and the stabilities of the embedded patterns, we propose that the domain of attraction of a network could be determined by a short-time (at least the first two-step) dynamics, in which both parameters begin to be visible.The first step overlap dynamics Q calculated by probability theory and the second step overlap dynamics for pseudo-inverse-model is obtained by extended Krauth's theory. The calculated domain of attraction for this model is in good agreement with the results obtained by computer simulation.     

Distribution of Overlap Profiles in the One-Dimensional Kac--Hopfield Model

We study a one-dimensional version of the Hopfield model with long, but finite range interactions below the critical temperature. In the thermodynamic limit we obtain large deviation estimates for the distribution of the “local” overlaps, the range of the interaction, , being the large parameter. We show in particular that the local overlaps in a typical Gibbs configuration are constant and equal to one of the mean-field equilibrium values on a scale . We also give estimates on the size of typical “jumps”, i.e. the regions where transitions from one equilibrium value to another take place. Contrary to the situation in the ferromagnetic Kac-model, the structure of the profiles is found to be governed by the quenched disorder rather than by entropy. Received: 14 February 1996 / Accepted: 30 September 1996     

A Hopfield Neural Network Model in a Transverse Field

A Hopfield model with transverse fields that induce tunneling among neurons is presented. A set of equations for the order parameters describing retrieval and spin glass phases of Hopfield model in a transverse field are obtained without using the tedious replica method, and the memory storage capacity of networks is andysed as a function of the temperatureand transverse field.     

On the Critical Capacity of the Hopfield Model

We estimate the critical capacity of the zero-temperature Hopfield model by using a novel and rigorous method. The probability of having a stable fixed point is one when α≤ 0.113 for a large number of neurons. This result is an advance on all rigorous results in the literature and the relationship between the capacity α and retrieval errors obtained here for small α coincides with replica calculation results. Received: 1 December 1999 / Accepted: 21 July 2000     

Metastates in the Hopfield Model in the Replica Symmetric Regime

We study the finite dimensional marginals of the Gibbs measure in the Hopfield model at low temperature when the number of patterns, M, is proportional to the volume with a sufficiently small proportionality constant > 0. It is shown that even when a single pattern is selected (by a magnetic field or by conditioning), the marginals do not converge almost surely, but only in law. The corresponding limiting law is constructed explicitly. We fit our result in the recently proposed language of metastates which we discuss some length. As a byproduct, in a certain regime of the parameters and (the inverse temperature), we also give a simple proof of Talagrands recent result that the replica symmetric solution found by Amit, Gutfreund, and Sompolinsky can be rigorously justified.     

Tricritical Points and Reentry in the Quantum Hopfield Neural-Network Model

We examine a quantum Hopfield neural-network model in the presence of trimodal random transverse fields and random neuronal thresholds within the method of statistical physics. We use the Trotter decomposition to map the problem into an equivalent classical random Hopfield-type Ising model and obtain phase transitions between the ferromagnetic retrieval and the paramagnetic phases. The influence of competition between the diluted random transverse fields and the diluted random thresholds on the system is discussed, and some interesting results such as tricritical points and reentrance are analyzed.     

基于矢量量化及Hopfield模型的灰度级图像识别

提出了一种新的识别灰度级图像的方法，该方法基于矢量量化的基本思想，通过对图像的分割，将灰度级图像映射成神经元仅取少数和几种状态的Ｈｏｐｆｉｅｌｄ神经网络模型，理论和模拟实验证明：这种低状态的ｏｐｆｉｅｌｄ与传统灰度图像识别模型相比，不仅神经元的数目较少，互连密度较低，而且网络具有较好的联想能力。     

Stochastic Model of Microtubule Dynamics

We introduce a continuous time stochastic process on strings made of two types of particle, whose dynamics mimics that of microtubules in a living cell. The long term behaviour of the system is described in terms of the velocity v of the string end. We show that v is an analytic function of its parameters and study its monotonicity properties. We give a complete characterisation of the phase diagram of the model and derive several criteria of the growth (\(v>0\)) and the shrinking (\(v<0\)) regimes of the dynamics.     

Friction in a Model of Hamiltonian Dynamics

We study the motion of a heavy tracer particle weakly coupled to a dense ideal Bose gas exhibiting Bose-Einstein condensation. In the so-called mean-field limit, the dynamics of this system approaches one determined by nonlinear Hamiltonian evolution equations describing a process of emission of Cerenkov radiation of sound waves into the Bose-Einstein condensate along the particle’s trajectory. The emission of Cerenkov radiation results in a friction force with memory acting on the tracer particle and causing it to decelerate until it comes to rest.

“A moving body will come to rest as soon as the force pushing it no longer acts on it in the manner necessary for its propulsion.”—— Aristotle     

Overlap in odd dimensions

In odd dimensions the lattice overlap formalism is simpler than in even dimensions. Masslessness of fermions can still be preserved without fine tuning and gauge invariance without gauge averaging can be maintained, although, sometimes, only at the expense of parity invariance. When parity invariance is enforced invariance under small gauge transformations can be maintained and continuum global gauge anomalies are reproduced.     

Spectator Model Dynamics in a Leakage Cavity

A spectator system in an atoms-cavity QED model is investigated. The subsystem initial state is prepared as one of the Bell states or one mixed state. It is shown that （i） the dynamics of Bell states are independent on the initial states; （ii） the concurrence dynamics can be engineered by a controlling light field.     

基于冲击力模型的分子马达动力学分析

从分子马达输运特点和实验现象出发,建立满足朗之万方程的冲击力模型,分析分子马达定向输运的动力学行为.研究发现:在合适的冲击力和噪声强度的共同作用下,分子马达可以稳定的梯跳跃迁运动和有效的输运;分子马达在轨运动的方向由冲击力的方向决定;另外,虽然在不同的噪声强度时平均速度都不为零,但是整个分子马达系综的高效输运对噪声强度有一定的选择性;系综的平均速度随着负载力的增大而减小,甚至会产生反方向的运动.     

Coarsening Dynamics in a Simplified DNLS Model

We investigate the coarsening evolution occurring in a simplified stochastic model of the Discrete NonLinear Schrödinger (DNLS) equation in the so-called negative-temperature region. We provide an explanation of the coarsening exponent n=1/3, by invoking an analogy with a suitable exclusion process. In spite of the equivalence with the exponent observed in other known universality classes, this model is certainly different, in that it refers to a dynamics with two conservation laws.     

Interest-Driven Model for Human Dynamics

Empirical observations indicate that the interevent time distribution of human actions exhibits heavy-tailed features. The queuing model based on task priorities is to some extent successful in explaining the origin of such heavy tails, however, it cannot explain all the temporal statistics of human behavior especially for the daily entertainments. We propose an interest-driven model, which can reproduce the power-law distribution of interevent time. The exponent can be analytically obtained and is in good accordance with the simulations. This model well explains the observed relationship between activities and power-law exponents, as reported recently for web-based behavior and the instant message communications.     

Dynamics of the Driven Jaynes-Cummings Model

We study the dynamical features of the Jaynes-Cummings model with the atomdriven by an external classical field in the case that the cavity field is initially in a Fock state.We find the dynamical variables by using dressed states in the bare atom representation. Weshow that the dynamical behavior of the cavity field can be strongly modified by the externalclassical field. We also find that the cavity field is super-Poissonian after some interaction timeif the external field is strong enough.     

多量子位Heisenberg模型中纠缠的时间演化特性

研究了多量子位Heisenberg模型中纠缠的时间演化特性, 并给出了平均纠缠度〈C〉和多体纠缠度Q的解析表达式. 结果发现无论是对〈C〉还是对Q随着时间t的不断增长, 它们均先线性的增大, 而后达到一近似稳定状态, 并绕一平衡值做无规则的上下震荡. 若进一步考察N〈C〉则还可以发现, 纠缠上下震荡的平衡值与Heisenberg链的长度几乎无关, 而仅由它们的次近邻耦合常数J决定.