Feedback controlled periodic states for different kinds of photorefractive nonlinear response

We investigate analytically and numerically the influence of the type of the photorefractive nonlinear response on the periodic states (attractors) which occur during feedback controlled 2W-coupling and correspond to almost 100% diffraction efficiency of the dynamic index grating. In addition to the case of the local response typical, for example, for LiNbO₃ crystals we consider the cases of nonlocal (diffusive) response (BaTiO₃, SBN) and resonant response (DC-biased BSO, BTO, and BGO crystals). It is shown that the conditions for the transition to the periodic states and their apparent characteristics are strongly different for the two limiting cases above. Received 16 July 2002 / Received in final form 29 October 2002 Published online 4 March 2003     

Interior point methods 25 years later

Interior point methods for optimization have been around for more than 25 years now. Their presence has shaken up the field of optimization. Interior point methods for linear and (convex) quadratic programming display several features which make them particularly attractive for very large scale optimization. Among the most impressive of them are their low-degree polynomial worst-case complexity and an unrivalled ability to deliver optimal solutions in an almost constant number of iterations which depends very little, if at all, on the problem dimension. Interior point methods are competitive when dealing with small problems of dimensions below one million constraints and variables and are beyond competition when applied to large problems of dimensions going into millions of constraints and variables.In this survey we will discuss several issues related to interior point methods including the proof of the worst-case complexity result, the reasons for their amazingly fast practical convergence and the features responsible for their ability to solve very large problems. The ever-growing sizes of optimization problems impose new requirements on optimization methods and software. In the final part of this paper we will therefore address a redesign of interior point methods to allow them to work in a matrix-free regime and to make them well-suited to solving even larger problems.     

无原子布氏代数理论的计算复杂性

研究无原子布氏代数的计算复杂性 .得到了下面的新定理 :定理 1　无原子布氏代数理论Δ具有完全的量词消去法 ,也就是说每一个式子都Δ等价于一个开式子 .定理 2　无原子布氏代数的初等型Γ (x1,… ,xn)是由型内的不含量词的全体开式子所唯一决定 .定理 3　无原子布氏代数的一个长度为 n的语句的判断过程所消耗的 Turing时间和空间都是属于 2 2 cn指数级 .     

求鳞状因子循环矩阵的逆阵及广义逆阵的快速付氏变换法

借助快速付立叶变换(FFT),本文给出一种求n阶鳞状因子循环矩阵的逆阵、自反g-逆、群逆、Moore-Penrose逆的快速算法,该算法的计算复杂性为O(nlog2n),最后给出的两个数值算例表明了该算法的有效性.     

Easy and hard instances of arc ranking in directed graphs

In this paper we deal with the arc ranking problem of directed graphs. We give some classes of graphs for which the arc ranking problem is polynomially solvable. We prove that deciding whether , where G is an acyclic orientation of a 3-partite graph is an NP-complete problem. In this way we answer an open question stated by Kratochvil and Tuza in 1999.     

Spatiotemporal and statistical symmetries

The notion of symmetries, either statistical or deterministic, can be useful for the characterization of complex systems and their bifurcations. In this paper, we investigate the connection between the (microscopic) spatiotemporal symmetries of a space-time functionu(x, t), on the one hand, and the (macroscopic) symmetries of statistical quantities such as the spatial (resp. temporal) two-point correlations and the spatial (resp. temporal) average, on the other hand. We show, how, under certain conditions, these symmetries are related to the symmetries of the orbits described byu(x, t) in the characteristic (phase) spaces. We also determine the largest group of spatiotemporal symmetries (in the sense introduced in our earlier work) satisfied by a given space-time functionu(x, t) and indicate how to extract the subgroups of point symmetries, namely those directly implemented on the space and time variables. Conversely, we determine all the functions invariant by a given space-time symmetry group. Finally, we illustrate all the previous points with specific examples.     

A physical organic mechanistic approach to understanding the complex reaction network of hemostasis (blood clotting)

This review focuses on how the mechanistic approach of physical organic chemistry can be used to elucidate the mechanisms behind complex biochemical networks. The dynamics of biochemical reaction networks is difficult to describe by considering their individual reactions, just as the dynamics of organic reactions is difficult to describe by considering individual electrons and atomic nuclei. Physical organic chemists have developed a useful set of tools to predict the outcome of organic reactions by separating the interacting molecules into modules (functional groups), and defining general rules for how these modules interact (mechanisms). This review shows how these tools of physical organic chemistry may be used to describe reaction networks. In addition, it describes the application of these tools to develop a mechanistic understanding of the dynamics of the complex network of hemostasis, which regulates blood clotting. Copyright © 2007 John Wiley & Sons, Ltd.     

Spin-glass energy landscape

We consider a nearest-neighbor-interaction ±J Ising spin glass in a square lattice. Inspired by natural evolution, we design a dynamic rule that includesselection, randomness, andmultibranch exploration. Following this rule, we succeed in walking along the space of states between local energy maxima and minima alternately. During the walk, we store various information about the spin states corresponding to these minima and maxima for later statistical analysis. In particular, we plot a histogram displaying how many times each minimum (or maximum) energy is visited as a function of the corresponding density value. Through finite-size scaling analysis, we conclude that a nonvanishing fraction of bonds remains unsatisfied (satisfied) at these energy minimum (maximum) states in the thermodynamic limit. This fraction measures the degree of unavoidable frustration of the system. Also in this limit, the width of these histograms vanishes, meaning that almost all metastable states occur at the same energy density value, with no dispersion.     

伽罗瓦环上的一类No序列的构造

近年来,伽罗瓦环上的序列理论成为人们研究的热点问题.有限域上的No序列是一类伪随机序列,它在序列密码中占具十分重要的角色.本文利用伽罗瓦环上的置换,构造了伽罗瓦环Z_(p~e)上的一类新的No序列,并且研究了其线性复杂度.研究的结果表明此类No序列具有相当大的线性复杂度.