Multidimensional large deviation local limit theorems

An earlier paper by the author ([4], 97–114) established large deviation local limit theorems for arbitrary sequences of real valued random variables. This work showed clearly the connection between the Cramér series and large deviation rates. In this article we present large deviation local limit theorems for arbitrary multidimensional random variables based solely on conditions imposed on their moment generating functions. These results generalize the theorems of [12], 100–106) for sums of independent and identically distributed random vectors.     

Large deviations from the hydrodynamical limit for a system of independent brownian particles

A large deviation principle for the hydrodynamical limit of independent Brownian motion is proved and an explicit expression of the rate function is given.     

Large deviation approach to non equilibrium processes in stochastic lattice gases

We present a review of recent work on the statistical mechanics of non equilibrium processes based on the analysis of large deviations properties of microscopic systems. Stochastic lattice gases are non trivial models of such phenomena and can be studied rigorously providing a source of challenging mathematical problems. In this way, some principles of wide validity have been obtained leading to interesting physical consequences.     

Integro-local theorems for sums of independent random vectors in the series scheme

Let S(n) = ξ(1)+?+ξ(n) be a sum of independent random vectors ξ(i) = ξ _(n)(i) with general distribution depending on a parameter n. We find sufficient conditions for the uniform version of the integro-local Stone theorem to hold for the asymptotics of the probability P(S(n) ∈ Δ[x), where Δ[x) is a cube with edge Δ and vertex at a point x.     

Limit Theorems for Multiplicative Processes

Let W be a non-negative random variable with EW=1, and let {W _i } be a family of independent copies of W, indexed by all the finite sequences i=i ₁i _n of positive integers. For fixed r and n the random multiplicative measure ⁿ _r has, on each r-adic interval at nth level, the density with respect to the Lebesgue measure on [0,1]. If EW log Wr, the sequence { ⁿ _r } _n converges a.s. weakly to the Mandelbrot measure _r . For each fixed 1n, we study asymptotic properties for the sequence of random measures { ⁿ _r } _r as r. We prove uniform laws of large numbers, functional central limit theorems, a functional law of iterated logarithm, and large deviation principles. The function-indexed processes is a natural extension to a tree-indexed process at nth level of the usual smoothed partial-sum process corresponding to n=1. The results extend the classical ones for { ¹ _r } _r , and the recent ones for the masses of { _r } _r established in Ref. 23.     

Multicriteria–multistage planning for the optimal path selection using hybrid genetic algorithms

The problem of the competence set expansion involves determining the optimal expansion path under the minimum cost and time. As we know, the conventional competence set model only considers the problems of the static situation and the single objective. However, the dynamic situation and the multicriteria should also be simultaneously considered in practice. In this paper, a multicriteria and multistage competence set model is proposed. In order to efficiently obtain an optimal expansion path, hybrid genetic algorithms (HGA) are employed. In addition, a numerical example is used to demonstrate the proposed method. On the basis of the numerical results, we can conclude that the proposed method can provide a sound competence set model by simultaneously considering the multicriteria and multistage situations.     

Toward routine billion‐variable optimization using genetic algorithms

The push for better understanding and design of complex systems requires the solution of challenging optimization problems with large numbers of decision variables. This note presents principled results demonstrating the scalable solution of a difficult test function on instances over a billion variables using a parallel implementation of a genetic algorithm (GA). The problem addressed is a noisy, blind problem over a vector of binary decision variables. Noise is added equaling a tenth of the deterministic objective function variance of the problem, thereby making it difficult for simple hillclimbers to find the optimal solution. The genetic algorithm used—the compact GA—is able to find the optimum in the presence of noise quickly, reliably, and accurately, and the solution scalability follows known convergence theories. These results on noisy problem together with other results on problems involving varying modularity, hierarchy, and overlap foreshadow routine solution of billion‐variable problems across the landscape of complexity science. © 2007 Wiley Periodicals, Inc. Complexity 12: 27–29, 2007     

Stock timing using genetic algorithms

In this paper, a genetic algorithm to search a set of technical trading rules which gives buying and selling advices about individual stocks is proposed. This approach is tested out of a sample of 24 French stocks among the most important stocks traded on the French market. We show that in most cases, the method outperforms a simple buy and hold strategy. However, we also illustrate the fact that the near‐optimal set of rules varies through time and across stocks. Copyright © 2002 John Wiley & Sons, Ltd.     

Global and local real-coded genetic algorithms based on parent-centric crossover operators

Parent-centric real-parameter crossover operators create the offspring in the neighbourhood of one of the parents, the female parent. The other parent, the male one, defines the range of the neighbourhood. With the aim of improving the behaviour of these crossover operators, we present three processes that are performed before their application. First, a female and male differentiation process determines the individuals in the population that may become female or/and male parents. Then, two different selection mechanisms choose the female and male parents from each group. In addition, we tackle the election of the most adequate evolution model to take out profit from these parent selection mechanisms. The experimental results confirm that these three processes may enhance the operation of the parent-centric crossover operators.     

Limit theorems for inverse process <Emphasis Type="Italic">T</Emphasis><Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> of Hawkes process

We consider linear Hawkes process N _t and its inverse process T _n . The limit theorems for N _t are well known and studied by many authors. In this paper, we study the limit theorems for T _n . In particular, we investigate the law of large numbers, the central limit theorem and the large deviation principle for T _n . The main tool of the proof is based on immigration-birth representation and the observations on the relation between N _t and T _n .     

Moderate deviations from the hydrodynamic limit of the symmetric exclusion process

We investigate the moderate deviations from the hydrodynamic limit of the empirical density ofparticles and obtain a moderate deviation principle for a symmetric exclusion process.     

On the controllability of predator-prey systems

In this paper, we obtain both global and local controllability results for a general nonautonomous predator-prey system using some techniques of nonlinear functional analysis such as the Schauder fixed-point theorem and contraction mapping principle.The first author would like to thank the Department of Science and Technology of India for sponsoring part of this work through Grant No. DST 12(21)/84-STP II.     

On genetic algorithms for the packing of polygons

A genetic algorithm for placing polygons on a rectangular board is proposed. The algorithm is improved by combination with deterministic methods.     

On the Pyatetskii-Shapiro Criterion of Normality

In this paper, the Postnikov--Pyatetskii-Shapiro criterion of normality is given a more modern form. We obtain its unimprovable analogs for finite Markov chains, continued fractions, and generalized Bernoulli shifts.     

On the Detection of Limit Cycles by the Variational Velocity Method

This paper summarizes, clarifies, and corrects some aspects of the variational velocity methodfor the detection of limit cycles. After definitions and statements of the most important theoremsassociated with this method, some aspects of the proof of the main theorem are corrected andreworked. An example from the original paper in Acta Appl. Math. 48 (1997),13–32, is then discussed and criticized. Finally, the limitations of this method are discussed,especially as it applies to systems involving multiple limit cycles (and therefore as it applies toHilberts XVIth Problem).     

利用遗传算法求一类非线性规划的最优解

针对一类非线性规则问题（Nonlinear Programming Problem)，采用遗传算法思想设计求解算法，实例表明，该遗传算法具有较高的计算效率。     

Improving crossover operator for real-coded genetic algorithms using virtual parents

The crossover operator is the most innovative and relevant operator in real-coded genetic algorithms. In this work we propose a new strategy to improve the performance of this operator by the creation of virtual parents obtained from the population parameters of localisation and dispersion of the best individuals. The idea consists of mating these virtual parents with individuals of the population. In this way, the offspring are created in the most promising regions. This strategy has been incorporated into several crossover operators. After analysing the results we can conclude that this strategy significantly improves the performance of the algorithm in most problems analysed.     

A learning process for fuzzy control rules using genetic algorithms

The purpose of this paper is to present a genetic learning process for learning fuzzy control rules from examples. It is developed in three stages: the first one is a fuzzy rule genetic generating process based on a rule learning iterative approach, the second one combines two kinds of rules, experts rules if there are and the previously generated fuzzy control rules, removing the redundant fuzzy rules, and the thrid one is a tuning process for adjusting the membership functions of the fuzzy rules. The three components of the learning process are developed formulating suitable genetic algorithms.     

Convergence behavior of decomposition algorithms for linear programs

This paper discusses plausible explanations of the somewhat folkloric, ‘tailing off’ convergence behavior of the Dantzig-Wolfe decomposition algorithm for linear programs. Is is argued that such beahvior may be used to numerical inaccuracy. Procedures to identify and mitigate such difficulties are outlined.     

ARMA model order and parameter estimation using genetic algorithms

A new method for simultaneously determining the order and the parameters of autoregressive moving average (ARMA) models is presented in this article. Given an ARMA (p, q) model in the absence of any information for the order, the correct order of the model (p, q) as well as the correct parameters will be simultaneously determined using genetic algorithms (GAs). These algorithms simply search the order and the parameter spaces to detect their correct values using the GA operators. The proposed method works on the principle of maximizing the GA fitness value relying on the deviation between the actual plant output, with or without an additive noise, and the estimated plant output. Simulation results show in detail the efficiency of the proposed approach. In addition to that, a practical model identification and parameter estimation is conducted in this article with results obtained as desired. The new method is compared with other well-known methods for ARMA model order and parameter estimation.