Combined random number generator via the generalized Chinese remainder theorem

The combined random number (RN) generator has been considered by many scholars as a good RN generator. One promising type of combined RN generator, recommended by L'Ecuyer (Oper. Res. 44 (1996) 816; 47 (1999) 159), is the combined multiple recursive generator (MRG). This paper analyzes the combined MRG via the Chinese remainder theorem. A new combined generator based on the generalized Chinese remainder theorem and on the Ore algorithm (Amer. Math. Monthly 59 (1952) 365) is presented. The proposed combined generator improves the combined MRG in terms of both the suitability for various types of RN generators and the restriction on the moduli of the individual generators. Therefore, the proposed combined generator is an ideal RN generator and is most recommended.     

倒向随机微分方程中生成元g的经济含义

将倒向随机微分方程看作金融市场中的一个定价机制,而该机制具体体现就是生成元g.本文通过经典的Black-Scholes模型探讨了生成元g的经济含义,首次提出了生成元g的表达式中含有折现的概念,同时详细分析并说明了不同的生成元g可以反应同一未定权益价格过程的不同形态.最后结合上面的讨论给出了关于一定形式的生成元g的类Jensen不等式性质.     

关于广义“缩减生成器”的概率模型

本文建立了以2值密钥流“缩减生成器”为特例的广义“缩减生成器”的概率模型,研究了它们的输出序列的概率性质,特别得到了其输出序列和原输入序列之间的符合率的表达式,据此可从概率论的角度对此类生成器的性能和得失进行分析.     

Generator,multiquadric generator,quasi-interpolation and multiquadric quasi-interpolation

The aim of this survey paper is to propose a new concept “generator”. In fact, generator is a single function that can generate the basis as well as the whole function space. It is a more fundamental concept than basis. Various properties of generator are also discussed. Moreover, a special generator named multiquadric function is introduced. Based on the multiquadric generator, the multiquadric quasi-interpolation scheme is constructed, and furthermore, the properties of this kind of quasi-interpolation are discussed to show its better capacity and stability in approximating the high order derivatives.     

Pseudorandom sequences constructed by the power generator

Summary We study the pseudorandom properties of the power generator (which includes as special cases the RSA generator and the Blum--Blum--Shub generator). In order to estimate the pseudorandom measures character sums with exponential functions are used.     

Local bases for refinable spaces

We provide a new representation of a refinable shift invariant space with a compactly supported generator, in terms of functions with a special property of homogeneity. In particular, these functions include all the homogeneous polynomials that are reproducible by the generator, which links this representation to the accuracy of the space. We completely characterize the class of homogeneous functions in the space and show that they can reproduce the generator. As a result we conclude that the homogeneous functions can be constructed from the vectors associated to the spectrum of the scale matrix (a finite square matrix with entries from the mask of the generator). Furthermore, we prove that the kernel of the transition operator has the same dimension as the kernel of this finite matrix. This relation provides an easy test for the linear independence of the integer translates of the generator. This could be potentially useful in applications to approximation theory, wavelet theory and sampling.

     

Scatter Search for the 0–1 Multidimensional Knapsack Problem

The evolutionary metaheuristic called scatter search has been applied successfully to optimization problems for several years. In this paper, we apply the scatter search technique to the well-known 0–1 multidimensional knapsack problem. We propose a new relaxation-based diversification generator, which produces an initial population with elite solutions. The computational results obtained for a set of classic and correlated instances clearly show that (1) this generator can also be used as a heuristic for solving the multidimensional knapsack problem; (2) using the population produced by our generator as a starting point for the scatter search algorithm leads to better performance. We also enhance the scatter search algorithm by integrating memory and by using adapted intensification phases. Overall, the results are interesting and competitive compared to other population-based algorithms, such as genetic algorithms.      

More efficient DDH pseudorandom generators

In this paper, we first show a DDH Lemma, which states that a multi-variable version of the decisional Diffie–Hellman problem is hard under the standard DDH assumption, where the group size is not necessarily known. Our proof, based on a self-reducibility technique, has a small reduction complexity. Using DDH Lemma, we extend the FSS pseudorandom generator of Farashahi et al. to a new one. The new generator is almost twice faster than FSS while still provably secure under the DDH assumption. Using the similar technique for the RSA modulus, we improve the Goldreich–Rosen generator. The new generator is provably secure under the factoring assumption and DDH assumption over \mathbbZ_N^*{\mathbb{Z}_N^*}. Evidently, to achieve the same security level, different generators may have different security parameters (e.g., distinct length of modulus). We compare our generators with other generators under the same security level. For simplicity, we make comparisons without any pre-computation. As a result, our first generator is the most efficient among all generators that are provably secure under standard assumptions. It has the similar efficiency as Gennaro generator, where the latter is proven secure under a non-standard assumption. Our second generator is more efficient than Goldreich–Rosen generator.     

Code generator matrices as RNG conditioners

We quantify precisely the distribution of the output of a binary random number generator (RNG) after conditioning with a binary linear code generator matrix by showing the connection between the Walsh spectrum of the resulting random variable and the weight distribution of the code. Previously known bounds on the performance of linear binary codes as entropy extractors can be derived by considering generator matrices as a selector of a subset of that spectrum. We also extend this framework to the case of non-binary codes.     

A GENERATOR AND A SIMPLEX SOLVER FOR NETWORK PIECEWISE LINEAR PROGRAMS

ＡＧＥＮＥＲＡＴＯＲＡＮＤＡＳＩＭＰＬＥＸＳＯＬＶＥＲＦＯＲＮＥＴＷＯＲＫＰＩＥＣＥＷＩＳＥＬＩＮＥＡＲＰＲＯＧＲＡＭＳＳＵＮＪＩＥ（孙捷）（ＩｎｓｔｉｔｕｔｅｏｆＡｐｐｌｉｅｄＭａｔｈｅｍｅｍａｔｉｃｓ，ｔｈｅＣｈｉｎｅｓｅＡｃａｄｅｍｙｏｆＳｃｉ...     

On generation of permutations through decomposition of symmetric groups into cosets

A hardware-oriented algorithm for generating permutations is presented that takes as a theoretic base an iterative decomposition of the symmetric groupS _n into cosets. It generates permutations in a new order. Simple ranking and unranking algorithms are given. The construction of a permutation generator is proposed which contains a cellular permutation network as a main component. The application of the permutation generator for solving a class of combinatorial problems on parallel computers is suggested.     

Generating Travelling-Salesman Problems with Known Optimal Tours

An algorithm is presented for randomly generating travelling-salesman problems (TSPs) for which the optimal tour is known. Both asymmetric and symmetric problems can be generated, with the option of having the distance matrix satisfying the triangle inequality. No limit exists to the number of nodes that can be considered, making the use of the generator attractive to those involved in the design and comparison of TSP solution approaches. Empirical testing of the generator indicates that the resultant problems are as difficult as problems generated in a completely random manner.     

Simulation Modelling Using an Interactive Simulation Program Generator

The development of an interactive simulation program generator which is available on micro and mainframe computers is outlined. The generator forms part of a simulation environment being researched into and constructed by a group of researchers at the London School of Economics. The generated programs are written in Pascal, using a suite of routines which assume a three-phase structure for simulation programs. Experiences of modelling using such a simulation modelling environment are outlined, as well as details of related research and future research plans.     

Bank-office Process Management in the Financial Services: a Simulation Approach Using a Model Generator

For the last ten years or so, developments in simulation software and methodology have been focused in two areas: (1) automating the model-building process; and (2) interfacing with other techniques and systems. That both academic and commercial research continues to be carried out in these areas is evidence of the continued popularity of the simulation technique. The most popular application areas where simulation modelling is used include manufacturing (engineering and process), warehousing and communications; not surprisingly, research and developments have therefore been concentrated in these areas. This paper describes the development of a simulation model generator for a different application area, that of clerical office processing of paper and documents for financial service companies. It outlines the reasons why there is a need for such a model generator and discusses the initial design requirements. The paper goes on to detail the developments and re-defined criteria required as the model generator brief changes as a result of practical applications.     

Estimation of Electricity Market Distribution Functions

In an electricity pool market the market distribution function gives the probability that a generator offering a certain quantity of power at a certain price will not be dispatched all of this quantity by the pool. It represents the uncertainty in a pool market associated with the offers of the other agents as well as demand. We present a general Bayesian update scheme for market distribution functions. To illustrate the approach a particular form of this procedure is applied to real data obtained from a New Zealand electricity generator.     

Probability model of Gunther generator

This paper constructs the probability model of Gunther generator at first,and the finite dimension union distribution of the output sequence is presented.The result shows that the output sequence is an independent and uniformly distributed 0,1 random variable sequence. It gives the theoretical foundation about why Gunther generator can avoid the statistic weakness of the output sequence of stop-and-go generator,and analyzes the coincidence between output sequence and input sequences of Gunther generator.The conclusions of this paper would offer theoretical references for designers and analyzers of clock-controlled generators.     

Market Price Calculations in Restructured Electricity Markets

In the traditional organisation of the power market, the generation Unit Commitment and Dispatch problem was solved as a cost minimisation problem. After deregulation of the electricity sector, the problem must be solved as a profit maximising problem. It is necessary to find feasible market prices. This is difficult, because simple marginal cost based prices not always cover startup and operation-independent costs, with the result that the generator would choose not to run with such prices. In this paper a market structure is proposed with a central market operator computing the market equilibrium for both energy and reserves, based on generator offers and consumer bids. It is shown that it is possible to find feasible market prices. Using a simple test system, it is shown that demand elasticity can have a profound impact on prices and generator revenues and profits during peaking hours.     

K[X]~m中模的生成基及其应用

本文研究了多项式环上的素模中的生成基理论和方法．通过建立新的约化准则,得到了模中生成基的结构和机械化计算方法．对于低维情形给出了素模中生成基的充分必要条件．文中的方法本质地简化了传统的模中Ｇｒｏｂｎｅｒ基方法．文中同时介绍了该方法在样条理论研究中的应用,并给出了一些计算例子．