Discreteness versus continuity in information technologies: Quantum calculus and its alternatives

In the paper, we discuss a role of quantum calculus, “differential calculus without taking limits” as a discrete analog of continuous mathematical analysis oriented on information technologies. We studied distinctive calculi that are alternative to quantum calculus and relate finite discriminators of values of an argument with finite discriminators of values of a function at their different combinations.     

Large-scale linear system solver using secondary storage: Self-energy in hybrid nanostructures

We present a Fortran library which can be used to solve large-scale dense linear systems, Ax=b. The library is based on the LU decomposition included in the parallel linear algebra library PLAPACK and on its out-of-core extension POOCLAPACK. The library is complemented with a code which calculates the self-polarization charges and self-energy potential of axially symmetric nanostructures, following an induced charge computation method. Illustrative calculations are provided for hybrid semiconductor–quasi-metal zero-dimensional nanostructures. In these systems, the numerical integration of the self-polarization equations requires using a very fine mesh. This translates into very large and dense linear systems, which we solve for ranks up to 3×¹⁰⁵. It is shown that the self-energy potential on the semiconductor–metal interface has important effects on the electronic wavefunction.

Program summary

Program title: HDSS (Huge Dense System Solver)Catalogue identifier: AEHU_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEHU_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 98 889No. of bytes in distributed program, including test data, etc.: 1 009 622Distribution format: tar.gzProgramming language: Fortran 90, CComputer: Parallel architectures: multiprocessors, computer clustersOperating system: Linux/UnixHas the code been vectorized or parallelized?: Yes. 4 processors used in the sample tests; tested from 1 to 288 processorsRAM: 2 GB for the sample tests; tested for up to 80 GBClassification: 7.3External routines: MPI, BLAS, PLAPACK, POOCLAPACK. PLAPACK and POOCLAPACK are included in the distribution file.Nature of problem: Huge scale dense systems of linear equations, Ax=B, beyond standard LAPACK capabilities. Application to calculations of self-energy potential in dielectrically mismatched semiconductor quantum dots.Solution method: The linear systems are solved by means of parallelized routines based on the LU factorization, using efficient secondary storage algorithms when the available main memory is insufficient. The self-energy solver relies on an induced charge computation method. The differential equation is discretized to yield linear systems of equations, which we then solve by calling the HDSS library.Restrictions: Simple precision. For the self-energy solver, axially symmetric systems must be considered.Running time: About 32 minutes to solve a system with approximately 100 000 equations and more than 6000 right-hand side vectors using a four-node commodity cluster with a total of 32 Intel cores.     

Prediction of rank deficiency in partition of unity-based methods with plane triangular or quadrilateral meshes

In the partition of unity (PU)-based methods, the global approximation is built by multiplying a partition of unity by local approximations. Within this framework, high-order approximations are achieved by directly adopting high-order polynomials as local approximations, and therefore nodes along sides or inside elements, which are usually adopted in the conventional finite element methods, are no more required. However, the PU-based approximation constructed in this way may suffer from rank deficiency due to the linear dependence of the global degrees of freedom. In this paper, the origin of the rank deficiency in the PU-based approximation space is first dissected at an element level, and then an approach to predict the rank deficiency for a mesh is proposed together with the principle of the increase of rank deficiency. Finally, examples are investigated to validate the present approach. The current work indicates such a fact that the rank deficiency is an unrelated issue to the nullity of the global matrix. It can be resolved in its own manner.     

Solving fracture problems using an asymptotic numerical method

The present work deals with the use of asymptotic numerical methods (ANM) to manage crack onset and crack growth in the framework of continuum damage mechanics (CDM). More specifically, an application of regularization techniques to a 1D cohesive model is proposed. The standard “triangle” damageable elastic model, which is often used in finite element codes to describe fracture of brittle materials, was chosen. Results associated with the load–unload cycle showed that ANM is convenient for numerically taking this specific irregular behavior into account. Moreover, the present paper also shows that the chosen damageable interface model can be introduced in the generalized standard material formalism, thus unabling us to define a complete energy balance associated with the damage process. In such a framework, the damage state is described by a new displacement variable. Finally, a 1D finite element application to a simple elastic damageable structure is shown to highlight the potential of this approach.     

Scheduling gain for frequency-selective Rayleigh-fading channels with application to self-organizing packet scheduling

This paper investigates packet scheduling in the context of Self-Optimizing Networks, and demonstrates how to improve coverage dynamically by adjusting the scheduling strategy. We focus on α-fair schedulers, and we provide methods for calculating the scheduling gain, including several closed form formulas. Scheduling gain is analyzed for different fading models, with a particular focus on the frequency-selective channel. We then propose a coverage-capacity self-optimization algorithm based on α-fair schedulers. A use case illustrates the implementation of the algorithm and simulation results show that important coverage gains are achieved at the expense of very little computing power.     

Defining the Web: the politics of search engines

Although the Web itself might truthfully claim a sovereign disinterested and unbiased attitude toward the people who use it, the authors claim that search engines, the tools that navigate the astronomical number of pages (800 million and counting), favor popular, wealthy, and powerful sites at the expense of others. Some researchers have estimated that, taken individually, none of the Web search engines studied indexes more than 16 percent of the total indexable Web. Combined, the results from all search engines they studied covered only about 42 percent of the Web. But what about those portions of the Web that remain hidden from view? The article looks at how search engine developers, designers, and producers grapple with the technical limits that restrict what their engines can find. The authors also examine influences that may determine systematic inclusion and exclusion of certain sites, and the wide-ranging factors that dictate systematic prominence for some sites while relegating others to systematic invisibility     

Fitting superellipses

In the literature, methods for fitting superellipses to data tend to be computationally expensive due to the nonlinear nature of the problem. This paper describes and tests several fitting techniques which provide different trade-offs between efficiency and accuracy. In addition, we describe various alternative error of fit measures that can be applied by most superellipse fitting methods     

Design of fault-tolerant large-scale VOD servers: With emphasis onhigh-performance and low-cost

Recent technological advances in digital signal processing, data compression techniques, and high-speed communication networks have made Video-on-Demand (VOD) servers feasible. A challenging task in such systems is servicing multiple clients simultaneously while satisfying real-time requirements of continuous delivery of objects at specified rates. To accomplish these tasks and realize economies of scale associated with servicing a large user population, a VOD server requires a large disk subsystem. Although a single disk is fairly reliable, a large disk farm can have an unacceptably high probability of disk failure. Furthermore, due to real-time constraints, the reliability requirements of VOD systems are even more stringent than those of traditional information systems. Traditional RAID solutions are inadequate due to poor resource usage. Thus, in this paper, we present alternative schemes which provide a high degree of reliability at low disk storage, bandwidth, and memory costs for on-demand multimedia servers. Moreover, we discuss some of the main issues and trade-offs associated with providing fault tolerance in multidisk VOD systems. We would like to impress upon the reader that one of the main points of this paper is the exposition of trade-offs and issues associated with designing fault-tolerant VOD servers. It is not the case that one fault tolerance scheme is absolutely better than another, but rather that one must understand the trade-offs as well as one's system constraints and then choose a fault tolerance scheme accordingly     

改进遗传算法搜索性能的研究

本文针对改进遗传算法的搜索性能,提出了一种新的变异算子－自适应多位变异算子,它根据每一代的每一个体在当代中的优劣程度,自适应地控制其发生变异的位数。适应度差的个体变异的位数多,一方面使差的模式生存机会少,另一方面增加了种群的多样性,同时也扩大了搜索范围。我们用模式定理证明了该算子的有效性,并且我们作的仿真实验也同样表明该算子能大大改进遗传算法的搜索性能。