A computational model for solid waste management with application

A model for regional solid waste management as a network flow problem is described, and a special purpose algorithm is developed. The model is applied to waste management and facility siting decisions in the Munich Metropolitan Area in the Federal Republic of Germany.     

A fully linear-time approximation algorithm for grammar-based compression

A linear-time approximation algorithm for the grammar-based compression is presented. This is an optimization problem to minimize the size of a context-free grammar deriving a given string. For each string of length n, the algorithm guarantees approximation ratio without suffix tree construction.     

SinaPlot: An Enhanced Chart for Simple and Truthful Representation of Single Observations Over Multiple Classes

Recent developments in data-driven science have led researchers to integrate data from several sources, over diverse experimental procedures, or databases. This alone poses a major challenge in truthfully visualizing data, especially when the number of data points varies between classes. To aid the representation of datasets with differing sample size, we have developed a new type of plot overcoming limitations of current standard visualization charts. SinaPlot is inspired by the strip chart and the violin plot and operates by letting the normalized density of points restrict the jitter along the x-axis. The plot displays the same contour as a violin plot but resembles a simple strip chart for a small number of data points. By normalizing jitter over all classes, the plot provides a fair representation for comparison between classes with a varying number of samples. In this way, the plot conveys information of both the number of data points, the density distribution, outliers and data spread in a very simple, comprehensible, and condensed format. The package for producing the plots is available for R through the CRAN network using base graphics package and as geom for ggplot through ggforce. We also provide access to a web-server accepting excel sheets to produce the plots (http://servers.binf.ku.dk:8890/sinaplot/).     

A novel group ranking model for revealing sequence and quantity knowledge

The aggregation of individuals’ preferences into a consensus ranking is a group ranking problem which has been widely utilized in various applications, such as decision support systems, recommendation systems, and voting systems. Gathering the comparison of preferences and aggregate them to gain consensuses is a conventional issue. For example, b > c ? d ? a indicates that b is favorable to c, and c (d) is somewhat favorable but not fully favorable to d (a), where > and ? are comparators, and a, b, c, and d are items. Recently, a new type of ranking model was proposed to provide temporal orders of items. The order, b&c → a, means that b and c can occur simultaneously and are also before a. Although this model can derive the order ranking of items, the knowledge about quantity-related items is also of importance to approach more real-life circumstances. For example, when enterprises or individuals handle their portfolios in financial management, two considerations, the sequences and the amount of money for investment objects, should be raised initially. In this study, we propose a model for discovering consensus sequential patterns with quantitative linguistic terms. Experiments using synthetic and real datasets showed the model’s computational efficiency, scalability, and effectiveness.     

A simple method for smoothing functions and compressing Hermite data

Let =(a=x₀<x₁<<x_n=b) be a partition of an interval [a,b] of R, and let f be a piecewise function of class C^k on [a,b] except at knots x_i where it is only of class , k_ik. We study in this paper a novel method which smooth the function f at x_i, 0in. We first define a new basis of the space of polynomials of degree 2k+1, and we describe algorithms for smoothing the function f. Then, as an application, we give a recursive computation of classical Hermite spline interpolants, and we present a method which allows us to compress Hermite data. The most part of these results are illustrated by some numerical examples. AMS subject classification 41A05, 41A15, 65D05, 65D07, 65D10     

Implementing PLS for distance-based regression: computational issues

Distance-based regression allows for a neat implementation of the partial least squares recurrence. In this paper, we address practical issues arising when dealing with moderately large datasets (n ~ 10⁴) such as those typical of automobile insurance premium calculations.     

A characterization for a graphic sequence to be potentially C r -graphic

Let r 3, n r and π = (d1, d2, . . . , dn) be a graphic sequence. If there exists a simple graph G on n vertices having degree sequence π such that G contains Cr (a cycle of length r) as a subgraph, then π is said to be potentially Cr-graphic. Li and Yin (2004) posed the following problem: characterize π = (d1, d2, . . . , dn) such that π is potentially Cr-graphic for r 3 and n r. Rao and Rao (1972) and Kundu (1973) answered this problem for the case of n = r. In this paper, this problem is solved completely.     

A central limit theorem and improved error bounds for a hybrid-Monte Carlo sequence with applications in computational finance

In problems of moderate dimensions, the quasi-Monte Carlo method usually provides better estimates than the Monte Carlo method. However, as the dimension of the problem increases, the advantages of the quasi-Monte Carlo method diminish quickly. A remedy for this problem is to use hybrid sequences; sequences that combine pseudorandom and low-discrepancy vectors. In this paper we discuss a particular hybrid sequence called the mixed sequence. We will provide improved discrepancy bounds for this sequence and prove a central limit theorem for the corresponding estimator. We will also provide numerical results that compare the mixed sequence with the Monte Carlo and randomized quasi-Monte Carlo methods.     

An RSA based public-key cryptosystem for secure communication

A new cryptosystem that uses modulo arithmetic operations is proposed. It is based on Rivest-Shamir-Adleman’s public key cryptosystem. A feature of the proposed system is that the encryption and decryption procedures are computationally less intensive, and hence the system is amenable for high data bit rate communications.     

A homotopy operator for Spencer’s sequence in the C ∞-case

The main result of the formal theory of overdetermined systems of differential equations says that any regular system Au = f with smooth coefficients on an open set U ⊂ ℝ ⁿ admits a solution in smooth sections of the bundle of formal power series provided that f satisfies a compatibility condition in U. Our contribution consists in detailed study of the dependence of formal solutions on the point of the base U of the bundle. We also parameterize these solutions by their Cauchy data. In doing so, we prove that, under absence of topological obstructions, there is a formal solution which smoothly depends on the point of the base. This leads to a concept of a finitely generated system (do not mix up it with holonomic or finite -type systems) for which we then prove a C ^∞-Poincaré lemma. The text was submitted by the authors in English.     

A positive finite-difference model in the computational simulation of complex biological film models

In this work, we design a linear, two-step, finite-difference method to approximate the solutions of a biological system that describes the interaction between a microbial colony and a surrounding substrate. The model is a system of four partial differential equations with nonlinear diffusion and reaction, and the colony is formed by an active portion, an inert component and the contribution of extracellular polymeric substances. In this work, we extend the computational approach proposed by Eberl and Demaret [A finite difference scheme for a degenerated diffusion equation arising in microbial ecology, Electr. J. Differ. Equ. 15 (2007) pp. 77–95], in order to design a numerical technique to approximate the solutions of a more complicated model proposed in the literature. As we will see in this work, this approach guarantees that positive and bounded initial solutions will evolve uniquely into positive and bounded, new approximations. We provide numerical simulations to evince the preservation of the positive character of solutions.     

A computational algebraic-geometry method for conditional-independence inference

We consider the problems of semi-graphoid inference and of independence implication from a set of conditional-independence statements. Based on ideas from R. Hemmecke et al. [Combin. Probab. Comput., 2008, 17: 239–257], we present algebraic-geometry characterizations of these two problems, and propose two corresponding algorithms. These algorithms can be realized with any computer algebra system when the number of variables is small.     

A computational approach for solving

We present a computational approach for finding all integral solutions of the equation for even values of . By reducing this problem to that of finding integral solutions of a certain class of quartic equations closely related to the Pell equations, we are able to apply the powerful computational machinery related to quadratic number fields. Using our approach, we determine all integral solutions for assuming the Generalized Riemann Hypothesis, and for unconditionally.

     

A fast computational algorithm for the Legendre-Fenchel transform

We investigate a fast algorithm, introduced by Brenier, which computes the Legendre-Fenchel transform of a real-valued function. We generalize his work to boxed domains and introduce a parameter in order to build an iterative algorithm. The new approach of separating primal and dual spaces allows a clearer understanding of the algorithm and yields better numerical behavior. We extend known complexity results and give new ones about the convergence of the algorithm.     

A comparison of computational strategies for geometric programs

Numerous algorithms for the solution of geometric programs have been reported in the literature. Nearly all are based on the use of conventional programming techniques specialized to exploit the characteristic structure of either the primal or the dual or a transformed primal problem. This paper attempts to elucidate, via computational comparisons, whether a primal, a dual, or a transformed primal solution approach is to be preferred.The authors wish to thank Captain P. A. Beck and Dr. R. S. Dembo for making available their codes. This research was supported in part under ONR Contract No. N00014-76-C-0551 with Purdue University.     

A computational method for minimization with nonlinear constraints

An iterative technique is developed to solve the problem of minimizing a functionf(y) subject to certain nonlinear constraintsg(y)=0. The variables are separated into the basic variablesx and the independent variablesu. Each iteration consists of a gradient phase and a restoration phase. The gradient phase involves a movement (on a surface that is linear in the basic variables and nonlinear in the independent variables) from a feasible point to a varied point in a direction based on the reduced gradient. The restoration phase involves a movement (in a hyperplane parallel tox-space) from the nonfeasible varied point to a new feasible point.The basic scheme is further modified to implement the method of conjugate gradients. The work required in the restoration phase is considerably reduced when compared with the existing methods.     

轨道运动方程数值解的一种加速算法

针对卫星轨道受大气阻力摄动的运动方程,提出了一种数值加速算法,该算法实现简单、计算量小、精度高,适合于各类卫星轨道的方程的求解.