. redlog is a package that extends the computer algebra system reduce to a computer logic system, i.e., a system that provides algorithms for the symbolic manipulation of first-order formulas over some temporarily fixed language and theory. In contrast to theorem provers, the methods applied know about the underlying algebraic theory and make use of it. Though the focus is on simplification, parametric linear optimization, and quantifier elimination, redlog is designed as a general-purpose system. We describe the functionality of redlog as it appears to the user, and explain the design issues and implementation techniques. ? The second author was supported by the dfg (Schwerpunktprogramm: Algorithmische Zahlentheorie und Algebra) 1 Introduction redlog stands for reduce logic system. It provides an extension of the computer algebra system (cas) reduce to a computer logic system (cls) implementing symbolic algorithms on first-order formulas w.r.t. temporarily fixed firstorder languag...

Abstract—The problem of finding the least-squares solution to a system of linear equations where the unknown vector is comprised of integers, but the matrix coefficient and given vector are comprised of real numbers, arises in many applications: communications, cryptography, GPS, to name a few. The problem is equivalent to finding the closest lattice point to a given point and is known to be NP-hard. In communications applications, however, the given vector is not arbitrary but rather is an unknown lattice point that has been perturbed by an additive noise vector whose statistical properties are known. Therefore, in this paper, rather than dwell on the worst-case complexity of the integer least-squares problem, we study its expected complexity, averaged over the noise and over the lattice. For the “sphere decoding” algorithm of Fincke and Pohst, we find a closed-form expression for the expected complexity, both for the infinite and finite lattice.

Regularization of ill-posed linear inverse problems via ℓ1 penalization has been proposed for cases where the solution is known to be (almost) sparse. One way to obtain the minimizer of such an ℓ1 penalized functional is via an iterative soft-thresholding algorithm. We propose an alternative implementation to ℓ1-constraints, using a gradient method, with projection on ℓ1-balls. The corresponding algorithm uses again iterative soft-thresholding, now with a variable thresholding parameter. We also propose accelerated versions of this iterative method, using ingredients of the (linear) steepest descent method. We prove convergence in norm for one of these projected gradient methods, without and with acceleration.

Dedicated to the memory of Gian-Carlo Rota who encouraged me to write this paper in the present style Abstract. In this paper we derive many infinite families of explicit exact formulas involving either squares or triangular numbers, two of which generalize Jacobi’s 4 and 8 squares identities to 4n 2 or 4n(n + 1) squares, respectively, without using cusp forms. In fact, we similarly generalize to infinite families all of Jacobi’s explicitly stated degree 2, 4, 6, 8 Lambert series expansions of classical theta functions. In addition, we extend Jacobi’s special analysis of 2 squares, 2 triangles, 6 squares, 6 triangles to 12 squares, 12 triangles, 20 squares, 20 triangles, respectively. Our 24 squares identity leads to a different formula for Ramanujan’s tau function τ(n), when n is odd. These results, depending on new expansions for powers of various products of classical theta functions, arise in the setting of Jacobi elliptic functions, associated continued fractions, regular C-fractions, Hankel or Turánian determinants, Fourier series, Lambert series, inclusion/exclusion, Laplace expansion formula for determinants, and Schur functions. The Schur function form of these infinite families of identities are analogous to the η-function identities of Macdonald. Moreover, the powers 4n(n + 1), 2n 2 + n, 2n 2 − n that appear in Macdonald’s work also arise at appropriate places in our analysis. A special case of our general methods yields a proof of the two Kac–Wakimoto conjectured identities involving representing

It is usually very hard, both for designers and users, to reason reliably about user interfaces. This article shows that ‘push button ’ and ‘point and click ’ user interfaces are algebraic structures. Users effectively do algebra when they interact, and therefore we can be precise about some important design issues and issues of usability. Matrix algebra, in particular, is useful for explicit calculation and for proof of various user interface properties. With matrix algebra, we are able to undertake with ease unusally thorough reviews of real user interfaces: this article examines a mobile phone, a handheld calculator and a digital multimeter as case studies, and draws general conclusions about the approach and its relevance to design.

This paper describes a computing environment named WBCSim that is intended to increase the productivity of wood scientists conducting research on wood-based composite materials. WBCSim integrates Fortran 77-based simulation codes with a graphical front end, an optimization tool, and a visualization tool. WBCSim serves as a prototype for the design, construction, and evaluation of larger scale problem solving (computing) environments. Several different wood-based composite material simulations are supported. A detailed description of the prototype's software architecture and a typical scenario of use are presented. The system converts output from the simulations to the Virtual Reality Modeling Language (VRML) for visualizing simulation results.

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We consider estimation in a particular semiparametric regression model for the mean of a counting process with “panel count ” data. The basic model assumption is that the conditional mean function of the counting process is of the form E{N(t)|Z} = exp(β T 0 Z)Λ0(t) where Z is a vector of covariates and Λ0 is the baseline mean function. The “panel count ” observation scheme involves observation of the counting process N for an individual at a random number K of random time points; both the number and the locations of these time points may differ across individuals. We study semiparametric maximum pseudo-likelihood and maximum likelihood estimators of the unknown parameters (β0,Λ0) derived on the basis of a nonhomogeneous Poisson process assumption. The pseudo-likelihood estimator is fairly easy to compute, while the maximum likelihood estimator poses more challenges from the computational perspective. We study asymptotic properties of both estimators assuming that the proportional mean model holds, but dropping the Poisson process assumption used to derive the estimators. In particular we establish asymptotic normality for the estimators of the regression parameter β0 under appropriate hypotheses. The results show that our estimation procedures are robust in the sense that the estimators converge to the truth regardless of the underlying counting process.

The computer science literature discusses code and algorithms extensively, but not always reliably. Tool support can help ensure integrity between code and explanation so that published papers are more reliable. A versatile, light-weight tool to support explaining code for publication is justified, described and compared with alternatives. The tool works with Java, C and similar languages, and provides support for publishing explanations of real code in LATEX, XML, HTML, etc.

Agent-based computing is increasingly regarded as an elegant and efficient way of providing access to computational resources. Several metacomputing research projects are using intelligent agents to manage a resource space and to map user computation to these resources in an optimal fashion. Such a project is NetSolve, developed at the University of Tennessee and Oak Ridge National Laboratory. NetSolve provides the user with a variety of interfaces that afford direct access to preinstalled, freely available numerical libraries. These libraries are embedded in computational servers. New numerical functionalities can be integrated easily into the servers by a specific framework. The NetSolve agent manages the coherency of the computational servers. It also uses predictions about the network and processor performances to assign user requests to the most suitable servers. This article reviews some of the basic concepts in agent-based design, discusses the NetSolve project and how its agent enhances ¯exibility and performance, and provides examples of other research efforts. Also discussed are future directions in agent-based computing in general and in NetSolve in particular.