Some recent results in the analysis of greedy algorithms for assignment problems

We survey some recent developments in the analysis of greedy algorithms for assignment and transportation problems. We focus on the linear programming model for matroids and linear assignment problems with Monge property, on general linear programs, probabilistic analysis for linear assignment and makespan minimization, and on-line algorithms for linear and non-linear assignment problems

Evaluation of the present theoretical basis for determination of planetary surface properties by earth-based radar

Spaceflight programs such as the planned Viking landing on Mars require the determination of planetary surface slopes and surface dielectric constants by earth-based methods. Heavy reliance is often placed on radar backscattering data for estimation of these surface properties. An assessment is presented of the basic theory by which the raw radar data are interpreted, and it is shown that serious difficulties and internal inconsistencies are present in the available theoretical formulas. The discussion brings into question the reliability of the presently available results for these surface properties as obtained by earth-based radar methods

RNA amplification for successful gene profiling analysis

The study of clinical samples is often limited by the amount of material available to study. While proteins cannot be multiplied in their natural form, DNA and RNA can be amplified from small specimens and used for high-throughput analyses. Therefore, genetic studies offer the best opportunity to screen for novel insights of human pathology when little material is available. Precise estimates of DNA copy numbers in a given specimen are necessary. However, most studies investigate static variables such as the genetic background of patients or mutations within pathological specimens without a need to assess proportionality of expression among different genes throughout the genome. Comparative genomic hybridization of DNA samples represents a crude exception to this rule since genomic amplification or deletion is compared among different specimens directly. For gene expression analysis, however, it is critical to accurately estimate the proportional expression of distinct RNA transcripts since such proportions directly govern cell function by modulating protein expression. Furthermore, comparative estimates of relative RNA expression at different time points portray the response of cells to environmental stimuli, indirectly informing about broader biological events affecting a particular tissue in physiological or pathological conditions. This cognitive reaction of cells is similar to the detection of electroencephalographic patterns which inform about the status of the brain in response to external stimuli. As our need to understand human pathophysiology at the global level increases, the development and refinement of technologies for high fidelity messenger RNA amplification have become the focus of increasing interest during the past decade. The need to increase the abundance of RNA has been met not only for gene specific amplification, but, most importantly for global transcriptome wide, unbiased amplification. Now gene-specific, unbiased transcriptome wide amplification accurately maintains proportionality among all RNA species within a given specimen. This allows the utilization of clinical material obtained with minimally invasive methods such as fine needle aspirates (FNA) or cytological washings for high throughput functional genomics studies. This review provides a comprehensive and updated discussion of the literature in the subject and critically discusses the main approaches, the pitfalls and provides practical suggestions for successful unbiased amplification of the whole transcriptome in clinical samples

Branched It\^o formula and natural It\^o-Stratonovich isomorphism

Branched rough paths, defined as characters over the Connes-Kreimer Hopf algebra $\mathcal{H}_\mathrm{CK}$, constitute integration theories that may fail to satisfy the usual integration by parts identity. Using known results on the primitive elements of $\mathcal{H}_\mathrm{CK}$ we can view it as a commutative cofree Hopf algebra (i.e. a commutative $\mathbf{B}_\infty$-algebra) and thus write an explicit change-of-variable formula for solutions to rough differential equations. This formula, which is realised through an explicit morphism from the Grossman-Larson Hopf algebra to the Hopf algebra of differential operators, restricts to the well-known It\^o formula in the very special case of semimartingales. In addition, we establish an isomorphism between $\mathcal{H}_\mathrm{CK}$ and the shuffle algebra over its primitives, which extends Hoffman's exponential for the quasi-shuffle algebra, and can therefore be viewed as a far-reaching generalisation of the usual It\^o-Stratonovich correction formula for semimartingales. Indeed, this can be stated as a characterisation of the algebra structure of any commutative $\mathbf{B}_\infty$-algebra. Compared to previous approaches, this transformation has the key property of being natural in the decorating vector space. We study the one-dimensional case more closely, by introducing the branched analogue of the Kailath-Segall polynomials and Dol\'eans-Dade exponential, and conclude with some examples of branched rough path lifts of a stochastic process which are not quasi-geometric.Comment: 54 pages, 1 figur

On the finite termination of an entropy function based smoothing Newton method for vertical linear complementarity problems

By using a smooth entropy function to approximate the non-smooth max-type function, a vertical linear complementarity problem (VLCP) can be treated as a family of parameterized smooth equations. A Newton-type method with a testing procedure is proposed to solve such a system. We show that the proposed algorithm finds an exact solution of VLCP in a finite number of iterations, under some conditions milder than those assumed in literature. Some computational results are included to illustrate the potential of this approach.Newton method;Finite termination;Entropy function;Smoothing approximation;Vertical linear complementarity problems

Old School Catalog 1924-25, The Engineering School

https://scholar.valpo.edu/oldschoolcatalogs/1002/thumbnail.jp

The Big One: Literature Discovers AIDS

Among the works discussed in this essay: An Intimate Desire to Survive, by Bill Becker; Epitaphs for the Plague Dead, by Robert Boucheron; A Cry in the Desert, by Jed A. Bryan; The World Can Break Your Heart, by Daniel Curzon; Safe Sex, by Harvey Fierstein; The Castro, in Cities on a Hill: A Journey Through Contemporary American Culture, by Frances FitzGerald; As Is, by William M. Hoffman; Plague: A Novel About Healing, by Toby Johnson; The Normal Heart, by Larry Kramer; To All the Girls I\u27ve Loved Before: An AIDS Diary, by J. W. Money; Facing It: A Novel of AIDS, by Paul Reed; And the Band Played On: Politics, People, and the AIDS Epidemic, by Randy Shilts; Men on Men: Best New Gay Fiction, edited by George Stambolian

Quasi-shuffle algebras and renormalisation of rough differential equations

The objective of this work is to compare several approaches to the process of renormalisation in the context of rough differential equations using the substitution bialgebra on rooted trees known from backward error analysis of $B$-series. For this purpose, we present a so-called arborification of the Hoffman--Ihara theory of quasi-shuffle algebra automorphisms. The latter are induced by formal power series, which can be seen to be special cases of the cointeraction of two Hopf algebra structures on rooted forests. In particular, the arborification of Hoffman's exponential map, which defines a Hopf algebra isomorphism between the shuffle and quasi-shuffle Hopf algebra, leads to a canonical renormalisation that coincides with Marcus' canonical extension for semimartingale driving signals. This is contrasted with the canonical geometric rough path of Hairer and Kelly by means of a recursive formula defined in terms of the coaction of the substitution bialgebra

The Community Is Their Textbook: Maryland\u27s Experiment with Mandatory Service for Students

At its best, service learning enriches both students and their communities. But creating good programs isn\u27t easy