Simplifications to A New Approach to the Covering Radius...”

We simplify the proofs of four results in [3], restating two of them for greater clarity. The main purpose of this note is to give a brief transparent proof of Theorem 7 of [3], the main upper bound of that paper. The secondary purpose is to give a more direct statement and proof of the integer programming determination of covering radius of [3]. Theorem 7 of [3] follows from a simple result in [2], which we state with the notation (for the linear code A)

Fault-Detection in Networks

To find broken links in networks we use the cut-set space. Information on which nodes can talk, or not, to which other nodes allows reduction of the problem to that of decoding the cut-set code of a graph. Special classes of such codes are known to have polynomial-time decoding algorithms. We present a simple algorithm to achieve the reduction and apply it in two examples

On Perfect Weighted Coverings with Small Radius

We extend the results of our previous paper [8] to the nonlinear case: The Lloyd polynomial of the covering has at least R distinct roots among 1, ... , n, where R is the covering radius. We investigate PWC with diameter 1, finding a partial characterization. We complete an investigation begun in [8] on linear PMC with distance 1 and diameter 2

Binary Perfect Weighted Coverings (PWC) I. The Linear Case

This paper deals with an extension of perfect codes to fractional (or weighted) coverings. We shall derive a Lloyd theorem --- a strong necessary condition of existence---and start a classification of these perfect coverings according to their diameter. We illustrate by pointing to list decoding

Weighted Coverings and Packings

In this paper we introduce a generalization of the concepts of coverings and packings in Hamming space called weighted coverings and packings. This allows us to formulate a number of well-known coding theoretical problems in a uniform manner. We study the existence of perfect weighted codes, discuss connections between weighted coverings and packings, and present many constructions for them

Covering Radius 1985-1994

We survey important developments in the theory of covering radius during the period 1985-1994. We present lower bounds, constructions and upper bounds, the linear and nonlinear cases, density and asymptotic results, normality, specific classes of codes, covering radius and dual distance, tables, and open problems

Concurrent sexual partnerships do not explain the HIV epidemics in Africa: a systematic review of the evidence

The notion that concurrent sexual partnerships are especially common in sub-Saharan Africa and explain the region's high HIV prevalence is accepted by many as conventional wisdom. In this paper, we evaluate the quantitative and qualitative evidence offered by the principal proponents of the concurrency hypothesis and analyze the mathematical model they use to establish the plausibility of the hypothesis

Classical limit in terms of symbolic dynamics for the quantum baker's map

We derive a simple closed form for the matrix elements of the quantum baker's map that shows that the map is an approximate shift in a symbolic representation based on discrete phase space. We use this result to give a formal proof that the quantum baker's map approaches a classical Bernoulli shift in the limit of a small effective Plank's constant.Comment: 12 pages, LaTex, typos correcte

Psychometric assessment of HIV/STI sexual risk scale among MSM: A Rasch model approach

<p>Abstract</p> <p>Background</p> <p>Little research has assessed the degree of severity and ordering of different types of sexual behaviors for HIV/STI infection in a measurement scale. The purpose of this study was to apply the Rasch model on psychometric assessment of an HIV/STI sexual risk scale among men who have sex with men (MSM).</p> <p>Methods</p> <p>A cross-sectional study using respondent driven sampling was conducted among 351 MSM in Shenzhen, China. The Rasch model was used to examine the psychometric properties of an HIV/STI sexual risk scale including nine types of sexual behaviors.</p> <p>Results</p> <p>The Rasch analysis of the nine items met the unidimensionality and local independence assumption. Although the person reliability was low at 0.35, the item reliability was high at 0.99. The fit statistics provided acceptable infit and outfit values. Item difficulty invariance analysis showed that the item estimates of the risk behavior items were invariant (within error).</p> <p>Conclusions</p> <p>The findings suggest that the Rasch model can be utilized for measuring the level of sexual risk for HIV/STI infection as a single latent construct and for establishing the relative degree of severity of each type of sexual behavior in HIV/STI transmission and acquisition among MSM. The measurement scale provides a useful measurement tool to inform, design and evaluate behavioral interventions for HIV/STI infection among MSM.</p