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)

Significance of low energy impact damage on modal parameters of composite beams by design of experiments

This paper presents an experimental study on the effects of multi-site damage on the vibration response of composite beams damaged by low energy impacts around the barely visible impact damage limit (BVID). The variation of the modal parameters with different levels of impact energy and density of damage is studied. Vibration tests have been carried out with both burst random and classical sine dwell excitations in order to compare that which of the methods among Polymax and Half Bandwidth Method is more suitable for damping estimation in the presence of damage. Design of experiments (DOE) performed on the experimental data show that natural frequency is a more sensitive parameter for damage detection than the damping ratio. It also highlighted energy of impact as the factor having a more significant effect on the modal parameters. Half Bandwidth Method is found to be unsuitable for damping estimation in the presence of damage

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

Aging and memory effects in beta-hydrochinone-clathrate

The out-of-equilibrium low-frequency complex susceptibility of the orientational glass methanol(73%)-beta-hydrochinone-clathrate is studied using temperature-stop protocols in aging experiments . Although the material does not have a sharp glass transition aging effects including rejuvenation and memory are found at low temperatures. However, they turn out to be much weaker, however, than in conventional magnetic spin glasses.Comment: 5 pages RevTeX, 6 eps-figures include

Off-Equilibrium Dynamics in Finite-Dimensional Spin Glass Models

The low temperature dynamics of the two- and three-dimensional Ising spin glass model with Gaussian couplings is investigated via extensive Monte Carlo simulations. We find an algebraic decay of the remanent magnetization. For the autocorrelation function $C(t,t_w)=[]_{av}$ a typical aging scenario with a $t/t_w$ scaling is established. Investigating spatial correlations we find an algebraic growth law $\xi(t_w)\sim t_w^{\alpha(T)}$ of the average domain size. The spatial correlation function $G(r,t_w)=[< S_i(t_w)S_{i+r}(t_w)>^2]_{av}$ scales with $r/\xi(t_w)$. The sensitivity of the correlations in the spin glass phase with respect to temperature changes is examined by calculating a time dependent overlap length. In the two dimensional model we examine domain growth with a new method: First we determine the exact ground states of the various samples (of system sizes up to $100\times 100$) and then we calculate the correlations between this state and the states generated during a Monte Carlo simulation.Comment: 38 pages, RevTeX, 14 postscript figure

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

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

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