On the state of strength‐three covering arrays

A covering array of size N, strength t, degree k, and order υ is a k × N array on υ symbols in which every t × N subarray contains every possible t × 1 column at least once. We present explicit constructions, constructive upper bounds on the size of various covering arrays, and compare our results with those of a commercial product. Applications of covering arrays include software testing, drug screening, and data compression. © 2002 Wiley Periodicals, Inc. J Combin Designs 10: 217–238, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/jcd.10002     

Filamentation “remote” sensing of chemical and biological agents/pollutants using only one femtosecond laser source

All matters in the path of filaments induced by an intense femtosecond laser pulse propagating in air could be fragmented and result in the emission of characteristic fluorescence spectra from the excited fragments. The fluorescence spectra exhibit specific signatures (fingerprints) that can be used for the identification of various substances including chemical and biological species. In this paper, we present an overview of the recent progress in our laboratory concerning the “remote” sensing of chemical and biological agents/pollutants in air using filamentation-induced nonlinear fluorescence techniques.     

Self quenching reaction of (Phenoxymethyl)chlorocarbene with diazirine

The combination of laser flash photolysis and product analysis demonstrates that even though (phenoxymethyl)chlorocarbene reacts with its diazirine precursor with a substantial rate constant of 3.5 x 10⁸ M^-1S^-1, the predicted azine product is not formed. These results indicate either carbene/diazirine reversibility or subsequent hydrogen migration of the carbene/diazirine adduct. Also, a rate constant of 2.0 x 10⁷ S^-1 for the 1,2-hydrogen atom migration in (p-nitrophenoxymethyl)chlorocarbene has been determined using the pyridinium ylide technique.     

Partially Observable Markov Decision Processes incorporating epistemic uncertainties

The use of Markov Decision Processes for Inspection Maintenance and Rehabilitation of civil engineering structures relies on the use of several transition matrices related to the stochastic degradation process, maintenance actions and imperfect inspections. Point estimators for these matrices are usually used and they are evaluated using statistical inference methods and/or expert evaluation methods. Thus, considerable epistemic uncertainty often veils the true values of these matrices. Our contribution through this paper is threefold. First, we present a methodology for incorporating epistemic uncertainties in dynamic programming algorithms used to solve finite horizon Markov Decision Processes (which may be partially observable). Second, we propose a methodology based on the use of Dirichlet distributions which answers, in our sense, much of the controversy found in the literature about estimating Markov transition matrices. Third, we show how the complexity resulting from the use of Monte-Carlo simulations for the transition matrices can be greatly overcome in the framework of dynamic programming. The proposed model is applied to concrete bridge under degradation, in order to provide the optimal strategy for inspection and maintenance. The influence of epistemic uncertainties on the optimal solution is underlined through sensitivity analysis regarding the input data.     

Statistical analysis of HDPE fatigue lifetime

Fatigue lifetime of HDPE structures such as pipes is recognized to show a large scatter. This study aims to compare different statistical methods and distributions, in order to give convenient modeling of tensile and fatigue test results of commercially available polyethylene compression molded sheets. The median rank, the maximum likelihood and the Kolmogorov-Smirnov fitting are compared for the estimation of Weibull parameters. The choice of the best distribution to fit fatigue lifetime is discussed on the basis of the goodness-of-fit results. It is found that whether the three-parameter distributions of Weibull and lognormal types are suitable for lifetime prediction, the two-parameter Weibull is more conservative for probabilistic fatigue design.     

Uncertainties of unidirectional composite strength under tensile loading and variation of environmental condition

A probabilistic strength model is developed for unidirectional composites with fibers in hexagonal arrays. The model assumes that, a central core of broken fibers surrounded by unbroken fibers which are subjected to unidirectional tensile loading. The proposed approach consists in using a modified shear lag model to calculate the ineffective lengths and stress concentrations around fiber breaks. The main feature in the model lies in incorporating the variation of composite properties due to temperature and moisture, in order to predict degradation of fibers and matrix characteristics. The strength degradation is often seen as a result of changes in ineffective lengths at fiber breaks, leading to stress concentrations in intact neighboring fibers. As fiber breaks are intrinsically random, the variability of input data allows us to describe the probabilistic model by using the Monte-Carlo method. The sensitivities of the mechanical response are evaluated regarding the uncertainties in design variables such as Young’s modulus of fibers and matrix, fiber reference strength, shear yield stress, fiber volume fraction and shear parameter defining the shear stress in the inelastic region.     

Slope packings and coverings,and generic algorithms for the discrete logarithm problem

We consider the set of slopes of lines formed by joining all pairs of points in some subset S of a Desarguesian affine plane of prime order p. If all the slopes are distinct and non‐infinite, we have a slope packing; if every possible non‐infinite slope occurs, then we have a slope covering. We review and unify some results on these problems that can be derived from the study of Sidon sets and sum covers. Then we report some computational results, we have obtained for small values of p. Finally, we point out some connections between slope packings and coverings and generic algorithms for the discrete logarithm problem in prime order (sub)groups. Our results provide a combinatorial characterization of such algorithms, in the sense that any generic algorithm implies the existence of a certain slope packing or covering, and conversely. © 2002 Wiley Periodicals, Inc. J Combin Designs 11: 36–50, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/jcd.10033     

Pooling, lattice square, and union jack designs

Simplified pooling designs employ rows, columns, and principal diagonals from square and rectangular plates. The requirement that every two samples be tested together in exactly one pool leads to a novel combinatorial configuration: The union jack design. Existence of union jack designs is settled affirmatively whenever the ordern is a prime andn3 (mod 4).     

Covering Arrays of Strength Three

A covering array of size N, degree k, order v and strength t is a k × N array with entries from a set of v symbols such that in any t × N subarray every t × 1 column occurs at least once. Covering arrays have been studied for their applications to drug screening and software testing. We present explicit constructions and give constructive upper bounds for the size of a covering array of strength three.     

Filament-induced breakdown remote spectroscopy in a polar environment

We demonstrate the feasibility of filament-induced breakdown spectroscopy (FIBS) for remote sensing of solid samples in a polar environment. FIBS spectra from an aluminum target induced by 800-nm laser pulses propagating in air were probed. The air visibility in an open winter field was as low as 3.2 km fluctuating with precipitation, pressure and relative humidity. Under such polar condition, clean spectral Al I lines from an aluminum target located at a distance of 60 m were obtained. This shows the technique FIBS could be potentially useful for sensing remote targets in a variety of polar environments.