Mutation analysis to verify feature matrices for isolating errors in simulation models

Software simulation models are computer programs that need to be verified and debugged like any other software. In previous work, a method for error isolation in simulation models has been proposed. The method relies on a set of feature matrices that can be used to determine which part of the model implementation is responsible for deviations in the output of the model. Currrently these feature matrices have to be generated by hand from the model implementation, which is a tedious and error-prone task. In this paper, a method based on mutation analysis, as well as prototype tool support for the verification of the manually generated feature matrices is presented. The application of the method and tool to a model for wastewater treatment shows that the feature matrices can be verified effectively using a minimal number of mutants.

Statistical physics of low density parity check error correcting codes

We study the performance of Low Density Parity Check (LDPC) error-correcting codes using the methods of statistical physics. LDPC codes are based on the generation of codewords using Boolean sums of the original message bits by employing two randomly-constructed sparse matrices. These codes can be mapped onto Ising spin models and studied using common methods of statistical physics. We examine various regular constructions and obtain insight into their theoretical and practical limitations. We also briefly report on results obtained for irregular code constructions, for codes with non-binary alphabet, and on how a finite system size effects the error probability.

Importance of tissue transglutaminase in repair of extracellular matrices and cell death of dermal fibroblasts after exposure to a solarium ultraviolet A source

Investigations were undertaken to study the role of the protein cross-linking enzyme tissue transglutaminase in changes associated with the extracellular matrix and in the cell death of human dermal fibroblasts following exposure to a solarium ultraviolet A source consisting of 98.8% ultraviolet A and 1.2% ultraviolet B. Exposure to nonlethal ultraviolet doses of 60 to 120 kJ per m2 resulted in increased tissue transglutaminase activity when measured either in cell homogenates, "in situ" by incorporation of fluorescein-cadaverine into the extracellular matrix or by changes in the epsilon(gamma-glutamyl) lysine cross-link. This increase in enzyme activity did not require de novo protein synthesis. Incorporation of fluorescein-cadaverine into matrix proteins was accompanied by the cross-linking of fibronectin and tissue transglutaminase into nonreducible high molecular weight polymers. Addition of exogenous tissue transglutaminase to cultured cells mimicking extensive cell leakage of the enzyme resulted in increased extracellular matrix deposition and a decreased rate of matrix turnover. Exposure of cells to 180 kJ per m2 resulted in 40% to 50% cell death with dying cells showing extensive tissue transglutaminase cross-linking of intracellular proteins and increased cross-linking of the surrounding extracellular matrix, the latter probably occurring as a result of cell leakage of tissue transglutaminase. These cells demonstrated negligible caspase activation and DNA fragmentation but maintained their cell morphology. In contrast, exposure of cells to 240 kJ per m2 resulted in increased cell death with caspase activation and some DNA fragmentation. These cells could be partially rescued from death by addition of caspase inhibitors. These data suggest that changes in cross-linking both in the intracellular and extracellular compartments elicited by tissue transglutaminase following exposure to ultraviolet provides a rapid tissue stabilization process following damage, but as such may be a contributory factor to the scarring process that results.

Integration of the Manakov-PMD Equation with Precomputed M(w) Matrices for PMD Simulation

A novel direct integration technique of the Manakov-PMD equation for the simulation of polarisation mode dispersion (PMD) in optical communication systems is demonstrated and shown to be numerically as efficient as the commonly used coarse-step method. The main advantage of using a direct integration of the Manakov-PMD equation over the coarse-step method is a higher accuracy of the PMD model. The new algorithm uses precomputed M(w) matrices to increase the computational speed compared to a full integration without loss of accuracy. The simulation results for the probability distribution function (PDF) of the differential group delay (DGD) and the autocorrelation function (ACF) of the polarisation dispersion vector for varying numbers of precomputed M(w) matrices are compared to analytical models and results from the coarse-step method. It is shown that the coarse-step method achieves a significantly inferior reproduction of the statistical properties of PMD in optical fibres compared to a direct integration of the Manakov-PMD equation.

Numerical implementation of the Manakov-PMD equation with precomputed M(Ω) matrices

The Manakov-PMD equation can be integrated with the same numerical efficiency as the coarse-step method by using precomputed M(Ω) matrices, which entirely avoids the somewhat ad-hoc rescaling of coefficients necessary in the coarse-step method.

Typical kernel size and number of sparse random matrices over Galois fields: a statistical physics approach

Using methods of statistical physics, we study the average number and kernel size of general sparse random matrices over GF(q), with a given connectivity profile, in the thermodynamical limit of large matrices. We introduce a mapping of GF(q) matrices onto spin systems using the representation of the cyclic group of order q as the q-th complex roots of unity. This representation facilitates the derivation of the average kernel size of random matrices using the replica approach, under the replica symmetric ansatz, resulting in saddle point equations for general connectivity distributions. Numerical solutions are then obtained for particular cases by population dynamics. Similar techniques also allow us to obtain an expression for the exact and average number of random matrices for any general connectivity profile. We present numerical results for particular distributions.

Properties of sparse random matrices over finite fields

Typical properties of sparse random matrices over finite (Galois) fields are studied, in the limit of large matrices, using techniques from the physics of disordered systems. For the case of a finite field GF(q) with prime order q, we present results for the average kernel dimension, average dimension of the eigenvector spaces and the distribution of the eigenvalues. The number of matrices for a given distribution of entries is also calculated for the general case. The significance of these results to error-correcting codes and random graphs is also discussed.