Special subsets and optimum codes based on lattices and cosets

This paper introduces the concept of special subsets when applied to generator matrices based on lattices and cosets as presented by Calder-bank and Sloane. By using the special subsets we propose a non exhaustive code search for optimum codes. Although non exhaustive, the search always results in optimum codes for given (k1, V, Λ/Λ′). Tables with binary and ternary optimum codes to partitions of lattices with 8, 9 e 16 cosets, were obtained.

Two matrix-based lattice construction techniques

Let m and n be integers greater than 1. Given lattices A and B of dimensions m and n, respectively, a technique for constructing a lattice from them of dimension m+n-1 is introduced. Furthermore, if A and B possess bases satisfying certain conditions, then a second technique yields a lattice of dimension m+n-2. The relevant parameters of the new lattices are given in terms of the respective parameters of A,B, and a lattice C isometric to a sublattice of A and B. Denser sphere packings than previously known ones in dimensions 52, 68, 84, 248, 520, and 4098 are obtained. © 2012 Elsevier Inc. All rights reserved.

Fast pseudorandom generator based on packed matrices

Pseudorandom generators are a basic foundation of many cryptographic services and information security protocols. We propose a modification of a previously published matricial pseudorandom generator that significantly improves performance and security. The resulting generator is successfully compared to world class standards.

An optimized pseudorandom generator using packed matrices

Most cryptographic services and information security protocols require a dependable source of random data; pseudorandom generators are convenient and efficient for this application working as one of the basic foundation blocks on which to build the required security infrastructure. We propose a modification of a previously published matricial pseudorandom generator that significantly improves performance and security by using word packed matrices and modifying key scheduling and bit extraction schemes. The resulting generator is then successfully compared to world class standards.

Krylov subspace methods for approximating functions of symmetric positive definite matrices with applications to applied statistics and anomalous diffusion

Matrix function approximation is a current focus of worldwide interest and finds application in a variety of areas of applied mathematics and statistics. In this thesis we focus on the approximation of A^(-α/2)b, where A ∈ ℝ^(n×n) is a large, sparse symmetric positive definite matrix and b ∈ ℝ^n is a vector. In particular, we will focus on matrix function techniques for sampling from Gaussian Markov random fields in applied statistics and the solution of fractional-in-space partial differential equations. Gaussian Markov random fields (GMRFs) are multivariate normal random variables characterised by a sparse precision (inverse covariance) matrix. GMRFs are popular models in computational spatial statistics as the sparse structure can be exploited, typically through the use of the sparse Cholesky decomposition, to construct fast sampling methods. It is well known, however, that for sufficiently large problems, iterative methods for solving linear systems outperform direct methods. Fractional-in-space partial differential equations arise in models of processes undergoing anomalous diffusion. Unfortunately, as the fractional Laplacian is a non-local operator, numerical methods based on the direct discretisation of these equations typically requires the solution of dense linear systems, which is impractical for fine discretisations. In this thesis, novel applications of Krylov subspace approximations to matrix functions for both of these problems are investigated. Matrix functions arise when sampling from a GMRF by noting that the Cholesky decomposition A = LL^T is, essentially, a `square root' of the precision matrix A. Therefore, we can replace the usual sampling method, which forms x = L^(-T)z, with x = A^(-1/2)z, where z is a vector of independent and identically distributed standard normal random variables. Similarly, the matrix transfer technique can be used to build solutions to the fractional Poisson equation of the form ϕn = A^(-α/2)b, where A is the finite difference approximation to the Laplacian. Hence both applications require the approximation of f(A)b, where f(t) = t^(-α/2) and A is sparse. In this thesis we will compare the Lanczos approximation, the shift-and-invert Lanczos approximation, the extended Krylov subspace method, rational approximations and the restarted Lanczos approximation for approximating matrix functions of this form. A number of new and novel results are presented in this thesis. Firstly, we prove the convergence of the matrix transfer technique for the solution of the fractional Poisson equation and we give conditions by which the finite difference discretisation can be replaced by other methods for discretising the Laplacian. We then investigate a number of methods for approximating matrix functions of the form A^(-α/2)b and investigate stopping criteria for these methods. In particular, we derive a new method for restarting the Lanczos approximation to f(A)b. We then apply these techniques to the problem of sampling from a GMRF and construct a full suite of methods for sampling conditioned on linear constraints and approximating the likelihood. Finally, we consider the problem of sampling from a generalised Matern random field, which combines our techniques for solving fractional-in-space partial differential equations with our method for sampling from GMRFs.

Bias in the nonlinear filter generator output sequence

Nonlinear filter generators are common components used in the keystream generators for stream ciphers and more recently for authentication mechanisms. They consist of a Linear Feedback Shift Register (LFSR) and a nonlinear Boolean function to mask the linearity of the LFSR output. Properties of the output of a nonlinear filter are not well studied. Anderson noted that the m-tuple output of a nonlinear filter with consecutive taps to the filter function is unevenly distributed. Current designs use taps which are not consecutive. We examine m-tuple outputs from nonlinear filter generators constructed using various LFSRs and Boolean functions for both consecutive and uneven (full positive difference sets where possible) tap positions. The investigation reveals that in both cases, the m-tuple output is not uniform. However, consecutive tap positions result in a more biased distribution than uneven tap positions, with some m-tuples not occurring at all. These biased distributions indicate a potential flaw that could be exploited for cryptanalysis.

Urban dynamic origin-destination matrices estimation

The aim of this paper is to explore a new approach to obtain better traffic demand (Origin-Destination, OD matrices) for dense urban networks. From reviewing existing methods, from static to dynamic OD matrix evaluation, possible deficiencies in the approach could be identified: traffic assignment details for complex urban network and lacks in dynamic approach. To improve the global process of traffic demand estimation, this paper is focussing on a new methodology to determine dynamic OD matrices for urban areas characterized by complex route choice situation and high level of traffic controls. An iterative bi-level approach will be used, the Lower level (traffic assignment) problem will determine, dynamically, the utilisation of the network by vehicles using heuristic data from mesoscopic traffic simulator and the Upper level (matrix adjustment) problem will proceed to an OD estimation using optimization Kalman filtering technique. In this way, a full dynamic and continuous estimation of the final OD matrix could be obtained. First results of the proposed approach and remarks are presented.

A new family of Marx generator based on resonant converter

This paper presents a novel topology to generate high voltage with utilization of slow and fast power switches. New concepts used in this topology include numbers of diode-capacitor units in parallel with resonant circuits which are connected to a positive buck-boost converter. The resonant circuit reverses the voltage polarity of the capacitors. This configuration has capability of generating a flexible high voltage with certain number of capacitors. The advantage of this topology is to use slow switches, less number of diodes and capacitors compare to Marx generator. Simulations have been performed to verify the proposed topology.

Mineralized human primary osteoblast matrices as a model system to analyse interactions of prostate cancer cells with the bone microenvironment

Prostate cancer metastasis is reliant on the reciprocal interactions between cancer cells and the bone niche/micro-environment. The production of suitable matrices to study metastasis, carcinogenesis and in particular prostate cancer/bone micro-environment interaction has been limited to specific protein matrices or matrix secreted by immortalised cell lines that may have undergone transformation processes altering signaling pathways and modifying gene or receptor expression. We hypothesize that matrices produced by primary human osteoblasts are a suitable means to develop an in vitro model system for bone metastasis research mimicking in vivo conditions. We have used a decellularized matrix secreted from primary human osteoblasts as a model for prostate cancer function in the bone micro-environment. We show that this collagen I rich matrix is of fibrillar appearance, highly mineralized, and contains proteins, such as osteocalcin, osteonectin and osteopontin, and growth factors characteristic of bone extracellular matrix (ECM). LNCaP and PC3 cells grown on this matrix, adhere strongly, proliferate, and express markers consistent with a loss of epithelial phenotype. Moreover, growth of these cells on the matrix is accompanied by the induction of genes associated with attachment, migration, increased invasive potential, Ca2+ signaling and osteolysis. In summary, we show that growth of prostate cancer cells on matrices produced by primary human osteoblasts mimics key features of prostate cancer bone metastases and thus is a suitable model system to study the tumor/bone micro-environment interaction in this disease.

A resonant based Marx generator

The configuration proposed in this paper aims to generate high voltage for pulsed power applications. The main idea is to charge two groups of capacitors in parallel through an inductor and take the advantage of resonant phenomena in charging each capacitor up to a double input voltage level. In each resonant half a cycle, one of those capacitor groups are charged, and finally the charged capacitors will be connected together in series and the summation of the capacitor voltages can be appeared at the output of the topology. This topology can be considered as a modified Marx generator which works based on the resonant concept. Simulation models of this converter have been investigated in Matlab/SIMULINK platform and the attained results fully satisfy the proper operation of the converter.

Osteogenic induction of human bone marrow-derived mesenchymal progenitor cells in novel synthetic polymer-hydrogel matrices

The aim of this project was to investigate the in vitro osteogenic potential of human mesenchymal progenitor cells in novel matrix architectures built by means of a three-dimensional bioresorbable synthetic framework in combination with a hydrogel. Human mesenchymal progenitor cells (hMPCs) were isolated from a human bone marrow aspirate by gradient centrifugation. Before in vitro engineering of scaffold-hMPC constructs, the adipogenic and osteogenic differentiation potential was demonstrated by staining of neutral lipids and induction of bone-specific proteins, respectively. After expansion in monolayer cultures, the cells were enzymatically detached and then seeded in combination with a hydrogel into polycaprolactone (PCL) and polycaprolactone-hydroxyapatite (PCL-HA) frameworks. This scaffold design concept is characterized by novel matrix architecture, good mechanical properties, and slow degradation kinetics of the framework and a biomimetic milieu for cell delivery and proliferation. To induce osteogenic differentiation, the specimens were cultured in an osteogenic cell culture medium and were maintained in vitro for 6 weeks. Cellular distribution and viability within three-dimensional hMPC bone grafts were documented by scanning electron microscopy, cell metabolism assays, and confocal laser microscopy. Secretion of the osteogenic marker molecules type I procollagen and osteocalcin was analyzed by semiquantitative immunocytochemistry assays. Alkaline phosphatase activity was visualized by p-nitrophenyl phosphate substrate reaction. During osteogenic stimulation, hMPCs proliferated toward and onto the PCL and PCL-HA scaffold surfaces and metabolic activity increased, reaching a plateau by day 15. The temporal pattern of bone-related marker molecules produced by in vitro tissue-engineered scaffold-cell constructs revealed that hMPCs differentiated better within the biomimetic matrix architecture along the osteogenic lineage.

In vitro characterization of natural and synthetic dermal matrices cultured with human dermal fibroblasts

The ideal dermal matrix should be able to provide the right biological and physical environment to ensure homogenous cell and extracellular matrix (ECM) distribution, as well as the right size and morphology of the neo-tissue required. Four natural and synthetic 3D matrices were evaluated in vitro as dermal matrices, namely (1) equine collagen foam, TissuFleece®, (2) acellular dermal replacement, Alloderm®, (3) knitted poly(lactic-co-glycolic acid) (10:90)–poly(-caprolactone) (PLGA–PCL) mesh, (4) chitosan scaffold. Human dermal fibroblasts were cultured on the specimens over 3 weeks. Cell morphology, distribution and viability were assessed by electron microscopy, histology and confocal laser microscopy. Metabolic activity and DNA synthesis were analysed via MTS metabolic assay and [3H]-thymidine uptake, while ECM protein expression was determined by immunohistochemistry. TissuFleece®, Alloderm® and PLGA–PCL mesh supported cell attachment, proliferation and neo-tissue formation. However, TissuFleece® contracted to 10% of the original size while Alloderm® supported cell proliferation predominantly on the surface of the material. PLGA–PCL mesh promoted more homogenous cell distribution and tissue formation. Chitosan scaffolds did not support cell attachment and proliferation. These results demonstrated that physical characteristics including porosity and mechanical stability to withstand cell contraction forces are important in determining the success of a dermal matrix material.

Bias in the nonlinear filter generator output sequence

Nonlinear filter generators are common components used in the keystream generators for stream ciphers and more recently for authentication mechanisms. They consist of a Linear Feedback Shift Register (LFSR) and a nonlinear Boolean function to mask the linearity of the LFSR output. Properties of the output of a nonlinear filter are not well studied. Anderson noted that the m-tuple output of a nonlinear filter with consecutive taps to the filter function is unevenly distributed. Current designs use taps which are not consecutive. We examine m-tuple outputs from nonlinear filter generators constructed using various LFSRs and Boolean functions for both consecutive and uneven (full positive difference sets where possible) tap positions. The investigation reveals that in both cases, the m-tuple output is not uniform. However, consecutive tap positions result in a more biased distribution than uneven tap positions, with some m-tuples not occurring at all. These biased distributions indicate a potential flaw that could be exploited for cryptanalysis

Engineered silk fibroin protein 3D matrices for in vitro tumor model

3D in vitro model systems that are able to mimic the in vivo microenvironment are now highly sought after in cancer research. Antheraea mylitta silk fibroin protein matrices were investigated as potential biomaterial for in vitro tumor modeling. We compared the characteristics of MDA-MB-231 cells on A. mylitta, Bombyx mori silk matrices, Matrigel, and tissue culture plates. The attachment and morphology of the MDA-MB-231 cell line on A. mylitta silk matrices was found to be better than on B. mori matrices and comparable to Matrigel and tissue culture plates. The cells grown in all 3D cultures showed more MMP-9 activity, indicating a more invasive potential. In comparison to B. mori fibroin, A. mylitta fibroin not only provided better cell adhesion, but also improved cell viability and proliferation. Yield coefficient of glucose consumed to lactate produced by cells on 3D A. mylitta fibroin was found to be similar to that of cancer cells in vivo. LNCaP prostate cancer cells were also cultured on 3D A. mylitta fibroin and they grew as clumps in long term culture. The results indicate that A. mylitta fibroin scaffold can provide an easily manipulated microenvironment system to investigate individual factors such as growth factors and signaling peptides, as well as evaluation of anticancer drugs.