Matrix Power S-box Analysis

* Work supported by the Lithuanian State Science and Studies Foundation.

Asymmetric Cipher Protocol Using Decomposition Problem

The asymmetric cipher protocol based on decomposition problem in matrix semiring M over semiring of natural numbers N is presented. The security parameters are defined and preliminary security analysis is presented.

Extended principal component analysis and its applications to image analysis

The objectives of this research are to analyze and develop a modified Principal Component Analysis (PCA) and to develop a two-dimensional PCA with applications in image processing. PCA is a classical multivariate technique where its mathematical treatment is purely based on the eigensystem of positive-definite symmetric matrices. Its main function is to statistically transform a set of correlated variables to a new set of uncorrelated variables over $\IR\sp{n}$ by retaining most of the variations present in the original variables.^ The variances of the Principal Components (PCs) obtained from the modified PCA form a correlation matrix of the original variables. The decomposition of this correlation matrix into a diagonal matrix produces a set of orthonormal basis that can be used to linearly transform the given PCs. It is this linear transformation that reproduces the original variables. The two-dimensional PCA can be devised as a two successive of one-dimensional PCA. It can be shown that, for an $m\times n$ matrix, the PCs obtained from the two-dimensional PCA are the singular values of that matrix.^ In this research, several applications for image analysis based on PCA are developed, i.e., edge detection, feature extraction, and multi-resolution PCA decomposition and reconstruction. ^

Correlation of detector dog alerts to cocaine decomposition products found in illicit forensic specimens

The volatile chemicals which comprise the odor of the illicit drug cocaine have been analyzed by adsorption onto activated charcoal followed by solvent elution and GC/MS analysis. A series of field tests have been performed to determine the dominant odor compound to which dogs alert. All of our data to date indicate that the dominant odor is due to the presence of methyl benzoate which is associated with the cocaine, rather than the cocaine itself. When methyl benzoate and cocaine are spiked onto U.S. currency, the threshold level of methyl benzoate required for a canine to signal an alert is typically 1-10 $\mu$g. Humans have been shown to have a sensitivity similar to dogs for methyl benzoate but with poorer selectivity/reliability. The dominant decomposition pathway for cocaine has been evaluated at elevated temperatures (up to 280$\sp\circ$C). Benzoic acid, but no detectable methyl benzoate, is formed. Solvent extraction and SFE were used to study the recovery of cocaine from U.S. currency. The amount of cocaine which could be recovered was found to decrease with time. ^

American Alligator Digestion Rate of Blue Crabs and Its Implications for Stomach Contents Analysis

Stomach contents analysis (SCA) provides a snap-shot observation of a consumer's diet. Interpretation of SCA data can be complicated by many factors, including variation in gastric residence times and digestion rates among prey taxa. Although some SCA methods are reported to efficiently remove all stomach contents, the effectiveness of these techniques has rarely been tested for large irregular shaped prey with hard exoskeletons. We used a controlled feeding trial to estimate gastric residency time and decomposition rate of a large crustacean prey item, the Blue Crab (Callinectes sapidus), which is consumed by American Alligators (Alligator mississippiensis), an abundant apex predator in coastal habitats of the southeastern United States. The decomposition rate of C. sapidus in the stomachs of A. mississippiensis followed a predictable pattern, and some crab pieces remained in stomachs for at least 14 days. We also found that certain portions of C. sapidus were prone to becoming caught within the stomach or esophagus, meaning not all crab parts are consistently recovered using gastric lavage techniques. However, because the state of decomposition of crabs was predictable, it is possible to estimate time since consumption for crabs recovered from wild alligators. This information, coupled with a detailed understanding of crab distributions and alligator movement tactics could help elucidate patterns of cross-ecosystem foraging by the American Alligator in coastal habitats.

Hydroperiod and seasonal effects on fish decomposition in an oligotrophic Everglades marsh

In the Everglades, the majority of fish detrital inputs occur during the dry scason, when waterlevel drawdown reduces aquatic habitat. While these mortality events are highly seasonal, the remineralization and recycling of fish detrital nutrients may represent an important stimulus to the ecosystem in the following wet season. The goal of this study was to quantify the rate of detrital fish decomposition during three periods of the year to determine seasonal variations in decomposition patterns in this ecosystem. A multiple regression analysis showed that hydroperiod and water depth both played a role in determining fish decomposition rates within this ecosystem. Decomposition rates ranged from a low of 13% day−1 in December 2000 to a high of 50% day−1 in April 2001, the height of the dry season. Phosphorus analysis showed that Gambusia holbrooki, the dominant small fish species in the Everglades, contains 7.169±1.46 mg P g−1 wet fish weight. Based on the observed decomposition rates and the average biomass added, the estimafed daily flux of phosphorus from the experimental detrital loading ranged from a low of 27.04 mg P day−1 to a high of 108.14 mg P day−1 during the decomposition period. We estimated that these inputs could represent an input of 43 μg P m−2 day−1 to the total temporal Everglades phosphorus budget. Although much of this phosphorus is likely incorporated into the macroinvertebrate pool, detrital inputs peak during the dry season when nutrients are most likely to be incorporated into the soil and occur when decomposition of vegetative material is moisture-limited. These inputs may therefore play an important role in stimulating vegetative production during the early wet season.

Method development for the analysis of smokeless powders and organic gunshot residue by ultra performance liquid chromatography with tandem mass spectrometry

The goal of this project was to develop a rapid separation and detection method for analyzing organic compounds in smokeless powders and then test its applicability on gunshot residue (GSR) samples. In this project, a total of 20 common smokeless powder additives and their decomposition products were separated by ultra performance liquid chromatography (UPLC) and confirmed by tandem mass spectrometry (MS/MS) using multiple reaction monitoring mode (MRM). Some of the targeted compounds included diphenylamines, centralites, nitrotoluenes, nitroglycerin, and various phthalates. The compounds were ionized in the MS source using simultaneous positive and negative electrospray ionization (ESI) with negative atmospheric pressure chemical ionization (APCI) in order to detect all compounds in a single analysis. The developed UPLC/MS/MS method was applied to commercially available smokeless powders and gunshot residue samples recovered from the hands of shooters, spent cartridges, and smokeless powder retrieved from unfired cartridges. Distinct compositions were identified for smokeless powders from different manufacturers and from separate manufacturing lots. The procedure also produced specific chemical profiles when tested on gunshot residues from different manufacturers. Overall, this thesis represents the development of a rapid and reproducible procedure capable of simultaneously detecting the widest possible range of components present in organic gunshot residue.^

Identification of characteristic volatile organic compounds released during the decomposition process of human remains and analogues

The manner in which remains decompose has been and is currently being researched around the world, yet little is still known about the generated scent of death. In fact, it was not until the Casey Anthony trial that research on the odor released from decomposing remains, and the compounds that it is comprised of, was brought to light. The Anthony trial marked the first admission of human decomposition odor as forensic evidence into the court of law; however, it was not "ready for prime time" as the scientific research on the scent of death is still in its infancy. This research employed the use of solid-phase microextraction (SPME) with gas chromatography-mass spectrometry (GC-MS) to identify the volatile organic compounds (VOCs) released from decomposing remains and to assess the impact that different environmental conditions had on the scent of death. Using human cadaver analogues, it was discovered that the environment in which the remains were exposed to dramatically affected the odors released by either modifying the compounds that it was comprised of or by enhancing/hindering the amount that was liberated. In addition, the VOCs released during the different stages of the decomposition process for both human remains and analogues were evaluated. Statistical analysis showed correlations between the stage of decay and the VOCs generated, such that each phase of decomposition was distinguishable based upon the type and abundance of compounds that comprised the odor. This study has provided new insight into the scent of death and the factors that can dramatically affect it, specifically, frozen, aquatic, and soil environments. Moreover, the results revealed that different stages of decomposition were distinguishable based upon the type and total mass of each compound present. Thus, based upon these findings, it is suggested that the training aids that are employed for human remains detection (HRD) canines should 1) be characteristic of remains that have undergone decomposition in different environmental settings, and 2) represent each stage of decay, to ensure that the HRD canines have been trained to the various odors that they are likely to encounter in an operational situation.

Seismic Response Analysis of a Full-Scale Base-Isolated Structure via Measurements and Modeling

The full-scale base-isolated structure studied in this dissertation is the only base-isolated building in South Island of New Zealand. It sustained hundreds of earthquake ground motions from September 2010 and well into 2012. Several large earthquake responses were recorded in December 2011 by NEES@UCLA and by GeoNet recording station nearby Christchurch Women's Hospital. The primary focus of this dissertation is to advance the state-of-the art of the methods to evaluate performance of seismic-isolated structures and the effects of soil-structure interaction by developing new data processing methodologies to overcome current limitations and by implementing advanced numerical modeling in OpenSees for direct analysis of soil-structure interaction.

This dissertation presents a novel method for recovering force-displacement relations within the isolators of building structures with unknown nonlinearities from sparse seismic-response measurements of floor accelerations. The method requires only direct matrix calculations (factorizations and multiplications); no iterative trial-and-error methods are required. The method requires a mass matrix, or at least an estimate of the floor masses. A stiffness matrix may be used, but is not necessary. Essentially, the method operates on a matrix of incomplete measurements of floor accelerations. In the special case of complete floor measurements of systems with linear dynamics, real modes, and equal floor masses, the principal components of this matrix are the modal responses. In the more general case of partial measurements and nonlinear dynamics, the method extracts a number of linearly-dependent components from Hankel matrices of measured horizontal response accelerations, assembles these components row-wise and extracts principal components from the singular value decomposition of this large matrix of linearly-dependent components. These principal components are then interpolated between floors in a way that minimizes the curvature energy of the interpolation. This interpolation step can make use of a reduced-order stiffness matrix, a backward difference matrix or a central difference matrix. The measured and interpolated floor acceleration components at all floors are then assembled and multiplied by a mass matrix. The recovered in-service force-displacement relations are then incorporated into the OpenSees soil structure interaction model.

Numerical simulations of soil-structure interaction involving non-uniform soil behavior are conducted following the development of the complete soil-structure interaction model of Christchurch Women's Hospital in OpenSees. In these 2D OpenSees models, the superstructure is modeled as two-dimensional frames in short span and long span respectively. The lead rubber bearings are modeled as elastomeric bearing (Bouc Wen) elements. The soil underlying the concrete raft foundation is modeled with linear elastic plane strain quadrilateral element. The non-uniformity of the soil profile is incorporated by extraction and interpolation of shear wave velocity profile from the Canterbury Geotechnical Database. The validity of the complete two-dimensional soil-structure interaction OpenSees model for the hospital is checked by comparing the results of peak floor responses and force-displacement relations within the isolation system achieved from OpenSees simulations to the recorded measurements. General explanations and implications, supported by displacement drifts, floor acceleration and displacement responses, force-displacement relations are described to address the effects of soil-structure interaction.

Using virtual topology operations to generate analysis topology

Virtual topology operations have been utilized to generate an analysis topology definition suitable for downstream mesh generation. Detailed descriptions are provided for virtual topology merge and split operations for all topological entities. Current virtual topology technology is extended to allow the virtual partitioning of volume cells and the topological queries required to carry out each operation are provided. Virtual representations are robustly linked to the underlying geometric definition through an analysis topology. The analysis topology and all associated virtual and topological dependencies are automatically updated after each virtual operation, providing the link to the underlying CAD geometry. Therefore, a valid description of the analysis topology, including relative orientations, is maintained. This enables downstream operations, such as the merging or partitioning of virtual entities, and interrogations, such as determining if a specific meshing strategy can be applied to the virtual volume cells, to be performed on the analysis topology description. As the virtual representation is a non-manifold description of the sub-divided domain the interfaces between cells are recorded automatically. This enables the advantages of non-manifold modelling to be exploited within the manifold modelling environment of a major commercial CAD system, without any adaptation of the underlying CAD model. A hierarchical virtual structure is maintained where virtual entities are merged or partitioned. This has a major benefit over existing solutions as the virtual dependencies are stored in an open and accessible manner, providing the analyst with the freedom to create, modify and edit the analysis topology in any preferred sequence, whilst the original CAD geometry is not disturbed. Robust definitions of the topological and virtual dependencies enable the same virtual topology definitions to be accessed, interrogated and manipulated within multiple different CAD packages and linked to the underlying geometry.

Study of Co-based hydrotalcite-derived mixed metal oxides partially modified with silver as potential catalysts for N2O decomposition

Co-Al-Ox mixed metal oxides partially modified with Cu or Mg, as well as Ag were successfully prepared, characterized and evaluated as potential catalysts for the N2O decomposition. The materials were characterized by the following techniques: X-Ray Diffraction, Thermogravimetric Analysis (TGA), N2 Physisorption, Hydrogen Temperature-Programmed Reduction (H2-TPR), and X-ray photoelectron spectroscopy (XPS). Ag-modified HT-derived mixed oxides showed enhanced activity compared to the undoped materials, the optimum composition was found for (1 wt.% Ag)CHT-Co3Al. The catalyst characterization studies suggested that the improved catalytic activity of Ag-promoted catalysts were mainly because of the altered redox properties of the materials.

A domain decomposition based algorithm for non-linear 2D inverse heat conduction problems

Inverse heat conduction problems (IHCPs) appear in many important scientific and technological fields. Hence analysis, design, implementation and testing of inverse algorithms are also of great scientific and technological interest. The numerical simulation of 2-D and –D inverse (or even direct) problems involves a considerable amount of computation. Therefore, the investigation and exploitation of parallel properties of such algorithms are equally becoming very important. Domain decomposition (DD) methods are widely used to solve large scale engineering problems and to exploit their inherent ability for the solution of such problems.

Time domain decomposition for European options in financial modelling

Finance is one of the fastest growing areas in modern applied mathematics with real world applications. The interest of this branch of applied mathematics is best described by an example involving shares. Shareholders of a company receive dividends which come from the profit made by the company. The proceeds of the company, once it is taken over or wound up, will also be distributed to shareholders. Therefore shares have a value that reflects the views of investors about the likely dividend payments and capital growth of the company. Obviously such value will be quantified by the share price on stock exchanges. Therefore financial modelling serves to understand the correlations between asset and movements of buy/sell in order to reduce risk. Such activities depend on financial analysis tools being available to the trader with which he can make rapid and systematic evaluation of buy/sell contracts. There are other financial activities and it is not an intention of this paper to discuss all of these activities. The main concern of this paper is to propose a parallel algorithm for the numerical solution of an European option. This paper is organised as follows. First, a brief introduction is given of a simple mathematical model for European options and possible numerical schemes of solving such mathematical model. Second, Laplace transform is applied to the mathematical model which leads to a set of parametric equations where solutions of different parametric equations may be found concurrently. Numerical inverse Laplace transform is done by means of an inversion algorithm developed by Stehfast. The scalability of the algorithm in a distributed environment is demonstrated. Third, a performance analysis of the present algorithm is compared with a spatial domain decomposition developed particularly for time-dependent heat equation. Finally, a number of issues are discussed and future work suggested.

A single-code software model for multiphysics analysis-engine on parallel and distributed computers with the PHYSICA toolkit

Abstract not available