Propagation of low power low divergence Gaussian fields in unbiased self-defocusing photorefractive media and their interactions

Many optical networks are limited in speed and processing capability due to the necessity for the optical signal to be converted to an electrical signal and back again. In addition, electronically manipulated interconnects in an otherwise optical network lead to overly complicated systems. Optical spatial solitons are optical beams that propagate without spatial divergence. They are capable of phase dependent interactions, and have therefore been extensively researched as suitable all optical interconnects for over 20 years. However, they require additional external components, initially high voltage power sources were required, several years later, high power background illumination had replaced the high voltage. However, these additional components have always remained as the greatest hurdle in realising the applications of the interactions of spatial optical solitons as all optical interconnects. Recently however, self-focusing was observed in an otherwise self-defocusing photorefractive crystal. This observation raises the possibility of the formation of soliton-like fields in unbiased self-defocusing media, without the need for an applied electrical field or background illumination. This thesis will present an examination of the possibility of the formation of soliton-like low divergence fields in unbiased self-defocusing photorefractive media. The optimal incident beam and photorefractive media parameters for the formation of these fields will be presented, together with an analytical and numerical study of the effect of these parameters. In addition, preliminary examination of the interactions of two of these fields will be presented. In order to complete an analytical examination of the field propagating through the photorefractive medium, the spatial profile of the beam after propagation through the medium was determined. For a low power solution, it was found that an incident Gaussian field maintains its Gaussian profile as it propagates. This allowed the beam at all times to be described by an individual complex beam parameter, while also allowing simple analytical solutions to the appropriate wave equation. An analytical model was developed to describe the effect of the photorefractive medium on the Gaussian beam. Using this model, expressions for the required intensity dependent change in both the real and imaginary components of the refractive index were found. Numerical investigation showed that under certain conditions, a low powered Gaussian field could propagate in self-defocusing photorefractive media with divergence of approximately 0.1 % per metre. An investigation into the parameters of a Ce:BaTiO3 crystal showed that the intensity dependent absorption is wavelength dependent, and can in fact transition to intensity dependent transparency. Thus, with careful wavelength selection, the required intensity dependent change in both the real and imaginary components of the refractive index for the formation of a low divergence Gaussian field are physically realisable. A theoretical model incorporating the dependence of the change in real and imaginary components of the refractive index on propagation distance was developed. Analytical and numerical results from this model are congruent with the results from the previous model, showing low divergence fields with divergence less than 0.003 % over the propagation length of the photorefractive medium. In addition, this approach also confirmed the previously mentioned self-focusing effect of the self-defocusing media, and provided an analogy to a negative index GRIN lens with an intensity dependent focal length. Experimental results supported the findings of the numerical analysis. Two low divergence fields were found to possess the ability to interact in a Ce:BaTiO3 crystal in a soliton-like fashion. The strength of these interactions was found to be dependent on the degree of divergence of the individual beams. This research found that low-divergence fields are possible in unbiased self-defocusing photorefractive media, and that soliton-like interactions between two of these fields are possible. However, in order for these types of fields to be used in future all optical interconnects, the manipulation of these interactions, together with the ability for these fields to guide a second beam at a different wavelength, must be investigated.

Flow regime transition criteria for two-phase flow at reduced gravity conditions

Flow regime transition criteria are of practical importance for two-phase flow analyses at reduced gravity conditions. Here, flow regime transition criteria which take the friction pressure loss effect into account were studied in detail. Criteria at reduced gravity conditions were developed by extending an existing model with various experimental datasets taken at microgravity conditions showed satisfactory agreement. Sample computations of the model were performed at various gravity conditions, such as 0.196, 1.62, 3.71, and 9.81 m/s2 corresponding to micro-gravity and lunar, Martian and Earth surface gravity, respectively. It was found that the effect of gravity on bubbly-slug and slug-annular (churn) transitions in a two-phase flow system was more pronounced at low liquid flow conditions, whereas the gravity effect could be ignored at high mixture volumetric flux conditions. While for the annular flow transitions due to flow reversal and onset of dropset entrainment, higher superficial gas velocity was obtained at higher gravity level.

Statistical eye model for normal eyes

Purpose. To create a binocular statistical eye model based on previously measured ocular biometric data. Methods. Thirty-nine parameters were determined for a group of 127 healthy subjects (37 male, 90 female; 96.8% Caucasian) with an average age of 39.9 ± 12.2 years and spherical equivalent refraction of −0.98 ± 1.77 D. These parameters described the biometry of both eyes and the subjects' age. Missing parameters were complemented by data from a previously published study. After confirmation of the Gaussian shape of their distributions, these parameters were used to calculate their mean and covariance matrices. These matrices were then used to calculate a multivariate Gaussian distribution. From this, an amount of random biometric data could be generated, which were then randomly selected to create a realistic population of random eyes. Results. All parameters had Gaussian distributions, with the exception of the parameters that describe total refraction (i.e., three parameters per eye). After these non-Gaussian parameters were omitted from the model, the generated data were found to be statistically indistinguishable from the original data for the remaining 33 parameters (TOST [two one-sided t tests]; P < 0.01). Parameters derived from the generated data were also significantly indistinguishable from those calculated with the original data (P > 0.05). The only exception to this was the lens refractive index, for which the generated data had a significantly larger SD. Conclusions. A statistical eye model can describe the biometric variations found in a population and is a useful addition to the classic eye models.

Anomalous event detection using a semi-two dimensional hidden Markov model

The rapid increase in the deployment of CCTV systems has led to a greater demand for algorithms that are able to process incoming video feeds. These algorithms are designed to extract information of interest for human operators. During the past several years, there has been a large effort to detect abnormal activities through computer vision techniques. Typically, the problem is formulated as a novelty detection task where the system is trained on normal data and is required to detect events which do not fit the learned `normal' model. Many researchers have tried various sets of features to train different learning models to detect abnormal behaviour in video footage. In this work we propose using a Semi-2D Hidden Markov Model (HMM) to model the normal activities of people. The outliers of the model with insufficient likelihood are identified as abnormal activities. Our Semi-2D HMM is designed to model both the temporal and spatial causalities of the crowd behaviour by assuming the current state of the Hidden Markov Model depends not only on the previous state in the temporal direction, but also on the previous states of the adjacent spatial locations. Two different HMMs are trained to model both the vertical and horizontal spatial causal information. Location features, flow features and optical flow textures are used as the features for the model. The proposed approach is evaluated using the publicly available UCSD datasets and we demonstrate improved performance compared to other state of the art methods.

Two novel numerical methods for solving the two-dimensional fractional Fitzhugh-Nagumo-monodomain model

Fractional mathematical models represent a new approach to modelling complex spatial problems in which there is heterogeneity at many spatial and temporal scales. In this paper, a two-dimensional fractional Fitzhugh-Nagumo-monodomain model with zero Dirichlet boundary conditions is considered. The model consists of a coupled space fractional diffusion equation (SFDE) and an ordinary differential equation. For the SFDE, we first consider the numerical solution of the Riesz fractional nonlinear reaction-diffusion model and compare it to the solution of a fractional in space nonlinear reaction-diffusion model. We present two novel numerical methods for the two-dimensional fractional Fitzhugh-Nagumo-monodomain model using the shifted Grunwald-Letnikov method and the matrix transform method, respectively. Finally, some numerical examples are given to exhibit the consistency of our computational solution methodologies. The numerical results demonstrate the effectiveness of the methods.

Stored blood products augment inflammation in a two-event model of Transfusion Related Acute Lung Injury (TRALI)

Aim/Background TRALI is hypothesised to develop via a two-event mechanism involving both the patieint's underlying morbidity and blood product factors. The storage of cellular products has been implicated in cases of non-antibody mediated TRALI, however the pathophysiological mechanisms are undefined. We investigated blood product storage-related modulation of inflmmatory cells and medicators involved in TRALI. Methods In an in vitro mode, fresh human whole blood was mixed with culture media (control) or LPS as a 1st event and "transfused" with 10% (v/v) pooled supernatant (SN) from Day 1 (d1, n=75) or Day 42 (D42, n=113) packed red blood cells (PRBCs) as a 2nd event. Following 6hrs, culture SN was used to assess the overall inflammatory response (cytometric bead array) and a duplicate assay containing protein transport inhibitor was used to assess neutrophil- and monocyte-specific inflmamatory responses using multi-colour flow cytometry. Panels: IL-6, IL-8, IL-10, IL-12, IL-1, TNF, MCP-1, IP-10, MIP-1. One-way ANOVA 95% CI. Results In the absence of LPS, exposure to D1 or D42 PRBC-SN reduced monocyte expression of IL-6, IL-8 and Il-10. D42 PRBC-SN also reduced monocyte IP-10, and the overall IL-8 production was increased. In the presence of LPS, D1-PRBC SN only modified overall IP-10 levels which were reduced. However, cf LPS alone, the combination of LPS and D42 PRBC-SN resulted in increased neutrophil and monocyte productionof IL-1 and IL-8 as well as reduced monocyte TNF production. Additionally, LPS and D42 PRBC-SN resulted in overall inflmmatory changes: elevated IL-8,

A two-stage item recommendation method using probabilistic ranking with reconstructed tensor model

In a tag-based recommender system, the multi-dimensional correlation should be modeled effectively for finding quality recommendations. Recently, few researchers have used tensor models in recommendation to represent and analyze latent relationships inherent in multi-dimensions data. A common approach is to build the tensor model, decompose it and, then, directly use the reconstructed tensor to generate the recommendation based on the maximum values of tensor elements. In order to improve the accuracy and scalability, we propose an implementation of the -mode block-striped (matrix) product for scalable tensor reconstruction and probabilistically ranking the candidate items generated from the reconstructed tensor. With testing on real-world datasets, we demonstrate that the proposed method outperforms the benchmarking methods in terms of recommendation accuracy and scalability.

An external field prior for the hidden Potts model with application to cone-beam computed tomography

In images with low contrast-to-noise ratio (CNR), the information gain from the observed pixel values can be insufficient to distinguish foreground objects. A Bayesian approach to this problem is to incorporate prior information about the objects into a statistical model. A method for representing spatial prior information as an external field in a hidden Potts model is introduced. This prior distribution over the latent pixel labels is a mixture of Gaussian fields, centred on the positions of the objects at a previous point in time. It is particularly applicable in longitudinal imaging studies, where the manual segmentation of one image can be used as a prior for automatic segmentation of subsequent images. The method is demonstrated by application to cone-beam computed tomography (CT), an imaging modality that exhibits distortions in pixel values due to X-ray scatter. The external field prior results in a substantial improvement in segmentation accuracy, reducing the mean pixel misclassification rate for an electron density phantom from 87% to 6%. The method is also applied to radiotherapy patient data, demonstrating how to derive the external field prior in a clinical context.

A cellular automata model to investigate immune cell–tumor cell interactions in growing tumors in two spatial dimensions

We develop a hybrid cellular automata model to describe the effect of the immune system and chemokines on a growing tumor. The hybrid cellular automata model consists of partial differential equations to model chemokine concentrations, and discrete cellular automata to model cell–cell interactions and changes. The computational implementation overlays these two components on the same spatial region. We present representative simulations of the model and show that increasing the number of immature dendritic cells (DCs) in the domain causes a decrease in the number of tumor cells. This result strongly supports the hypothesis that DCs can be used as a cancer treatment. Furthermore, we also use the hybrid cellular automata model to investigate the growth of a tumor in a number of computational “cancer patients.” Using these virtual patients, the model can explain that increasing the number of DCs in the domain causes longer “survival.” Not surprisingly, the model also reflects the fact that the parameter related to tumor division rate plays an important role in tumor metastasis.

Numerical treatment of a two-dimensional variable-order fractional nonlinear reaction-diffusion model

A two-dimensional variable-order fractional nonlinear reaction-diffusion model is considered. A second-order spatial accurate semi-implicit alternating direction method for a two-dimensional variable-order fractional nonlinear reaction-diffusion model is proposed. Stability and convergence of the semi-implicit alternating direct method are established. Finally, some numerical examples are given to support our theoretical analysis. These numerical techniques can be used to simulate a two-dimensional variable order fractional FitzHugh-Nagumo model in a rectangular domain. This type of model can be used to describe how electrical currents flow through the heart, controlling its contractions, and are used to ascertain the effects of certain drugs designed to treat arrhythmia.

Mixture models of nucleotide sequence evolution that account for heterogeneity in the substitution process across sites and across lineages

Molecular phylogenetic studies of homologous sequences of nucleotides often assume that the underlying evolutionary process was globally stationary, reversible, and homogeneous (SRH), and that a model of evolution with one or more site-specific and time-reversible rate matrices (e.g., the GTR rate matrix) is enough to accurately model the evolution of data over the whole tree. However, an increasing body of data suggests that evolution under these conditions is an exception, rather than the norm. To address this issue, several non-SRH models of molecular evolution have been proposed, but they either ignore heterogeneity in the substitution process across sites (HAS) or assume it can be modeled accurately using the distribution. As an alternative to these models of evolution, we introduce a family of mixture models that approximate HAS without the assumption of an underlying predefined statistical distribution. This family of mixture models is combined with non-SRH models of evolution that account for heterogeneity in the substitution process across lineages (HAL). We also present two algorithms for searching model space and identifying an optimal model of evolution that is less likely to over- or underparameterize the data. The performance of the two new algorithms was evaluated using alignments of nucleotides with 10 000 sites simulated under complex non-SRH conditions on a 25-tipped tree. The algorithms were found to be very successful, identifying the correct HAL model with a 75% success rate (the average success rate for assigning rate matrices to the tree's 48 edges was 99.25%) and, for the correct HAL model, identifying the correct HAS model with a 98% success rate. Finally, parameter estimates obtained under the correct HAL-HAS model were found to be accurate and precise. The merits of our new algorithms were illustrated with an analysis of 42 337 second codon sites extracted from a concatenation of 106 alignments of orthologous genes encoded by the nuclear genomes of Saccharomyces cerevisiae, S. paradoxus, S. mikatae, S. kudriavzevii, S. castellii, S. kluyveri, S. bayanus, and Candida albicans. Our results show that second codon sites in the ancestral genome of these species contained 49.1% invariable sites, 39.6% variable sites belonging to one rate category (V1), and 11.3% variable sites belonging to a second rate category (V2). The ancestral nucleotide content was found to differ markedly across these three sets of sites, and the evolutionary processes operating at the variable sites were found to be non-SRH and best modeled by a combination of eight edge-specific rate matrices (four for V1 and four for V2). The number of substitutions per site at the variable sites also differed markedly, with sites belonging to V1 evolving slower than those belonging to V2 along the lineages separating the seven species of Saccharomyces. Finally, sites belonging to V1 appeared to have ceased evolving along the lineages separating S. cerevisiae, S. paradoxus, S. mikatae, S. kudriavzevii, and S. bayanus, implying that they might have become so selectively constrained that they could be considered invariable sites in these species.

Interference of Two Closely Spaced Strip Footings on Sand Using Model Tests

By using small scale model tests, the interference effect on the ultimate bearing capacity of two closely spaced strip footings, placed on the surface of dry sand, was investigated. At any time, the footings were assumed to (1) carry exactly the same magnitude of load; and (2) settle to the same extent. No tilt of the footing was allowed. The effect of clear spacing (s) between two footings was explicitly studied. An interference of footings leads to a significant increase in their bearing capacity; the interference effect becomes even more substantial with an increase in the relative density of sand. The bearing capacity attains a peak magnitude at a certain (critical) spacing between two footings. The experimental observations presented in this technical note were similar to those given by different available theories. However, in a quantitative sense, the difference between the experiments and theories was seen to be still significant and it emphasizes the need of doing a further rigorous analysis in which the effect of stress level on the shear strength parameters of soil mass can be incorporated properly.

Working covariance model selection for generalized estimating equations

We investigate methods for data-based selection of working covariance models in the analysis of correlated data with generalized estimating equations. We study two selection criteria: Gaussian pseudolikelihood and a geodesic distance based on discrepancy between model-sensitive and model-robust regression parameter covariance estimators. The Gaussian pseudolikelihood is found in simulation to be reasonably sensitive for several response distributions and noncanonical mean-variance relations for longitudinal data. Application is also made to a clinical dataset. Assessment of adequacy of both correlation and variance models for longitudinal data should be routine in applications, and we describe open-source software supporting this practice.