A Bayesian Spatial Mixture Model for FMRI Analysis

We develop, implement and study a new Bayesian spatial mixture model (BSMM). The proposed BSMM allows for spatial structure in the binary activation indicators through a latent thresholded Gaussian Markov random field. We develop a Gibbs (MCMC) sampler to perform posterior inference on the model parameters, which then allows us to assess the posterior probabilities of activation for each voxel. One purpose of this article is to compare the HJ model and the BSMM in terms of receiver operating characteristics (ROC) curves. Also we consider the accuracy of the spatial mixture model and the BSMM for estimation of the size of the activation region in terms of bias, variance and mean squared error. We perform a simulation study to examine the aforementioned characteristics under a variety of configurations of spatial mixture model and BSMM both as the size of the region changes and as the magnitude of activation changes.

Limit Theorems for Branching Processes with Random Migration Components

The classical Bienaymé-Galton-Watson (BGW) branching process can be interpreted as mathematical model of population dynamics when the members of an isolated population reproduce themselves independently of each other according to a stochastic law.

Branching Processes in Autoregressive Random Environment

2000 Mathematics Subject Classification: 60J80, 60K05.

Em Algorithm for MLE of a Probit Model for Multiple Ordinal Outcomes

The correlated probit model is frequently used for multiple ordered data since it allows to incorporate seamlessly different correlation structures. The estimation of the probit model parameters based on direct maximization of the limited information maximum likelihood is a numerically intensive procedure. We propose an extension of the EM algorithm for obtaining maximum likelihood estimates for a correlated probit model for multiple ordinal outcomes. The algorithm is implemented in the free software environment for statistical computing and graphics R. We present two simulation studies to examine the performance of the developed algorithm. We apply the model to data on 121 women with cervical or endometrial cancer. Patients developed normal tissue reactions as a result of post-operative external beam pelvic radiotherapy. In this work we focused on modeling the effects of a genetic factor on early skin and early urogenital tissue reactions and on assessing the strength of association between the two types of reactions. We established that there was an association between skin reactions and polymorphism XRCC3 codon 241 (C>T) (rs861539) and that skin and urogenital reactions were positively correlated. ACM Computing Classification System (1998): G.3.

NLSE-based modelling of a random distributed feedback fiber laser

Random distributed feedback (DFB) fiber lasers have attracted a great attention since first demonstration [1]. Despite big advance in practical laser systems, random DFB fiber laser spectral properties are far away to be understood or even numerically modelled. Up to date, only generation power could be calculated and optimized numerically [1,2] or analytically [3] within the power balance model. However, spectral and statistical properties of random DFB fiber laser can not be found in this way. Here we present first numerical modelling of the random DFB fiber laser, including its spectral and statistical properties, using NLSE-based model. © 2013 IEEE.

Power optimization of random distributed feedback fiber lasers

We present a comprehensive study of power output characteristics of random distributed feedback Raman fiber lasers. The calculated optimal slope efficiency of the backward wave generation in the one-arm configuration is shown to be as high as ∼90% for 1 W threshold. Nevertheless, in real applications a presence of a small reflection at fiber ends can appreciably deteriorate the power performance. The developed numerical model well describes the experimental data. © 2012 Optical Society of America.

The development and analysis of a field project model curriculum and its impact on achievement and attitude toward science and the environment with at-risk eleventh and twelfth grade students

This study was an evaluation of a Field Project Model Curriculum and its impact on achievement, attitude toward science, attitude toward the environment, self-concept, and academic self-concept with at-risk eleventh and twelfth grade students. One hundred eight students were pretested and posttested on the Piers-Harris Children's Self-Concept Scale, PHCSC (1985); the Self-Concept as a Learner Scale, SCAL (1978); the Marine Science Test, MST (1987); the Science Attitude Inventory, SAI (1970); and the Environmental Attitude Scale, EAS (1972). Using a stratified random design, three groups of students were randomly assigned according to sex and stanine level, to three treatment groups. Group one received the field project method, group two received the field study method, and group three received the field trip method. All three groups followed the marine biology course content as specified by Florida Student Performance Objectives and Frameworks. The intervention occurred for ten months with each group participating in outside-of-classroom activities on a trimonthly basis. Analysis of covariance procedures were used to determine treatment effects. F-ratios, p-levels and t-tests at p $<$.0062 (.05/8) indicated that a significant difference existed among the three treatment groups. Findings indicated that groups one and two were significantly different from group three with group one displaying significantly higher results than group two. There were no significant differences between males and females in performance on the five dependent variables. The tenets underlying environmental education are congruent with the recommendations toward the reform of science education. These include a value analysis approach, inquiry methods, and critical thinking strategies that are applied to environmental issues. ^

A Markov chain location-allocation meta-model for hurricane relief

An emergency is a deviation from a planned course of events that endangers people, properties, or the environment. It can be described as an unexpected event that causes economic damage, destruction, and human suffering. When a disaster happens, Emergency Managers are expected to have a response plan to most likely disaster scenarios. Unlike earthquakes and terrorist attacks, a hurricane response plan can be activated ahead of time, since a hurricane is predicted at least five days before it makes landfall. This research looked into the logistics aspects of the problem, in an attempt to develop a hurricane relief distribution network model. We addressed the problem of how to efficiently and effectively deliver basic relief goods to victims of a hurricane disaster. Specifically, where to preposition State Staging Areas (SSA), which Points of Distributions (PODs) to activate, and the allocation of commodities to each POD. Previous research has addressed several of these issues, but not with the incorporation of the random behavior of the hurricane's intensity and path. This research presents a stochastic meta-model that deals with the location of SSAs and the allocation of commodities. The novelty of the model is that it treats the strength and path of the hurricane as stochastic processes, and models them as Discrete Markov Chains. The demand is also treated as stochastic parameter because it depends on the stochastic behavior of the hurricane. However, for the meta-model, the demand is an input that is determined using Hazards United States (HAZUS), a software developed by the Federal Emergency Management Agency (FEMA) that estimates losses due to hurricanes and floods. A solution heuristic has been developed based on simulated annealing. Since the meta-model is a multi-objective problem, the heuristic is a multi-objective simulated annealing (MOSA), in which the initial solution and the cooling rate were determined via a Design of Experiments. The experiment showed that the initial temperature (T0) is irrelevant, but temperature reduction (δ) must be very gradual. Assessment of the meta-model indicates that the Markov Chains performed as well or better than forecasts made by the National Hurricane Center (NHC). Tests of the MOSA showed that it provides solutions in an efficient manner. Thus, an illustrative example shows that the meta-model is practical.

The transducer model for contrast detection and discrimination: formal relations, implications, and an empirical test.

The transducer function mu for contrast perception describes the nonlinear mapping of stimulus contrast onto an internal response. Under a signal detection theory approach, the transducer model of contrast perception states that the internal response elicited by a stimulus of contrast c is a random variable with mean mu(c). Using this approach, we derive the formal relations between the transducer function, the threshold-versus-contrast (TvC) function, and the psychometric functions for contrast detection and discrimination in 2AFC tasks. We show that the mathematical form of the TvC function is determined only by mu, and that the psychometric functions for detection and discrimination have a common mathematical form with common parameters emanating from, and only from, the transducer function mu and the form of the distribution of the internal responses. We discuss the theoretical and practical implications of these relations, which have bearings on the tenability of certain mathematical forms for the psychometric function and on the suitability of empirical approaches to model validation. We also present the results of a comprehensive test of these relations using two alternative forms of the transducer model: a three-parameter version that renders logistic psychometric functions and a five-parameter version using Foley's variant of the Naka-Rushton equation as transducer function. Our results support the validity of the formal relations implied by the general transducer model, and the two versions that were contrasted account for our data equally well.

Toy model to describe the effect of positional blocklike disorder in metamaterials composites

We study theoretically the effect of a new type of blocklike positional disorder on the effective electromagnetic properties of one-dimensional chains of resonant, high-permittivity dielectric particles, where particles are arranged into perfectly well-ordered blocks whose relative position is a random variable. This creates a finite order correlation length that mimics the situation encountered in metamaterials fabricated through self-assembled techniques, whose structures often display short-range order between near neighbors but long-range disorder, due to stacking defects. Using a spectral theory approach combined with a principal component statistical analysis, we study, in the long-wavelength regime, the evolution of the electromagnetic response when the composite filling fraction and the block size are changed. Modifications in key features of the resonant response (amplitude, width, etc.) are investigated, showing a regime transition for a filling fraction around 50%.

A model for the modular evolution of rna addressing open questions on the origin of life

A main unsolved problem in the RNA world scenario for the origin of life is how a template-dependent RNA polymerase ribozyme emerged from short RNA oligomers generated by random polymerization of ribonucleotides (Joyce and Orgel 2006). Current estimates establish a minimum size about 165 nt long for such a ribozyme (Johnston et al. 2001), a length three to four times that of the longest RNA oligomers obtained by random polymerization on clay mineral surfaces (Huang and Ferris 2003, 2006). To overcome this gap, we have developed a stepwise model of ligation-based, modular evolution of RNA (Briones et al. 2009) whose main conceptual steps are summarized in Figure 1. This scenario has two main advantages with respect to previous hypotheses put forward for the origin of the RNA world: i) short RNA....

Posterior Probability Modeling and Image Classification for Archaeological Site Prospection: Building a Survey Efficacy Model for Identifying Neolithic Felsite Workshops in the Shetland Islands

The application of custom classification techniques and posterior probability modeling (PPM) using Worldview-2 multispectral imagery to archaeological field survey is presented in this paper. Research is focused on the identification of Neolithic felsite stone tool workshops in the North Mavine region of the Shetland Islands in Northern Scotland. Sample data from known workshops surveyed using differential GPS are used alongside known non-sites to train a linear discriminant analysis (LDA) classifier based on a combination of datasets including Worldview-2 bands, band difference ratios (BDR) and topographical derivatives. Principal components analysis is further used to test and reduce dimensionality caused by redundant datasets. Probability models were generated by LDA using principal components and tested with sites identified through geological field survey. Testing shows the prospective ability of this technique and significance between 0.05 and 0.01, and gain statistics between 0.90 and 0.94, higher than those obtained using maximum likelihood and random forest classifiers. Results suggest that this approach is best suited to relatively homogenous site types, and performs better with correlated data sources. Finally, by combining posterior probability models and least-cost analysis, a survey least-cost efficacy model is generated showing the utility of such approaches to archaeological field survey.

Random Access over Multi-Packet Reception Channels: A Mean-Field Approach

Thesis (Ph.D.)--University of Washington, 2016-06

Markov Random Fields in Cancer Mutation Dependencies

Even though a large amount of evidence would suggest that PP2A serine/threonine protein phosphatase acts as a tumour suppressor the genomics data to support this claim is limited. We fit a sparse binary Markov random field with individual sample's total mutational frequency as an additional covariate to model the dependencies between the mutations occurring in the PP2A encoding genes. We utilize the data from recent large scale cancer genomics studies, where the whole genome from a human tumour biopsy has been analysed. Our results show a complex network of interactions between the occurrence of mutations in our twenty examined genes. According to our analysis the mutations occurring in the genes PPP2R1A, PPP2R3A, and PPP2R2B are identified as the key mutations. These genes form the core of the network of conditional dependency between the mutations in the investigated twenty genes. Additionally, we note that the mutations occurring in PPP2R4 seem to be more influential in samples with higher number of total mutations. The mutations occurring in the set of genes suggested by our results has been shown to contribute to the transformation of human cells. We conclude that our evidence further supports the claim that PP2A acts as a tumour suppressor and restoring PP2A activity is an appealing therapeutic strategy.

A stylized software model to explore the free market equality/efficiency tradeoff

This paper provides an agent-based software exploration of the wellknown free market efficiency/equality trade-off. Our study simulates the interaction of agents producing, trading and consuming goods in the presence of different market structures, and looks at how efficient the producers/consumers mapping turn out to be as well as the resulting distribution of welfare among agents at the end of an arbitrarily large number of iterations. Two market mechanisms are compared: the competitive market (a double auction market in which agents outbid each other in order to buy and sell products) and the random one (in which products are allocated randomly). Our results confirm that the superior efficiency of the competitive market (an effective and never stopping producers/consumers mapping and a superior aggregative welfare) comes at a very high price in terms of inequality (above all when severe budget constraints are in play).