SURVIVAL PREDICTION FOR BRAIN TUMOR PATIENTS USING GENE EXPRESSION DATA

Brain tumor is one of the most aggressive types of cancer in humans, with an estimated median survival time of 12 months and only 4% of the patients surviving more than 5 years after disease diagnosis. Until recently, brain tumor prognosis has been based only on clinical information such as tumor grade and patient age, but there are reports indicating that molecular profiling of gliomas can reveal subgroups of patients with distinct survival rates. We hypothesize that coupling molecular profiling of brain tumors with clinical information might improve predictions of patient survival time and, consequently, better guide future treatment decisions. In order to evaluate this hypothesis, the general goal of this research is to build models for survival prediction of glioma patients using DNA molecular profiles (U133 Affymetrix gene expression microarrays) along with clinical information. First, a predictive Random Forest model is built for binary outcomes (i.e. short vs. long-term survival) and a small subset of genes whose expression values can be used to predict survival time is selected. Following, a new statistical methodology is developed for predicting time-to-death outcomes using Bayesian ensemble trees. Due to a large heterogeneity observed within prognostic classes obtained by the Random Forest model, prediction can be improved by relating time-to-death with gene expression profile directly. We propose a Bayesian ensemble model for survival prediction which is appropriate for high-dimensional data such as gene expression data. Our approach is based on the ensemble "sum-of-trees" model which is flexible to incorporate additive and interaction effects between genes. We specify a fully Bayesian hierarchical approach and illustrate our methodology for the CPH, Weibull, and AFT survival models. We overcome the lack of conjugacy using a latent variable formulation to model the covariate effects which decreases computation time for model fitting. Also, our proposed models provides a model-free way to select important predictive prognostic markers based on controlling false discovery rates. We compare the performance of our methods with baseline reference survival methods and apply our methodology to an unpublished data set of brain tumor survival times and gene expression data, selecting genes potentially related to the development of the disease under study. A closing discussion compares results obtained by Random Forest and Bayesian ensemble methods under the biological/clinical perspectives and highlights the statistical advantages and disadvantages of the new methodology in the context of DNA microarray data analysis.

Time-Series Panel Analysis (TSPA): Multivariate Modeling of Temporal Associations in Psychotherapy Process.

Objective: Processes occurring in the course of psychotherapy are characterized by the simple fact that they unfold in time and that the multiple factors engaged in change processes vary highly between individuals (idiographic phenomena). Previous research, however, has neglected the temporal perspective by its traditional focus on static phenomena, which were mainly assessed at the group level (nomothetic phenomena). To support a temporal approach, the authors introduce time-series panel analysis (TSPA), a statistical methodology explicitly focusing on the quantification of temporal, session-to-session aspects of change in psychotherapy. TSPA-models are initially built at the level of individuals and are subsequently aggregated at the group level, thus allowing the exploration of prototypical models. Method: TSPA is based on vector auto-regression (VAR), an extension of univariate auto-regression models to multivariate time-series data. The application of TSPA is demonstrated in a sample of 87 outpatient psychotherapy patients who were monitored by postsession questionnaires. Prototypical mechanisms of change were derived from the aggregation of individual multivariate models of psychotherapy process. In a 2nd step, the associations between mechanisms of change (TSPA) and pre- to postsymptom change were explored. Results: TSPA allowed a prototypical process pattern to be identified, where patient's alliance and self-efficacy were linked by a temporal feedback-loop. Furthermore, therapist's stability over time in both mastery and clarification interventions was positively associated with better outcomes. Conclusions: TSPA is a statistical tool that sheds new light on temporal mechanisms of change. Through this approach, clinicians may gain insight into prototypical patterns of change in psychotherapy.

REGRESSION ANALYSIS FOR STANDARDIZED MORTALITY RATIOS WITH APPLICATION TO OCCUPATIONAL FOLLOW-UP STUDIES

Traditional comparison of standardized mortality ratios (SMRs) can be misleading if the age-specific mortality ratios are not homogeneous. For this reason, a regression model has been developed which incorporates the mortality ratio as a function of age. This model is then applied to mortality data from an occupational cohort study. The nature of the occupational data necessitates the investigation of mortality ratios which increase with age. These occupational data are used primarily to illustrate and develop the statistical methodology.^ The age-specific mortality ratio (MR) for the covariates of interest can be written as MR(,ij...m) = ((mu)(,ij...m)/(theta)(,ij...m)) = r(.)exp (Z('')(,ij...m)(beta)) where (mu)(,ij...m) and (theta)(,ij...m) denote the force of mortality in the study and chosen standard populations in the ij...m('th) stratum, respectively, r is the intercept, Z(,ij...m) is the vector of covariables associated with the i('th) age interval, and (beta) is a vector of regression coefficients associated with these covariables. A Newton-Raphson iterative procedure has been used for determining the maximum likelihood estimates of the regression coefficients.^ This model provides a statistical method for a logical and easily interpretable explanation of an occupational cohort mortality experience. Since it gives a reasonable fit to the mortality data, it can also be concluded that the model is fairly realistic. The traditional statistical method for the analysis of occupational cohort mortality data is to present a summary index such as the SMR under the assumption of constant (homogeneous) age-specific mortality ratios. Since the mortality ratios for occupational groups usually increase with age, the homogeneity assumption of the age-specific mortality ratios is often untenable. The traditional method of comparing SMRs under the homogeneity assumption is a special case of this model, without age as a covariate.^ This model also provides a statistical technique to evaluate the relative risk between two SMRs or a dose-response relationship among several SMRs. The model presented has application in the medical, demographic and epidemiologic areas. The methods developed in this thesis are suitable for future analyses of mortality or morbidity data when the age-specific mortality/morbidity experience is a function of age or when there is an interaction effect between confounding variables needs to be evaluated. ^

Calidad del agua en el área regadía del río Mendoza : temperatura, pH, iones solubles y sólidos

El río Mendoza riega el oasis Norte en el que se encuentra asentada la población del Gran Mendoza. El crecimiento urbano avanzó sobre áreas originalmente agrícolas, rodeándolas y atravesándolas con una intrincada red de canales y desagües de riego y colectores de desagües urbano-pluviales. Para conocer la evolución de la calidad del agua de esta cuenca se seleccionaron, estratégicamente, diversos sitios de muestreo: tres puntos (RI a RIII) a lo largo del río a partir del derivador (dique Cipolletti), cinco en la red de canales (CI a CV) y siete ubicados en los colectores de drenaje (DI a DVII). En ellos se realizó el análisis de las variables temperatura, pH, iones solubles y sólidos (en suspensión, sedimentables 10 minutos, totales, fijos y volátiles). En la red de drenaje sólo se analizaron los tres primeros parámetros. La metodología estadística incluyó el análisis descriptivo, inferencial y espacial de cada variable. Los resultados indican que en el río no hay diferencias entre los puntos de muestreo en lo que respecta a pH y sólidos totales volátiles. En cambio, sí se encuentran diferencias en todas las demás variables, y en general entre RIII y RII respecto de RI. En canales y RI no hay diferencias entre los puntos de muestreo en carbonatos y sólidos totales volátiles y sí en todas las demás variables analizadas.

Reseña sobre las metodologías de campo, analíticas y estadísticas empleadas en la determinación y manejo de datos de los elementos de tierras raras en el sistema suelo-planta

El presente artículo es una revisión detallada de estudios científicos publicados que tratan el tema relacionado con la determinación de los elementos de las tierras raras (REEs) en el sistema suelo-planta. Los estudios han sido llevados a cabo principalmente en países europeos y asiáticos. Cabe señalar que la investigación en los países latinoamericanos es muy escasa; sin embargo, es creciente el interés de analizar la aportación de estos elementos al suelo y la planta, lo cual se debe a la aplicación de fertilizantes que contienen dosis elevadas de estos elementos en su composición. Diversas técnicas de muestreo, experimentación y análisis han sido empleadas para la determinación de los REEs. No obstante, se considera que el manejo de los datos ha sido incorrecto estadísticamente. El contenido del presente artículo aborda: (i) las generalidades de los REEs; (ii) el análisis de la bibliografía disponible con el fin de conocer las metodologías de muestreo y análisis más utilizadas en 37 artículos en total, señalando algunos puntos que se consideran todavía deficientes; (iii) dos ejemplos de la aplicación de técnicas estadísticas (intervalo de confianza de la media y pruebas de significancia de la relación F de Fisher y t de Student) utilizando datos reportados en dos artículos. Los resultados mostraron, con los datos del primer artículo analizado, que: a) no se aplicó una metodología estadística para evaluar la calidad de datos; b) al aplicar estadística se encontró que existen diferencias sistemáticas entre los datos determinados en el laboratorio y los certificados. En el segundo artículo analizado se demostró, mediante pruebas de significancia, que existen diferencias significativas en las medias de Ce y Eu (los dos elementos tomados como ejemplos) en las plantas de un sitio a otro.

Cenozoic oxygen isotopic values for benthic foraminifera from DSDP and ODP low and high latitude marine sediment cores

The climate during the Cenozoic era changed in several steps from ice-free poles and warm conditions to ice-covered poles and cold conditions. Since the 1950s, a body of information on ice volume and temperature changes has been built up predominantly on the basis of measurements of the oxygen isotopic composition of shells of benthic foraminifera collected from marine sediment cores. The statistical methodology of time series analysis has also evolved, allowing more information to be extracted from these records. Here we provide a comprehensive view of Cenozoic climate evolution by means of a coherent and systematic application of time series analytical tools to each record from a compilation spanning the interval from 4 to 61 Myr ago. We quantitatively describe several prominent features of the oxygen isotope record, taking into account the various sources of uncertainty (including measurement, proxy noise, and dating errors). The estimated transition times and amplitudes allow us to assess causal climatological-tectonic influences on the following known features of the Cenozoic oxygen isotopic record: Paleocene-Eocene Thermal Maximum, Eocene-Oligocene Transition, Oligocene-Miocene Boundary, and the Middle Miocene Climate Optimum. We further describe and causally interpret the following features: Paleocene-Eocene warming trend, the two-step, long-term Eocene cooling, and the changes within the most recent interval (Miocene-Pliocene). We review the scope and methods of constructing Cenozoic stacks of benthic oxygen isotope records and present two new latitudinal stacks, which capture besides global ice volume also bottom water temperatures at low (less than 30°) and high latitudes. This review concludes with an identification of future directions for data collection, statistical method development, and climate modeling.

Significado empírico de la multifractalidad de la precipitación

El objetivo central de la presente investigación es profundizar la interpretación de los parámetros multifractales en el caso de las series de precipitación. Para ello se aborda, en primer lugar, la objetivación de la selección de la parte lineal de las curvas log-log que se encuentra en la base de los métodos de análisis fractal y multifractal; y, en segundo lugar, la generación de series artificiales de precipitación, con características similares a las reales, que permitan manipular los datos y evaluar la influencia de las modificaciones controladas de las series en los resultados de los parámetros multifractales derivados. En cuanto al problema de la selección de la parte lineal de las curvas log-log se desarrollaron dos métodos: a. Cambio de tendencia, que consiste en analizar el cambio de pendiente de las rectas ajustadas a dos subconjuntos consecutivos de los datos. b. Eliminación de casos, que analiza la mejora en el p-valor asociado al coeficiente de correlación al eliminar secuencialmente los puntos finales de la regresión. Los resultados obtenidos respecto a la regresión lineal establecen las siguientes conclusiones: - La metodología estadística de la regresión muestra la dificultad para encontrar el valor de la pendiente de tramos rectos de curvas en el procedimiento base del análisis fractal, indicando que la toma de decisión de los puntos a considerar redunda en diferencias significativas de las pendientes encontradas. - La utilización conjunta de los dos métodos propuestos ayuda a objetivar la toma de decisión sobre la parte lineal de las familias de curvas en el análisis fractal, pero su utilidad sigue dependiendo del número de datos de que se dispone y de las altas significaciones que se obtienen. En cuanto al significado empírico de los parámetros multifratales de la precipitación, se han generado 19 series de precipitación por medio de un simulador de datos diarios en cascada a partir de estimaciones anuales y mensuales, y en base a estadísticos reales de 4 estaciones meteorológicas españolas localizadas en un gradiente de NW a SE. Para todas las series generadas, se calculan los parámetros multifractales siguiendo la técnica de estimación de la DTM (Double Trace Moments - Momentos de Doble Traza) desarrollado por Lavalle et al. (1993) y se observan las modificaciones producidas. Los resultados obtenidos arrojaron las siguientes conclusiones: - La intermitencia, C1, aumenta al concentrar las precipitaciones en menos días, al hacerla más variable, o al incrementar su concentración en los días de máxima, mientras no se ve afectado por la modificación en la variabilidad del número de días de lluvia. - La multifractalidad, α, se ve incrementada con el número de días de lluvia y la variabilidad de la precipitación, tanto anual como mensual, así como también con la concentración de precipitación en el día de máxima. - La singularidad probable máxima, γs, se ve incrementada con la concentración de la lluvia en el día de precipitación máxima mensual y la variabilidad a nivel anual y mensual. - El grado no- conservativo, H, depende del número de los días de lluvia que aparezcan en la serie y secundariamente de la variabilidad general de la lluvia. - El índice de Hurst generalizado se halla muy ligado a la singularidad probable máxima. ABSTRACT The main objective of this research is to interpret the multifractal parameters in the case of precipitation series from an empirical approach. In order to do so the first proposed task was to objectify the selection of the linear part of the log-log curves that is a fundamental step of the fractal and multifractal analysis methods. A second task was to generate precipitation series, with real like features, which allow evaluating the influence of controlled series modifications on the values of the multifractal parameters estimated. Two methods are developed for selecting the linear part of the log-log curves in the fractal and multifractal analysis: A) Tendency change, which means analyzing the change in slope of the fitted lines to two consecutive subsets of data. B) Point elimination, which analyzes the improvement in the p- value associated to the coefficient of correlation when the final regression points are sequentially eliminated. The results indicate the following conclusions: - Statistical methodology of the regression shows the difficulty of finding the slope value of straight sections of curves in the base procedure of the fractal analysis, pointing that the decision on the points to be considered yield significant differences in slopes values. - The simultaneous use of the two proposed methods helps to objectify the decision about the lineal part of a family of curves in fractal analysis, but its usefulness are still depending on the number of data and the statistical significances obtained. Respect to the empiric meaning of the precipitation multifractal parameters, nineteen precipitation series were generated with a daily precipitation simulator derived from year and month estimations and considering statistics from actual data of four Spanish rain gauges located in a gradient from NW to SE. For all generated series the multifractal parameters were estimated following the technique DTM (Double Trace Moments) developed by Lavalle et al. (1993) and the variations produced considered. The results show the following conclusions: 1. The intermittency, C1, increases when precipitation is concentrating for fewer days, making it more variable, or when increasing its concentration on maximum monthly precipitation days, while it is not affected due to the modification in the variability in the number of days it rained. 2. Multifractility, α, increases with the number of rainy days and the variability of the precipitation, yearly as well as monthly, as well as with the concentration of precipitation on the maximum monthly precipitation day. 3. The maximum probable singularity, γs, increases with the concentration of rain on the day of the maximum monthly precipitation and the variability in yearly and monthly level. 4. The non-conservative degree, H’, depends on the number of rainy days that appear on the series and secondly on the general variability of the rain. 5. The general Hurst index is linked to the maximum probable singularity.

Las posibilidades de las fuentes de información sociodemográficas para el monitoreo del derecho a la salud de las personas mayores en la Argentina, 1999-2013

En el artículo se propone analizar y sistematizar el alcance, las limitaciones y los desafíos de las fuentes de información producidas oficialmente en la Argentina en los últimos 15 años, para el monitoreo del ejercicio del derecho a la salud de las personas mayores. Se realiza una compilación de indicadores propuestos principalmente por el Centro Latinoamericano y Caribeño de Demografía (CELADE)-División de Población de la Comisión Económica para América Latina y el Caribe (CEPAL) en el marco de diferentes conferencias internacionales y se analizan las posibilidades de implementación, con una mirada desde el enfoque basado en los derechos humanos. Entre las principales conclusiones, se destaca que la Argentina cuenta con un conjunto de fuentes de información que permiten abordar una cantidad importante de indicadores. Sin embargo, para medidas clave en este grupo poblacional, las principales fuentes de información no permiten monitorear diferencias entre distintos grupos socioeconómicos y geográficos ni su evolución, por lo que no admiten una mirada desde el enfoque de derechos.

The Relationship between Adolescent Social Network Structure and Perceptions of School Climate

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

Motor unit number estimation - A Bayesian approach

All muscle contractions are dependent on the functioning of motor units. In diseases such as amyotrophic lateral sclerosis (ALS), progressive loss of motor units leads to gradual paralysis. A major difficulty in the search for a treatment for these diseases has been the lack of a reliable measure of disease progression. One possible measure would be an estimate of the number of surviving motor units. Despite over 30 years of motor unit number estimation (MUNE), all proposed methods have been met with practical and theoretical objections. Our aim is to develop a method of MUNE that overcomes these objections. We record the compound muscle action potential (CMAP) from a selected muscle in response to a graded electrical stimulation applied to the nerve. As the stimulus increases, the threshold of each motor unit is exceeded, and the size of the CMAP increases until a maximum response is obtained. However, the threshold potential required to excite an axon is not a precise value but fluctuates over a small range leading to probabilistic activation of motor units in response to a given stimulus. When the threshold ranges of motor units overlap, there may be alternation where the number of motor units that fire in response to the stimulus is variable. This means that increments in the value of the CMAP correspond to the firing of different combinations of motor units. At a fixed stimulus, variability in the CMAP, measured as variance, can be used to conduct MUNE using the "statistical" or the "Poisson" method. However, this method relies on the assumptions that the numbers of motor units that are firing probabilistically have the Poisson distribution and that all single motor unit action potentials (MUAP) have a fixed and identical size. These assumptions are not necessarily correct. We propose to develop a Bayesian statistical methodology to analyze electrophysiological data to provide an estimate of motor unit numbers. Our method of MUNE incorporates the variability of the threshold, the variability between and within single MUAPs, and baseline variability. Our model not only gives the most probable number of motor units but also provides information about both the population of units and individual units. We use Markov chain Monte Carlo to obtain information about the characteristics of individual motor units and about the population of motor units and the Bayesian information criterion for MUNE. We test our method of MUNE on three subjects. Our method provides a reproducible estimate for a patient with stable but severe ALS. In a serial study, we demonstrate a decline in the number of motor unit numbers with a patient with rapidly advancing disease. Finally, with our last patient, we show that our method has the capacity to estimate a larger number of motor units.

Pedagogia da Autonomia: Os Limitadores da Docência no Exercício da Autonomia na Instituição Escolar

O principal objetivo deste trabalho é identificar se existem elementos presentes nas atividades diárias do professor que interferem em seu ministério e quantificar sua influência, utilizando como referencial teórico o livro A Pedagogia da Autonomia de Paulo Freire e as bases conceituais da pedagogia freiriana. Foi feito um levantamento da rotina das instituições para comprovar a existência e a extensão do que chamaremos aqui limitadores da autonomia do trabalho docente responsáveis pela redução da capacidade do docente em seu trabalho junto aos alunos. Dessa forma, eventos cuja origem se acha fora da ação do professor, muitas vezes, distante mesmo do ambiente escolar, em um contexto em que a própria instituição se insere, têm sua participação na redução dessa autonomia. Outros limitadores têm sua gênese dentro do próprio ambiente educacional, dificultando e às vezes impedindo, essa ação. São limitadores que por sua ligação intrínseca com a instituição, do ponto de vista de contexto, neste ensaio classifico como institucionais. O excesso de atividades a que o professor se encontra sujeito, bem como a avalanche burocrática obrigando-o por vezes a levar parte de suas atividades para dentro de sua vida pessoal, aparecem aqui como limitadores funcionais, por estarem intimamente ligados aos aspectos da própria prática do docente. Mesmo as barreiras físicas e assecuratórias da tranqüilidade do ambiente escolar, como: crachás, portões, catracas e outros, são tratados aqui como limitadores físicos, compondo com os demais as categorias em torno das quais o tema aqui tratado se desenvolve. Existem de fato, limitadores da ação educacional? Em que medida produzem seus efeitos e em que proporção são sentidos pelos profissionais da educação? São questões cujas análises se embasarão em respostas dadas por professores da Educação Infantil, do Ensino Fundamental I e II além do Ensino Médio, a um questionário, que compiladas e estatisticamente tratadas, desembocarão na conclusão hipótese deste ensaio: A atividade educacional padece dos efeitos provocados pelos limitadores da ação docente . Para tanto faremos o estabelecimento das bases referenciais no capítulo primeiro, recortando da obra do eminente educador os elementos que servirão para seu embasamento teórico. Partindo dos aspectos mais genéricos para os mais específicos, que têm conotação com o presente tema, passamos no capítulo segundo ao levantamento das diversas atividades próprias da prática educativa, das quais o professor não tem como se eximir, classificando-as didaticamente, em uma preparação para um momento posterior de levantamento de dados. No capítulo terceiro é apresentado o questionário e seus resultados; a metodologia estatística empregada foi a qualitativa, porém com avaliações que permitem mensurar o grau de interferência de cada categoria presente no resultado final. Desta forma concluí, de acordo com a hipótese inicial, pela existência dos limitadores como fatores inerentes à prática educacional e sua relevância como agentes inibidores da ação docente dentro do universo estudado.(AU)

An empirical investigation on firm-level performance of cross border mergers and acquisitions

This empirical study investigates the performance of cross border M&A. The first stage is to identify the determinants of making cross border M&A complete. One focus here is to extend the existing empirical evidence in the field of cross border M&A and exploit the likelihood of M&A from a different perspective. Given the determinants of cross border M&A completions, the second stage is to investigate the effects of cross border M&A on post-acquisition firm performance for both targets and acquirers. The thesis exploits a hitherto unused data base, which consists of those firms that are rumoured to be undertaking M&A, and then follow the deal to completion or abandonment. This approach highlights a number of limitations to the previous literature, which relies on statistical methodology to identify potential but non-existent mergers. This thesis changes some conventional understanding for M&A activity. Cross border M&A activity is underpinned by various motives such as synergy, management discipline, and acquisition of complementary resources. Traditionally, it is believed that these motives will boost the international M&A activity and improve firm performance after takeovers. However, this thesis shows that such factors based on these motives as acquirer’s profitability and liquidity and target’s intangible resource actually deter the completion of cross border M&A in the period of 2002-2011. The overall finding suggests that the cross border M&A is the efficiency-seeking activity rather than the resource-seeking activity. Furthermore, compared with firms in takeover rumours, the completion of M&A lowers firm performance. More specifically, the difficulties in transfer of competitive advantages and integration of strategic assets lead to low firm performance in terms of productivity. Besides, firms cannot realise the synergistic effect and managerial disciplinary effect once a cross border M&A is completed, which suggests a low post-acquisition profitability level.

Laminar-turbulent transition in Raman fiber lasers:a first passage statistics based analysis

Loss of coherence with increasing excitation amplitudes and spatial size modulation is a fundamental problem in designing Raman fiber lasers. While it is known that ramping up laser pump power increases the amplitude of stochastic excitations, such higher energy inputs can also lead to a transition from a linearly stable coherent laminar regime to a non-desirable disordered turbulent state. This report presents a new statistical methodology, based on first passage statistics, that classifies lasing regimes in Raman fiber lasers, thereby leading to a fast and highly accurate identification of a strong instability leading to a laminar-turbulent phase transition through a self-consistently defined order parameter. The results have been consistent across a wide range of pump power values, heralding a breakthrough in the non-invasive analysis of fiber laser dynamics.

Bayesian alignment of continuous molecular shapes using random fields

Statistical methodology is proposed for comparing molecular shapes. In order to account for the continuous nature of molecules, classical shape analysis methods are combined with techniques used for predicting random fields in spatial statistics. Applying a modification of Procrustes analysis, Bayesian inference is carried out using Markov chain Monte Carlo methods for the pairwise alignment of the resulting molecular fields. Superimposing entire fields rather than the configuration matrices of nuclear positions thereby solves the problem that there is usually no clear one--to--one correspondence between the atoms of the two molecules under consideration. Using a similar concept, we also propose an adaptation of the generalised Procrustes analysis algorithm for the simultaneous alignment of multiple molecular fields. The methodology is applied to a dataset of 31 steroid molecules.

GIS-integrated mathematical modeling of social phenomena at macro- and micro- levels—a multivariate geographically-weighted regression model for identifying locations vulnerable to hosting terrorist safe-houses: France as case study

Adaptability and invisibility are hallmarks of modern terrorism, and keeping pace with its dynamic nature presents a serious challenge for societies throughout the world. Innovations in computer science have incorporated applied mathematics to develop a wide array of predictive models to support the variety of approaches to counterterrorism. Predictive models are usually designed to forecast the location of attacks. Although this may protect individual structures or locations, it does not reduce the threat—it merely changes the target. While predictive models dedicated to events or social relationships receive much attention where the mathematical and social science communities intersect, models dedicated to terrorist locations such as safe-houses (rather than their targets or training sites) are rare and possibly nonexistent. At the time of this research, there were no publically available models designed to predict locations where violent extremists are likely to reside. This research uses France as a case study to present a complex systems model that incorporates multiple quantitative, qualitative and geospatial variables that differ in terms of scale, weight, and type. Though many of these variables are recognized by specialists in security studies, there remains controversy with respect to their relative importance, degree of interaction, and interdependence. Additionally, some of the variables proposed in this research are not generally recognized as drivers, yet they warrant examination based on their potential role within a complex system. This research tested multiple regression models and determined that geographically-weighted regression analysis produced the most accurate result to accommodate non-stationary coefficient behavior, demonstrating that geographic variables are critical to understanding and predicting the phenomenon of terrorism. This dissertation presents a flexible prototypical model that can be refined and applied to other regions to inform stakeholders such as policy-makers and law enforcement in their efforts to improve national security and enhance quality-of-life.