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.

The efficiency of multivariate macroeconomic forecasts

We examine the efficiency of multivariate macroeconomic forecasts by estimating a vector autoregressive model on the forecast revisions of four variables (GDP, inflation, unemployment and wages). Using a data set of professional forecasts for the G7 countries, we find evidence of cross‐series revision dynamics. Specifically, forecasts revisions are conditionally correlated to the lagged forecast revisions of other macroeconomic variables, and the sign of the correlation is as predicted by conventional economic theory. This indicates that forecasters are slow to incorporate news across variables. We show that this finding can be explained by forecast underreaction.

Multivariate orthogonal polynomials and integrable systems

Multivariate orthogonal polynomials in D real dimensions are considered from the perspective of the Cholesky factorization of a moment matrix. The approach allows for the construction of corresponding multivariate orthogonal polynomials, associated second kind functions, Jacobi type matrices and associated three term relations and also Christoffel-Darboux formulae. The multivariate orthogonal polynomials, their second kind functions and the corresponding Christoffel-Darboux kernels are shown to be quasi-determinants as well as Schur complements of bordered truncations of the moment matrix; quasi-tau functions are introduced. It is proven that the second kind functions are multivariate Cauchy transforms of the multivariate orthogonal polynomials. Discrete and continuous deformations of the measure lead to Toda type integrable hierarchy, being the corresponding flows described through Lax and Zakharov-Shabat equations; bilinear equations are found. Varying size matrix nonlinear partial difference and differential equations of the 2D Toda lattice type are shown to be solved by matrix coefficients of the multivariate orthogonal polynomials. The discrete flows, which are shown to be connected with a Gauss-Borel factorization of the Jacobi type matrices and its quasi-determinants, lead to expressions for the multivariate orthogonal polynomials and their second kind functions in terms of shifted quasi-tau matrices, which generalize to the multidimensional realm, those that relate the Baker and adjoint Baker functions to ratios of Miwa shifted tau-functions in the 1D scenario. In this context, the multivariate extension of the elementary Darboux transformation is given in terms of quasi-determinants of matrices built up by the evaluation, at a poised set of nodes lying in an appropriate hyperplane in R^D, of the multivariate orthogonal polynomials. The multivariate Christoffel formula for the iteration of m elementary Darboux transformations is given as a quasi-determinant. It is shown, using congruences in the space of semi-infinite matrices, that the discrete and continuous flows are intimately connected and determine nonlinear partial difference-differential equations that involve only one site in the integrable lattice behaving as a Kadomstev-Petviashvili type system. Finally, a brief discussion of measures with a particular linear isometry invariance and some of its consequences for the corresponding multivariate polynomials is given. In particular, it is shown that the Toda times that preserve the invariance condition lay in a secant variety of the Veronese variety of the fixed point set of the linear isometry.

Multivariate analysis of lifestyle, constitutive and body composition factors influencing bone health in community-dwelling older adults from Madeira, Portugal

info:eu-repo/semantics/publishedVersion

Structural brain connectivity and cognitive ability differences: A multivariate distance matrix regression analysis

Neuroimaging research involves analyses of huge amounts of biological data that might or might not be related with cognition. This relationship is usually approached using univariate methods, and, therefore, correction methods are mandatory for reducing false positives. Nevertheless, the probability of false negatives is also increased. Multivariate frameworks have been proposed for helping to alleviate this balance. Here we apply multivariate distance matrix regression for the simultaneous analysis of biological and cognitive data, namely, structural connections among 82 brain regions and several latent factors estimating cognitive performance. We tested whether cognitive differences predict distances among individuals regarding their connectivity pattern. Beginning with 3,321 connections among regions, the 36 edges better predicted by the individuals' cognitive scores were selected. Cognitive scores were related to connectivity distances in both the full (3,321) and reduced (36) connectivity patterns. The selected edges connect regions distributed across the entire brain and the network defined by these edges supports high-order cognitive processes such as (a) (fluid) executive control, (b) (crystallized) recognition, learning, and language processing, and (c) visuospatial processing. This multivariate study suggests that one widespread, but limited number, of regions in the human brain, supports high-level cognitive ability differences. Hum Brain Mapp, 2016. © 2016 Wiley Periodicals, Inc.

Using multivariate sequential patterns to improve survival prediction in intensive care burn unit

Resuscitation and stabilization are key issues in Intensive Care Burn Units and early survival predictions help to decide the best clinical action during these phases. Current survival scores of burns focus on clinical variables such as age or the body surface area. However, the evolution of other parameters (e.g. diuresis or fluid balance) during the first days is also valuable knowledge. In this work we suggest a methodology and we propose a Temporal Data Mining algorithm to estimate the survival condition from the patient’s evolution. Experiments conducted on 480 patients show the improvement of survival prediction.

Geometrical Methods in Multivariate Risk Management: Algorithms and Applications

This thesis builds a framework for evaluating downside risk from multivariate data via a special class of risk measures (RM). The peculiarity of the analysis lies in getting rid of strong data distributional assumptions and in orientation towards the most critical data in risk management: those with asymmetries and heavy tails. At the same time, under typical assumptions, such as the ellipticity of the data probability distribution, the conformity with classical methods is shown. The constructed class of RM is a multivariate generalization of the coherent distortion RM, which possess valuable properties for a risk manager. The design of the framework is twofold. The first part contains new computational geometry methods for the high-dimensional data. The developed algorithms demonstrate computability of geometrical concepts used for constructing the RM. These concepts bring visuality and simplify interpretation of the RM. The second part develops models for applying the framework to actual problems. The spectrum of applications varies from robust portfolio selection up to broader spheres, such as stochastic conic optimization with risk constraints or supervised machine learning.

An application of two techniques for the analysis of short, multivariate non-stationary time-series of Mauritanian trawl survey data

Min/max autocorrelation factor analysis (MAFA) and dynamic factor analysis (DFA) are complementary techniques for analysing short (> 15-25 y), non-stationary, multivariate data sets. We illustrate the two techniques using catch rate (cpue) time-series (1982-2001) for 17 species caught during trawl surveys off Mauritania, with the NAO index, an upwelling index, sea surface temperature, and an index of fishing effort as explanatory variables. Both techniques gave coherent results, the most important common trend being a decrease in cpue during the latter half of the time-series, and the next important being an increase during the first half. A DFA model with SST and UPW as explanatory variables and two common trends gave good fits to most of the cpue time-series. (c) 2004 International Council for the Exploration of the Sea. Published by Elsevier Ltd. All rights reserved.

Identification of deep water lantern sharks (Chondrichthyes : Etmopteridae) using morphometric data and multivariate analysis

Taxonomic distinction to species level of deep water sharks is complex and often impossible to achieve during fisheries-related studies. The species of the genus Etmopterus are particularly difficult to identify, so they often appear without species assignation as Etmopetrus sp. or spp. in studies, even those focusing on elasmobranchs. During this work, the morphometric traits of two species of Etmopterus, E. spinax and E. pusillus were studied using 27 different morphological measurements, relatively easy to obtain even in the field. These measurements were processed with multivariate analysis in order to find out the most important ones likely to separate the two species. Sexual dimorphism was also assessed using the same techniques, and it was found that it does not occur in these species. The two Etmopterus species presented in this study share the same habitats in the overlapping ranges of distribution and are caught together on the outer shelves and slopes of the north-eastern Atlantic.

Trammel net catch species composition, catch rates and metiers in southern European waters: A multivariate approach

We identified and quantified the effect of season, depth, and inner and outer panel mesh size on the trammel net catch species composition and catch rates in four southern European areas (Northeast Atlantic: Basque Country, Spain; Algarve, Portugal; Gulf of Cadiz, Spain; Mediterranean: Cyclades, Greece), all of which are characterised by important trammel net fisheries. In each area, we conducted, in 1999-2000, seasonal, experimental fishing trials at various depths with trammel nets of six different inner/outer panel mesh combinations (i.e., two large outer panel meshes and three small inner panel meshes). Overall, our study covered some of the most commonly used inner panel mesh sizes, ranging from 40 to 140 mm (stretched). We analysed the species composition and catch rates of the different inner/outer panel combinations with regression, multivariate analysis (cluster analysis and multidimensional scaling) and other 'community' techniques (number of species, dominance curves). All our analyses indicated that the outer panel mesh sizes used in the present study did not significantly affect the catch characteristics in terms of number of species, catch rates and species composition. Multivariate analyses and seasonal dominance plots indicated that in Basque, Algarve and Cyclades waters, where sampling covered wide depth ranges, both season and depth strongly affected catch species compositions. For the Gulf of Cadiz, where sampling was restricted to depths 10-30 m, season was the only factor affecting catch species composition and thus group formation. In contrast, the inner panel mesh size did not generally affect multidimensional group formation in all areas but affected the dominance of the species caught in the Algarve and the Gulf of Cadiz. Multivariate analyses also revealed 11 different metiers (i.e., season-depth-species-inner panel mesh size combinations) in the four areas. This clearly indicated the existence of trammel net 'hot spots', which represent essential habitats (e.g., spawning, nursery or wintering grounds) of the life history of the targeted and associated species. The number of specimens caught declined significantly with inner panel mesh size in all areas. We attributed this to the exponential decline in abundance with size, both within- and between-species. In contrast, the number of species caught in each area was not related to the inner mesh size. This was unexpected and might be a consequence of the wide size-selective range of trammel nets. (c) 2006 Elsevier B.V All rights reserved.

Multivariate analysis of lifestyle, constitutive and body composition factors influencing bone health in community-dwelling older adults from Madeira, Portugal

info:eu-repo/semantics/publishedVersion

Uncertainty evaluation of multivariate quantities: A case study on electrical impedance

The paper discusses the evaluation of the uncertainty of a multivariate quantity using the Law of Propagation of Uncertainty defined in the Guide to the Expression of Uncertainty in Measurement (GUM) and a Monte Carlo method according to the GUM’s Supplement 2. The quantity analysed is the electrical impedance, which is not a scalar but a complex quantity. The used measuring method allows the evaluation of the impedance and of its uncertainty in different ways and the corresponding results are presented, compared and discussed. For comparison purposes, results of the impedance uncertainty obtained using the NIST Uncertainty Machine are also presented.

Improving multivariate data streams clustering.

Clustering data streams is an important task in data mining research. Recently, some algorithms have been proposed to cluster data streams as a whole, but just few of them deal with multivariate data streams. Even so, these algorithms merely aggregate the attributes without touching upon the correlation among them. In order to overcome this issue, we propose a new framework to cluster multivariate data streams based on their evolving behavior over time, exploring the correlations among their attributes by computing the fractal dimension. Experimental results with climate data streams show that the clusters' quality and compactness can be improved compared to the competing method, leading to the thoughtfulness that attributes correlations cannot be put aside. In fact, the clusters' compactness are 7 to 25 times better using our method. Our framework also proves to be an useful tool to assist meteorologists in understanding the climate behavior along a period of time.

Selection of mango rosa genotypes in a breeding population using the multivariate-biplot method.

Mango (Mangifera indica L.) trees stand out among the main fruit trees cultivated in Brazil. The mango rosa fruit is a very popular local variety (landrace), especially because of their superior technological characteristics such as high contents of Vitamin C and soluble solids (SS), as well as attractive taste and color. The objective of this study was to select a breeding population of mango rosa (polyclonal variety; ≥5 individuals) that can simultaneously meet the fresh and processed fruit Vmarkets, using the multivariate method of principal components and the biplot graphic.

Breed comparison for heat adaptation in rams using multivariate analysis.

2016