Order-Related Problems Parameterized by Width

In the main body of this thesis, we study two different order theoretic problems. The first problem, called Completion of an Ordering, asks to extend a given finite partial order to a complete linear order while respecting some weight constraints. The second problem is an order reconfiguration problem under width constraints. While the Completion of an Ordering problem is NP-complete, we show that it lies in FPT when parameterized by the interval width of ρ. This ordering problem can be used to model several ordering problems stemming from diverse application areas, such as graph drawing, computational social choice, and computer memory management. Each application yields a special partial order ρ. We also relate the interval width of ρ to parameterizations for these problems that have been studied earlier in the context of these applications, sometimes improving on parameterized algorithms that have been developed for these parameterizations before. This approach also gives some practical sub-exponential time algorithms for ordering problems. In our second main result, we combine our parameterized approach with the paradigm of solution diversity. The idea of solution diversity is that instead of aiming at the development of algorithms that output a single optimal solution, the goal is to investigate algorithms that output a small set of sufficiently good solutions that are sufficiently diverse from one another. In this way, the user has the opportunity to choose the solution that is most appropriate to the context at hand. It also displays the richness of the solution space. There, we show that the considered diversity version of the Completion of an Ordering problem is fixed-parameter tractable with respect to natural paramaters that capture the notion of diversity and the notion of sufficiently good solutions. We apply this algorithm in the study of the Kemeny Rank Aggregation class of problems, a well-studied class of problems lying in the intersection of order theory and social choice theory. Up to this point, we have been looking at problems where the goal is to find an optimal solution or a diverse set of good solutions. In the last part, we shift our focus from finding solutions to studying the solution space of a problem. There we consider the following order reconfiguration problem: Given a graph G together with linear orders τ and τ ′ of the vertices of G, can one transform τ into τ ′ by a sequence of swaps of adjacent elements in such a way that at each time step the resulting linear order has cutwidth (pathwidth) at most w? We show that this problem always has an affirmative answer when the input linear orders τ and τ ′ have cutwidth (pathwidth) at most w/2. Using this result, we establish a connection between two apparently unrelated problems: the reachability problem for two-letter string rewriting systems and the graph isomorphism problem for graphs of bounded cutwidth. This opens an avenue for the study of the famous graph isomorphism problem using techniques from term rewriting theory. In addition to the main part of this work, we present results on two unrelated problems, namely on the Steiner Tree problem and on the Intersection Non-emptiness problem from automata theory.Doktorgradsavhandlin

Essays on a study of statistical power in economics.

Knowing the statistical power of an empirical analysis after it is completed can be very useful. Among other things, it can help one determine whether a finding of statistical insignificance is due to a small effect size or insufficient statistical power. This thesis consists of five studies linked together by my attempts to study how best to calculate ex post statistical power. Chapter One provides an introduction and the background for this thesis. In Chapter Two, I detail what is meant by statistical power (including ex ante and ex post power) and why it is important to researchers. I also identify the various factors that affect statistical power. Chapter Three explains why ex post power has a “bad reputation.” A common practice for calculating ex post power employs an inappropriate method known as “observed power.” “Observed power” uses the estimated effect size as the assumed true effect size and then calculates the associated power. Though widely used, this method has been demonstrated to produce biased estimates of statistical power (Yuan & Maxwell, 2005). I present two approaches for calculating ex post power suggested by researchers to avoid the problems of “observed power”. Chapter Four begins by replicating a recent paper by Brown, Lambert and Wojan (2019). BLW use a bootstrapping procedure to calculate ex post power and apply it to a benefit-cost analysis of a U.S. conservation program. I reproduce BLW’s results. I call their method for calculating ex post power BLW1. I then propose a variant of their method, which I call BLW2. I use Monte Carlo experiments to compare both methods in a simple data environment where there is no clustering. In Chapter Five, I detail two more methods for calculating ex post power. The first procedure is taken from a blog post by David McKenzie and Owen Ozier (2019). I call this approach the SE-ES Method (for Standard Error – Effect Size). I then propose yet another variant of the BLW method, BLW3, which uses a wild-cluster bootstrap for handling clustered data. Chapter Five subjects all four methods to an extensive set of Monte Carlo experiments to assess their reliability in calculating ex post statistical power. I find that the SE-ES method is superior to BLW’s method (BLW1, BLW2 and BLW3) and has good overall performance. Chapter Six applies the SE-ES method to a set of 23 development studies that were funded by the International Initiative for Impact Evaluation (3ie), a non-profit organization that supports research on ways to help the poor in low- and middle-income countries. I analyze the ex post power of these studies and explore factors that may be responsible for differences between ex ante and ex post statistical power. Chapter Seven concludes this thesis. It provides an overview of my chapters, as well as a summary of my main findings

New developments in frontier models for objective assessments

This dissertation is the result of some innovative proposals, in the wide framework of production efficiency frontier models, that have the common goal of reducing subjective choices of the researcher by using, as far as possible, objective methods. In particular, the first proposal links the economic efficiency theory to the spatial econometrics with the aim of taking into account - in the efficiency evaluation of a productive unit - the neighborhood effects in a global way avoiding the subjective selection of a set of variables identifying territorial effects. The method called Spatial Stochastic Frontier Analysis (SSFA) has been published in Fusco and Vidoli (2013) for the production efficiency analysis and generalized in this thesis to be able to also analyze the cost efficiency. The second proposal, instead aims to introduce enhancements in the methods using frontier techniques to aggregate simple indicators in a composite indicator. Subjectivity is avoided in the identification of the set of aggregation weights necessary for constructing the composite indicator, in the definition of a preference structure among simple indicators and in the extreme values and outliers influence removal. The two methods proposed, called respectively Directional Benefit of the Doubt (D-BoD) and Robust Directional Benefit of the Doubt (RD-BoD), have been published in Fusco (2015) and Vidoli, Fusco and Mazziotta (2015). The dissertation consists of four parts: the first one introduces the foundations of the economic efficiency analysis and gives key economic concepts and definitions needed for a proper understanding of the following parts, focusing both on parametric and on nonparametric methods for cross-sectional and panel data and for mono-output and multi-output production processes; the second one discusses the fundamentals of the spatial econometrics, on the main connection proposals with the efficiency theory and shows in detail the SSFA method and the related R package called SSFA implemented to allow other researchers to use it; in the third part the concept of composite indicator and the required steps for its construction are discussed and D-BoD and RD-BoD are shown, moreover the related R package Compind is presented; all proposed methods have been tested both on simulated data and on real data and the results are shown in the fourth part. In the last part, two innovative applications, respectively on the estimation of non performing loans of commercial banks (Fusco and Maggi, 2016) and on the estimation of the local governments’ expenditure needs (Vidoli and Fusco, 2017) by using the efficiency and spatial theories, are also included

Graph-based Support Vector Machines for Patient Response Prediction Using Pathway and Gene Expression Data

Over the past decade, multiple function genomic datasets studying chromosomal aberrations and their downstream implications on gene expression have accumulated across a variety of cancer types. With the majority being paired copy number/gene expression profiles originating from the same patient groups, this time frame has also induced a wealth of integrative attempts in hope that the concurrent analysis between both genomic structures will result in optimized downstream results. Borrowing the concept, this dissertation presents a novel contribution to the development of statistical methodology for integrating copy number and gene expression data for purposes of predicting treatment response in multiple myeloma patients

Geostatistical methods for disease prevalence mapping

Geostatistical methods are increasingly used in low-resource settings where disease registries are either non-existent or geographically incomplete. In this thesis, which is comprised of four papers, we address some of the common issues that arise from analysing disease prevalence data. In the first paper we consider the problem of combining data from multiple spatially referenced surveys so as to account for two main sources of variation: temporal variation, when surveys are repeated over time; data-quality variation, e.g. between randomised and non-randomised surveys. We then propose a multivariate binomial geostatistical model for the combined analysis of data from multiple surveys. We also show an application to malaria prevalence data from three surveys conducted in two consecutive years in Chikwawa District, Malawi, one of which used a more economical convenience sampling strategy. In the second paper, we analyse river-blindness prevalence data from a survey conducted in 20 African countries enrolled in the African Programme of Onchocerciasis Control (APOC). The main challenge of this analysis is computational, as a binomial geostatistical model has to be fitted to more than 14,000 village locations and predictions carried out on about 10 millions locations across Africa. To make the computation feasible and efficient, we then develop a low rank approximation based on a convolution-kernel representation which avoids matrix inversion. The third paper is a tutorial on the use of a new R package, namely “PrevMap”, which provides functions for both likelihood-based and Bayesian analysis of spatially referenced prevalence data. In the fourth paper, we present some extensions of the standard geostatistical model for spatio-temporal analysis of prevalence data and modelling of spatially structured zero-inflation. We then describe three applications that have arisen through our collaborations with researchers and public health programmers in African countries

Life Among the Muses: Papers in Honor of James S. Findley

Edited volume of papers Preface; Terry L. Yates The Academic Offspring of James S. Findley; Kenneth N. Geluso and Don E. Wilson Annotated Bibliography of James Smith Findley; William L. Gannon and Don E. Wilson Biogeography of Baja California Peninsular Desert Mammals; David J. Hafner and Brett R. Riddle Annotated Checklist of the Recent Land Mammals of Sonora, Mexico; William Caire On the Status of Neotoma varia from Isla Datil, Sonora; Michael A. Bogan Systematics, Distribution, and Ecology of the Mammals of Catamarca Province, Argentina; Michael A. Mares, Ricardo A. Ojeda, Janet K. Braun, and Ruben M. Barquez Similarity Coefficients and Relationships of Wisconsin-Age Faunas New Mexico and Trans-Pecos Texas; Arthur H. Harris Historical Implications and Characteristics of Assemblages of Small Mammals in West-Central Kansas; E.D. Fleharty and Rob Channell Mammal Species of Concern in New Mexico; Clyde Jones and C. Gregory Schmitt Non-Human Mortality, Injuries, and Possible Cannibalism in Utah Black Bears; Hal L. Black Skeletal Architecture of the Forelimbs in Kangaroo Rats (Heteromyidae: Dipodomys): Adaptations for Digging and Food Handling; Kerry S. Kilburn Puncturing Ability of Bat Canine Teeth: The Tip; Patricia W. Freeman and William N. Weins The Effects of Daily and Seasonal Temperature Variation on a Model of Competing Lizard Species; J.S. Scheibe A Comparison of Morphometric Techniques to Distinguish Sympatric Mussel Species (Family Unionidae) with Similar Shell Morphology; Patricia Mehlhop and Richard L. Cifelli Evaluation of Methods for Permanently Marking Kangaroo Rats (Dipodomys: Heteromyidae); Daniel F. Williams, Walter Tordoff Ill, and David J. Germano Influence of Proximity to Rivers on Chipmunk Vocalization Patterns; William L. Gannon Subnivean Foraging by Abert\u27s Squirrels; Richard B. Forbe