Generalized anxiety disorder (GAD) is a prevalent anxiety disorder that is characterized by persistent excessive worrying that is often difficult to control. The pathology of GAD has been associated with abnormal neural activity and functional connectivity. This systematic review has examined the central neural correlates of GAD which are the prefrontal cortex (PFC), the anterior cingulate cortex (ACC) and the amygdala and how activation and functional connectivity in these brain areas differ between patients with GAD and healthy controls. This review also investigated how abnormal functional connectivity and activation in these brain regions relates to worry which is the most prominent psychological symptom in patients with GAD. A systematic review was conducted and seven original functional magnetic resonance imaging (fMRI) studies were included after a literature search on PubMed, Scopus and, Web of Science. The main findings from this review revealed decreased activation in the PFC and ACC and enhanced activation in the amygdala during the viewing of negative stimuli in patients with GAD. Identifying the neural correlates of GAD and how it relates to worry may provide improved treatment in the future such as developing more effective psychotropic drugs or improved psychotherapy. GAD has been associated with lower well-being and life satisfaction and may even be a risk factor for suicidal thoughts. One of the limitations from this review is that several of the included studies recruited patients with comorbidities and for that reason results from these studies cannot be generalized and applied to individuals with GAD.

Minimax D-optimal designs for regression models with heteroscedastic errors are studied and constructed. These designs are robust against possible misspecification of the error variance in the model. We propose a flexible assumption for the error variance and use a minimax approach to define robust designs. As usual it is hard to find robust designs analytically, since the associated design problem is not a convex optimization problem. However, the minimax D-optimal design problem has an objective function as a difference of two convex functions. An effective algorithm is developed to compute minimax D-optimal designs under the least squares estimator and generalized least squares estimator. The algorithm can be applied to construct minimax D-optimal designs for any linear or nonlinear regression model with heteroscedastic errors. In addition, several theoretical results are obtained for the minimax D-optimal designs. / Graduate

The Finkelstein and Schoenfeld (FS) test is a popular generalized pairwise comparison approach to analyze prioritized composite endpoints (e.g., components are assessed in order of clinical importance). Power and sample size estimation for the FS test, however, are generally done via simulation studies. This simulation approach can be extremely computationally burdensome, compounded by an increasing number of composite endpoints and with increasing sample size. We propose an analytic solution to calculate power and sample size for commonly encountered two-component hierarchical composite endpoints. The power formulas are derived assuming underlying distributions in each of the component outcomes on the population level, which provide a computationally efficient and practical alternative to the standard simulation approach. The proposed analytic approach is extended to derive conditional power formulas, which are used in combination with the promising zone methodology to perform sample size re-estimation in the setting of adaptive clinical trials. Prioritized composite endpoints with more than two components are also investigated. Extensive Monte Carlo simulation studies were conducted to demonstrate that the performance of the proposed analytic approach is consistent with that of the standard simulation approach. We also demonstrate through simulations that the proposed methodology possesses generally desirable objective properties including robustness to mis-specified underlying distributional assumptions. We illustrate our proposed methods through application of the proposed formulas by calculating power and sample size for the Transthyretin Amyloidosis Cardiomyopathy Clinical Trial (ATTR-ACT) and the EMPULSE trial for empagliozin treatment of acute heart failure.

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The thesis studies truncated moment problems and related reconstruction techniques. It transfers the main aspects of Prony's method from finitely-supported measures to the classes of signed or non-negative measures supported on algebraic varieties of any dimension. The Zariski closure of the support of these measures is shown to be determined by finitely many moments and can be computed from the kernel of moment matrices. Moreover, several reconstruction algorithms are developed which are based on the computation of generalized eigenvalues and allow to recover the components of mixtures of such measures.

For different input contexts (sequence of previous words), to predict the next word, a neural word-level language model outputs a probability distribution over all the words in the vocabulary using a softmax function. When the log of probability outputs for all such contexts are stacked together, the resulting matrix is a log probability matrix which can be denoted as Q_theta, where theta denotes the model parameters. When language modeling is formulated as a matrix factorization problem, the matrix to be factorized Q_theta is expected to be high-rank as natural language is highly context-dependent. But existing softmax based word-level language models have a limitation of not being able to produce such matrices; this is known as the softmax bottleneck. There are several works that attempted to overcome the limitations introduced by softmax bottleneck, such as the models that can produce high-rank Q_theta. During the process of reproducing the results of these works, we observed that the rank of Q_theta does not always positively correlate with better performance (i.e., lower test perplexity). This puzzling observation triggered us to conduct a systematic investigation to check the influence of rank of Q_theta on better performance of a language model. We first introduce a new family of activation functions called the Generalized SigSoftmax (GSS). By controlling the parameters of GSS, we were able to construct language models that can produce Q_theta with diverse ranks (i.e., low, medium, and high ranks). For models that use GSS with different parameters, we observe that rank does not have a strong positive correlation with perplexity on the test data, reinforcing the support of our initial observation. By inspecting the top-5 predictions made by different models for a selected set of input contexts, we observe that a high-rank Q_theta does not guarantee a strong qualitative performance. Then, we conduct experiments to check if there are any other additional benefits in having models that can produce high-rank Q_theta. We expose that Q_theta rather suffers from the phenomenon of fast singular value decay. Additionally, we also propose an alternative metric to denote the rank of any matrix known as epsilon-effective rank, which can be useful to approximately quantify the singular value distribution when different values for epsilon are used. We conclude by showing that it is the regularization which has played a positive role in the performance of these high-rank models in comparison to the chosen baselines, and there is no single model yet which truly gains improved expressiveness just because of breaking the softmax bottleneck.

<p>This theses is dedicated to the study of generalized diagonal dominance and its<br />various beneflts. The starting point is the well known nonsingularity result of strictly diagonally dominant matrices, from which generalizations were formed in difierent directions. In theses, after a short overview of very well known results, special attention was turned to contemporary contributions, where overview of already published original material is given, together with new obtained results. Particulary, Ger&bull;sgorin-type localization theory for matrix pencils is developed, and application of the results in wireless sensor networks optimization problems is shown.</p> / <p><span class="fontstyle0">Ova teza je posvećena izučavanju generalizovane dijagonalne dominacije i njenih brojnih prednosti. Osnovu čini poznati rezultat o regularnosti strogo dijagonalnih matrica,<br />čija su uop&scaron;tenja formirana u brojnim pravcima. U tezi, nakon kratkog pregleda dobro poznatih rezultata, posebna pažnja je posvećena savremenim doprinosima, gde je dat i pregled već objavljenih autorovih rezultata, kao i detaljan tretman novih dobijenih rezultata. Posebno je razvijena teorija lokalizacije Ger&scaron;gorinovog tipa generalizovanih karakterističnih korena i pokazana je primena rezultata u problemima optimizacije bežičnih senzor mreža.</span></p>

Are individuals that trust strangers more likely to have children, and can they be expected to have more children than their lower trusting counterparts? This article assesses two perspectives that hold this as a likely outcome. One perspective has trusting individuals as more likely to hand over the care of their children to strangers, thereby reconciling work and family dilemmas for women. In the Five-Factor Model of Personality, trusting individuals increase their odds of parenthood through several paths, including better relationship quality and outward behavior. The two perspectives also suggest different macro-level conditions for the associations. The former maintains that trust is more important for fertility in high trusting countries and where women have a high share of highly educated. The latter holds that trust is more important in low trusting countries. It also suggests that men benefit more from being trusting. This article tests these two perspectives quantitatively using a sample of eight countries that participated in the Generations and Genders Survey. The method being logistic regression with a longitudinal design. The second perspective found most support from the analysis. A positive significant association between trust and the likelihood of parenthood was more clearly found among male respondents. This result suggests that researchers on fertility and personality can be recommended to include generalized trust in their statistical models.

Understanding tuberculosis transmission is vital for efforts at interrupting the spread of disease. Household contact studies that follow persons sharing a household with a TB case—so-called household contacts—and test for latent TB infection by tuberculin skin test conversion give investigators vital information about risk factors for TB transmission. In these studies, investigators often assume secondary cases are infected by the primary TB case, despite substantial evidence that infection from a source outside the home is often equally likely, especially in high-prevalence settings. Investigators may discard information on contacts who test positive at study initiation due to uncertainty of the infection source, or assume infected contacts were infected from the index case prior to study initiation. With either assumption, information on transmission dynamics is lost or incomplete, and estimates of household risk factors for transmission will be biased. This dissertation describes an approach to modeling TB transmission that accounts for community-acquired transmission in the estimation of transmission risk factors from household contact study data. The proposed model generates population-specific estimates of the probability a contact of an infectious case will be infected from a source outside the home—a vital statistic for planning effective interventions to halt disease spread—in additional to estimates of household transmission predictors. We first describe the model analytically, and then apply it to synthetic datasets under different risk scenarios. We then fit the model to data taken from three household contact studies in different locations: Brazil, India, and Uganda. Infection predictors such as contact sleeping proximity to the index case and index case disease severity are underestimated in standard models compared to the proposed method, and non-household TB infection risk increases with age stratum, reflecting longer at-risk duration for community-based exposure for older contacts. This analysis will aid public health planners in understanding how best to interrupt TB spread in disparate populations by characterizing where transmission risk is greatest and which risk factors influence household-acquired transmission. Finally, we present an open-source software package in the R environment titled upmfit for modular implementation of the Bayesian Markov Chain Monte Carlo methods used to estimate the model. / 2018-05-10T00:00:00Z

Generalized algebraic data types (GADTs) are a type system extension to algebraic data types that allows the type of an algebraic data value to vary with its shape. The GADT type system allows programmers to express detailed program properties as types (for example, that a function should return a list of the same length as its input), and a general-purpose type checker will automatically check those properties at compile time. Type inference for the GADT type system and the properties of the type system are both currently areas of active research. In this dissertation, I attack both problems simultaneously by exploiting the symbiosis between type system research and type inference research. Deficiencies of GADT type inference algorithms motivate research on specific aspects of the type system, and discoveries about the type system bring in new insights that lead to improved GADT type inference algorithms. The technical contributions of this dissertation are therefore twofold: in addition to new GADT type system properties (such as the prevalence of pointwise type information flow in GADT patterns, a generalized notion of existential types, and the effects of enforcing the GADT branch reachability requirement), I will also present a new GADT type inference algorithm that is significantly more powerful than existing algorithms. These contributions should help programmers use the GADT type system more effectively, and they should also enable language implementers to provide better support for the GADT type system.