Hypothesis Test for Manifolds and Networks

Statistical inference of high-dimensional data is crucial for science and engineering. Such high-dimensional data are often structured. For example, they can be data from a certain manifold or a large network. Motivated by the problems that arise in recommendation systems, power systems, and social media, etc., this dissertation aims to provide statistical modeling for such problems and perform statistical inferences. This dissertation focus on two problems. (i) statistical modeling for smooth manifold and inferences for the corresponding characteristic rank; (ii) detection of change-points for sequential data in a network. For the first topic. We start with the rank selection problem in the matrix completion problem. We addressed the problem of rank identifiability in minimum rank matrix completion problem and proposed a statistical model for the low-rank matrix approximation problem. We then generalize the problem to a more general smooth manifold. For the second topic. We study the problem of cascading failure motivated by the study of the power system. We proposed a model for failure propagation and a fast algorithm to perform the test procedure of detecting the cascading failure. The other problem we study in change-points detection is to detect the change of event data. We use the multivariate Hawkes process to capture the self and cross excitation between the events and proposed a test procedure base on scan score statistics.Ph.D

Improved micro-contact resistance model that considers material deformation, electron transport and thin film characteristics

This paper reports on an improved analytic model forpredicting micro-contact resistance needed for designing microelectro-mechanical systems (MEMS) switches. The originalmodel had two primary considerations: 1) contact materialdeformation (i.e. elastic, plastic, or elastic-plastic) and 2) effectivecontact area radius. The model also assumed that individual aspotswere close together and that their interactions weredependent on each other which led to using the single effective aspotcontact area model. This single effective area model wasused to determine specific electron transport regions (i.e. ballistic,quasi-ballistic, or diffusive) by comparing the effective radius andthe mean free path of an electron. Using this model required thatmicro-switch contact materials be deposited, during devicefabrication, with processes ensuring low surface roughness values(i.e. sputtered films). Sputtered thin film electric contacts,however, do not behave like bulk materials and the effects of thinfilm contacts and spreading resistance must be considered. Theimproved micro-contact resistance model accounts for the twoprimary considerations above, as well as, using thin film,sputtered, electric contact

Social welfare policies and child poverty in South Africa: a microsimulation model on the child support grant

Philosophiae Doctor - PhDThe study assessed the extent of child poverty in South Africa using five different policy scenarios, and modelled the impact on poverty and inequalities of people living in households with children using the Foster-Greer-Thorbecke (FGT) index of poverty measurement, including poverty rate P0, (headcount index ratio), poverty gap index P1, (the depth of poverty), and the severity of poverty P2 (squared poverty gap index). Societal welfare inequalities have been measured using the Gini co-efficient. In general, the scenario analysis was based on the 2007 population baseline and 2008 government policy rules. The results of the study clearly indicate that there is a positive correlation between cash transfer (Child Support Grant) and a reduction in poverty and the inequalities of people living in households with children in South Africa. An increase in the Child Support Grant amount and the number of child beneficiaries, in modelling, produced a positive effect in addressing increasing child poverty and vulnerability. In addition, the research process identified four interrelated gaps that hinder the successful implementation of the social welfare policies underlying the Child Support Grant to reduce the poverty and inequality profile of people living in households with children in South Africa. First, inadequate understanding of the constitutional rights of the child exists. Second, failure to use proven best practice of institutional arrangements and implementation modalities was identified. Third, lack of political will for the championship of a universal basic income grant (UBIG) is present. Fourth, insufficient research, monitoring and evaluation (M&E) and dissemination of best practices is done. Within the context of the above mentioned analysis, the study finally brings into focus general observations gained from the investigation and provides recommendations to policy makers and other stakeholders.South Afric

Batch Control and Diagnosis

Batch processes are becoming more and more important in the chemical process industry, where they are used in the manufacture of specialty materials, which often are highly profitable. Some examples where batch processes are important are the manufacturing of pharmaceuticals, polymers, and semiconductors. The focus of this thesis is exception handling and fault detection in batch control. In the first part an internal model approach for exception handling is proposed where each equipment object in the control system is extended with a state-machine based model that is used on-line to structure and implement the safety interlock logic. The thesis treats exception handling both at the unit supervision level and at the recipe level. The goal is to provide a structure, which makes the implementation of exception handling in batch processes easier. The exception handling approach has been implemented in JGrafchart and tested on the batch pilot plant Procel at Universitat Politècnica de Catalunya in Barcelona, Spain. The second part of the thesis is focused on fault detection in batch processes. A process fault can be any kind of malfunction in a dynamic system or plant, which leads to unacceptable performance such as personnel injuries or bad product quality. Fault detection in dynamic processes is a large area of research where several different categories of methods exist, e.g., model-based and process history-based methods. The finite duration and non-linear behavior of batch processes where the variables change significantly over time and the quality variables are only measured at the end of the batch lead to that the monitoring of batch processes is quite different from the monitoring of continuous processes. A benchmark batch process simulation model is used for comparison of several fault detection methods. A survey of multivariate statistical methods for batch process monitoring is performed and new algorithms for two of the methods are developed. It is also shown that by combining model-based estimation and multivariate methods fault detection can be improved even though the process is not fully observable

Scalable Low-rank Matrix and Tensor Decomposition on Graphs

In many signal processing, machine learning and computer vision applications, one often has to deal with high dimensional and big datasets such as images, videos, web content, etc. The data can come in various forms, such as univariate or multivariate time series, matrices or high dimensional tensors. The goal of the data mining community is to reveal the hidden linear or non-linear structures in the datasets. Over the past couple of decades matrix factorization, owing to its intrinsic association with dimensionality reduction has been adopted as one of the key methods in this context. One can either use a single linear subspace to approximate the data (the standard Principal Component Analysis (PCA) approach) or a union of low dimensional subspaces where each data class belongs to a different subspace. In many cases, however, the low dimensional data follows some additional structure. Knowledge of such structure is beneficial, as we can use it to enhance the representativity of our models by adding structured priors. A nowadays standard way to represent pairwise affinity between objects is by using graphs. The introduction of graph-based priors to enhance matrix factorization models has recently brought them back to the highest attention of the data mining community. Representation of a signal on a graph is well motivated by the emerging field of signal processing on graphs, based on notions of spectral graph theory. The underlying assumption is that high-dimensional data samples lie on or close to a smooth low-dimensional manifold. Interestingly, the underlying manifold can be represented by its discrete proxy, i.e. a graph. A primary limitation of the state-of-the-art low-rank approximation methods is that they do not generalize for the case of non-linear low-rank structures. Furthermore, the standard low-rank extraction methods for many applications, such as low-rank and sparse decomposition, are computationally cumbersome. We argue, that for many machine learning and signal processing applications involving big data, an approximate low-rank recovery suffices. Thus, in this thesis, we present solutions to the above two limitations by presenting a new framework for scalable but approximate low-rank extraction which exploits the hidden structure in the data using the notion of graphs. First, we present a novel signal model, called `Multilinear low-rank tensors on graphs (MLRTG)' which states that a tensor can be encoded as a multilinear combination of the low-frequency graph eigenvectors, where the graphs are constructed along the various modes of the tensor. Since the graph eigenvectors have the interpretation of \textit{non-linear} embedding of a dataset on the low-dimensional manifold, we propose a method called `Graph Multilinear SVD (GMLSVD)' to recover PCA based linear subspaces from these eigenvectors. Finally, we propose a plethora of highly scalable matrix and tensor based problems for low-rank extraction which implicitly or explicitly make use of the GMLSVD framework. The core idea is to replace the expensive iterative SVD operations by updating the linear subspaces from the fixed non-linear ones via low-cost operations. We present applications in low-rank and sparse decomposition and clustering of the low-rank features to evaluate all the proposed methods. Our theoretical analysis shows that the approximation error of the proposed framework depends on the spectral properties of the graph Laplacian

The geological environment of post-caledonian base-metal mineralization in Ireland

The Dlnantian host and wall rocks to the Ballyvergin, Gortdrum, Oola, Carrickittle and Tynagh base-metal deposits were analysed for a variety of trace elements with a view to establishing a local sedimentary syngenetic contribution of metals. Against expectation all the trace element aureoles examined proved the epigenetic nature of the sulphide mineralization. The aureoles are of two kinds corresponding to the sulphide deposit types. The copper deposits in the Lower Limestone Shales and the argillaceous Lower Limestones; Ballyvergin, Gortdrum and Oola, are fringed with enrichments of arsenic and lead, whereas the Waulsortian wall rocks to the Tynagh and Carrickittle lead-zinc deposits contain uneven enrichments of many trace elements. A reconnaissance survey in the Waulsortian mud bank complex to the west north west of Tynagh revealed what may be an extensive syngenetic manganese aureole to the Tynagh chert-hematite deposit. The exhalative origin proposed by Derry, Clark and Gillatt (1965) for the Tynagh iron deposit is supported by chemical analysis. Thus hot springs were in existence at Tynagh in mid-Dinantian times. This was probably the case too at Silvermines (Graham 1970). The iron deposit at Keel as well as the thick developments of chert at Silvermines and Aherlow are taken here as additional evidence for a mid-Dinantian age for the onset of mineralization. Although the local structural controls to the sulphide deposits may be related to the Armorican Orogeny, the distribution of the ore deposits is more easily explained in terms of north-south geofracturing caused by the tensile stresses which eventually led to the formation of the Atlantic (Rockall Trough) margin. The recent discovery of the Navan sulphide deposit was broadly predictable by this theory

Applied Fracture Mechanics

The book "Applied Fracture Mechanics" presents a collection of articles on application of fracture mechanics methods to materials science, medicine, and engineering. In thirteen chapters, a wide range of topics is discussed, including strength of biological tissues, safety of nuclear reactor components, fatigue effects in pipelines, environmental effects on fracture among others. In addition, the book presents mathematical and computational methods underlying the fracture mechanics applications, and also developments in statistical modeling of fatigue. The work presented in this book will be useful, effective, and beneficial to mechanical engineers, civil engineers, and material scientists from industry, research, and education

A systems approach to sub-typing of rheumatoid arthritis

The current health care system is severely challenged by for instance rising costs, fewer new blockbuster drugs and increasing numbers of hospitalizations due to side effects. Especially in the area of chronic diseases the current disease fighting strategy is failing and a more personalized medicine approach is needed. In this thesis new sub-types of rheumatoid arthritis are characterized with metabolomics analysis and symptoms patterns. The sub-types are based on diagnostic knowledge from Chinese medicine. The two sub-types of RA patients were found to have differences in apoptosis regulation of T-cells and differences in urine acylcarnitine levels. A questionnaire was designed to distinguish the two sub-types and to evaluate symptom patterns of arthritis patients. In the future the response to treatment of these sub-types of patients can be studied and specific treatment can be targeted to these sub-types.LEI Universiteit LeidenArtrose & Reuma StichtingAnalyse en stochastie

Resampling-based tests of functional categories in gene expression studies

DNA microarrays allow researchers to measure the coexpression of thousands of genes, and are commonly used to identify changes in expression either across experimental conditions or in association with some clinical outcome. With increasing availability of gene annotation, researchers have begun to ask global questions of functional genomics that explore the interactions of genes in cellular processes and signaling pathways. A common hypothesis test for gene categories is constructed as a post hoc analysis performed once a list of significant genes is identified, using classically derived tests for 2x2 contingency tables. We note several drawbacks to this approach including the violation of an independence assumption by the correlation in expression that exists among genes. To test gene categories in a more appropriate manner, we propose a flexible, permutation-based framework, termed SAFE (for Significance Analysis of Function and Expression). SAFE is a two-stage approach, whereby gene-specific statistics are calculated for the association between expression and the response of interest and then a global statistic is used to detect a shift within a gene category to more extreme associations. Significance is assessed by repeatedly permuting whole arrays whereby the correlation between all genes is held constant and accounted for. This permutation scheme also preserves the relatedness of categories containing overlapping genes, such that error rate estimates can be readily obtained for multiple dependent tests. Through a detailed survey of gene category tests and simulations based on real microarray, we demonstrate how SAFE generates appropriate Type I error rates as compared to other methods. Under a more rigorously defined null hypothesis, permutation-based tests of gene categories are shown to be conservative by inducing a special case with a maximum variance for the test statistic. A bootstrap-based approach to hypothesis testing is incorporated into the SAFE framework providing better coverage and improved power under a defined class of alternatives. Lastly, we extend the SAFE framework to consider gene categories in a probabilistic manner. This allows for a hypothesis test of co-regulation, using models of transcription factor binding sites to score for the presence of motifs in the upstream regions of genes