Hyperspaces, shape theory and computational topology

Esta tesis trata sobre aproximaciones de espacios métricos compactos. La aproximación y reconstrucción de espacios topológicos mediante otros más sencillos es un tema antigüo en topología geométrica. La idea es construir un espacio muy sencillo lo más parecido posible al espacio original. Como es muy difícil (o incluso no tiene sentido) intentar obtener una copia homeomorfa, el objetivo será encontrar un espacio que preserve algunas propriedades topológicas (algebraicas o no) como compacidad, conexión, axiomas de separación, tipo de homotopía, grupos de homotopía y homología, etc. Los primeros candidatos como espacios sencillos con propiedades del espacio original son los poliedros. Ver el artículo [45] para los resultados principales. En el germen de esta idea, destacamos los estudios de Alexandroff en los años 20, relacionando la dimensión del compacto métrico con la dimensión de ciertos poliedros a través de aplicaciones con imágenes o preimágenes controladas (en términos de distancias). En un contexto más moderno, la idea de aproximación puede ser realizada construyendo un complejo simplicial basado en el espacio original, como el complejo de Vietoris-Rips o el complejo de Cech y comparar su realización con él. En este sentido, tenemos el clásico lema del nervio [12, 21] el cual establece que para un recubrimiento por abiertos “suficientemente bueno" del espacio (es decir, un recubrimiento con miembros e intersecciones contractibles o vacías), el nervio del recubrimiento tiene el tipo de homotopía del espacio original. El problema es encontrar estos recubrimientos (si es que existen). Para variedades Riemannianas, existen algunos resultados en este sentido, utilizando los complejos de Vietoris-Rips. Hausmann demostró [35] que la realización del complejo de Vietoris-Rips de la variedad, para valores suficientemente bajos del parámetro, tiene el tipo de homotopía de dicha variedad. En [40], Latschev demostró una conjetura establecida por Hausmann: El tipo de homotopía de la variedad se puede recuperar utilizando un conjunto finito de puntos (suficientemente denso) para el complejo de Vietoris-Rips. Los resultados de Petersen [58], comparando la distancia Gromov-Hausdorff de los compactos métricos con su tipo de homotopía, son también interesantes. Aquí, los poliedros salen a relucir en las demostraciones, no en los resultados...

The Inner Corona Algebra of a C0(X)-Algebra

Date of Acceptance: 15/07/2015

The Inner Corona Algebra of a C0(X)-Algebra

Date of Acceptance: 15/07/2015

Production of Referring Expressions for an Unknown Audience : a Computational Model of Communal Common Ground

The research reported in this article is based on the Ph.D. project of Dr. RK, which was funded by the Scottish Informatics and Computer Science Alliance (SICSA). KvD acknowledges support from the EPSRC under the RefNet grant (EP/J019615/1).

The mechanism of ϕC31 integrase directionality : experimental analysis and computational modelling

Acknowledgments We thank Sally Rowland for helpful comments on the manuscript. © The Author(s) 2016. Published by Oxford University Press on behalf of Nucleic Acids Research.

A Comparative Review of Computational Methods as Applied to Gold(I) Complexes and Mechanisms

In the last two decades, the field of homogeneous gold catalysis has been

extremely active, growing at a rapid pace. Another rapidly-growing field—that of

computational chemistry—has often been applied to the investigation of various gold-

catalyzed reaction mechanisms. Unfortunately, a number of recent mechanistic studies

have utilized computational methods that have been shown to be inappropriate and

inaccurate in their description of gold chemistry. This work presents an overview of

available computational methods with a focus on the approximations and limitations

inherent in each, and offers a review of experimentally-characterized gold(I) complexes

and proposed mechanisms as compared with their computationally-modeled

counterparts. No aim is made to identify a “recommended” computational method for

investigations of gold catalysis; rather, discrepancies between experimentally and

computationally obtained values are highlighted, and the systematic errors between

different computational methods are discussed.

Computational Methods for Identifying Hypertrophic Cardiomyopathy using 12-lead ECG

Hypertrophic cardiomyopathy (HCM) is a cardiovascular disease where the heart muscle is partially thickened and blood flow is - potentially fatally - obstructed. It is one of the leading causes of sudden cardiac death in young people. Electrocardiography (ECG) and Echocardiography (Echo) are the standard tests for identifying HCM and other cardiac abnormalities. The American Heart Association has recommended using a pre-participation questionnaire for young athletes instead of ECG or Echo tests due to considerations of cost and time involved in interpreting the results of these tests by an expert cardiologist. Initially we set out to develop a classifier for automated prediction of young athletes’ heart conditions based on the answers to the questionnaire. Classification results and further in-depth analysis using computational and statistical methods indicated significant shortcomings of the questionnaire in predicting cardiac abnormalities. Automated methods for analyzing ECG signals can help reduce cost and save time in the pre-participation screening process by detecting HCM and other cardiac abnormalities. Therefore, the main goal of this dissertation work is to identify HCM through computational analysis of 12-lead ECG. ECG signals recorded on one or two leads have been analyzed in the past for classifying individual heartbeats into different types of arrhythmia as annotated primarily in the MIT-BIH database. In contrast, we classify complete sequences of 12-lead ECGs to assign patients into two groups: HCM vs. non-HCM. The challenges and issues we address include missing ECG waves in one or more leads and the dimensionality of a large feature-set. We address these by proposing imputation and feature-selection methods. We develop heartbeat-classifiers by employing Random Forests and Support Vector Machines, and propose a method to classify full 12-lead ECGs based on the proportion of heartbeats classified as HCM. The results from our experiments show that the classifiers developed using our methods perform well in identifying HCM. Thus the two contributions of this thesis are the utilization of computational and statistical methods for discovering shortcomings in a current screening procedure and the development of methods to identify HCM through computational analysis of 12-lead ECG signals.

Computational models for improved diagnosis and prognosis of stroke using robot-based biomarkers

Stroke is a leading cause of death and permanent disability worldwide, affecting millions of individuals. Traditional clinical scores for assessment of stroke-related impairments are inherently subjective and limited by inter-rater and intra-rater reliability, as well as floor and ceiling effects. In contrast, robotic technologies provide objective, highly repeatable tools for quantification of neurological impairments following stroke. KINARM is an exoskeleton robotic device that provides objective, reliable tools for assessment of sensorimotor, proprioceptive and cognitive brain function by means of a battery of behavioral tasks. As such, KINARM is particularly useful for assessment of neurological impairments following stroke. This thesis introduces a computational framework for assessment of neurological impairments using the data provided by KINARM. This is done by achieving two main objectives. First, to investigate how robotic measurements can be used to estimate current and future abilities to perform daily activities for subjects with stroke. We are able to predict clinical scores related to activities of daily living at present and future time points using a set of robotic biomarkers. The findings of this analysis provide a proof of principle that robotic evaluation can be an effective tool for clinical decision support and target-based rehabilitation therapy. The second main objective of this thesis is to address the emerging problem of long assessment time, which can potentially lead to fatigue when assessing subjects with stroke. To address this issue, we examine two time reduction strategies. The first strategy focuses on task selection, whereby KINARM tasks are arranged in a hierarchical structure so that an earlier task in the assessment procedure can be used to decide whether or not subsequent tasks should be performed. The second strategy focuses on time reduction on the longest two individual KINARM tasks. Both reduction strategies are shown to provide significant time savings, ranging from 30% to 90% using task selection and 50% using individual task reductions, thereby establishing a framework for reduction of assessment time on a broader set of KINARM tasks. All in all, findings of this thesis establish an improved platform for diagnosis and prognosis of stroke using robot-based biomarkers.

Using Computational Significance and Resilience in System Software Stacks.:Keynote Talk

This talk explores how the runtime system and operating system can leverage metrics that express the significance and resilience of application components in order to reduce the energy footprint of parallel applications. We will explore in particular how software can tolerate and indeed exploit higher error rates in future processors and memory technologies that may operate outside their safe margins.

Deterministic Genericity and the Computation of homological Invariants

The main goal of this thesis is to discuss the determination of homological invariants of polynomial ideals. Thereby we consider different coordinate systems and analyze their meaning for the computation of certain invariants. In particular, we provide an algorithm that transforms any ideal into strongly stable position if char k = 0. With a slight modification, this algorithm can also be used to achieve a stable or quasi-stable position. If our field has positive characteristic, the Borel-fixed position is the maximum we can obtain with our method. Further, we present some applications of Pommaret bases, where we focus on how to directly read off invariants from this basis. In the second half of this dissertation we take a closer look at another homological invariant, namely the (absolute) reduction number. It is a known fact that one immediately receives the reduction number from the basis of the generic initial ideal. However, we show that it is not possible to formulate an algorithm – based on analyzing only the leading ideal – that transforms an ideal into a position, which allows us to directly receive this invariant from the leading ideal. So in general we can not read off the reduction number of a Pommaret basis. This result motivates a deeper investigation of which properties a coordinate system must possess so that we can determine the reduction number easily, i.e. by analyzing the leading ideal. This approach leads to the introduction of some generalized versions of the mentioned stable positions, such as the weakly D-stable or weakly D-minimal stable position. The latter represents a coordinate system that allows to determine the reduction number without any further computations. Finally, we introduce the notion of β-maximal position, which provides lots of interesting algebraic properties. In particular, this position is in combination with weakly D-stable sufficient for the weakly D-minimal stable position and so possesses a connection to the reduction number.

Begreppens roll vid inlärning av algebra : En litteraturstudie om den roll begrepp och begreppsförmåga spelar vid inlärning av algebra för elever i årskurs 4-6

Svenska elever har presterat dåligt i internationella undersökningar en längre tid när det gäller algebraområdet i matematik. Elevernas begreppsförståelse har pekats ut som en faktor som spelar in i de dåliga resultaten för svenska elever del. Syftet med denna studie har därför varit att ta reda på den roll som begrepp och begreppsförmåga spelar vid inlärning av algebra samt vilken begreppsförståelse elever i årskurs 4-6 har. Genom en systematisk litteraturstudie har frågeställningarna besvarats. Resultaten visar att brister i begreppsförståelse i algebra också leder till brister i kunskap i algebra. Undervisning med fokus på begrepp leder till bättre förståelse för begrepp samtidigt som det även leder till procedurell kunskap. Elever i årskurs 4-6 kan hantera variabler och använda dem i matematiska uttryck. Fördelar med en tidig introduktion av variabelbegreppet är att elever bygger en bättre förståelse för begreppet.