COMPUTATIONAL IMPROVEMENTS FOR STOCHASTIC SIMULATION WITH MULTILEVEL MONTE CARLO

In this work we implement various techniques to improve the multilevel Monte Carlo (MLMC) method as it is applied to a variety of stochastic models. In each case we were able to show a quantifiable computational benefit.First we explore the use of a parallel antithetic MLMC algorithm to simulate systems of stochastic differential equations (SDEs) with correlated noise. Since Le ́vy area approxima- tion is unnecessary with antithetic MLMC, it is a natural choice for the solution of systems with non-diagonal, non-commutative noise. The Milstein method used with antithetic MLMC provides a computation complexity of O(ε^−2) root-mean-square error. Furthermore, MLMC uses independent sampling, which is naturally suited for parallel algorithms. We display the advantages of this approach with a case study in stochastic pricing models.Secondly, we analyze the effects of stiffness on the convergence rate to the solution of a system of SDEs. Similarly to their deterministic counterparts, stochastic differential solvers can be unstable when used with a stiff system. When unstable step sizes are taken on the lower levels of MLMC, convergence is not guaranteed. We examine two approaches to remedy this problem: 1) the use of a semi-implicit method with a larger step-size stability region and 2) simply using a more fine discretization as the initial level for the MLMC simulator. We apply this approach to a case study in biochemical reaction networks.Lastly, we improve a recently developed MLMC algorithm, which uses an iterative solver for the solution a partial differential equation (PDE) with random input. The innovation of the original algorithm is that each sample utilizes data gathered from all previously computed samples to create a better initial guess for the iterative solver. The drawback of this method is that the computation of a sample is no longer independent in a computational sense. We use a K-dimensional tree to sort the random input initially so that groups of locally distributed samples may be computed in batches at each parallel computing node.Ph.D

Challenges for identifying the neural mechanisms that support spatial navigation: the impact of spatial scale.

Spatial navigation is a fascinating behavior that is essential for our everyday lives. It involves nearly all sensory systems, it requires numerous parallel computations, and it engages multiple memory systems. One of the key problems in this field pertains to the question of reference frames: spatial information such as direction or distance can be coded egocentrically-relative to an observer-or allocentrically-in a reference frame independent of the observer. While many studies have associated striatal and parietal circuits with egocentric coding and entorhinal/hippocampal circuits with allocentric coding, this strict dissociation is not in line with a growing body of experimental data. In this review, we discuss some of the problems that can arise when studying the neural mechanisms that are presumed to support different spatial reference frames. We argue that the scale of space in which a navigation task takes place plays a crucial role in determining the processes that are being recruited. This has important implications, particularly for the inferences that can be made from animal studies in small scale space about the neural mechanisms supporting human spatial navigation in large (environmental) spaces. Furthermore, we argue that many of the commonly used tasks to study spatial navigation and the underlying neuronal mechanisms involve different types of reference frames, which can complicate the interpretation of neurophysiological data

Alternative perceptions of reality: dyslexia

My MVA work, Alternative Perceptions of Reality: Dyslexia, revolves around dyslexia and ways in which dyslexic artists, like myself, represent reality in their art. I focus on how dyslexics perceive space and time, how this is represented in their work and how it manifests in my own work. The introduction describes why dyslexia is relevant to art, provides more detail on dyslexia itself and ways dyslexia can affect perception. Surrealism and Symbolism are discussed in order to draw parallels with dyslexic perception. Chapter 1 describes the influences on my own work, including dyslexia, primitive art and symbolism. The second chapter profiles two well known artists with dyslexia: Robert Rauschenberg and Pablo Picasso. I examine ways in which they represent space or reality and how dyslexic perception is apparent in their works. Similarly, in Chapter 3, I discuss the works of the contemporary dyslexic artists Terry A. Orchard and Katharine Dowson, including the results of interviews and surveys I conducted. Throughout this dissertation, I also discuss my own experience of dyslexia and how it is expressed through my paintings. In the conclusion, I discuss what I have learned about the work of myself and other dyslexic artists: How our paintings are a glimpse of alternative inner realities

Synthetic Approaches to Novel Pyridine and Indole Derivatives as Potential Agents for the Treatment of Neurodegenerative Disorders

Alzheimer’s Disease (AD), Parkinson’s Disease (PD) and Lewy Body Disease (LBD) are some of the many neurodegenerative disorders associated with dementia, for which there is no ultimate cure. It is widely accepted that central nervous system (CNS) nicotinic acetylcholine receptors (nAChRs) may be strongly implicated in the pathology of these devastating disorders, and that stimulation of nAChRs can enhance cognitive behaviour in animals and humans. Nicotine and other nicotinic receptor binding compounds have, over many years, been explored as potential therapies for disorders such as AD and PD. This thesis describes the preparation and pharmacological investigation of a series of 3- substituted and 3,5-disubstitued pyridine derivatives as potential novel and selective nictotinic receptor agonists. Chapter Two details the synthesis of targeted compounds using the generation of [(pyridin-3-yl)methyl]lithium and [(5-methylpyridin-3- yl)methyl]lithium, respectively and subsequent reaction with various electrophiles. Unsuccessful attempts at the synthesis of enantiomerically pure 4-substituted arylpyridin-3-yl-ethanol derivatives by reduction of prochiral 4-substituted arylpyridin-3-yl-ethanone derivatives were made using both catalytic and enzymatic approaches; however, a pair of enantiomerically pure alcohols were isolated via the resolution of diastereomeric esters (prepared by reaction with (S)-O-acetyl mandelic acid) and subsequent hydrolysis. iv Chapter Three explores the synthesis of targeted compounds using halogen-lithium exchange reactions of 3-bromopyridine using n-BuLi and ring-opening by the resultant pyridin-3-yllithium of 4-substituted aryl epoxides. As an extension, Sonogashira cross-coupling of 3- bromopyridine and 4-substituted arylacetylenes and subsequent hydration as an approach to 4-substituted pyridin-3-yl-ethanone derivatives is described. A series of indole derivatives were synthesised using identical approaches. Using methodology developed in previous Chapters, Chapter Four describes approaches to symmetrical and asymmetrical 3,5- bis(arylethynyl)pyridine derivatives, the corresponding bis(ketones), alcohols and 3,5-disubstituted keto-alcohol products. Chapter Five details preliminary pharmacological data (binding and functional assays) performed by our collaborators at Institut de Recherches Servier

Miscarriage and stillbirth following maternal Zika virus infection in nonhuman primates.

Zika virus (ZIKV) infection is associated with congenital defects and pregnancy loss. Here, we found that 26% of nonhuman primates infected with Asian/American ZIKV in early gestation experienced fetal demise later in pregnancy despite showing few clinical signs of infection. Pregnancy loss due to asymptomatic ZIKV infection may therefore be a common but under-recognized adverse outcome related to maternal ZIKV infection

Replay as wavefronts and theta sequences as bump oscillations in a grid cell attractor network.

Grid cells fire in sequences that represent rapid trajectories in space. During locomotion, theta sequences encode sweeps in position starting slightly behind the animal and ending ahead of it. During quiescence and slow wave sleep, bouts of synchronized activity represent long trajectories called replays, which are well-established in place cells and have been recently reported in grid cells. Theta sequences and replay are hypothesized to facilitate many cognitive functions, but their underlying mechanisms are unknown. One mechanism proposed for grid cell formation is the continuous attractor network. We demonstrate that this established architecture naturally produces theta sequences and replay as distinct consequences of modulating external input. Driving inhibitory interneurons at the theta frequency causes attractor bumps to oscillate in speed and size, which gives rise to theta sequences and phase precession, respectively. Decreasing input drive to all neurons produces traveling wavefronts of activity that are decoded as replays

Marc Chagall sees America

Eleven-year old upper middle-class boy Eugene Sparrow begins a friendship with the Mexican immigrant boy, Marcos Cervantes. Through their relationship, as well as through his conversation in a secret garden with his dead older sister, Eugene is led to question authority, family, friendship, loyalty, class separations- the very foundations of the society in which he has been raised, and the values he has been taught to accept as true.California State University, Northridge. Department of English