Knot concordance and Heegaard Floer homology invariants in branched covers

By studying the Heegaard Floer homology of the preimage of a knot K in S^3 inside its double branched cover, we develop simple obstructions to K having finite order in the classical smooth concordance group. As an application, we prove that all 2-bridge knots of crossing number at most 12 for which the smooth concordance order was previously unknown have infinite smooth concordance order.Comment: Expanded references; 25 pages, 5 figure

Hierarchical reinforcement learning in a biologically plausible neural architecture

Humans and other animals have an impressive ability to quickly adapt to unfamiliar environments, with only minimal feedback. Computational models have been able to provide intriguing insight into these processes, by making connections between abstract computational theories of reinforcement learning (RL) and neurophysiological data. However, the ability of these models falls well below the level of real neural systems, thus it is clear that there are important aspects of the neural computation not being captured by our models. In this work we explore how new developments from the computational study of RL can be expanded to the realm of neural modelling. Specifically, we examine the field of hierarchical reinforcement learning (HRL), which extends RL by dividing the RL process into a hierarchy of actions, where higher level decisions guide the choices made at lower levels. The advantages of HRL have been demonstrated from a computational perspective, but HRL has never been implemented in a neural model. Thus it is unclear whether HRL is a purely abstract theory, or whether it could help explain the RL ability of real brains. Here we show that all the major components of HRL can be implemented in an integrated, biologically plausible neural model. The core of this system is a model of ``flat'' RL that implements the processing of a single layer. This includes computing action values given the current state, selecting an output action based on those values, computing a temporal difference error based on the result of that action, and using that error to update the action values. We then show how the design of this system allows multiple layers to be combined hierarchically, where inputs are received from higher layers and outputs delivered to lower layers. We also provide a detailed neuroanatomical mapping, showing how the components of the model fit within known neuroanatomical structures. We demonstrate the performance of the model in a range of different environments, in order to emphasize the aim of understanding the brain's general, flexible reinforcement learning ability. These results show that the model compares well to previous modelling work and demonstrates improved performance as a result of its hierarchical ability. We also show that the model's output is consistent with available data on human hierarchical RL. Thus we believe that this work, as the first biologically plausible neural model of HRL, brings us closer to understanding the full range of RL processing in real neural systems. We conclude with a discussion of the design decisions made throughout the course of this work, as well as some of the most important avenues for the model's future development. Two of the most critical of these are the incorporation of model-based reasoning and the autonomous development of hierarchical structure, both of which are important aspects of the full HRL process that are absent in the current model. We also discuss some of the predictions that arise from this model, and how they might be tested experimentally.4 month

A neural modelling approach to investigating general intelligence

One of the most well-respected and widely used tools in the study of general intelligence is the Raven's Progressive Matrices test, a nonverbal task wherein subjects must induce the rules that govern the patterns in an arrangement of shapes and figures. This thesis describes the first neurally based, biologically plausible model that can dynamically generate the rules needed to solve Raven's matrices. We demonstrate the success and generality of the rules generated by the model, as well as interesting insights the model provides into the causes of individual differences, at both a low (neural capacity) and high (subject strategy) level. Throughout this discussion we place our research within the broader context of intelligence research, seeking to understand how the investigation and modelling of Raven's Progressive Matrices can contribute to our understanding of general intelligence

Fetal age assessment based on 2nd trimester ultrasound in Africa and the effect of ethnicity

<p>Abstract</p> <p>Background</p> <p>The African population is composed of a variety of ethnic groups, which differ considerably from each other. Some studies suggest that ethnic variation may influence dating. The aim of the present study was to establish reference values for fetal age assessment in Cameroon using two different ethnic groups (Fulani and Kirdi).</p> <p>Methods</p> <p>This was a prospective cross sectional study of 200 healthy pregnant women from Cameroon. The participants had regular menstrual periods and singleton uncomplicated pregnancies, and were recruited after informed consent. The head circumference (HC), outer-outer biparietal diameter (BPDoo), outer-inner biparietal diameter and femur length (FL), also called femur diaphysis length, were measured using ultrasound at 12–22 weeks of gestation. Differences in demographic factors and fetal biometry between ethnic groups were assessed by t- and Chi-square tests.</p> <p>Results</p> <p>Compared with Fulani women (N = 96), the Kirdi (N = 104) were 2 years older (p = 0.005), 3 cm taller (p = 0.001), 6 kg heavier (p < 0.0001), had a higher body mass index (BMI) (p = 0.001), but were not different with regard to parity. Ethnicity had no effect on BPDoo (p = 0.82), HC (p = 0.89) or FL (p = 00.24). Weight, height, maternal age and BMI had no effect on HC, BPDoo and FL (p = 0.2–0.58, 0.1–0.83, and 0.17–0.6, respectively).</p> <p>When comparing with relevant European charts based on similar design and statistics, we found overlapping 95% CI for BPD (Norway & UK) and a 0–4 day difference for FL and HC.</p> <p>Conclusion</p> <p>Significant ethnic differences between mothers were not reflected in fetal biometry at second trimester. The results support the recommendation that ultrasound in practical health care can be used to assess gestational age in various populations with little risk of error due to ethnic variation.</p

Computing Khovanov-Rozansky homology and defect fusion

We compute the categorified sl(N) link invariants as defined by Khovanov and Rozansky, for various links and values of N. This is made tractable by an algorithm for reducing tensor products of matrix factorisations to finite rank, which we implement in the computer algebra package Singular.Comment: 35 pages; v2: exposition shortened and reorganised; v3: typos in Section 4 correcte