Supercongruences satisfied by coefficients of 2F1 hypergeometric series

Recently, Chan, Cooper and Sica conjectured two congruences for coefficients of classical 2F1 hypergeometric series which also arise from power series expansions of modular forms in terms of modular functions. We prove these two congruences using combinatorial properties of the coefficients.Comment: 13 page

Quintessence with quadratic coupling to dark matter

We introduce a new form of coupling between dark energy and dark matter that is quadratic in their energy densities. Then we investigate the background dynamics when dark energy is in the form of exponential quintessence. The three types of quadratic coupling all admit late-time accelerating critical points, but these are not scaling solutions. We also show that two types of coupling allow for a suitable matter era at early times and acceleration at late times, while the third type of coupling does not admit a suitable matter era.Comment: 11 pages, 8 figures, revte

An Electronic Market-Maker

This paper presents an adaptive learning model for market-making under the reinforcement learning framework. Reinforcement learning is a learning technique in which agents aim to maximize the long-term accumulated rewards. No knowledge of the market environment, such as the order arrival or price process, is assumed. Instead, the agent learns from real-time market experience and develops explicit market-making strategies, achieving multiple objectives including the maximizing of profits and minimization of the bid-ask spread. The simulation results show initial success in bringing learning techniques to building market-making algorithms

Simultaneous lesion and neuroanatomy segmentation in Multiple Sclerosis using deep neural networks

Segmentation of both white matter lesions and deep grey matter structures is an important task in the quantification of magnetic resonance imaging in multiple sclerosis. Typically these tasks are performed separately: in this paper we present a single segmentation solution based on convolutional neural networks (CNNs) for providing fast, reliable segmentations of multimodal magnetic resonance images into lesion classes and normal-appearing grey- and white-matter structures. We show substantial, statistically significant improvements in both Dice coefficient and in lesion-wise specificity and sensitivity, compared to previous approaches, and agreement with individual human raters in the range of human inter-rater variability. The method is trained on data gathered from a single centre: nonetheless, it performs well on data from centres, scanners and field-strengths not represented in the training dataset. A retrospective study found that the classifier successfully identified lesions missed by the human raters. Lesion labels were provided by human raters, while weak labels for other brain structures (including CSF, cortical grey matter, cortical white matter, cerebellum, amygdala, hippocampus, subcortical GM structures and choroid plexus) were provided by Freesurfer 5.3. The segmentations of these structures compared well, not only with Freesurfer 5.3, but also with FSL-First and Freesurfer 6.0