1,286 research outputs found

    A periodicity criterion and the section problem on the Mapping Class Group

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    Some years ago, V. Markovic proved that there is no section of the Mapping Class Group for a closed surface of genus g larger than 5 (in the case of homeomorphims) and more recently generalized this result with D. Saric to the case where g is larger than 1. We will state a periodicity criterion and will use it to simplify some of the arguments given by Markovic and Saric in the proof of their theorem. The periodicity criterion tells us that a homeomorphism of a connected surface must be periodic if the set of connected periodic open sets generates the topology of the surface.Comment: 40 page

    Deep Learning can Replicate Adaptive Traders in a Limit-Order-Book Financial Market

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    We report successful results from using deep learning neural networks (DLNNs) to learn, purely by observation, the behavior of profitable traders in an electronic market closely modelled on the limit-order-book (LOB) market mechanisms that are commonly found in the real-world global financial markets for equities (stocks & shares), currencies, bonds, commodities, and derivatives. Successful real human traders, and advanced automated algorithmic trading systems, learn from experience and adapt over time as market conditions change; our DLNN learns to copy this adaptive trading behavior. A novel aspect of our work is that we do not involve the conventional approach of attempting to predict time-series of prices of tradeable securities. Instead, we collect large volumes of training data by observing only the quotes issued by a successful sales-trader in the market, details of the orders that trader is executing, and the data available on the LOB (as would usually be provided by a centralized exchange) over the period that the trader is active. In this paper we demonstrate that suitably configured DLNNs can learn to replicate the trading behavior of a successful adaptive automated trader, an algorithmic system previously demonstrated to outperform human traders. We also demonstrate that DLNNs can learn to perform better (i.e., more profitably) than the trader that provided the training data. We believe that this is the first ever demonstration that DLNNs can successfully replicate a human-like, or super-human, adaptive trader operating in a realistic emulation of a real-world financial market. Our results can be considered as proof-of-concept that a DLNN could, in principle, observe the actions of a human trader in a real financial market and over time learn to trade equally as well as that human trader, and possibly better.Comment: 8 pages, 4 figures. To be presented at IEEE Symposium on Computational Intelligence in Financial Engineering (CIFEr), Bengaluru; Nov 18-21, 201

    Prime ends rotation numbers and periodic points

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    We study the problem of existence of a periodic point in the boundary of an invariant domain for a surface homeomorphism. In the area-preserving setting, a complete classification is given in terms of rationality of Carath\'eordory's prime ends rotation number, similar to Poincar\'e's theory for circle homeomorphisms. In particular, we prove the converse of a classic result of Cartwright and Littlewood. This has a number of consequences for generic area preserving surface diffeomorphisms. For instance, we extend previous results of J. Mather on the boundary of invariant open sets for CrC^r-generic area preserving diffeomorphisms. Most results are proved in a general context, for homeomorphisms of arbitrary surfaces with a weak nonwandering-type hypothesis. This allows us to prove a conjecture of R. Walker about co-basin boundaries, and it also has applications in holomorphic dynamics.Comment: 50 pages, 15 figure

    Biochemical prevention and treatment of viral infections – A new paradigm in medicine for infectious diseases

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    For two centuries, vaccination has been the dominating approach to develop prophylaxis against viral infections through immunological prevention. However, vaccines are not always possible to make, are ineffective for many viral infections, and also carry certain risk for a small, yet significant portion of the population. In the recent years, FDA's approval and subsequent market acceptance of Synagis, a monoclonal antibody indicated for prevention and treatment of respiratory syncytial virus (RSV) has heralded a new era for viral infection prevention and treatment. This emerging paradigm, herein designated "Biochemical Prevention and Treatment", currently involves two aspects: (1) preventing viral entry via passive transfer of specific protein-based anti-viral molecules or host cell receptor blockers; (2) inhibiting viral amplification by targeting the viral mRNA with anti-sense DNA, ribozyme, or RNA interference (RNAi). This article summarizes the current status of this field

    A finite dimensional proof of a result of Hutchings about irrational pseudo-rotations

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    We prove that the Calabi invariant of a C1C^1 pseudo-rotation of the unit disk, that coincides with a rotation on the unit circle, is equal to its rotation number. This result has been shown some years ago by Michael Hutchings (under very slightly stronger hypothesis). While the original proof used Embedded Contact Homology techniques, the proof of this article uses generating functions and the dynamics of the induced gradient flow
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