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    ABSTRACT: This paper describes the operation of a new design of wave energy converter. The design consists of a buoyant tethered submerged circular cylinder which is allowed to pitch freely about an axis below its centre. Within the body of the cylinder a fluid half fills an annular tank whose shaped inner walls allow the fundamental sloshing mode of the fluid be to tuned to any period of interest. The pitching motion of the cylinder in waves induces a sloshing motion inside the annular tank which in turns drives an air turbine connecting air chambers above the two isolated internal free surfaces. The concept behind this design is to couple resonances of the pitching cylinder with natural sloshing resonances of the internal water tank and thus achieve a broadbanded power response over a wide range of physically-relevant wave periods. Mathematically, the problem introduces new techniques to solve the series of complex internal forced sloshing problems that arise and to efficiently determine key hydrodynamic coefficients needed for the calculation of the power from the device. The results show that practical configurations can be found in which the efficiency of a two-dimensional cylindrical device is close to its maximum theoretical limit over the target range of periods from 55 to 1111 seconds.
    European Journal of Mechanics - B/Fluids 09/2014; 47. DOI:10.1016/j.euromechflu.2014.03.008
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    ABSTRACT: We extend to the function field setting the heuristic previously developed, by Conrey, Farmer, Keating, Rubinstein and Snaith, for the integral moments and ratios of L -functions defined over number fields. Specifically, we give a heuristic for the moments and ratios of a family of L -functions associated with hyperelliptic curves of genus g over a fixed finite field FqFq in the limit as g→∞g→∞. Like in the number field case, there is a striking resemblance to the corresponding formulae for the characteristic polynomials of random matrices. As an application, we calculate the one-level density for the zeros of these L-functions.
    Journal of Number Theory 09/2014; 142:102–148. DOI:10.1016/j.jnt.2014.02.019
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    ABSTRACT: Continuous action space games are ubiquitous in economics. However, whilst learning dynamics in normal form games with finite action sets are now well studied, it is not until recently that their continuous action space counterparts have been examined. We extend stochastic fictitious play to the continuous action space framework. In normal form games with finite action sets the limiting behaviour of a discrete time learning process is often studied using its continuous time counterpart via stochastic approximation. In this paper we study stochastic fictitious play in games with continuous action spaces using the same method. This requires the asymptotic pseudo-trajectory approach to stochastic approximation to be extended to Banach spaces. In particular the limiting behaviour of stochastic fictitious play is studied using the associated smooth best response dynamics on the space of finite signed measures. Using this approach, stochastic fictitious play is shown to converge to an equilibrium point in two-player zero-sum games and a stochastic fictitious play-like process is shown to converge to an equilibrium in negative definite single population games.
    Journal of Economic Theory 07/2014; 152. DOI:10.1016/j.jet.2014.04.008
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    ABSTRACT: We consider an elastic plate of infinite length and constant width supported simply along its two parallel edges and having a finite length crack along its centreline. In particular, we look for and find trapped modes (localised oscillations) in the presence of the crack. An explicit wide-spacing approximation based on the Wiener–Hopf technique applied to incident wave scattering by semi-infinite cracks is complemented by an exact formulation of the problem in the form of integro-differential equations. An application of a Galerkin method for the numerical calculation of results from the latter method leads to a novel explicit ‘small-spacing’ approximation. In combination with the wide-spacing results this is shown to provide accurate results for all lengths of crack.
    Wave Motion 04/2014; DOI:10.1016/j.wavemoti.2014.01.002
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    ABSTRACT: Rationale: A recent study published in Circulation Research by Gao et al used sinoatrial node (SAN)-targeted, incomplete Ncx1 knockout in mice to explore the role of the Na(+)/Ca(2+) exchanger (NCX) in cardiac pacemaker. The authors concluded that NCX is required for increasing sinus rates, but not for maintaining resting heart rate. This conclusion was based, in part, on numeric model simulations performed by Gao et al that reproduced their experimental results of unchanged action potentials in the knockout SAN cells. The authors, however, did not simulate the NCX current (INCX), that is, the subject of the study. Objective: We extended numeric examinations to simulate INCX in their incomplete knockout SAN cells that is crucial to interpret the study results. Methods and Results: INCX and Ca(2+) dynamics were simulated using different contemporary numeric models of SAN cells. We found that minimum diastolic Ca(2+) levels and INCX amplitudes generated by remaining NCX molecules (only 20% of control) remained almost unchanged. Simulations using a new local Ca(2+) control model indicate that these powerful compensatory mechanisms involve complex local cross-talk of Ca(2+) cycling proteins and NCX. Specifically, lower NCX expression facilitates Ca(2+)-induced Ca(2+) release and larger local Ca(2+) releases that stabilize diastolic INCX. Further reduction of NCX expression results in arrhythmia and halt of automaticity. Conclusions: Remaining NCX molecules in the incomplete knockout model likely produce almost the same diastolic INCX as in wild-type cells. INCX contribution is crucially important for both basal automaticity of SAN cells and during the fight-or-flight reflex.
    Circulation Research 10/2013; 113(10):e94-e100. DOI:10.1161/CIRCRESAHA.113.302465
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    ABSTRACT: We study reaction dynamics on a model potential energy surface exhibiting post-transition state bifurcation in the vicinity of a valley ridge inflection (VRI) point. We compute fractional yields of products reached after the VRI region is traversed, both with and without dissipation. It is found that apparently minor variations in the potential lead to significant changes in the reaction dynamics. Moreover, when dissipative effects are incorporated, the product ratio depends in a complicated and highly non-monotonic fashion on the dissipation parameter. Dynamics in the vicinity of the VRI point itself play essentially no role in determining the product ratio, except in the highly dissipative regime.
    The Journal of Chemical Physics 10/2013; 139(15):154108. DOI:10.1063/1.4825155
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    ABSTRACT: Does information play a significant role in the foundations of physics? Information is the abstraction that allows us to refer to the states of systems when we choose to ignore the systems themselves. This is only possible in very particular frameworks, like in classical or quantum theory, or more generally, whenever there exists an information unit such that the state of any system can be reversibly encoded in a sufficient number of such units. In this work, we show how the abstract formalism of quantum theory can be deduced solely from the existence of an information unit with suitable properties, together with two further natural assumptions: the continuity and reversibility of dynamics, and the possibility of characterizing the state of a composite system by local measurements. This constitutes a set of postulates for quantum theory with a simple and direct physical meaning, like the ones of special relativity or thermodynamics, and it articulates a strong connection between physics and information.
    Proceedings of the National Academy of Sciences 09/2013; 110(41). DOI:10.1073/pnas.1304884110
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    ABSTRACT: The challenge of understanding complex systems often gives rise to a mul-tiplicity of models. It is natural to consider whether the outputs of these models can be combined to produce a system prediction that is more infor-mative than the output of any one of the models taken in isolation. And, in particular, to consider the relationship between the spread of model out-puts and system uncertainty. We describe a statistical framework for such a combination, based on the exchangeability of the models, and their co-exchangeability with the system. We demonstrate the simplest implemen-tation of our framework in the context of climate prediction. Throughout we work entirely in means and variances, to avoid the necessity of specifying higher-order quantities for which we often lack well-founded judgements.
    Journal of the American Statistical Association 09/2013; 108(503). DOI:10.1080/01621459.2013.802963
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    ABSTRACT: Most examples of the application of evolutionary game theory to problems in biology involve highly simplified models. I contend that it is time to move on and include much more richness in models. In particular, more thought needs to be given to the importance of (i) between-individual variation; (ii) the interaction between individuals, and hence the process by which decisions are reached; (iii) the ecological and life-history context of the situation; (iv) the traits that are under selection, and (v) the underlying psychological mechanisms that lead to behaviour. I give examples where including variation between individuals fundamentally changes predicted outcomes of a game. Variation also selects for real-time responses, again resulting in changed outcomes. Variation can select for other traits, such as choosiness and social sensitivity. More generally, many problems involve coevolution of more than one trait. I identify situations where a reductionist approach, in which a game is isolated from is ecological setting, can be misleading. I also highlight the need to consider flexibility of behaviour, mental states and other issues concerned with the evolution of mechanism.
    Journal of The Royal Society Interface 08/2013; 10(88):20130544. DOI:10.1098/rsif.2013.0544
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    ABSTRACT: In 1964, Bell discovered that quantum mechanics is a nonlocal theory. Three years later, in a seemingly unconnected development, Harsanyi introduced the concept of Bayesian games. Here we show that, in fact, there is a deep connection between Bell nonlocality and Bayesian games, and that the same concepts appear in both fields. This link offers interesting possibilities for Bayesian games, namely of allowing the players to receive advice in the form of nonlocal correlations, for instance using entangled quantum particles or more general no-signalling boxes. This will lead to novel joint strategies, impossible to achieve classically. We characterize games for which nonlocal resources offer a genuine advantage over classical ones. Moreover, some of these strategies represent equilibrium points, leading to the notion of quantum/no-signalling Nash equilibrium. Finally, we describe new types of question in the study of nonlocality, namely the consideration of nonlocal advantage given a set of Bell expressions.
    Nature Communications 07/2013; 4:2057. DOI:10.1038/ncomms3057
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