The Master Equation for Large Population Equilibriums

We use a simple N-player stochastic game with idiosyncratic and common noises to introduce the concept of Master Equation originally proposed by Lions in his lectures at the Coll\`ege de France. Controlling the limit N tends to the infinity of the explicit solution of the N-player game, we highlight the stochastic nature of the limit distributions of the states of the players due to the fact that the random environment does not average out in the limit, and we recast the Mean Field Game (MFG) paradigm in a set of coupled Stochastic Partial Differential Equations (SPDEs). The first one is a forward stochastic Kolmogorov equation giving the evolution of the conditional distributions of the states of the players given the common noise. The second is a form of stochastic Hamilton Jacobi Bellman (HJB) equation providing the solution of the optimization problem when the flow of conditional distributions is given. Being highly coupled, the system reads as an infinite dimensional Forward Backward Stochastic Differential Equation (FBSDE). Uniqueness of a solution and its Markov property lead to the representation of the solution of the backward equation (i.e. the value function of the stochastic HJB equation) as a deterministic function of the solution of the forward Kolmogorov equation, function which is usually called the decoupling field of the FBSDE. The (infinite dimensional) PDE satisfied by this decoupling field is identified with the \textit{master equation}. We also show that this equation can be derived for other large populations equilibriums like those given by the optimal control of McKean-Vlasov stochastic differential equations. The paper is written more in the style of a review than a technical paper, and we spend more time and energy motivating and explaining the probabilistic interpretation of the Master Equation, than identifying the most general set of assumptions under which our claims are true

Novel Characteristics of Valveless Pumping

This study investigates the occurrence of valveless pumping in a fluidfilled system consisting of two open tanks connected by an elastic tube. We show that directional flow can be achieved by introducing a periodic pinching applied at an asymmetrical location along the tube, and that the flow direction depends on the pumping frequency. We propose a relation between wave propagation velocity, tube length, and resonance frequencies associated with shifts in the pumping direction using numerical simulations. The eigenfrequencies of the system are estimated from the linearized system, and we show that these eigenfrequencies constitute the resonance frequencies and the horizontal slope frequencies of the system; 'horizontal slope frequency' being a new concept. A simple model is suggested, explaining the effect of the gravity driven part of the oscillation observed in response to the tank and tube diameter changes. Results are partly compared with experimental findings.Art. no. 22450

The male handicap: male-biased mortality explains skewed sex ratios in brown trout embryos

Juvenile sex ratios are often assumed to be equal for many species with genetic sex determination, but this has rarely been tested in fish embryos due to their small size and absence of sex-specific markers. We artificially crossed three populations of brown trout and used a recently developed genetic marker for sexing the offspring of both pure and hybrid crosses. Sex ratios (SR = proportion of males) varied widely one month after hatching ranging from 0.15 to 0.90 (mean = 0.39 ± 0.03). Families with high survival tended to produce balanced or male-biased sex ratios, but SR was significantly female-biased when survival was low, suggesting that males sustain higher mortality during development. No difference in SR was found between pure and hybrid families, but the existence of sire × dam interactions suggests that genetic incompatibility may play a role in determining sex ratios. Our findings have implications for animal breeding and conservation because skewed sex ratios will tend to reduce effective population size and bias selection estimates

Historical changes in the phenology of British Odonata are related to climate

Responses of biota to climate change take a number of forms including distributional shifts, behavioural changes and life history changes. This study examined an extensive set of biological records to investigate changes in the timing of life history transitions (specifically emergence) in British Odonata between 1960 and 2004. The results show that there has been a significant, consistent advance in phenology in the taxon as a whole over the period of warming that is mediated by life history traits. British odonates significantly advanced the leading edge (first quartile date) of the flight period by a mean of 1.51 ±0.060 (SEM, n=17) days per decade or 3.08±1.16 (SEM, n=17) days per degree rise in temperature when phylogeny is controlled for. This study represents the first review of changes in odonate phenology in relation to climate change. The results suggest that the damped temperature oscillations experienced by aquatic organisms compared with terrestrial organisms are sufficient to evoke phenological responses similar to those of purely terrestrial taxa

Demography and disorders of German Shepherd Dogs under primary veterinarycare in the UK

The German Shepherd Dog (GSD) has been widely used for a variety of working roles. However, concerns for the health and welfare of the GSD have been widely aired and there is evidence that breed numbers are now in decline in the UK. Accurate demographic and disorder data could assist with breeding and clinical prioritisation. The VetCompassTM Programme collects clinical data on dogs under primary veterinary care in the UK. This study included all VetCompassTM dogs under veterinary care during 2013. Demographic, mortality and clinical diagnosis data on GSDs were extracted and reported

Factorization and resummation of s-channel single top quark production

In this paper we study the factorization and resummation of s-channel single top quark production in the Standard Model at both the Tevatron and the LHC. We show that the production cross section in the threshold limit can be factorized into a convolution of hard function, soft function and jet function via soft-collinear-effective-theory (SCET), and resummation can be performed using renormalization group equation in the momentum space resummation formalism. We find that in general, the resummation effects enhance the Next-to-Leading-Order (NLO) cross sections by about $3$ at both the Tevatron and the LHC, and significantly reduce the factorization scale dependence of the total cross section at the Tevatron, while at the LHC we find that the factorization scale dependence has not been improved, compared with the NLO results.Comment: 29 pages, 7 figures; version published in JHE

A Semi-Lagrangian scheme for a modified version of the Hughes model for pedestrian flow

In this paper we present a Semi-Lagrangian scheme for a regularized version of the Hughes model for pedestrian flow. Hughes originally proposed a coupled nonlinear PDE system describing the evolution of a large pedestrian group trying to exit a domain as fast as possible. The original model corresponds to a system of a conservation law for the pedestrian density and an Eikonal equation to determine the weighted distance to the exit. We consider this model in presence of small diffusion and discuss the numerical analysis of the proposed Semi-Lagrangian scheme. Furthermore we illustrate the effect of small diffusion on the exit time with various numerical experiments

Jet Shapes and Jet Algorithms in SCET

Jet shapes are weighted sums over the four-momenta of the constituents of a jet and reveal details of its internal structure, potentially allowing discrimination of its partonic origin. In this work we make predictions for quark and gluon jet shape distributions in N-jet final states in e+e- collisions, defined with a cone or recombination algorithm, where we measure some jet shape observable on a subset of these jets. Using the framework of Soft-Collinear Effective Theory, we prove a factorization theorem for jet shape distributions and demonstrate the consistent renormalization-group running of the functions in the factorization theorem for any number of measured and unmeasured jets, any number of quark and gluon jets, and any angular size R of the jets, as long as R is much smaller than the angular separation between jets. We calculate the jet and soft functions for angularity jet shapes \tau_a to one-loop order (O(alpha_s)) and resum a subset of the large logarithms of \tau_a needed for next-to-leading logarithmic (NLL) accuracy for both cone and kT-type jets. We compare our predictions for the resummed \tau_a distribution of a quark or a gluon jet produced in a 3-jet final state in e+e- annihilation to the output of a Monte Carlo event generator and find that the dependence on a and R is very similar.Comment: 62 pages plus 21 pages of Appendices, 13 figures, uses JHEP3.cls. v2: corrections to finite parts of NLO jet functions, minor changes to plots, clarified discussion of power corrections. v3: Journal version. Introductory sections significantly reorganized for clarity, classification of logarithmic accuracy clarified, results for non-Mercedes-Benz configurations adde

Photoswitchable diacylglycerols enable optical control of protein kinase C.

Increased levels of the second messenger lipid diacylglycerol (DAG) induce downstream signaling events including the translocation of C1-domain-containing proteins toward the plasma membrane. Here, we introduce three light-sensitive DAGs, termed PhoDAGs, which feature a photoswitchable acyl chain. The PhoDAGs are inactive in the dark and promote the translocation of proteins that feature C1 domains toward the plasma membrane upon a flash of UV-A light. This effect is quickly reversed after the termination of photostimulation or by irradiation with blue light, permitting the generation of oscillation patterns. Both protein kinase C and Munc13 can thus be put under optical control. PhoDAGs control vesicle release in excitable cells, such as mouse pancreatic islets and hippocampal neurons, and modulate synaptic transmission in Caenorhabditis elegans. As such, the PhoDAGs afford an unprecedented degree of spatiotemporal control and are broadly applicable tools to study DAG signaling

Proteomic identification of immunodiagnostic antigens for <i>Trypanosoma vivax </i>infections in cattle and generation of a proof-of-concept lateral flow test diagnostic device

Trypanosoma vivax is one of the causative agents of Animal African Trypanosomosis in cattle, which is endemic in sub-Saharan Africa and transmitted primarily by the bite of the tsetse fly vector. The parasite can also be mechanically transmitted, and this has allowed its spread to South America. Diagnostics are limited for this parasite and in farm settings diagnosis is mainly symptom-based. We set out to identify, using a proteomic approach, candidate diagnostic antigens to develop into an easy to use pen-side lateral flow test device. Two related members the invariant surface glycoprotein family, TvY486_0045500 and TvY486_0019690, were selected. Segments of these antigens, lacking N-terminal signal peptides and C-terminal transmembrane domains, were expressed in E. coli. Both were developed into ELISA tests and one of them, TvY486_0045500, was developed into a lateral flow test prototype. The tests were all evaluated blind with 113 randomised serum samples, taken from 37 calves before and after infection with T. vivax or T. congolense. The TvY486_0045500 and TvY486_0019690 ELISA tests gave identical sensitivity and specificity values for T. vivax infection of 94.5% (95% CI, 86.5% to 98.5%) and 88.0% (95% CI, 75.7% to 95.5%), respectively, and the TvY486_0045500 lateral flow test prototype a sensitivity and specificity of 92.0% (95% CI, 83.4% to 97.0%) and 89.8% (95% CI, 77.8% to 96.6%), respectively. These data suggest that recombinant TvY486_0045500 shows promise for the development of a pen-side lateral flow test for the diagnosis of T. vivax animal African trypanosomosis