Bigger Yields From Everbearing Strawberries

Many home gardeners and commercial producers of strawberries in Iowa have had discouraging results with everbearing strawberries. One reason is the hot, dry weather we usually have during July and August. Because moisture is short, the late summer crop often consists mostly of small fruits or nubbins - sometimes not even worth harvesting

A new representation for non--local operators and path integrals

We derive an alternative representation for the relativistic non--local kinetic energy operator and we apply it to solve the relativistic Salpeter equation using the variational sinc collocation method. Our representation is analytical and does not depend on an expansion in terms of local operators. We have used the relativistic harmonic oscillator problem to test our formula and we have found that arbitrarily precise results are obtained, simply increasing the number of grid points. More difficult problems have also been considered, observing in all cases the convergence of the numerical results. Using these results we have also derived a new representation for the quantum mechanical Green's function and for the corresponding path integral. We have tested this representation for a free particle in a box, recovering the exact result after taking the proper limits, and we have also found that the application of the Feynman--Kac formula to our Green's function yields the correct ground state energy. Our path integral representation allows to treat hamiltonians containing non--local operators and it could provide to the community a new tool to deal with such class of problems.Comment: 9 pages ; 1 figure ; refs added ; title modifie

Dynamics of a lattice Universe

We find a solution to Einstein field equations for a regular toroidal lattice of size L with equal masses M at the centre of each cell; this solution is exact at order M/L. Such a solution is convenient to study the dynamics of an assembly of galaxy-like objects. We find that the solution is expanding (or contracting) in exactly the same way as the solution of a Friedman-Lema\^itre-Robertson-Walker Universe with dust having the same average density as our model. This points towards the absence of backreaction in a Universe filled with an infinite number of objects, and this validates the fluid approximation, as far as dynamics is concerned, and at the level of approximation considered in this work.Comment: 14 pages. No figure. Accepted version for Classical and Quantum Gravit

Repeated games for eikonal equations, integral curvature flows and non-linear parabolic integro-differential equations

The main purpose of this paper is to approximate several non-local evolution equations by zero-sum repeated games in the spirit of the previous works of Kohn and the second author (2006 and 2009): general fully non-linear parabolic integro-differential equations on the one hand, and the integral curvature flow of an interface (Imbert, 2008) on the other hand. In order to do so, we start by constructing such a game for eikonal equations whose speed has a non-constant sign. This provides a (discrete) deterministic control interpretation of these evolution equations. In all our games, two players choose positions successively, and their final payoff is determined by their positions and additional parameters of choice. Because of the non-locality of the problems approximated, by contrast with local problems, their choices have to "collect" information far from their current position. For integral curvature flows, players choose hypersurfaces in the whole space and positions on these hypersurfaces. For parabolic integro-differential equations, players choose smooth functions on the whole space

Topology and Homoclinic Trajectories of Discrete Dynamical Systems

We show that nontrivial homoclinic trajectories of a family of discrete, nonautonomous, asymptotically hyperbolic systems parametrized by a circle bifurcate from a stationary solution if the asymptotic stable bundles Es(+{\infty}) and Es(-{\infty}) of the linearization at the stationary branch are twisted in different ways.Comment: 19 pages, canceled the appendix (Properties of the index bundle) in order to avoid any text overlap with arXiv:1005.207

Distinguishing importation from diversification of quinolone-resistant Neisseria gonorrhoeae by molecular evolutionary analysis

<p>Abstract</p> <p>Background</p> <p>Distinguishing the recent introduction of quinolone resistant gonococci into a population from diversification of resistant strains already in the population is important for planning effective infection control strategies. We applied molecular evolutionary analyses to DNA sequences from 9 housekeeping genes and <it>gyrA</it>, <it>parC </it>and <it>porB </it>of 24 quinolone resistant <it>N. gonorrhoeae </it>(QRNG) and 24 quinolone sensitive isolates collected in Israel during 2000–2001.</p> <p>Results</p> <p>Phylogenetic and eBURST analyses and estimates of divergence time indicated QRNG were introduced on 3 separate occasions and underwent limited diversification by mutation, deletion and horizontal gene transfer. Reconstruction of <it>N. gonorrhoeae </it>demography showed a slowly declining effective strain population size from 1976 to 1993, rapid decline between 1994 and 1999, and an increase from 1999 to 2001. This is partially attributable to declining gonorrhea case rates from 1973 to 1994. Additional contributing factors are selective sweeps of antibiotic resistant gonococci and increased transmission from sex workers. The abrupt decline in the mid-1990s heralded an increased incidence of gonorrhea from 1997 to the present. The subsequent increase in effective strain population size since 1999 reflects the increased gonococcal census population and introduction of quinolone resistance strains.</p> <p>Conclusion</p> <p>Our study demonstrates the effective use of population genetic approaches to assess recent and historical population dynamics of <it>N. gonorrhoeae</it>.</p

Spectral zeta functions of a 1D Schr\"odinger problem

We study the spectral zeta functions associated to the radial Schr\"odinger problem with potential V(x)=x^{2M}+alpha x^{M-1}+(lambda^2-1/4)/x^2. Using the quantum Wronskian equation, we provide results such as closed-form evaluations for some of the second zeta functions i.e. the sum over the inverse eigenvalues squared. Also we discuss how our results can be used to derive relationships and identities involving special functions, using a particular 5F_4 hypergeometric series as an example. Our work is then extended to a class of related PT-symmetric eigenvalue problems. Using the fused quantum Wronskian we give a simple method for calculating the related spectral zeta functions. This method has a number of applications including the use of the ODE/IM correspondence to compute the (vacuum) nonlocal integrals of motion G_n which appear in an associated integrable quantum field theory.Comment: 15 pages, version

The heart of a convex body

We investigate some basic properties of the {\it heart} $\heartsuit(\mathcal{K})$ of a convex set $\mathcal{K}.$ It is a subset of $\mathcal{K},$ whose definition is based on mirror reflections of euclidean space, and is a non-local object. The main motivation of our interest for $\heartsuit(\mathcal{K})$ is that this gives an estimate of the location of the hot spot in a convex heat conductor with boundary temperature grounded at zero. Here, we investigate on the relation between $\heartsuit(\mathcal{K})$ and the mirror symmetries of $\mathcal{K};$ we show that $\heartsuit(\mathcal{K})$ contains many (geometrically and phisically) relevant points of $\mathcal{K};$ we prove a simple geometrical lower estimate for the diameter of $\heartsuit(\mathcal{K});$ we also prove an upper estimate for the area of $\heartsuit(\mathcal{K}),$ when $\mathcal{K}$ is a triangle.Comment: 15 pages, 3 figures. appears as "Geometric Properties for Parabolic and Elliptic PDE's", Springer INdAM Series Volume 2, 2013, pp 49-6

Weak versus D-solutions to linear hyperbolic first order systems with constant coefficients

We establish a consistency result by comparing two independent notions of generalized solutions to a large class of linear hyperbolic first-order PDE systems with constant coefficients, showing that they eventually coincide. The first is the usual notion of weak solutions defined via duality. The second is the new notion of D-solutions which we recently introduced and arose in connection to the vectorial calculus of variations in L∞ and fully nonlinear elliptic systems. This new approach is a duality-free alternative to distributions and is based on the probabilistic representation of limits of difference quotients

Mesoscopic structure and social aspects of human mobility

The individual movements of large numbers of people are important in many contexts, from urban planning to disease spreading. Datasets that capture human mobility are now available and many interesting features have been discovered, including the ultra-slow spatial growth of individual mobility. However, the detailed substructures and spatiotemporal flows of mobility - the sets and sequences of visited locations - have not been well studied. We show that individual mobility is dominated by small groups of frequently visited, dynamically close locations, forming primary "habitats" capturing typical daily activity, along with subsidiary habitats representing additional travel. These habitats do not correspond to typical contexts such as home or work. The temporal evolution of mobility within habitats, which constitutes most motion, is universal across habitats and exhibits scaling patterns both distinct from all previous observations and unpredicted by current models. The delay to enter subsidiary habitats is a primary factor in the spatiotemporal growth of human travel. Interestingly, habitats correlate with non-mobility dynamics such as communication activity, implying that habitats may influence processes such as information spreading and revealing new connections between human mobility and social networks.Comment: 7 pages, 5 figures (main text); 11 pages, 9 figures, 1 table (supporting information