Hybrid modelling of individual movement and collective behaviour

Mathematical models of dispersal in biological systems are often written in terms of partial differential equations (PDEs) which describe the time evolution of population-level variables (concentrations, densities). A more detailed modelling approach is given by individual-based (agent-based) models which describe the behaviour of each organism. In recent years, an intermediate modelling methodology – hybrid modelling – has been applied to a number of biological systems. These hybrid models couple an individual-based description of cells/animals with a PDEmodel of their environment. In this chapter, we overview hybrid models in the literature with the focus on the mathematical challenges of this modelling approach. The detailed analysis is presented using the example of chemotaxis, where cells move according to extracellular chemicals that can be altered by the cells themselves. In this case, individual-based models of cells are coupled with PDEs for extracellular chemical signals. Travelling waves in these hybrid models are investigated. In particular, we show that in contrary to the PDEs, hybrid chemotaxis models only develop a transient travelling wave

Crocodylus intermedius

Number of Pages: 2Integrative BiologyGeological Science

Vortex-boson duality in four space-time dimensions

A continuum version of the vortex-boson duality in (3+1) dimensions is formulated and its implications studied in the context of a pair Wigner crystal in underdoped cuprate superconductors. The dual theory to a phase fluctuating superconductor (or superfluid) is shown to be a theory of bosonic strings interacting through a Kalb-Ramond rank-2 tensorial gauge field. String condensation produces Higgs mass for the gauge field and the expected Wigner crystal emerges as an interesting space-time analog of the Abrikosov lattice.Comment: 4 pages REVTeX; for related work and info visit http://www.physics.ubc.ca/~fran

Fractionalization in a square-lattice model with time-reversal symmetry

We propose a two-dimensional time-reversal invariant system of essentially non-interacting electrons on a square lattice that exhibits configurations with fractional charges e/2. These are vortex-like topological defects in the dimerization order parameter describing spatial modulation in the electron hopping amplitudes. Charge fractionalization is established by a simple counting argument, analytical calculation within the effective low-energy theory, and by an exact numerical diagonalization of the lattice Hamiltonian. We comment on the exchange statistics of fractional charges and possible realizations of the system.Comment: 4 pages, 3 figures, RevTex 4. (v2) improved discussion of lattice effects and confinement; clearer figure

On chaos in mean field spin glasses

We study the correlations between two equilibrium states of SK spin glasses at different temperatures or magnetic fields. The question, presiously investigated by Kondor and Kondor and V\'egs\"o, is approached here constraining two copies of the same system at different external parameters to have a fixed overlap. We find that imposing an overlap different from the minimal one implies an extensive cost in free energy. This confirms by a different method the Kondor's finding that equilibrium states corresponding to different values of the external parameters are completely uncorrelated. We also consider the Generalized Random Energy Model of Derrida as an example of system with strong correlations among states at different temperatures.Comment: 19 pages, Late

Covariant spectator theory of np scattering: Effective range expansions and relativistic deuteron wave functions

We present the effective range expansions for the 1S_0 and 3S_1 scattering phase shifts, and the relativistic deuteron wave functions that accompany our recent high precision fits (with chi^2/N{data} approx 1) to the 2007 world np data below 350 MeV. The wave functions are expanded in a series of analytical functions (with the correct asymptotic behavior at both large and small arguments) that can be Fourier-transformed from momentum to coordinate space and are convenient to use in any application. A fortran subroutine to compute these wave functions can be obtained from the authors.Comment: 32 pages, 14 figure

Dietary flavonoid intake and incidence of erectile dysfunction

Background: The predominant etiology for erectile dysfunction (ED) is vascular, however limited data are available on the role of diet. A higher intake of several flavonoids reduces diabetes and cardiovascular disease (CVD) risk but no studies have examined associations between flavonoids and erectile function.   Objective: To examine the relationship between habitual flavonoid sub-class intakes and incidence of ED.   Methods: We conducted a prospective study among 25,096 men from the Health Professionals Follow-up Study. Total flavonoid and subclass intakes were calculated from food frequency questionnaires collected every 4 years. Participants rated their erectile function in 2000 (with historical reporting from 1986) and again in 2004 and 2008.   Results: During 10 years of follow-up, 35.6% reported incident ED. After multivariate adjustment, including classic CVD risk factors, several sub-classes were associated with reduced ED incidence; specifically flavones (RR 0.91:95%CI=0.85,0.97; p-trend=0.006), flavanones (RR 0.89;95%CI=0.83,0.95; p-trend=0.0009), and anthocyanins (RR 0.91;95%CI=0.85,0.98; p-trend=0.002) comparing extreme intakes. The results remained significant after additional adjustment for a composite dietary intake score. In analyses stratified by age, a higher intake of flavanones, anthocyanins and flavones was significantlyassociated with a reduction in risk of erectile dysfunction only in men <70 years old and not older men (11-16% reduction in risk (p - interaction 0.002, 0.03, 0.007 for flavones, flavanones and anthocyanins respectively). In food-based analysis, higher total fruit intake, major sources of anthocyanins and flavanones, was associated with 14% reduction in risk of ED (RR 0.86;95%CI=0.79,0.92; p=0.002).The American Journal of Clinical Nutrition AJCN/2015/122010 Version 3.    Conclusions : These data suggest that a higher habitual intake of specific 24 flavonoid-rich foods are associated with reduced ED incidence. Intervention trials are needed to further examine the impact of increasing intakes of commonly consumed flavonoid-rich foods on men’s health

Vortices, zero modes and fractionalization in bilayer-graphene exciton condensate

A real-space formulation is given for the recently discussed exciton condensate in a symmetrically biased graphene bilayer. We show that in the continuum limit an oddly-quantized vortex in this condensate binds exactly one zero mode per valley index of the bilayer. In the full lattice model the zero modes are split slightly due to intervalley mixing. We support these results by an exact numerical diagonalization of the lattice Hamiltonian. We also discuss the effect of the zero modes on the charge content of these vortices and deduce some of their interesting properties.Comment: (v2) A typo in Fig. 1 and a slight error in Eq. (4) corrected; all the main results and conclusions remain unchange