Linear Relationship Statistics in Diffusion Limited Aggregation

We show that various surface parameters in two-dimensional diffusion limited aggregation (DLA) grow linearly with the number of particles. We find the ratio of the average length of the perimeter and the accessible perimeter of a DLA cluster together with its external perimeters to the cluster size, and define a microscopic schematic procedure for attachment of an incident new particle to the cluster. We measure the fractal dimension of the red sites (i.e., the sites upon cutting each of them splits the cluster) equal to that of the DLA cluster. It is also shown that the average number of the dead sites and the average number of the red sites have linear relationships with the cluster size.Comment: 4 pages, 5 figure

Families Facing the Demands of Military Life: New Research Directions

Military families, whether Active-duty, Reserve, or National Guard, face a multitude of demands in times of both peace and war, and these demands will shift throughout a Servicemember’s career. Our research at the Walter Reed Army Institute of Research (WRAIR), as well as research done at other institutions, has shown that the demands experienced by military families have both negative and positive effects in terms of health, marital satisfaction, and satisfaction with the Army. Appraisal of these demands and the ability to obtain the necessary resources to deal with them are important determinants of a variety of well-being–, family-, and Army-related outcomes. This chapter will focus on the findings of family studies conducted by researchers at WRAIR and examine the road ahead with studying military families based on the outcomes discussed

Accelerated Overlap Fermions

Numerical evaluation of the overlap Dirac operator is difficult since it contains the sign function $\epsilon(H_w)$ of the Hermitian Wilson-Dirac operator $H_w$ with a negative mass term. The problems are due to $H_w$ having very small eigenvalues on the equilibrium background configurations generated in current day Monte Carlo simulations. Since these are a consequence of the lattice discretisation and do not occur in the continuum version of the operator, we investigate in this paper to what extent the numerical evaluation of the overlap can be accelerated by making the Wilson-Dirac operator more continuum-like. Specifically, we study the effect of including the clover term in the Wilson-Dirac operator and smearing the link variables in the irrelevant terms. In doing so, we have obtained a factor of two speedup by moving from the Wilson action to a FLIC (Fat Link Irrelevant Clover) action as the overlap kernel.Comment: 15 pages, 6 figures; V2 contains major revision of the introduction and motivation sections. Conclusion and results unchanged v2.1: formatting chang

Fast Fourier Transform algorithm design and tradeoffs

The Fast Fourier Transform (FFT) is a mainstay of certain numerical techniques for solving fluid dynamics problems. The Connection Machine CM-2 is the target for an investigation into the design of multidimensional Single Instruction Stream/Multiple Data (SIMD) parallel FFT algorithms for high performance. Critical algorithm design issues are discussed, necessary machine performance measurements are identified and made, and the performance of the developed FFT programs are measured. Fast Fourier Transform programs are compared to the currently best Cray-2 FFT program

A retrospective study of the prevalence of the canine degenerative myelopathy associated superoxide dismutase 1 mutation (SOD1: c. 118G> A) in a referral population of German Shepherd dogs from the UK

BACKGROUND: Canine degenerative myelopathy (CDM) is an adult onset, progressive neurodegenerative disease of the spinal cord. The disease was originally described in the German Shepherd dog (GSD), but it is now known to occur in many other dog breeds. A previous study has identified a mutation in the superoxide dismutase 1 gene (SOD1:c.118G > A) that is associated with susceptibility to CDM. In the present study, restriction fragment length polymorphism (RFLP) analysis was used to genotype GSD for SOD1:c.118G > A in order to estimate the prevalence of the mutation in a referral population of GSD in the UK. RESULTS: This study demonstrated that the RFLP assay, based on use of PCR and subsequent digestion with the Eco571 enzyme, provided a simple genotyping test for the SOD1:c.118G > A mutation. In a young GSD population (i.e. dogs less than 6 years of age, before clinical signs of the disease usually become apparent), 8 of 50 dogs were found to be homozygous and a further 19 were heterozygous for the mutation. In dogs over 8 years of age, 21 of 50 dogs admitted to a tertiary referral hospital with pelvic limb ataxia as a major clinical sign were homozygous for the mutation, compared to none of 50 dogs of similar age, but where no neurological disease was reported on referral. CONCLUSIONS: This data suggests that genotyping for the SOD1:c.118G > A mutation is clinically applicable and that the mutation has a high degree of penetrance. Genotyping might also be useful for screening the GSD population to avoid mating of two carriers, but since the allele frequency is relatively high in the UK population of GSD, care should be taken to avoid reduction in genetic diversity within the breed

Feedback and Fluctuations in a Totally Asymmetric Simple Exclusion Process with Finite Resources

We revisit a totally asymmetric simple exclusion process (TASEP) with open boundaries and a global constraint on the total number of particles [Adams, et. al. 2008 J. Stat. Mech. P06009]. In this model, the entry rate of particles into the lattice depends on the number available in the reservoir. Thus, the total occupation on the lattice feeds back into its filling process. Although a simple domain wall theory provided reasonably good predictions for Monte Carlo simulation results for certain quantities, it did not account for the fluctuations of this feedback. We generalize the previous study and find dramatically improved predictions for, e.g., the density profile on the lattice and provide a better understanding of the phenomenon of "shock localization."Comment: 11 pages, 3 figures, v2: Minor change

The Influence of Cross-immunity on the Coexistence, Invasion and Evolution of Pathogen Strains

Several epidemic models with many co-circulating strains have shown that partial crossimmunity between otherwise identical strains of a pathogen can lead to three solutions: stable coexistence of all strains, stable coexistence of a subset of strains, coexistence of some or all strains in complex cycles. Here we step back to a three strain model to examine the mechanisms behind some of these solutions. Using a one-dimensional antigenic space, we consider a host population in which two strains are endemic and ask when it can be invaded by a third strain. If the function relating antigenic distance to cross-immunity is linear or a square-root this is always possible. If the function is parabolic it depends on the degree of antigenic similarity between strains and the basic reproductive number. We show that the differences between functional forms occur because their shape determines the importance of secondary infection. These results suggest that pathogens for which the relationship between antigenic distance and cross-immunity has a square-root form will exist as a cloud of strains without significant antigenic structuring. Conversely, pathogens for which the relationship is parabolic will exist in populations with strong antigenic structuring and the number of strains limited by the basic reproductive number. Furthermore, numerical simulation showssimulation shows that the maximum sustainable number of strains in such populations requires significant instantaneous changes in antigenic structure and cannot be achieved by a sequence of small point mutations alone

Antigenic distance and cross-immunity, invisibility and coexistence of pathogen strains in an epidemiological model with discrete antigenic space

In models of pathogen interaction and evolution discrete genotypes in the form of bit strings may be mapped to points in a discrete phenotype space based on similarity in antigenic structure. Cross-immunity between strains, that is the reduction in susceptibility to strain A conferred to a host by infection with strain B, can then be defined for pairs of points in the antigenic space by a specified function. Analysis of an SIR type model shows that, if two strains are at equilibrium, the shape of the cross-immunity function has a strong influence on the invasion and coexistence of a third strain and, consequently, the expected evolutionary pathway. A function that is constant except for discontinuities at the end points is expected to result in the accumulation of diversity until a pair of discordant strains occurs that can, depending on parameter values, exclude all other strains. For a function of the form f(h)=h^q, where h is the antigenic distance between two strains, invasion and coexistence is always possible if q1 invasion and coexistence may be impossible, depending on parameter values, and the pathogen population is expected to show significant antigenic structuring. In addition to illuminating the role of cross-immunity in pathogen evolution, this analysis indicates that the choice of cross-immunity function, the representation of immunity acquired from multiple previous infections and the number of elements used to characterize the antigenic space must be carefully considered in the development and interpretation of more sophisticated models of pathogen dynamics and evolution