THE OPTIMAL N-BODY METHOD FOR STABILITY STUDIES OF GALAXIES

The stability of a galaxy model is most easily assessed through N-body simulation. Particle-mesh codes have been widely used for this purpose, since they enable the largest numbers of particles to be employed. We show that the functional expansion technique, originally proposed by Clutton-Brock for other simulation problems, is in fact superior for stability work. For simulations of linear evolution it is not much slower than grid methods using the same number of particles, and reproduces analytical results with much greater accuracy. This success rests on its ability to represent global modes with a modest number of basis functions; grid methods may be more effective for other applications, however. Our conclusions are based on implementations of functional expansion and grid algorithms for disk galaxies.Comment: Accepted for publication in The Astrophysical Journal, to appear October 1, 1995; 16 pages including 4 figures, self-unpacking uuencoded gzipped postscript, also available by email from [email protected]

Age-specific mortality during the 1918 influenza pandemic: unravelling the mystery of high young adult mortality.

The worldwide spread of a novel influenza A (H1N1) virus in 2009 showed that influenza remains a significant health threat, even for individuals in the prime of life. This paper focuses on the unusually high young adult mortality observed during the Spanish flu pandemic of 1918. Using historical records from Canada and the U.S., we report a peak of mortality at the exact age of 28 during the pandemic and argue that this increased mortality resulted from an early life exposure to influenza during the previous Russian flu pandemic of 1889-90. We posit that in specific instances, development of immunological memory to an influenza virus strain in early life may lead to a dysregulated immune response to antigenically novel strains encountered in later life, thereby increasing the risk of death. Exposure during critical periods of development could also create holes in the T cell repertoire and impair fetal maturation in general, thereby increasing mortality from infectious diseases later in life. Knowledge of the age-pattern of susceptibility to mortality from influenza could improve crisis management during future influenza pandemics

Generation of potential/surface density pairs in flat disks Power law distributions

We report a simple method to generate potential/surface density pairs in flat axially symmetric finite size disks. Potential/surface density pairs consist of a ``homogeneous'' pair (a closed form expression) corresponding to a uniform disk, and a ``residual'' pair. This residual component is converted into an infinite series of integrals over the radial extent of the disk. For a certain class of surface density distributions (like power laws of the radius), this series is fully analytical. The extraction of the homogeneous pair is equivalent to a convergence acceleration technique, in a matematical sense. In the case of power law distributions, the convergence rate of the residual series is shown to be cubic inside the source. As a consequence, very accurate potential values are obtained by low order truncation of the series. At zero order, relative errors on potential values do not exceed a few percent typically, and scale with the order N of truncation as 1/N**3. This method is superior to the classical multipole expansion whose very slow convergence is often critical for most practical applications.Comment: Accepted for publication in Astronomy & Astrophysics 7 pages, 8 figures, F90-code available at http://www.obs.u-bordeaux1.fr/radio/JMHure/intro2applawd.htm

Delay-induced Synchronization Phenomena in an Array of Globally Coupled Logistic Maps

We study the synchronization of a linear array of globally coupled identical logistic maps. We consider a time-delayed coupling that takes into account the finite velocity of propagation of the interactions. We find globally synchronized states in which the elements of the array evolve along a periodic orbit of the uncoupled map, while the spatial correlation along the array is such that an individual map sees all other maps in his present, current, state. For values of the nonlinear parameter such that the uncoupled maps are chaotic, time-delayed mutual coupling suppress the chaotic behavior by stabilizing a periodic orbit which is unstable for the uncoupled maps. The stability analysis of the synchronized state allows us to calculate the range of the coupling strength in which global synchronization can be obtained.Comment: 8 pages, 7 figures, changed content, added reference

Determinants of Influenza Mortality Trends: Age-Period-Cohort Analysis of Influenza Mortality in the United States, 1959-2016.

This study examines the roles of age, period, and cohort in influenza mortality trends over the years 1959-2016 in the United States. First, we use Lexis surfaces based on Serfling models to highlight influenza mortality patterns as well as to identify lingering effects of early-life exposure to specific influenza virus subtypes (e.g., H1N1, H3N2). Second, we use age-period-cohort (APC) methods to explore APC linear trends and identify changes in the slope of these trends (contrasts). Our analyses reveal a series of breakpoints where the magnitude and direction of birth cohort trends significantly change, mostly corresponding to years in which important antigenic drifts or shifts took place (i.e., 1947, 1957, 1968, and 1978). Whereas child, youth, and adult influenza mortality appear to be influenced by a combination of cohort- and period-specific factors, reflecting the interaction between the antigenic experience of the population and the evolution of the influenza virus itself, mortality patterns of the elderly appear to be molded by broader cohort factors. The latter would reflect the processes of physiological capital improvement in successive birth cohorts through secular changes in early-life conditions. Antigenic imprinting, cohort morbidity phenotype, and other mechanisms that can generate the observed cohort effects, including the baby boom, are discussed

Quantum Computing of Classical Chaos: Smile of the Arnold-Schrodinger Cat

We show on the example of the Arnold cat map that classical chaotic systems can be simulated with exponential efficiency on a quantum computer. Although classical computer errors grow exponentially with time, the quantum algorithm with moderate imperfections is able to simulate accurately the unstable chaotic classical dynamics for long times. The algorithm can be easily implemented on systems of a few qubits.Comment: revtex, 4 pages, 4 figure

Exponential Gain in Quantum Computing of Quantum Chaos and Localization

We present a quantum algorithm which simulates the quantum kicked rotator model exponentially faster than classical algorithms. This shows that important physical problems of quantum chaos, localization and Anderson transition can be modelled efficiently on a quantum computer. We also show that a similar algorithm simulates efficiently classical chaos in certain area-preserving maps.Comment: final published versio

An adaptive algorithm for n-body field expansions

An expansion of a density field or particle distribution in basis functions which solve the Poisson equation both provides an easily parallelized n-body force algorithm and simplifies perturbation theories. The expansion converges quickly and provides the highest computational advantage if the lowest-order potential-density pair in the basis looks like the unperturbed galaxy or stellar system. Unfortunately, there are only a handful of such basis in the literature which limits this advantage. This paper presents an algorithm for deriving these bases to match a wide variety of galaxy models. The method is based on efficient numerical solution of the Sturm-Liouville equation and can be used for any geometry with a separable Laplacian. Two cases are described in detail. First for the spherical case, the lowest order basis function pair may be chosen to be exactly that of the underlying model. The profile may be cuspy or have a core and truncated or of infinite extent. Secondly, the method yields a three-dimensional cylindrical basis appropriate for studying galaxian disks. In this case, the vertical and radial bases are coupled; the lowest order radial part of the basis function can be chosen to match the underlying profile only in the disk plane. Practically, this basis is still a very good match to the overall disk profile and converges in a small number of terms.Comment: 16 pages, 5 figures, submitted to A

The impact of the demographic transition on dengue in Thailand: Insights from a statistical analysis and mathematical modeling

Background: An increase in the average age of dengue hemorrhagic fever (DHF) cases has been reported in Thailand. The cause of this increase is not known. Possible explanations include a reduction in transmission due to declining mosquito populations, declining contact between human and mosquito, and changes in reporting. We propose that a demographic shift toward lower birth and death rates has reduced dengue transmission and lengthened the interval between large epidemics. Methods and Findings: Using data from each of the 72 provinces of Thailand, we looked for associations between force of infection (a measure of hazard, defined as the rate per capita at which susceptible individuals become infected) and demographic and climactic variables. We estimated the force of infection from the age distribution of cases from 1985 to 2005. We find that the force of infection has declined by 2% each year since a peak in the late 1970s and early 1980s. Contrary to recent findings suggesting that the incidence of DHF has increased in Thailand, we find a small but statistically significant decline in DHF incidence since 1985 in a majority of provinces. The strongest predictor of the change in force of infection and the mean force of infection is the median age of the population. Using mathematical simulations of dengue transmission we show that a reduced birth rate and a shift in the population's age structure can explain the shift in the age distribution of cases, reduction of the force of infection, and increase in the periodicity of multiannual oscillations of DHF incidence in the absence of other changes. Conclusions: Lower birth and death rates decrease the flow of susceptible individuals into the population and increase the longevity of immune individuals. The increase in the proportion of the population that is immune increases the likelihood that an infectious mosquito will feed on an immune individual, reducing the force of infection. Though the force of infection has decreased by half, we find that the critical vaccination fraction has not changed significantly, declining from an average of 85% to 80%. Clinical guidelines should consider the impact of continued increases in the age of dengue cases in Thailand. Countries in the region lagging behind Thailand in the demographic transition may experience the same increase as their population ages. The impact of demographic changes on the force of infection has been hypothesized for other diseases, but, to our knowledge, this is the first observation of this phenomenon

Plankton lattices and the role of chaos in plankton patchiness

Spatiotemporal and interspecies irregularities in planktonic populations have been widely observed. Much research into the drivers of such plankton patches has been initiated over the past few decades but only recently have the dynamics of the interacting patches themselves been considered. We take a coupled lattice approach to model continuous-in-time plankton patch dynamics, as opposed to the more common continuum type reaction-diffusion-advection model, because it potentially offers a broader scope of application and numerical study with relative ease. We show that nonsynchronous plankton patch dynamics (the discrete analog of spatiotemporal irregularity) arise quite naturally for patches whose underlying dynamics are chaotic. However, we also observe that for parameters in a neighborhood of the chaotic regime, smooth generalized synchronization of nonidentical patches is more readily supported which reduces the incidence of distinct patchiness. We demonstrate that simply associating the coupling strength with measurements of (effective) turbulent diffusivity results in a realistic critical length of the order of 100 km, above which one would expect to observe unsynchronized behavior. It is likely that this estimate of critical length may be reduced by a more exact interpretation of coupling in turbulent flows