Periodic pattern formation in reaction-diffusion systems -an introduction for numerical simulation

The aim of the present review is to provide a comprehensive explanation of Turing reaction–diffusion systems in sufficient detail to allow readers to perform numerical calculations themselves. The reaction–diffusion model is widely studied in the field of mathematical biology, serves as a powerful paradigm model for self-organization and is beginning to be applied to actual experimental systems in developmental biology. Despite the increase in current interest, the model is not well understood among experimental biologists, partly because appropriate introductory texts are lacking. In the present review, we provide a detailed description of the definition of the Turing reaction–diffusion model that is comprehensible without a special mathematical background, then illustrate a method for reproducing numerical calculations with Microsoft Excel. We then show some examples of the patterns generated by the model. Finally, we discuss future prospects for the interdisciplinary field of research involving mathematical approaches in developmental biology

Emotional engagements predict and enhance social cognition in young chimpanzees

Social cognition in infancy is evident in coordinated triadic engagements, that is, infants attending jointly with social partners and objects. Current evolutionary theories of primate social cognition tend to highlight species differences in cognition based on human-unique cooperative motives. We consider a developmental model in which engagement experiences produce differential outcomes. We conducted a 10-year-long study in which two groups of laboratory-raised chimpanzee infants were given quantifiably different engagement experiences. Joint attention, cooperativeness, affect, and different levels of cognition were measured in 5- to 12-month-old chimpanzees, and compared to outcomes derived from a normative human database. We found that joint attention skills significantly improved across development for all infants, but by 12 months, the humans significantly surpassed the chimpanzees. We found that cooperativeness was stable in the humans, but by 12 months, the chimpanzee group given enriched engagement experiences significantly surpassed the humans. Past engagement experiences and concurrent affect were significant unique predictors of both joint attention and cooperativeness in 5- to 12-month-old chimpanzees. When engagement experiences and concurrent affect were statistically controlled, joint attention and cooperation were not associated. We explain differential social cognition outcomes in terms of the significant influences of previous engagement experiences and affect, in addition to cognition. Our study highlights developmental processes that underpin the emergence of social cognition in support of evolutionary continuity

Local variations in spatial synchrony of influenza epidemics

Background: Understanding the mechanism of influenza spread across multiple geographic scales is not complete. While the mechanism of dissemination across regions and states of the United States has been described, understanding the determinants of dissemination between counties has not been elucidated. The paucity of high resolution spatial-temporal influenza incidence data to evaluate disease structure is often not available. Methodology and Findings: We report on the underlying relationship between the spread of influenza and human movement between counties of one state. Significant synchrony in the timing of epidemics exists across the entire state and decay with distance (regional correlation = 62%). Synchrony as a function of population size display evidence of hierarchical spread with more synchronized epidemics occurring among the most populated counties. A gravity model describing movement between two populations is a stronger predictor of influenza spread than adult movement to and from workplaces suggesting that non-routine and leisure travel drive local epidemics. Conclusions: These findings highlight the complex nature of influenza spread across multiple geographic scales. © 2012 Stark et al

Abundances of Baade's Window Giants from Keck/HIRES Spectra: I. Stellar Parameters and [Fe/H] Values

We present the first results of a new abundance survey of the Milky Way bulge based on Keck/HIRES spectra of 27 K-giants in the Baade's Window ($l = 1$, $b = -4$) field. The spectral data used in this study are of much higher resolution and signal-to-noise than previous optical studies of Galactic bulge stars. The [Fe/H] values of our stars, which range between -1.29 and $+0.51$, were used to recalibrate large low resolution surveys of bulge stars. Our best value for the mean [Fe/H] of the bulge is $-0.10 \pm 0.04$. This mean value is similar to the mean metallicity of the local disk and indicates that there cannot be a strong metallicity gradient inside the solar circle. The metallicity distribution of stars confirms that the bulge does not suffer from the so-called ``G-dwarf'' problem. This paper also details the new abundance techniques necessary to analyze very metal-rich K-giants, including a new Fe line list and regions of low blanketing for continuum identification.Comment: Accepted for publication in January 2006 Astrophysical Journal. Long tables 3--6 withheld to save space (electronic tables in journal paper). 53 pages, 10 figures, 9 table

Modeling seismic wave propagation and amplification in 1D/2D/3D linear and nonlinear unbounded media

To analyze seismic wave propagation in geological structures, it is possible to consider various numerical approaches: the finite difference method, the spectral element method, the boundary element method, the finite element method, the finite volume method, etc. All these methods have various advantages and drawbacks. The amplification of seismic waves in surface soil layers is mainly due to the velocity contrast between these layers and, possibly, to topographic effects around crests and hills. The influence of the geometry of alluvial basins on the amplification process is also know to be large. Nevertheless, strong heterogeneities and complex geometries are not easy to take into account with all numerical methods. 2D/3D models are needed in many situations and the efficiency/accuracy of the numerical methods in such cases is in question. Furthermore, the radiation conditions at infinity are not easy to handle with finite differences or finite/spectral elements whereas it is explicitely accounted in the Boundary Element Method. Various absorbing layer methods (e.g. F-PML, M-PML) were recently proposed to attenuate the spurious wave reflections especially in some difficult cases such as shallow numerical models or grazing incidences. Finally, strong earthquakes involve nonlinear effects in surficial soil layers. To model strong ground motion, it is thus necessary to consider the nonlinear dynamic behaviour of soils and simultaneously investigate seismic wave propagation in complex 2D/3D geological structures! Recent advances in numerical formulations and constitutive models in such complex situations are presented and discussed in this paper. A crucial issue is the availability of the field/laboratory data to feed and validate such models.Comment: of International Journal Geomechanics (2010) 1-1

Mode transitions in a model reaction-diffusion system driven by domain growth and noise

Pattern formation in many biological systems takes place during growth of the underlying domain. We study a specific example of a reaction–diffusion (Turing) model in which peak splitting, driven by domain growth, generates a sequence of patterns. We have previously shown that the pattern sequences which are presented when the domain growth rate is sufficiently rapid exhibit a mode-doubling phenomenon. Such pattern sequences afford reliable selection of certain final patterns, thus addressing the robustness problem inherent of the Turing mechanism. At slower domain growth rates this regular mode doubling breaks down in the presence of small perturbations to the dynamics. In this paper we examine the breaking down of the mode doubling sequence and consider the implications of this behaviour in increasing the range of reliably selectable final patterns