Zeroes of partial sums of the zeta-function

This article considers the positive integers $N$ for which $\zeta_{N}(s) = \sum_{n=1}^{N} n^{-s}$ has zeroes in the half-plane $\Re(s)>1$. Building on earlier results, we show that there are no zeroes for $1\leq N\leq 18$ and for $N=20, 21, 28$. For all other $N$ there are infinitely many zeroes.Comment: 5 Pages - Final Version will appear in LMS JC

On the Sum of Two Squares and At Most Two Powers of 2

We demonstrate that there are infinitely many integers that cannot be expressed as the sum of two squares of integers and up to two non-negative integer powers of 2.Comment: 5 pages; to appear in Amer. Math. Monthl

Host adapted serotypes of <i>Salmonella enterica</i>

Salmonella constitutes a genus of zoonotic bacteria of worldwide economic and health importance. The current view of salmonella taxonomy assigns the members of this genus to two species: S. enterica and S. bongori. S. enterica itself is divided into six subspecies, enterica, salamae, arizonae, diarizonae, indica, and houtenae, also known as subspecies I, II, IIIa, IIIb, IV, and VI, respectively. Members of Salmonella enterica subspecies enterica are mainly associated with warm-blooded vertebrates and are usually transmitted by ingestion of food or water contaminated by infected faeces. The pathogenicity of most of the distinct serotypes remains undefined, and even within the most common serotypes, many questions remain to be answered regarding the interactions between the organism and the infected host. Salmonellosis manifests itself in three major forms: enteritis, septicaemia, and abortion, each of which may be present singly or in combination, depending on both the serotype and the host involved. Although currently over 2300 serovars of Salmonella are recognized, only about 50 serotypes are isolated in any significant numbers as human or animal pathogens and they all belong to subspecies enterica. Of these, most cause acute gastroenteritis characterized by a short incubation period and a severe systemic disease in man or animals, characterized by septicaemia, fever and/or abortion, and such serotypes are often associated with one or few host species. It is the intention of this review to present a summary of current knowledge of these host-adapted serotypes of S. enterica. The taxonomic relationships between the serotypes will be discussed together with a comparison of the pathology and pathogenesis of the disease that they cause in their natural host(s). Since much of our knowledge on salmonellosis is based on the results of work on Typhimurium, this serotype will often be used as the baseline in discussion. It is hoped that an appreciation of the differences that exist in the way these serotypes interact with the host will lead to a greater understanding of the complex host–parasite relationship that characterizes salmonella infections

Temporal Subsampling Diminishes Small Spatial Scales in Recurrent Neural Network Emulators of Geophysical Turbulence

The immense computational cost of traditional numerical weather and climate models has sparked the development of machine learning (ML) based emulators. Because ML methods benefit from long records of training data, it is common to use datasets that are temporally subsampled relative to the time steps required for the numerical integration of differential equations. Here, we investigate how this often overlooked processing step affects the quality of an emulator's predictions. We implement two ML architectures from a class of methods called reservoir computing: (1) a form of Nonlinear Vector Autoregression (NVAR), and (2) an Echo State Network (ESN). Despite their simplicity, it is well documented that these architectures excel at predicting low dimensional chaotic dynamics. We are therefore motivated to test these architectures in an idealized setting of predicting high dimensional geophysical turbulence as represented by Surface Quasi-Geostrophic dynamics. In all cases, subsampling the training data consistently leads to an increased bias at small spatial scales that resembles numerical diffusion. Interestingly, the NVAR architecture becomes unstable when the temporal resolution is increased, indicating that the polynomial based interactions are insufficient at capturing the detailed nonlinearities of the turbulent flow. The ESN architecture is found to be more robust, suggesting a benefit to the more expensive but more general structure. Spectral errors are reduced by including a penalty on the kinetic energy density spectrum during training, although the subsampling related errors persist. Future work is warranted to understand how the temporal resolution of training data affects other ML architectures

Updating models for restoration and management of fiery ecosystems

© 2015 Elsevier B.V. Scientific models that guide restoration/management protocols should be reviewed periodically as new data become available. We examine ecological concepts used to guide restoration of pine savannas and woodlands, historically prominent but now rare habitats in the southern North American Coastal Plain. For many decades, pine savanna management has been guided predominantly by a biome-centric succession model. Pine savannas have been considered early-successional communities that, in the absence of fire, transition rapidly toward closed-canopy hardwood forests. Recurrent fires have been viewed as exogenous disturbances that maintain savanna ecosystems as a sub-climax, blocking succession to an equilibrium steady state (closed-canopy forests). Over recent decades, a vegetation-fire feedback model has emerged in which pine savannas are conceptualized as persistent, non-equilibrium communities maintained by endogenous, co-evolutionary vegetation-fire feedbacks. Endemic plant species are resistant to fires and specialized for post-fire conditions generated by frequent lightning fires, primarily within a distinct fire season. These species produce pyrogenic fine fuels that are easily ignited. The resulting fire regimes, entrained by these vegetation-fire feedbacks, are predicted to result in persistent pine savannas. Local variation over space and time in evolutionary feedback mechanisms between pyrogenic vegetation and fire regimes produces heterogeneous landscapes. Disturbances of these feedbacks, such as human fire suppression, are postulated to result in rapid transition to communities lacking feedback elements, such as closed-canopy forest and those without pyrogenic species. Succession-based management focuses on reversing the transition to forest, primarily by removing hardwoods and reintroducing fire as a disturbance. However, we advocate restoration and management approaches that target reinstitution of functional vegetation-fire feedbacks. Such approaches should favor native pyrogenic plant species and reinstitute fire regimes that mimic historical, evolutionarily derived fire regimes. Vegetation-fire feedback concepts should be useful in addressing resistance and resilience of fiery ecosystems worldwide to inherent changes in feedback mechanisms, constituting a framework useful in addressing global management challenges