Jensen polynomials for the Riemann zeta function and other sequences

In 1927 P\'olya proved that the Riemann Hypothesis is equivalent to the hyperbolicity of Jensen polynomials for the Riemann zeta function $\zeta(s)$ at its point of symmetry. This hyperbolicity has been proved for degrees $d\leq 3$. We obtain an asymptotic formula for the central derivatives $\zeta^{(2n)}(1/2)$ that is accurate to all orders, which allows us to prove the hyperbolicity of a density $1$ subset of the Jensen polynomials of each degree. Moreover, we establish hyperbolicity for all $d\leq 8$. These results follow from a general theorem which models such polynomials by Hermite polynomials. In the case of the Riemann zeta function, this proves the GUE random matrix model prediction in derivative aspect. The general theorem also allows us to prove a conjecture of Chen, Jia, and Wang on the partition function.Comment: 11 page

Modelling the spread of an invasive woody taxon: Rhododendron ponticum L.

Simulation of the present-day distribution and abundance of rialRhododendron ponticum L. at the Glen Etive study site in the Western Highlands of Scotland was achieved using a simple deterministic model (MIGRATE). The model utilises the demographic and dispersal parameters characteristic to a species and a knowledge of the environmental history of the area through which it spreads to simulate patterns of spread. Biotic parameter values were derived from simple field measures and from data in the literature. "Habitat maps" were constructed on the basis of observations made in the field as to the likely relationships of Rhododendron to biotic and abiotic features of the habitat. Habitat features and their attributes were digitised and recorded in an ARC/INFO Geographical Information System (GIS). The simulation of changes in habitat through time was attempted using different habitat maps composed of cells containing unique values for relative carrying capacities, which were representative of the state of the habitat at a certain time. These habitat maps could only influence the dynamics of spread at the intervals between generations. Implementation of habitat changes was dependent on the cohort structure of the model which limited the resolution and exact order of changes that could be taken into account. Model simulations were tested for accuracy against the present-day distribution and abundance of the invading population as mapped in the field, and as seen in aerial photographs from 1946."Null" simulations showed that environmental factors were important determinants of the migration rate. Having achieved accurate simulation of a past and present distribution at a fine spatial scale from two initial foci of introduction in 1910, predictions were made as to the likely pattern of future spread. Predictions for the future were then made considering the effects of control regimes. The importance of the implications of the pattern of spread to migration research and to conservationists, considering the ecological impacts of Rhododendron observed at the study site are discussed in relation to previous findings. More specifically the importance of the long-distance dispersal function to the invasion process is highlighted, and it is suggested that evolution should favour strategies resulting in long-distance dispersal. The reason for large seed crops is discussed in this light. This project represents an integration of field techniques, biotic data available from the literature, a deterministic model, a GIS and aerial photography

The distribution and abundance of the rook corvus frugilegus L. as influenced by habitat suitability and competitive interactions.

Rooks (Corvus frugilegus) are colonially breeding corvids found in most agricultural landscapes. Colonies in the County Durham area tend to be clustered at distances up to 500 m, but otherwise show little pattern in terms of spacing or size. Colony size was comparable between sites as changes in colony nest counts were allowed to stabilise before the whole area was surveyed. When measuring nest build-up at a sample of colonies in 1996, no further significant increases occurred after 9th April. The spatial size distribution of colonies was maintained between years. The distribution and size of breeding colonies is modelled in relation to the interaction between the spatial distribution of the foraging habitat and potential intraspecific competitors, with the identification of the distance over which this interaction is strongest. The satellite derived habitat data used for the modelling were part of the ITE Land Cover Map of Great Britain. However, their correspondence with ground reference data was found to be severely lacking. Thus, for modelling the availability of nesting habitat, OS woodland data were used as these identified more of the extant rookery sites, whilst the ITE data were retained for quantifying the foraging habitat. Logistic regression showed that the distribution of colony sites was influenced by the availability of woodland blocks large enough to hold a colony, proximity to roads and buildings, and by the amount of pasture within 1 km. Other suitable sites with these characteristics remained unoccupied within the distribution. Partial Correlations showed that interactions between the spatial distribution of the foraging habitat and competitors influenced colony size at distances up to 6 km, suggesting their effect outside of the breeding season. The multiple regression model built with variable values for this distance explained 31% of the variance in colony size. When applied to the potential breeding sites identified using the logistic regression, most sites still remained suitable. This suggests the distribution is not saturated and that limited availability of breeding habitat is not the cause of the nesting aggregations. The broad correlation of Rook abundance to foraging habitat and potential competitors corresponds to an ideal free distribution of individuals across colony sites. This is supported by models of Rook numbers in relation to parish agricultural statistics produced by MAFF. These again show the importance of pasture as a probable foraging resource, and how pasture quality could be important to Rook numbers. The models also supported the ideal free predictions of spatial variation in Rook abundance in relation to habitat, and the response of colony sizes to temporal change in habitat quality

A new molecular diagnostic tool for surveying and monitoring Triops cancriformis populations

© 2017 Sellers et al. The tadpole shrimp, Triops cancriformis, is a freshwater crustacean listed as endangered in the UK and Europe living in ephemeral pools. Populations are threatened by habitat destruction due to land development for agriculture and increased urbanisation. Despite this, there is a lack of efficient methods for discovering and monitoring populations. Established macroinvertebrate monitoring methods, such as net sampling, are unsuitable given the organism's life history, that include long lived diapausing eggs, benthic habits and ephemerally active populations. Conventional hatching methods, such as sediment incubation, are both time consuming and potentially confounded by bet-hedging hatching strategies of diapausing eggs. Here we develop a new molecular diagnostic method to detect viable egg banks of T. cancriformis, and compare its performance to two conventional monitoring methods involving diapausing egg hatching. We apply this method to a collection of pond sediments from the Wildfowl & Wetlands Trust Caerlaverock National Nature Reserve, which holds one of the two remaining British populations of T. cancriformis. DNA barcoding of isolated eggs, using newly designed species-specific primers for a large region of mtDNA, was used to estimate egg viability. These estimates were compared to those obtained by the conventional methods of sediment and isolation hatching. Our method outperformed the conventional methods, revealing six ponds holding viable T. cancriformis diapausing egg banks in Caerlaverock. Additionally, designed species-specific primers for a short region of mtDNA identified degraded, inviable eggs and were used to ascertain the levels of recent mortality within an egg bank. Together with efficient sugar flotation techniques to extract eggs from sediment samples, our molecular method proved to be a faster and more powerful alternative for assessing the viability and condition of T. cancriformis diapausing egg banks

Race, Memory, and Historical Responsibility: What Do Southerners Do with a Difficult Past?

Newly emerging, transitional societies –– that is, societies that traded dictatorial or authoritarian rule for some form of open or liberal polity –– face at least three interdependent problems of what is called in legal scholarship and social science “transitional justice”: the first is how (if at all) to hold the old regime’s autocratic, often violence-laden leadership responsible for its wrongdoings while in power; the second is what (if anything) to do with thousands upon thousands of ordinary folk whose participation in, or compliance with, the old regime helped legitimate and thus perpetuate the wrongdoing; and the third task how (if at all) to deal with the victims of the old regime. By situating the American South in the global context of the need of newly democratizing societies for transitional justice, we explore how the South’s similarities with and differences from other such societies have shaped the timing and character of its peoples’ post-Jim Crow era restorative justice and racial reconciliation projects, paying particular attention to criminal trials for perpetrators of past crimes, apology, truth and reconciliation-type commissions, and memorialization. We then document the extent of racial inequalities in employment, income, poverty status, and morbidity and mortality, arguing both that past racial injustices result in contemporary racial inequalities and that restorative justice points forward in time--and thus must deal with current inequities –– as well as backward

Revisiting A Festival of Violence : Two Comments, A Response [Book Review]

When, more than thirty years ago, I was writing my second graduate research paper, I was strongly advised by the professor in the course, John Morton Blum, to stop trying to weigh the factors I hypothesized might have caused the phenomenon I was trying to explain. Just list all the causes for which there is any credible evidence, I was told; don’t even try to rank them, and certainly don’t waste your time attempting to reject any. It’s not the historian’s job, and it’s probably not possible, anyway. Tell a good story, with interesting characters and active verbs. If you must, explain, but above all, entertain-that was the Blumian credo. I largely ignored the adjuration, reinforcing the then-department chairman’s view of me as a rebel with too few causes

Lunar Architecture Team - Phase 2 Habitat Volume Estimation: "Caution When Using Analogs"

The lunar surface habitat will serve as the astronauts' home on the moon, providing a pressurized facility for all crew living functions and serving as the primary location for a number of crew work functions. Adequate volume is required for each of these functions in addition to that devoted to housing the habitat systems and crew consumables. The time constraints of the LAT-2 schedule precluded the Habitation Team from conducting a complete "bottoms-up" design of a lunar surface habitation system from which to derive true volumetric requirements. The objective of this analysis was to quickly derive an estimated total pressurized volume and pressurized net habitable volume per crewmember for a lunar surface habitat, using a principled, methodical approach in the absence of a detailed design. Five "heuristic methods" were used: historical spacecraft volumes, human/spacecraft integration standards and design guidance, Earth-based analogs, parametric "sizing" tools, and conceptual point designs. Estimates for total pressurized volume, total habitable volume, and volume per crewmember were derived using these methods. All method were found to provide some basis for volume estimates, but values were highly variable across a wide range, with no obvious convergence of values. Best current assumptions for required crew volume were provided as a range. Results of these analyses and future work are discussed