Numerical Computation of a Certain Dirichlet Series Attached to Siegel Modular Forms of Degree Two

The Rankin convolution type Dirichlet series D-F,D-G(s) of Siegel modular forms F and G of degree two, which was introduced by Kohnen and the second author, is computed numerically for various F and G. In particular, we prove that the series D-F,D-G(s), which shares the same functional equation and analytic behavior with the spinor L-functions of eigenforms of the same weight are not linear combinations of those. In order to conduct these experiments a numerical method to compute the Petersson scalar products of Jacobi Forms is developed and discussed in detail.

Efficient computation of discrete polynomial transforms

This letter presents a new recursive method for computing discrete polynomial transforms. The method is shown for forward and inverse transforms of the Hermite, binomial, and Laguerre transforms. The recursive flow diagrams require only 2 additions, 2( +1) memory units, and +1multipliers for the +1-point Hermite and binomial transforms. The recursive flow diagram for the +1-point Laguerre transform requires 2 additions, 2( +1) memory units, and 2( +1) multipliers. The transform computation time for all of these transforms is ( )

Computation of discrete cosine transform using Clenshaw's recurence formula

Clenshaw’s recurrenee formula is used to derive recursive algorithms for the discrete cosine transform @CT) and the inverse discrete cosine transform (IDCT). The recursive DCT algorithm presented here requires one fewer delay element per coefficient and one fewer multiply operation per coeflident compared with two recently proposed methods. Clenshaw’s recurrence formula provides a unified development for the recursive DCT and IDCT algorithms. The M v e al gorithms apply to arbitrary lengtb algorithms and are appropriate for VLSI implementation.

Citizen science reveals unexpected continental-scale evolutionary change in a model organism

Organisms provide some of the most sensitive indicators of climate change and evolutionary responses are becoming apparent in species with short generation times. Large datasets on genetic polymorphism that can provide an historical benchmark against which to test for recent evolutionary responses are very rare, but an exception is found in the brown-lipped banded snail (Cepaea nemoralis). This species is sensitive to its thermal environment and exhibits several polymorphisms of shell colour and banding pattern affecting shell albedo in the majority of populations within its native range in Europe. We tested for evolutionary changes in shell albedo that might have been driven by the warming of the climate in Europe over the last half century by compiling an historical dataset for 6,515 native populations of C. nemoralis and comparing this with new data on nearly 3,000 populations. The new data were sampled mainly in 2009 through the Evolution MegaLab, a citizen science project that engaged thousands of volunteers in 15 countries throughout Europe in the biggest such exercise ever undertaken. A known geographic cline in the frequency of the colour phenotype with the highest albedo (yellow) was shown to have persisted and a difference in colour frequency between woodland and more open habitats was confirmed, but there was no general increase in the frequency of yellow shells. This may have been because snails adapted to a warming climate through behavioural thermoregulation. By contrast, we detected an unexpected decrease in the frequency of Unbanded shells and an increase in the Mid-banded morph. Neither of these evolutionary changes appears to be a direct response to climate change, indicating that the influence of other selective agents, possibly related to changing predation pressure and habitat change with effects on micro-climate.

The evolutionary importance of cell ratio between notochordal and nucleus pulposus cells: an experimental 3-D co-culture study

Notochordal cells and nucleus pulposus cells are co-existing in the intervertebral disc at various ratios among different mammalians. This fact rises the question about the interactions and the evolutionary relevance of this phenomenon. It has been described that these relatively large notochordal cells are mainly dominant in early lifetime of all vertebrates and then differences occur with ageing. Human, cattle, sheep, and goat lose the cells with age, whereas rodents and lagomorphs maintain these throughout their lifetime.

Evolutionary forces shaping genomic islands of population differentiation in humans

Background Levels of differentiation among populations depend both on demographic and selective factors: genetic drift and local adaptation increase population differentiation, which is eroded by gene flow and balancing selection. We describe here the genomic distribution and the properties of genomic regions with unusually high and low levels of population differentiation in humans to assess the influence of selective and neutral processes on human genetic structure. Methods Individual SNPs of the Human Genome Diversity Panel (HGDP) showing significantly high or low levels of population differentiation were detected under a hierarchical-island model (HIM). A Hidden Markov Model allowed us to detect genomic regions or islands of high or low population differentiation. Results Under the HIM, only 1.5% of all SNPs are significant at the 1% level, but their genomic spatial distribution is significantly non-random. We find evidence that local adaptation shaped high-differentiation islands, as they are enriched for non-synonymous SNPs and overlap with previously identified candidate regions for positive selection. Moreover there is a negative relationship between the size of islands and recombination rate, which is stronger for islands overlapping with genes. Gene ontology analysis supports the role of diet as a major selective pressure in those highly differentiated islands. Low-differentiation islands are also enriched for non-synonymous SNPs, and contain an overly high proportion of genes belonging to the 'Oncogenesis' biological process. Conclusions Even though selection seems to be acting in shaping islands of high population differentiation, neutral demographic processes might have promoted the appearance of some genomic islands since i) as much as 20% of islands are in non-genic regions ii) these non-genic islands are on average two times shorter than genic islands, suggesting a more rapid erosion by recombination, and iii) most loci are strongly differentiated between Africans and non-Africans, a result consistent with known human demographic history.

Evidence of Adaptive Evolutionary Divergence during Biological Invasion

Rapid phenotypic diversification during biological invasions can either arise by adaptation to alternative environments or by adaptive phenotypic plasticity. Where experimental evidence for adaptive plasticity is common, support for evolutionary diversification is rare. Here, we performed a controlled laboratory experiment using full-sib crosses between ecologically divergent threespine stickleback populations to test for a genetic basis of adaptation. Our populations are from two very different habitats, lake and stream, of a recently invaded range in Switzerland and differ in ecologically relevant morphological traits. We found that in a lake-like food treatment lake fish grow faster than stream fish, resembling the difference among wild type individuals. In contrast, in a stream-like food treatment individuals from both populations grow similarly. Our experimental data suggest that genetically determined diversification has occurred within less than 140 years after the arrival of stickleback in our studied region.