Abstract:
We examine the number of vanishings of quadratic twists of the L-function associated to an elliptic curve. Applying a conjecture for the full asymptotics of the moments of critical L-values we obtain a conjecture for the first two terms in the ratio of the number of vanishings of twists sorted according to arithmetic progressions.

Abstract:
We give some heuristics for counting elliptic curves with certain properties. In particular, we re-derive the Brumer-McGuinness heuristic for the number of curves with positive/negative discriminant up to $X$, which is an application of lattice-point counting. We then introduce heuristics (with refinements from random matrix theory) that allow us to predict how often we expect an elliptic curve $E$ with even parity to have $L(E,1)=0$. We find that we expect there to be about $c_1X^{19/24}(\log X)^{3/8}$ curves with $|\Delta|

Abstract:
We explain how to find a rational point on a rational elliptic curve of rank 1 using Heegner points. We give some examples, and list new algorithms that are due to Cremona and Delaunay. These are notes from a short course given at the Institut Henri Poincare in December 2004.

Abstract:
In 1987, Zagier and Kramarz published a paper in which they presented evidence that a positive proportion of the even-signed cubic twists of the elliptic curve $x^3+y^3=1$ should have positive rank. We extend their data, showing that it is more likely that the proportion goes to zero.

Abstract:
We derive an explicit zero-free region for symmetric square L-functions of elliptic curves, and use this to derive an explicit lower bound for the modular degree of rational elliptic curves. The techniques are similar to those used in the classical derivation of zero-free regions for Dirichlet L-functions, but here, due to the work of Goldfield-Hoffstein-Lieman, we know that there are no Siegel zeros, which leads to a strengthened result.

Abstract:
Here we present a novel method for identifying nearly all insertions of a ME subfamily in the whole genomes of multiple individuals and simultaneously genotyping (for presence or absence) those insertions that are variable in the population. We use ME-specific primers to construct DNA libraries that contain the junctions of all ME insertions of the subfamily, with their flanking genomic sequences, from many individuals. Individual-specific "index" sequences are designed into the oligonucleotide adapters used to construct the individual libraries. These libraries are then pooled and sequenced using a ME-specific sequencing primer. Mobile element insertion loci of the target subfamily are uniquely identified by their junction sequence, and all insertion junctions are linked to their individual libraries by the corresponding index sequence. To test this method's feasibility, we apply it to the human AluYb8 and AluYb9 subfamilies. In four individuals, we identified a total of 2,758 AluYb8 and AluYb9 insertions, including nearly all those that are present in the reference genome, as well as 487 that are not. Index counts show the sequenced products from each sample reflect the intended proportions to within 1%. At a sequencing depth of 355,000 paired reads per sample, the sensitivity and specificity of ME-Scan are both approximately 95%.Mobile Element Scanning (ME-Scan) is an efficient method for quickly genotyping mobile element insertions with very high sensitivity and specificity. In light of recent improvements to high-throughput sequencing technology, it should be possible to employ ME-Scan to genotype insertions of almost any mobile element family in many individuals from any species.Mobile elements (MEs) are DNA sequences that can replicate and insert themselves into new loci within larger host genomes. This strategy has proved very successful: MEs are evolutionarily ancient, highly diversified in form, ubiquitous in distribution, and often extremely numerous with

Abstract:
The discretisation problem for even quadratic twists is almost understood, with the main question now being how the arithmetic Delaunay heuristic interacts with the analytic random matrix theory prediction. The situation for odd quadratic twists is much more mysterious, as the height of a point enters the picture, which does not necessarily take integral values (as does the order of the Shafarevich-Tate group). We discuss a couple of models and present data on this question.

Novel aspects of T
cells containing TCRVβ20-1 are
numerous, ranging from pathogen specific reactivity to specific tissue homing,
or possible T cell subsets. Recently, it was demonstrated that TCR itself could
become reactive by binding to small molecules free of the pHLA interface. Our
work here was to identify a natural ligand binding to an identified pocket on
the CDR2β loop of these TCR. Using
docking of suspected ligands, we were able to show Guanine and Adenine diand
tri-nucleotides readily bind to the identified site. Comparing these with small
molecule sites found on other TCR types, we show this interaction is novel. With
further molecular dynamic simulations, these sites are shown to be plausible by
conducting simple computational based solubility tests as cross validation. Combined
with simple proliferative responses, the identified nucleotides are also shown
to have functional consequences by inducing T cell proliferation for CD4/Vβ20-1 + T cells, while failing to induce
proliferation in other T cell isolates. Merging computational and simple cell
assays, this work establishes a role of nucleotides in T cells found to contain
this TCR subtype.

Activation and expansion of drug reactive T cells are key
features in drug hypersensitivity reactions. Drugs may interact directly with immune
receptors such as the human leukocyte antigens (HLA) or the T-cell receptors
(TCR) itself, the pharmacological interaction [p-i] concept. To analyze whether
the drug sulfamethoxazole (SMX) interacts directly
with the TCR and thereby contributing to signaling and T cell activation, we
analyze two SMX specific T cell clones (TCC “1.3”and “H13”).
Proliferation to SMX and 11 related sulfanilamides, Ca++ influx in drug
stimulated T-cells and the inhibitory effect of non-reactive sulfanilamides on
SMX stimulation were analyzed. In silico docking of SMX and related sulfanilamide to the TCR were used to identify
possible drug binding sites, and correlated to in vitro data to find the correct docking. In Ca++ influx assays,
reactions occurred as early as 14 sec after adding SMX to TCC and APC. The
broadly reactive clone (“H13”)
was stimulated by 5 additional sulfanilamide, while one TCC (“1.3”) was reactive exclusively with SMX
but not other sulfanilamides. Competition experiments with sulfanilamide
inhibited SMX induced Ca++ influx and proliferation of the TCC1.3 ina dose dependent way. Docking experiments
with SMX and related sulfanilamides confirmed and explained the in vitro data as docking localized
binding sites for SMX and the 5 stimulating sulfanilamides on the CDR2β domain of the clone H13, while the 6
non-stimulatory SA failed to bind. In TCC 1.3, SMX could be docked on the CDR3α
of the TCR. The other, non-stimulatory but inhibitory SA could also be docked
to the same site. The combined analysis of in
vitro and in silico

Abstract:
The conjectures of Deligne, Be\u\i linson, and Bloch-Kato assert that there should be relations between the arithmetic of algebro-geometric objects and the special values of their $L$-functions. We make a numerical study for symmetric power $L$-functions of elliptic curves, obtaining data about the validity of their functional equations, frequency of vanishing of central values, and divisibility of Bloch-Kato quotients.