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Search Results: 1 - 10 of 311657 matches for " Mark J. Watkins "
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Secondary terms in the number of vanishings of quadratic twists of elliptic curve L-functions
J. Brian Conrey,Atul Pokharel,Michael O. Rubinstein,Mark Watkins
Mathematics , 2005,
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.
Some heuristics about elliptic curves
Mark Watkins
Mathematics , 2006,
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|
Some remarks on Heegner point computations
Mark Watkins
Mathematics , 2005,
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.
Rank distribution in a family of cubic twists
Mark Watkins
Mathematics , 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.
Explicit lower bounds on the modular degree of an elliptic curve
Mark Watkins
Mathematics , 2004,
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.
Mobile element scanning (ME-Scan) by targeted high-throughput sequencing
David J Witherspoon, Jinchuan Xing, Yuhua Zhang, W Scott Watkins, Mark A Batzer, Lynn B Jorde
BMC Genomics , 2010, DOI: 10.1186/1471-2164-11-410
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
Discretisation for odd quadratic twists
J. Brian Conrey,Michael O. Rubinstein,Nina C. Snaith,Mark Watkins
Mathematics , 2005,
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.
T cell receptor variable β20-1 harbors a nucleotide binding pocket in the CDR2β loop  [PDF]
Stephan Watkins, Werner J. Pichler
Open Journal of Immunology (OJI) , 2013, DOI: 10.4236/oji.2013.33021
Abstract:

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.

Activating interactions of sulfanilamides with T cell receptors  [PDF]
Stephan Watkins, Werner J. Pichler
Open Journal of Immunology (OJI) , 2013, DOI: 10.4236/oji.2013.33019
Abstract:

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

Symmetric powers of elliptic curve L-functions
Phil Martin,Mark Watkins
Mathematics , 2006,
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.
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