Cubic Curves, Finite Geometry and Cryptography

Some geometry on non-singular cubic curves, mainly over finite fields, is surveyed. Such a curve has 9,3,1 or 0 points of inflexion, and cubic curves are classified accordingly. The group structure and the possible numbers of rational points are also surveyed. A possible strengthening of the security of elliptic curve cryptography is proposed using a `shared secret' related to the group law. Cubic curves are also used in a new way to construct sets of points having various combinatorial and geometric properties that are of particular interest in finite Desarguesian planes.Comment: This is a version of our article to appear in Acta Applicandae Mathematicae. In this version, we have corrected a sentence in the third paragraph. The final publication is available at springerlink.com at http://www.springerlink.com/content/xh85647871215644

On operad structures of moduli spaces and string theory

Recent algebraic structures of string theory, including homotopy Lie algebras, gravity algebras and Batalin-Vilkovisky algebras, are deduced from the topology of the moduli spaces of punctured Riemann spheres. The principal reason for these structures to appear is as simple as the following. A conformal field theory is an algebra over the operad of punctured Riemann surfaces, this operad gives rise to certain standard operads governing the three kinds of algebras, and that yields the structures of such algebras on the (physical) state space naturally.Comment: 33 pages (An elaboration of minimal area metrics and new references are added

Relativistic Description of Exclusive Semileptonic Decays of Heavy Mesons

Using quasipotential approach, we have studied exclusive semileptonic decays of heavy mesons with the account of relativistic effects. Due to more complete relativistic description of the $s$ quark more precise expressions for semileptonic form factors are obtained. Various differential distributions in exclusive semileptonic decays of heavy mesons are calculated. It is argued that consistent account of relativistic effects and HQET motivated choice of the parameters of quark-antiquark potential allow to get reliable value for the ratio $A_2(0)/A_1(0)$ in the $D\to K^*l\nu_l$ decay as well as the ratio~$\Gamma(D\to K^*l\nu_l)/\Gamma(D\to Kl\nu_l)$. All calculated branching ratios are in accord with available experimental data.Comment: 18 pages, LATEX, 2 figures inclosed + 4 Postscript figure

Signaling via a CD27-TRAF2-SHP-1 axis during naive T cell activation promotes memory-associated gene regulatory networks.

The interaction of the tumor necrosis factor receptor (TNFR) family member CD27 on naive CD8 <sup>+</sup> T (Tn) cells with homotrimeric CD70 on antigen-presenting cells (APCs) is necessary for T cell memory fate determination. Here, we examined CD27 signaling during Tn cell activation and differentiation. In conjunction with T cell receptor (TCR) stimulation, ligation of CD27 by a synthetic trimeric CD70 ligand triggered CD27 internalization and degradation, suggesting active regulation of this signaling axis. Internalized CD27 recruited the signaling adaptor TRAF2 and the phosphatase SHP-1, thereby modulating TCR and CD28 signals. CD27-mediated modulation of TCR signals promoted transcription factor circuits that induced memory rather than effector associated gene programs, which are induced by CD28 costimulation. CD27-costimulated chimeric antigen receptor (CAR)-engineered T cells exhibited improved tumor control compared with CD28-costimulated CAR-T cells. Thus, CD27 signaling during Tn cell activation promotes memory properties with relevance to T cell immunotherapy

Recurrent mutations in the U2AF1 splicing factor in myelodysplastic syndromes

Myelodysplastic syndromes (MDS) are hematopoietic stem cell disorders that often progress to chemotherapy-resistant secondary acute myeloid leukemia (sAML). We used whole-genome sequencing to perform an unbiased comprehensive screen to discover the somatic mutations in a sample from an individual with sAML and genotyped the loci containing these mutations in the matched MDS sample. Here we show that a missense mutation affecting the serine at codon 34 (Ser34) in U2AF1 was recurrently present in 13 out of 150 (8.7%) subjects with de novo MDS, and we found suggestive evidence of an increased risk of progression to sAML associated with this mutation. U2AF1 is a U2 auxiliary factor protein that recognizes the AG splice acceptor dinucleotide at the 3' end of introns, and the alterations in U2AF1 are located in highly conserved zinc fingers of this protein. Mutant U2AF1 promotes enhanced splicing and exon skipping in reporter assays in vitro. This previously unidentified, recurrent mutation in U2AF1 implicates altered pre-mRNA splicing as a potential mechanism for MDS pathogenesis

Semileptonic Meson Decays in the Quark Model: An Update

We present the predictions of ISGW2, an update of the ISGW quark model for semileptonic meson decays. The updated model incorporates a number of features which should make it more reliable, including the constraints imposed by Heavy Quark Symmetry, hyperfine distortions of wavefunctions, and form factors with more realistic high recoil behaviors.Comment: All text and tables contained in the ".latex" file and all figures (14) contained in the ".uu" file