Quantum Thetas on Noncommutative T^4 from Embeddings into Lattice

In this paper we investigate the theta vector and quantum theta function over noncommutative T^4 from the embedding of R x Z^2. Manin has constructed the quantum theta functions from the lattice embedding into vector space (x finite group). We extend Manin's construction of the quantum theta function to the embedding of vector space x lattice case. We find that the holomorphic theta vector exists only over the vector space part of the embedding, and over the lattice part we can only impose the condition for Schwartz function. The quantum theta function built on this partial theta vector satisfies the requirement of the quantum theta function. However, two subsequent quantum translations from the embedding into the lattice part are non-additive, contrary to the additivity of those from the vector space part.Comment: 20 pages, LaTeX, version to appear in J. Phys.

Theta Vectors and Quantum Theta Functions

In this paper, we clarify the relation between Manin's quantum theta function and Schwarz's theta vector in comparison with the kq representation, which is equivalent to the classical theta function, and the corresponding coordinate space wavefunction. We first explain the equivalence relation between the classical theta function and the kq representation in which the translation operators of the phase space are commuting. When the translation operators of the phase space are not commuting, then the kq representation is no more meaningful. We explain why Manin's quantum theta function obtained via algebra (quantum tori) valued inner product of the theta vector is a natural choice for quantum version of the classical theta function (kq representation). We then show that this approach holds for a more general theta vector with constant obtained from a holomorphic connection of constant curvature than the simple Gaussian one used in the Manin's construction. We further discuss the properties of the theta vector and of the quantum theta function, both of which have similar symmetry properties under translation.Comment: LaTeX 21 pages, give more explicit explanations for notions given in the tex

d=3 Bosonic Vector Models Coupled to Chern-Simons Gauge Theories

We study three dimensional O(N)_k and U(N)_k Chern-Simons theories coupled to a scalar field in the fundamental representation, in the large N limit. For infinite k this is just the singlet sector of the O(N) (U(N)) vector model, which is conjectured to be dual to Vasiliev's higher spin gravity theory on AdS_4. For large k and N we obtain a parity-breaking deformation of this theory, controlled by the 't Hooft coupling lambda = 4 \pi N / k. For infinite N we argue (and show explicitly at two-loop order) that the theories with finite lambda are conformally invariant, and also have an exactly marginal (\phi^2)^3 deformation. For large but finite N and small 't Hooft coupling lambda, we show that there is still a line of fixed points parameterized by the 't Hooft coupling lambda. We show that, at infinite N, the interacting non-parity-invariant theory with finite lambda has the same spectrum of primary operators as the free theory, consisting of an infinite tower of conserved higher-spin currents and a scalar operator with scaling dimension \Delta=1; however, the correlation functions of these operators do depend on lambda. Our results suggest that there should exist a family of higher spin gravity theories, parameterized by lambda, and continuously connected to Vasiliev's theory. For finite N the higher spin currents are not conserved.Comment: 34 pages, 29 figures. v2: added reference

Microevolution of Helicobacter pylori during prolonged infection of single hosts and within families

Our understanding of basic evolutionary processes in bacteria is still very limited. For example, multiple recent dating estimates are based on a universal inter-species molecular clock rate, but that rate was calibrated using estimates of geological dates that are no longer accepted. We therefore estimated the short-term rates of mutation and recombination in Helicobacter pylori by sequencing an average of 39,300 bp in 78 gene fragments from 97 isolates. These isolates included 34 pairs of sequential samples, which were sampled at intervals of 0.25 to 10.2 years. They also included single isolates from 29 individuals (average age: 45 years) from 10 families. The accumulation of sequence diversity increased with time of separation in a clock-like manner in the sequential isolates. We used Approximate Bayesian Computation to estimate the rates of mutation, recombination, mean length of recombination tracts, and average diversity in those tracts. The estimates indicate that the short-term mutation rate is 1.4×10−6 (serial isolates) to 4.5×10−6 (family isolates) per nucleotide per year and that three times as many substitutions are introduced by recombination as by mutation. The long-term mutation rate over millennia is 5–17-fold lower, partly due to the removal of non-synonymous mutations due to purifying selection. Comparisons with the recent literature show that short-term mutation rates vary dramatically in different bacterial species and can span a range of several orders of magnitude

Epidermal growth factor receptor kinase domain mutations are rare in salivary gland carcinomas

Activating mutations within the epidermal growth factor (EGFR) tyrosine kinase domain identify non-small cell lung cancer patients with improved clinical response to tyrosine kinase inhibitor therapy. Recently, we identified two EGFR mutations in a cohort of 25 salivary gland carcinomas (SGCs) by screening the tumour samples for the both most common hotspot mutations in exons 19 and 21 by allele-specific PCR. Here, we present a comprehensive sequencing analysis of the entire critical EGFR tyrosine kinase domain in 65 SGC of the main histopathological types. We found EGFR mutations in the tyrosine kinase domain to be a rare event in SGCs. No additional mutations other than the two known exon 19 deletions (c.2235_2249del15) in a mucoepidermoid carcinoma and an adenoid cystic carcinoma have been detected. Other putative predictive markers for EGFR-targeted therapy in SGCs might be relevant and should be investigated

A Two-Stage Random Forest-Based Pathway Analysis Method

Pathway analysis provides a powerful approach for identifying the joint effect of genes grouped into biologically-based pathways on disease. Pathway analysis is also an attractive approach for a secondary analysis of genome-wide association study (GWAS) data that may still yield new results from these valuable datasets. Most of the current pathway analysis methods focused on testing the cumulative main effects of genes in a pathway. However, for complex diseases, gene-gene interactions are expected to play a critical role in disease etiology. We extended a random forest-based method for pathway analysis by incorporating a two-stage design. We used simulations to verify that the proposed method has the correct type I error rates. We also used simulations to show that the method is more powerful than the original random forest-based pathway approach and the set-based test implemented in PLINK in the presence of gene-gene interactions. Finally, we applied the method to a breast cancer GWAS dataset and a lung cancer GWAS dataset and interesting pathways were identified that have implications for breast and lung cancers

New genetic loci implicated in fasting glucose homeostasis and their impact on type 2 diabetes risk.

Levels of circulating glucose are tightly regulated. To identify new loci influencing glycemic traits, we performed meta-analyses of 21 genome-wide association studies informative for fasting glucose, fasting insulin and indices of beta-cell function (HOMA-B) and insulin resistance (HOMA-IR) in up to 46,186 nondiabetic participants. Follow-up of 25 loci in up to 76,558 additional subjects identified 16 loci associated with fasting glucose and HOMA-B and two loci associated with fasting insulin and HOMA-IR. These include nine loci newly associated with fasting glucose (in or near ADCY5, MADD, ADRA2A, CRY2, FADS1, GLIS3, SLC2A2, PROX1 and C2CD4B) and one influencing fasting insulin and HOMA-IR (near IGF1). We also demonstrated association of ADCY5, PROX1, GCK, GCKR and DGKB-TMEM195 with type 2 diabetes. Within these loci, likely biological candidate genes influence signal transduction, cell proliferation, development, glucose-sensing and circadian regulation. Our results demonstrate that genetic studies of glycemic traits can identify type 2 diabetes risk loci, as well as loci containing gene variants that are associated with a modest elevation in glucose levels but are not associated with overt diabetes

Studying the Underlying Event in Drell-Yan and High Transverse Momentum Jet Production at the Tevatron

We study the underlying event in proton-antiproton collisions by examining the behavior of charged particles (transverse momentum pT > 0.5 GeV/c, pseudorapidity |\eta| < 1) produced in association with large transverse momentum jets (~2.2 fb-1) or with Drell-Yan lepton-pairs (~2.7 fb-1) in the Z-boson mass region (70 < M(pair) < 110 GeV/c2) as measured by CDF at 1.96 TeV center-of-mass energy. We use the direction of the lepton-pair (in Drell-Yan production) or the leading jet (in high-pT jet production) in each event to define three regions of \eta-\phi space; toward, away, and transverse, where \phi is the azimuthal scattering angle. For Drell-Yan production (excluding the leptons) both the toward and transverse regions are very sensitive to the underlying event. In high-pT jet production the transverse region is very sensitive to the underlying event and is separated into a MAX and MIN transverse region, which helps separate the hard component (initial and final-state radiation) from the beam-beam remnant and multiple parton interaction components of the scattering. The data are corrected to the particle level to remove detector effects and are then compared with several QCD Monte-Carlo models. The goal of this analysis is to provide data that can be used to test and improve the QCD Monte-Carlo models of the underlying event that are used to simulate hadron-hadron collisions.Comment: Submitted to Phys.Rev.