Superrigid subgroups and syndetic hulls in solvable Lie groups

This is an expository paper. It is not difficult to see that every group homomorphism from the additive group Z of integers to the additive group R of real numbers extends to a homomorphism from R to R. We discuss other examples of discrete subgroups D of connected Lie groups G, such that the homomorphisms defined on D can ("virtually") be extended to homomorphisms defined on all of G. For the case where G is solvable, we give a simple proof that D has this property if it is Zariski dense. The key ingredient is a result on the existence of syndetic hulls.Comment: 17 pages. This is the final version that will appear in the volume "Rigidity in Dynamics and Geometry," edited by M. Burger and A. Iozzi (Springer, 2002

Equidistribution Rates, Closed String Amplitudes, and the Riemann Hypothesis

We study asymptotic relations connecting unipotent averages of $Sp(2g,\mathbb{Z})$ automorphic forms to their integrals over the moduli space of principally polarized abelian varieties. We obtain reformulations of the Riemann hypothesis as a class of problems concerning the computation of the equidistribution convergence rate in those asymptotic relations. We discuss applications of our results to closed string amplitudes. Remarkably, the Riemann hypothesis can be rephrased in terms of ultraviolet relations occurring in perturbative closed string theory.Comment: 15 page

Eluding SUSY at every genus on stable closed string vacua

In closed string vacua, ergodicity of unipotent flows provide a key for relating vacuum stability to the UV behavior of spectra and interactions. Infrared finiteness at all genera in perturbation theory can be rephrased in terms of cancelations involving only tree-level closed strings scattering amplitudes. This provides quantitative results on the allowed deviations from supersymmetry on perturbative stable vacua. From a mathematical perspective, diagrammatic relations involving closed string amplitudes suggest a relevance of unipotent flows dynamics for the Schottky problem and for the construction of the superstring measure.Comment: v2, 17 pages, 8 figures, typos corrected, new figure added with 3 modular images of long horocycles,(obtained with Mathematica

Convergence of measures on compactifications of locally symmetric spaces

We conjecture that the set of homogeneous probability measures on the maximal Satake compactification of an arithmetic locally symmetric space S=Γ∖G/K is compact. More precisely, given a sequence of homogeneous probability measures on S, we expect that any weak limit is homogeneous with support contained in precisely one of the boundary components (including S itself). We introduce several tools to study this conjecture and we prove it in a number of cases, including when G=SL3(R) and Γ=SL3(Z)

Nicotine exposure and transgenerational impact: a prospective study on small regulatory microRNAs

Early developmental stages are highly sensitive to stress and it has been reported that pre-conditioning with tobacco smoking during adolescence predisposes those youngsters to become smokers as adults. However, the molecular mechanisms of nicotine-induced transgenerational consequences are unknown. In this study, we genome-widely investigated the impact of nicotine exposure on small regulatory microRNAs (miRNAs) and its implication on health disorders at a transgenerational aspect. Our results demonstrate that nicotine exposure, even at the low dose, affected the global expression profiles of miRNAs not only in the treated worms (F0 parent generation) but also in two subsequent generations (F1 and F2, children and grandchildren). Some miRNAs were commonly affected by nicotine across two or more generations while others were specific to one. The general miRNA patterns followed a “two-hit� model as a function of nicotine exposure and abstinence. Target prediction and pathway enrichment analyses showed daf-4, daf-1, fos-1, cmk-1, and unc-30 to be potential effectors of nicotine addiction. These genes are involved in physiological states and phenotypes that paralleled previously published nicotine induced behavior. Our study offered new insights and further awareness on the transgenerational effects of nicotine exposed during the vulnerable post-embryonic stages, and identified new biomarkers for nicotine addiction.ECU Open Access Publishing Support Fun

The cloud aerosol interaction and precipitation enhancement experiment (CAIPEEX): Overview and preliminary results

While the demand for enhancing rainfall through cloud seeding is strong and persistent in the country, considerable uncertainty exists on the success of such an endeavour at a given location. To understand the pathways of aerosol-cloud interaction through which this might be achieved, a national experiment named Cloud Aerosol Interaction and Precipitation Enhancement EXperiment (CAIPEEX) in two phases, was carried out. The rationale of CAIPEEX, the strategy for conducting the experiment, data quality and potential for path-breaking science are described in this article. Pending completion of quality control and calibration of the CAIPEEX phase-II data, here we present some initial results of CAIPEEX phase-I aimed at documenting the prevailing microphysical characteristics of aerosols and clouds and associated environmental conditions over different regions of the country and under different monsoon conditions with the help of an instrumented research aircraft. First-time simultaneous observations of aerosol, cloud condensation nuclei (CCN) and cloud droplet number concentration (CDNC) over the Ganges Valley during monsoon season show very high concentrations (> 1000 cm-3) of CCN at elevated layers. Observations of elevated layers with high aerosol concentration over the Gangetic valley extending up to 6 km and relatively less aerosol concentration in the boundary layer are also documented. We also present evidence of strong cloud- aerosol interaction in the moist environments with an increase in the cloud droplet effective radius. Our observations also show that pollution increases CDNC and the warm rain depth, and delays its initiation. The critical effective radius for warm rain initiation is found to be between 10 and 12 μm in the polluted clouds and it is between 12 and 14 μm in cleaner monsoon clouds

Extremality and dynamically defined measures, part I: Diophantine properties of quasi-decaying measures

We present a new method of proving the Diophantine extremality of various dynamically defined measures, vastly expanding the class of measures known to be extremal. This generalizes and improves the celebrated theorem of Kleinbock and Margulis (’98) resolving Sprindžuk’s conjecture, as well as its extension by Kleinbock, Lindenstrauss, and Weiss (’04), hereafter abbreviated KLW. As applications we prove the extremality of all hyperbolic measures of smooth dynamical systems with sufficiently large Hausdorff dimension, of the Patterson–Sullivan measures of all nonplanar geometrically finite groups, and of the Gibbs measures (including conformal measures) of infinite iterated function systems. The key technical idea, which has led to a plethora of new applications, is a significant weakening of KLW’s sufficient conditions for extremality. In Part I, we introduce and develop a systematic account of two classes of measures, which we call quasi-decaying and weakly quasi-decaying. We prove that weak quasi-decay implies strong extremality in the matrix approximation framework, thus proving a conjecture of KLW. We also prove the “inherited exponent of irrationality” version of this theorem, describing the relationship between the Diophantine properties of certain subspaces of the space of matrices and measures supported on these subspaces. In subsequent papers, we exhibit numerous examples of quasi-decaying measures, in support of the thesis that “almost any measure from dynamics and/or fractal geometry is quasi-decaying”. We also discuss examples of non-extremal measures coming from dynamics, illustrating where the theory must halt

Smoking Cessation Pharmacogenetics: Analysis of Varenicline and Bupropion in Placebo-Controlled Clinical Trials

Despite effective therapies for smoking cessation, most smokers find quitting difficult and most successful quitters relapse. Considerable evidence supports a genetic risk for nicotine dependence; however, less is known about the pharmacogenetics of smoking cessation. In the first pharmacogenetic investigation of the efficacy of varenicline and bupropion, we examined whether genes important in the pharmacodynamics and pharmacokinetics of these drugs and nicotine predict medication efficacy and adverse events. Subjects participated in randomized, double-blind, placebo-controlled smoking cessation clinical trials, comparing varenicline, a nicotinic acetylcholine receptor (nAChR) partial agonist, with bupropion, a norepinephrine/dopamine reuptake inhibitor, and placebo. Primary analysis included 1175 smokers of European ancestry, and 785 single nucleotide polymorphisms from 24 genes, representing 254 linkage disequilibrium (LD) bins (genes included nAChR subunits, additional varenicline-specific genes, and genes involved in nicotine or bupropion metabolism). For varenicline, continuous abstinence (weeks 9–12) was associated with multiple nAChR subunit genes (including CHRNB2, CHRNA5, and CHRNA4) (OR=1.76; 95% CI: 1.23–2.52) (p<0.005); for bupropion, abstinence was associated with CYP2B6 (OR=1.78; 95% CI: 1.27–2.50) (p<0.001). Incidence of nausea was associated with several nAChR subunit genes (OR=0.50; 95% CI: 0.36–0.70) (p<0.0001) and time to relapse after quitting was associated with HTR3B (HR=1.97; 95% CI: 1.45–2.68) (p<0.0001). These data provide evidence for multiple genetic loci contributing to smoking cessation and therapeutic response. Different loci are associated with varenicline vs bupropion response, suggesting that additional research may identify clinically useful markers to guide treatment decisions

Glutamate regulation of calcium and IP3 oscillating and pulsating dynamics in astrocytes

Recent years have witnessed an increasing interest in neuron-glia communication. This interest stems from the realization that glia participates in cognitive functions and information processing and is involved in many brain disorders and neurodegenerative diseases. An important process in neuron-glia communications is astrocyte encoding of synaptic information transfer: the modulation of intracellular calcium dynamics in astrocytes in response to synaptic activity. Here, we derive and investigate a concise mathematical model for glutamate-induced astrocytic intracellular Ca2+ dynamics that captures the essential biochemical features of the regulatory pathway of inositol 1,4,5-trisphosphate (IP3). Starting from the well-known two-state Li-Rinzel model for calcium-induced-calcium release, we incorporate the regulation of the IP3 production and phosphorylation. Doing so we extended it to a three-state model (referred as the G-ChI model), that could account for Ca2+ oscillations triggered by endogenous IP3 metabolism as well as by IP3 production by external glutamate signals. Compared to previous similar models, our three-state models include a more realistic description of the IP3 production and degradation pathways, lumping together their essential nonlinearities within a concise formulation. Using bifurcation analysis and time simulations, we demonstrate the existence of new putative dynamical features. The cross-couplings between IP3 and Ca2+ pathways endows the system with self-consistent oscillator properties and favor mixed frequency-amplitude encoding modes over pure amplitude modulation ones. These and additional results of our model are in general agreement with available experimental data and may have important implications on the role of astrocytes in the synaptic transfer of information.Comment: 42 pages, 16 figures, 1 table. Figure filenames mirror figure order in the paper. Ending "S" in figure filenames stands for "Supplementary Figure". This article was selected by the Faculty of 1000 Biology: "Genevieve Dupont: Faculty of 1000 Biology, 4 Sep 2009" at http://www.f1000biology.com/article/id/1163674/evaluatio

Badly approximable points on manifolds

Addressing a problem of Davenport we show that any finite intersection of the sets of weighted badly approximable points on any analytic nondegenerate manifold in has full dimension. This also extends Schmidt's conjecture on badly approximable points to arbitrary dimensions