Same-sign trileptons as a signal of sneutrino lightest supersymmetric partlcle

Contrary to common expectation, a left-sneutrinos can occasionally be the lightest supersymmet- ric particle. This has important implications in both collider and dark matter studies. We show that same-sign tri-lepton (SS3L) events at the Large Hadron Collider, with any lepton having opposite sign vetoed, distinguish such scenarios, up to gluino masses exceeding 2 TeV. The jets + M ET signal rate is somewhat suppressed in this case, thus enhancing the scope of leptonic signals.Comment: Version published in Phys.Lett.

Generalized Dantzig Selector: Application to the k-support norm

We propose a Generalized Dantzig Selector (GDS) for linear models, in which any norm encoding the parameter structure can be leveraged for estimation. We investigate both computational and statistical aspects of the GDS. Based on conjugate proximal operator, a flexible inexact ADMM framework is designed for solving GDS, and non-asymptotic high-probability bounds are established on the estimation error, which rely on Gaussian width of unit norm ball and suitable set encompassing estimation error. Further, we consider a non-trivial example of the GDS using $k$-support norm. We derive an efficient method to compute the proximal operator for $k$-support norm since existing methods are inapplicable in this setting. For statistical analysis, we provide upper bounds for the Gaussian widths needed in the GDS analysis, yielding the first statistical recovery guarantee for estimation with the $k$-support norm. The experimental results confirm our theoretical analysis.Comment: Updates to boun

Applications of asymptotic expansions to some statistical problems

The dissertation is composed of four research papers. In all the papers asymptotic methods and techniques are the main tools used to reach conclusions. [1] A Berry-Esseen theorem for Hypergeometric probabilities under minimal conditions. [2] Normal Approximation to the Hypergeometric distribution in nonstandard cases and a sub-Gaussian Berry-Esseen Theorem. [3] Asymptotic properties of sample quantiles from a finite population. [4] Edgeworth expansions for Spectral density estimates.;The papers [1]-[3] consider the problem of quantile estimation in a finite population setup and related asymptotic results regarding Normal approximation to Hypergeometric random variables. The asymptotic properties of the sample quantile are derived under a superpopulation model. It is shown that the sample quantile is asymptotically normal and the scaled sample variance of the sample quantile converges to the asymptotic variance under a slight moment condition. The performance of the bootstrap is also investigated. We show that the usual bootstrap suggested by Gross (1980) fails in this case. A suitably modified version of the bootstrapped sample quantile converges in distribution to the same asymptotic normal distribution as the sample quantile. Consistency of the modified bootstrap variance estimate is proved under the same moment conditions.;The paper [4] considers the problem of Edgeworth expansion of spectral density estimators of a stationary time series. The spectral density estimate at each frequency is based on tapered periodograms of overlapping blocks of observations. We give conditions for the validity of a general order Edgeworth expansion under an approximate strong mixing condition on the random variables, and also establish a moderate deviation inequality. We also verify the conditions explicitly for linear time series, which are satisfied under mild and easy-to-check conditions on the innovation variables and on their nonrandom co-efficients. The work makes use of the results of Lahiri (2007) where general order Edgeworth expansions for functions of blocks of weakly dependent random variables are derived. In our work we relax the assumption of Gaussianity, which was used by Velasco and Robinson (2001) to obtain similar Edgeworth expansions

Molecular modeling and SAR studies of CDK5/p25 selective inhibitors

Alzheimer\u27s disease (AD) is one of the most dreaded forms of progressive neurodegenerative diseases. The two main hallmarks of AD are the formation of amyloid senile plaques and neurofibrillary tangles. Cyclin dependent kinase 5 (CDK5) is a proline directed serine/threonine kinase, which expressed primarily in the central nervous system. In the biochemical process the CDK5-natural activator, p35 is cleaved by calpain to a shorter protein p25, which in turn hyperphosphorylates Tau, forms neurofibrillary tangles and causes AD. CDK5 deregulation is also indicated in other neurodegenerative diseases, such as Huntington\u27s chorea, stroke, Parkinson\u27s disease, amyotrophic lateral sclerosis, major depression and substance abuse. We chose to design CDK5/p25 inhibitors as a target against neurodegeneration leading to Alzheimer\u27s disease. One of our major goals was to design CDK5/p25 inhibitors selective over CDK2. Since we were targeting neurodegeneration we wanted to avoid any undesired cell cycle mediated apoptotic effects of CDK2 inhibition. The task was very challenging, because the two kinases possessed very high levels of sequence homology. In our approach we decided to achieve selectivity through structure based virtual screening strategy, validate the hits through biological screening and explore structure activity relationship (SAR) modifications around the lead structure. To identify de-novo templates, we decided to use the structure based E-pharmacophore models coupled with docking based virtual screening workflow to screen a commercially available database containing 2.84 million compounds. The biological screening was performed using radiometric filter binding assays with full length hCDK5/p25 and hCDK2/E kinases. An ATP non-competitive and selective inhibitor with ligand efficiency of 0.3 was identified as the lead molecule. We developed an efficient six-step synthesis of a key intermediate starting from aniline utilizing a sequence of Friedel-Crafts, Vilsmeier-Haack, nucleophilic aromatic substitution and cyclization reactions. We also developed an easy derivatization approach utilizing convergent analog synthesis to study SAR around the lead structure. Further SAR optimization led to the discovery of several low micromolar ATP non-competitive CDK5/p25 inhibitors with much greater CDK2/E selectivity. This new series of compounds can be further evaluated in in-vitro and in-vivo AD models to develop future drug candidates