On Tightness of the Tsaknakis-Spirakis Algorithm for Approximate Nash Equilibrium

Finding the minimum approximate ratio for Nash equilibrium of bi-matrix games has derived a series of studies, started with 3/4, followed by 1/2, 0.38 and 0.36, finally the best approximate ratio of 0.3393 by Tsaknakis and Spirakis (TS algorithm for short). Efforts to improve the results remain not successful in the past 14 years. This work makes the first progress to show that the bound of 0.3393 is indeed tight for the TS algorithm. Next, we characterize all possible tight game instances for the TS algorithm. It allows us to conduct extensive experiments to study the nature of the TS algorithm and to compare it with other algorithms. We find that this lower bound is not smoothed for the TS algorithm in that any perturbation on the initial point may deviate away from this tight bound approximate solution. Other approximate algorithms such as Fictitious Play and Regret Matching also find better approximate solutions. However, the new distributed algorithm for approximate Nash equilibrium by Czumaj et al. performs consistently at the same bound of 0.3393. This proves our lower bound instances generated against the TS algorithm can serve as a benchmark in design and analysis of approximate Nash equilibrium algorithms

B-meson dileptonic decays enhanced by supersymmetry with large tan⁡β\tan\beta

We examined the rare decays $B\to X_s\ell^+\ell^-$ and $B_s\to\ell^+\ell^-\gamma$ in the minimal supersymmetric model with large $\tan\beta$. Taking into account the gluino-loop and neutralino-loop effects, we found that for a large $\tan\beta$ the neutral Higgs exchanging diagrams could enhance $Br(B\to X_s\tau^+\tau^-)$ by a factor of 5 and $Br(B_s\to\tau^+\tau^-\gamma)$ by a couple of orders in some part of supersymmetric parameter space allowed by current experiments such as $b\to s\gamma, B\to K^{(*)}\ell^+\ell^-$ and $B_s\to\ell^+\ell^-$. The forward-backward asymmetry and the distributions of differential branching ratios are also found to differ significantly from the standard model results. Such enhanced branching ratios reach the level of $10^{-5}$ and thus might be observable in the new generation of B experiments.Comment: 17 pages,9 figures, a detail contribution and reference adde

FVGWAS: Fast voxelwise genome wide association analysis of large-scale imaging genetic data

More and more large-scale imaging genetic studies are being widely conducted to collect a rich set of imaging, genetic, and clinical data to detect putative genes for complexly inherited neuropsychiatric and neurodegenerative disorders. Several major big-data challenges arise from testing genome-wide (NC > 12 million known variants) associations with signals at millions of locations (NV ~ 106) in the brain from thousands of subjects (n ~ 103). The aim of this paper is to develop a Fast Voxelwise Genome Wide Association analysiS (FVGWAS) framework to e ciently carry out whole-genome analyses of whole-brain data. FVGWAS consists of three components including a heteroscedastic linear model, a global sure independence screening (G-SIS) procedure, and a detection procedure based on wild bootstrap methods. Specifically, for standard linear association, the computational complexity is O(nNV NC) for voxelwise genome wide association analysis (VGWAS) method compared with O((NC + NV)n2) for FVGWAS. Simulation studies show that FVGWAS is an effcient method of searching sparse signals in an extremely large search space, while controlling for the family-wise error rate. Finally, we have successfully applied FVGWAS to a large-scale imaging genetic data analysis of ADNI data with 708 subjects, 193,275 voxels in RAVENS maps, and 501,584 SNPs, and the total processing time was 203,645 seconds for a single CPU. Our FVG-WAS may be a valuable statistical toolbox for large-scale imaging genetic analysis as the field is rapidly advancing with ultra-high-resolution imaging and whole-genome sequencing

Muon anomalous magnetic moment in technicolor models

Contributions to the muon anomalous magnetic moment are evaluated in the technicolor model with scalars and topcolor assisted technicolor model. In the technicolor model with scalars, the additional contributions come from the loops of scalars, which were found sizable only for a very large $f/f^{'}$ disfavored by the experiment of $b\to s\gamma$. The topcolor effect is also found to be large only for an unnaturally large $\tan\theta'$, and thus the previously evaluated loop effects of extended technicolor bosons, suppressed by $m_{\mu}^2/M_{ETC}^2$, must be resorted to account for the E821 experiment. So, if the E821 experiment result persists, it would be a challenge to technicolor models.Comment: refs and comments adde

SUSY-Induced Top Quark FCNC Processes at Linear Colliders

In the Minimal Supersymmetric Model (MSSM) the hitherto unconstrained flavor mixing between top-squark and charm-squark will induce the flavor-changing neutral-current (FCNC) interaction between top quark and charm quark, which then give rise to various processes at the next generation linear collider (NLC), i.e., the top-charm associated productions via $e^+ e^-$, $e^- \gamma$ and $\gamma \gamma$ collisions as well as the top quark rare decays $t \to c V$ ($V=g$, $\gamma$ or $Z$). All these processes involve the same part of the parameter space of the MSSM. Through a comparative analysis for all these processes at the NLC, we found the best channel to probe such SUSY-induced top quark FCNC is the top-charm associated production in $\gamma \gamma$ collision, which occurs at a much higher rate than $e^+ e^-$ or $e^- \gamma$ collision and may reach the detectable level for some part of the parameter space. Since the rates predicted by the Standard Model are far below the detectable level, the observation of such FCNC events would be a robust indirect evidence of SUSY.Comment: 12 pages, 8 figures (more refs added, discussions extended

Global Analysis of UDP Glucose Pyrophosphorylase (UDPGP) Gene Family in Plants: Conserved Evolution Involved in Cell Death

UDP glucose pyrophosphorylase (UDPGP) family genes have been reported to play essential roles in cell death or individual survival. However, a systematic analysis on UDPGP gene family has not been performed yet. In this study, a total of 454 UDPGP proteins from 76 different species were analyzed. The analyses of the phylogenetic tree and orthogroups divided UDPGPs into three clades, including UDP-N-acetylglucosamine pyrophosphorylase (UAP), UDP-glucose pyrophosphorylase (UGP, containing UGP-A and UGP-B), and UDP-sugar pyrophosphorylase (USP). The evolutionary history of the UDPGPs indicated that the members of UAP, USP, and UGP-B were relatively conserved while varied in UGP-A. Homologous sequences of UGP-B and USP were found only in plants. The expression profile of UDPGP genes in Oryza sativa was mainly motivated under jasmonic acid (JA), abscisic acid (ABA), cadmium, and cold treatments, indicating that UDPGPs may play an important role in plant development and environment endurance. The key amino acids regulating the activity of UDPGPs were analyzed, and almost all of them were located in the NB-loop, SB-loop, or conserved motifs. Analysis of the natural variants of UDPGPs in rice revealed that only a few missense mutants existed in coding sequences (CDSs), and most of the resulting variations were located in the non-motif sites, indicating the conserved structure and function of UDPGPs in the evolution. Furthermore, alternative splicing may play a key role in regulating the activity of UDPGPs. The spatial structure prediction, enzymatic analysis, and transgenic verification of UAP isoforms illustrated that the loss of N- and C-terminal sequences did not affect the overall 3D structures, but the N- and C-terminal sequences are important for UAP genes to maintain their enzymatic activity. These results revealed a conserved UDPGP gene family and provided valuable information for further deep functional investigation of the UDPGP gene family in plants