Small representations of finite classical groups

Finite group theorists have established many formulas that express interesting properties of a finite group in terms of sums of characters of the group. An obstacle to applying these formulas is lack of control over the dimensions of representations of the group. In particular, the representations of small dimensions tend to contribute the largest terms to these sums, so a systematic knowledge of these small representations could lead to proofs of important conjectures which are currently out of reach. Despite the classification by Lusztig of the irreducible representations of finite groups of Lie type, it seems that this aspect remains obscure. In this note we develop a language which seems to be adequate for the description of the "small" representations of finite classical groups and puts in the forefront the notion of rank of a representation. We describe a method, the "eta correspondence", to construct small representations, and we conjecture that our construction is exhaustive. We also give a strong estimate on the dimension of small representations in terms of their rank. For the sake of clarity, in this note we describe in detail only the case of the finite symplectic groups.Comment: 18 pages, 9 figures, accepted for publications in the proceedings of the conference on the occasion of Roger Howe's 70th birthday (1-5 June 2015, Yale University, New Haven, CT

Pattern Comparator Trigger (PACT) for the muon system of the CMS experiment

The general scheme for the fast, pipelined first level trigger on high pt muons in the CMS detector at LHC is presented. The prototype PACT system was tested in the high momentum muon beams in the RD5 experiment during 1993/94 runs. The obtained efficiency curves are shown

Is Thermosensing Property of RNA Thermometers Unique?

A large number of studies have been dedicated to identify the structural and sequence based features of RNA thermometers, mRNAs that regulate their translation initiation rate with temperature. It has been shown that the melting of the ribosome-binding site (RBS) plays a prominent role in this thermosensing process. However, little is known as to how widespread this melting phenomenon is as earlier studies on the subject have worked with a small sample of known RNA thermometers. We have developed a novel method of studying the melting of RNAs with temperature by computationally sampling the distribution of the RNA structures at various temperatures using the RNA folding software Vienna. In this study, we compared the thermosensing property of 100 randomly selected mRNAs and three well known thermometers - rpoH, ibpA and agsA sequences from E. coli. We also compared the rpoH sequences from 81 mesophilic proteobacteria. Although both rpoH and ibpA show a higher rate of melting at their RBS compared with the mean of non-thermometers, contrary to our expectations these higher rates are not significant. Surprisingly, we also do not find any significant differences between rpoH thermometers from other -proteobacteria and E. coli non-thermometers

Eisenstein series for infinite-dimensional U-duality groups

We consider Eisenstein series appearing as coefficients of curvature corrections in the low-energy expansion of type II string theory four-graviton scattering amplitudes. We define these Eisenstein series over all groups in the E_n series of string duality groups, and in particular for the infinite-dimensional Kac-Moody groups E9, E10 and E11. We show that, remarkably, the so-called constant term of Kac-Moody-Eisenstein series contains only a finite number of terms for particular choices of a parameter appearing in the definition of the series. This resonates with the idea that the constant term of the Eisenstein series encodes perturbative string corrections in BPS-protected sectors allowing only a finite number of corrections. We underpin our findings with an extensive discussion of physical degeneration limits in D<3 space-time dimensions.Comment: 69 pages. v2: Added references and small additions, to be published in JHE

Analysis and Prediction of Translation Rate Based on Sequence and Functional Features of the mRNA

Protein concentrations depend not only on the mRNA level, but also on the translation rate and the degradation rate. Prediction of mRNA's translation rate would provide valuable information for in-depth understanding of the translation mechanism and dynamic proteome. In this study, we developed a new computational model to predict the translation rate, featured by (1) integrating various sequence-derived and functional features, (2) applying the maximum relevance & minimum redundancy method and incremental feature selection to select features to optimize the prediction model, and (3) being able to predict the translation rate of RNA into high or low translation rate category. The prediction accuracies under rich and starvation condition were 68.8% and 70.0%, respectively, evaluated by jackknife cross-validation. It was found that the following features were correlated with translation rate: codon usage frequency, some gene ontology enrichment scores, number of RNA binding proteins known to bind its mRNA product, coding sequence length, protein abundance and 5′UTR free energy. These findings might provide useful information for understanding the mechanisms of translation and dynamic proteome. Our translation rate prediction model might become a high throughput tool for annotating the translation rate of mRNAs in large-scale

A Genome-Wide Analysis of Promoter-Mediated Phenotypic Noise in Escherichia coli

Gene expression is subject to random perturbations that lead to fluctuations in the rate of protein production. As a consequence, for any given protein, genetically identical organisms living in a constant environment will contain different amounts of that particular protein, resulting in different phenotypes. This phenomenon is known as “phenotypic noise.” In bacterial systems, previous studies have shown that, for specific genes, both transcriptional and translational processes affect phenotypic noise. Here, we focus on how the promoter regions of genes affect noise and ask whether levels of promoter-mediated noise are correlated with genes' functional attributes, using data for over 60% of all promoters in Escherichia coli. We find that essential genes and genes with a high degree of evolutionary conservation have promoters that confer low levels of noise. We also find that the level of noise cannot be attributed to the evolutionary time that different genes have spent in the genome of E. coli. In contrast to previous results in eukaryotes, we find no association between promoter-mediated noise and gene expression plasticity. These results are consistent with the hypothesis that, in bacteria, natural selection can act to reduce gene expression noise and that some of this noise is controlled through the sequence of the promoter region alon

A Genetic Strategy for Stochastic Gene Activation with Regulated Sparseness (STARS)

It remains a challenge to establish a straightforward genetic approach for controlling the probability of gene activation or knockout at a desired level. Here, we developed a method termed STARS: stochastic gene activation with genetically regulated sparseness. The stochastic expression was achieved by two cross-linked, mutually-exclusive Cre-mediated recombinations. The stochastic level was further controlled by regulating Cre/lox reaction kinetics through varying the intrachromosomal distance between the lox sites mediating one of the recombinations. In mammalian cell lines stably transfected with a single copy of different STARS transgenes, the activation/knockout of reporter genes was specifically controlled to occur in from 5% to 50% of the cell population. STARS can potentially provide a convenient way for genetic labeling as well as gene expression/knockout in a population of cells with a desired sparseness level

Gravitational Waves From Known Pulsars: Results From The Initial Detector Era

We present the results of searches for gravitational waves from a large selection of pulsars using data from the most recent science runs (S6, VSR2 and VSR4) of the initial generation of interferometric gravitational wave detectors LIGO (Laser Interferometric Gravitational-wave Observatory) and Virgo. We do not see evidence for gravitational wave emission from any of the targeted sources but produce upper limits on the emission amplitude. We highlight the results from seven young pulsars with large spin-down luminosities. We reach within a factor of five of the canonical spin-down limit for all seven of these, whilst for the Crab and Vela pulsars we further surpass their spin-down limits. We present new or updated limits for 172 other pulsars (including both young and millisecond pulsars). Now that the detectors are undergoing major upgrades, and, for completeness, we bring together all of the most up-to-date results from all pulsars searched for during the operations of the first-generation LIGO, Virgo and GEO600 detectors. This gives a total of 195 pulsars including the most recent results described in this paper.United States National Science FoundationScience and Technology Facilities Council of the United KingdomMax-Planck-SocietyState of Niedersachsen/GermanyAustralian Research CouncilInternational Science Linkages program of the Commonwealth of AustraliaCouncil of Scientific and Industrial Research of IndiaIstituto Nazionale di Fisica Nucleare of ItalySpanish Ministerio de Economia y CompetitividadConselleria d'Economia Hisenda i Innovacio of the Govern de les Illes BalearsNetherlands Organisation for Scientific ResearchPolish Ministry of Science and Higher EducationFOCUS Programme of Foundation for Polish ScienceRoyal SocietyScottish Funding CouncilScottish Universities Physics AllianceNational Aeronautics and Space AdministrationOTKA of HungaryLyon Institute of Origins (LIO)National Research Foundation of KoreaIndustry CanadaProvince of Ontario through the Ministry of Economic Development and InnovationNational Science and Engineering Research Council CanadaCarnegie TrustLeverhulme TrustDavid and Lucile Packard FoundationResearch CorporationAlfred P. Sloan FoundationAstronom