A Panorama Of Physical Mathematics c. 2022

What follows is a broad-brush overview of the recent synergistic interactions between mathematics and theoretical physics of quantum field theory and string theory. The discussion is forward-looking, suggesting potentially useful and fruitful directions and problems, some old, some new, for further development of the subject. This paper is a much extended version of the Snowmass whitepaper on physical mathematics [1]

Goodness-of-Fit Tests and Model Diagnostics for Negative Binomial Regression of RNA Sequencing Data

This work is about assessing model adequacy for negative binomial (NB) regression, particularly (1) assessing the adequacy of the NB assumption, and (2) assessing the appropriateness of models for NB dispersion parameters. Tools for the first are appropriate for NB regression generally; those for the second are primarily intended for RNA sequencing (RNA-Seq) data analysis. The typically small number of biological samples and large number of genes in RNA-Seq analysis motivate us to address the trade-offs between robustness and statistical power using NB regression models. One widely-used power-saving strategy, for example, is to assume some commonalities of NB dispersion parameters across genes via simple models relating them to mean expression rates, and many such models have been proposed. As RNA-Seq analysis is becoming ever more popular, it is appropriate to make more thorough investigations into power and robustness of the resulting methods, and into practical tools for model assessment. In this article, we propose simulation-based statistical tests and diagnostic graphics to address model adequacy. We provide simulated and real data examples to illustrate that our proposed methods are effective for detecting the misspecification of the NB mean-variance relationship as well as judging the adequacy of fit of several NB dispersion models

Higher order asymptotics for negative binomial regression inferences from RNA-sequencing data

RNA sequencing (RNA-Seq) is the current method of choice for characterizing transcriptomes and quantifying gene expression changes. This next generation sequencing-based method provides unprecedented depth and resolution. The negative binomial (NB) probability distribution has been shown to be a useful model for frequencies of mapped RNA-Seq reads and consequently provides a basis for statistical analysis of gene expression. Negative binomial exact tests are available for two-group comparisons but do not extend to negative binomial regression analysis, which is important for examining gene expression as a function of explanatory variables and for adjusted group comparisons accounting for other factors. We address the adequacy of available large-sample tests for the small sample sizes typically available from RNA-Seq studies and consider a higher-order asymptotic (HOA) adjustment to likelihood ratio tests. We demonstrate that 1) the HOA-adjusted likelihood ratio test is practically indistinguishable from the exact test in situations where the exact test is available, 2) the type I error of the HOA test matches the nominal specification in regression settings we examined via simulation, and 3) the power of the likelihood ratio test does not appear to be affected by the HOA adjustment. This work helps clarify the accuracy of the unadjusted likelihood ratio test and the degree of improvement available with the HOA adjustment. Furthermore, the HOA test may be preferable even when the exact test is available because it does not require ad hoc library size adjustments.Keywords: Regression, RNA-Seq, Overdispersion, Extra- Poisson variation, Negative binomial, Higher-order asymptotic

Preliminary safety assessment of a membrane-bound delta 9 desaturase candidate protein for transgenic oilseed crops

AbstractA gene encoding delta 9 desaturase (D9DS), an integral membrane protein, is being considered for incorporation into oilseed crops to reduce saturated fatty acids and thus improve human nutritional value. Typically, a safety assessment for transgenic crops involves purifying heterologously produced transgenic proteins in an active form for use in safety studies. Membrane-bound proteins have been very difficult to isolate in an active form due to their inherent physicochemical properties. Described here are methods used to derive enriched preparations of the active D9DS protein for use in early stage safety studies. Results of these studies, in combination with bioinformatic results and knowledge of the mode of action of the protein, along with a history of safe consumption of related proteins, provides a weight of evidence supporting the safety of the D9DS protein in food and feed

Geometric Configurations, Regular Subalgebras of E10 and M-Theory Cosmology

We re-examine previously found cosmological solutions to eleven-dimensional supergravity in the light of the E_{10}-approach to M-theory. We focus on the solutions with non zero electric field determined by geometric configurations (n_m, g_3), n\leq 10. We show that these solutions are associated with rank $g$ regular subalgebras of E_{10}, the Dynkin diagrams of which are the (line) incidence diagrams of the geometric configurations. Our analysis provides as a byproduct an interesting class of rank-10 Coxeter subgroups of the Weyl group of E_{10}.Comment: 48 pages, 27 figures, 5 tables, references added, typos correcte

Charged, conformal non-relativistic hydrodynamics

We embed a holographic model of an U(1) charged fluid with Galilean invariance in string theory and calculate its specific heat capacity and Prandtl number. Such theories are generated by a R-symmetry twist along a null direction of a N=1 superconformal theory. We study the hydrodynamic properties of such systems employing ideas from the fluid-gravity correspondence.Comment: 31 pages, 1 figure, JHEP3 style, refs added, typos corrected, missing terms in spatial charge current and field corrections added, to be published in JHE

Genomic and expression analysis of multiple Sry loci from a single Rattus norvegicus Y chromosome

BACKGROUND: Sry is a gene known to be essential for testis determination but is also transcribed in adult male tissues. The laboratory rat, Rattus norvegicus, has multiple Y chromosome copies of Sry while most mammals have only a single copy. DNA sequence comparisons with other rodents with multiple Sry copies are inconsistent in divergence patterns and functionality of the multiple copies. To address hypotheses of divergence, gene conversion and functional constraints, we sequenced Sry loci from a single R. norvegicus Y chromosome from the Spontaneously Hypertensive Rat strain (SHR) and analyzed DNA sequences for homology among copies. Next, to determine whether all copies of Sry are expressed, we developed a modification of the fluorescent marked capillary electrophoresis method to generate three different sized amplification products to identify Sry copies. We applied this fragment analysis method to both genomic DNA and cDNA prepared from mRNA from testis and adrenal gland of adult male rats. RESULTS: Y chromosome fragments were amplified and sequenced using primers that included the entire Sry coding region and flanking sequences. The analysis of these sequences identified six Sry loci on the Y chromosome. These are paralogous copies consistent with a single phylogeny and the divergence between any two copies is less than 2%. All copies have a conserved reading frame and amino acid sequence consistent with function. Fragment analysis of genomic DNA showed close approximations of experimental with predicted values, validating the use of this method to identify proportions of each copy. Using the fragment analysis procedure with cDNA samples showed the Sry copies expressed were significantly different from the genomic distribution (testis p < 0.001, adrenal gland p < 0.001), and the testis and adrenal copy distribution in the transcripts were also significantly different from each other (p < 0.001). Total Sry transcript expression, analyzed by real-time PCR, showed significantly higher levels of Sry in testis than adrenal gland (p, 0.001). CONCLUSION: The SHR Y chromosome contains at least 6 full length copies of the Sry gene. These copies have a conserved coding region and conserved amino acid sequence. The pattern of divergence is not consistent with gene conversion as the mechanism for this conservation. Expression studies show multiple copies expressed in the adult male testis and adrenal glands, with tissue specific differences in expression patterns. Both the DNA sequence analysis and RNA transcript expression analysis are consistent with more than one copy having function and selection preventing divergence although we have no functional evidence

Search for Branons at LEP

We search, in the context of extra-dimension scenarios, for the possible existence of brane fluctuations, called branons. Events with a single photon or a single Z-boson and missing energy and momentum collected with the L3 detector in e^+ e^- collisions at centre-of-mass energies sqrt{s}=189-209$ GeV are analysed. No excess over the Standard Model expectations is found and a lower limit at 95% confidence level of 103 GeV is derived for the mass of branons, for a scenario with small brane tensions. Alternatively, under the assumption of a light branon, brane tensions below 180 GeV are excluded

Measurement of Exclusive rho^0 rho^0 Production in Two-Photon Collisions at High Q^2 at LEP

Exclusive rho rho production in two-photon collisions involving a single highly virtual photon is studied with data collected at LEP at centre-of-mass energies 89GeV < \sqrt{s} < 209GeV with a total integrated luminosity of 854.7pb^-1 The cross section of the process gamma gamma^* -> rho rho is determined as a function of the photon virtuality, Q^2 and the two-photon centre-of-mass energy, Wgg, in the kinematic region: 1.2GeV^2 < Q^2 < 30GeV^2 and 1.1GeV < Wgg < 3GeV

Search for a Higgs Boson Decaying into Two Photons at LEP

A Higgs particle produced in association with a Z boson and decaying into two photons is searched for in the data collected by the L3 experiment at LEP. All possible decay modes of the Z boson are investigated. No signal is observed in 447.5 pb^-1 of data recorded at centre-of-mass energies up to 209 GeV. Limits on the branching fraction of the Higgs boson decay into two photons as a function of the Higgs mass are derived. A lower limit on the mass of a fermiophobic Higgs boson is set at 105.4 GeV at 95% confidence level