Abstract:
Monstrous moonshine relates distinguished modular functions to the representation theory of the monster. The celebrated observations that 196884=1+196883 and 21493760=1+196883+21296876, etc., illustrate the case of the modular function j-744, whose coefficients turn out to be sums of the dimensions of the 194 irreducible representations of the monster. Such formulas are dictated by the structure of the graded monstrous moonshine modules. Recent works in moonshine suggest deep relations between number theory and physics. Number theoretic Kloosterman sums have reappeared in quantum gravity, and mock modular forms have emerged as candidates for the computation of black hole degeneracies. This paper is a survey of past and present research on moonshine. We also compute the quantum dimensions of the monster orbifold, and obtain exact formulas for the multiplicities of the irreducible components of the moonshine modules. These formulas imply that such multiplicities are asymptotically proportional to dimensions.

Abstract:
The two Rogers-Ramanujan $q$-series \[ \sum_{n=0}^{\infty}\frac{q^{n(n+\sigma)}}{(1-q)\cdots (1-q^n)}, \] where $\sigma=0,1$, play many roles in mathematics and physics. By the Rogers-Ramanujan identities, they are essentially modular functions. Their quotient, the Rogers-Ramanujan continued fraction, has the special property that its singular values are algebraic integral units. We find a framework which extends the Rogers-Ramanujan identities to doubly-infinite families of $q$-series identities. If $a\in\{1,2\}$ and $m,n\geq 1$, then we have \[ \sum_{\substack{\lambda \\ \lambda_1\leq m}} q^{a|\lambda|} P_{2\lambda}(1,q,q^2,\dots;q^n) =\textrm{"Infinite product modular function"}, \] where the $P_{\lambda}(x_1,x_2,\dots;q)$ are Hall-Littlewood polynomials. These $q$-series are specialized characters of affine Kac--Moody algebras. Generalizing the Rogers-Ramanujan continued fraction, we prove in the case of $\textrm{A}_{2n}^{(2)}$ that the relevant $q$-series quotients are integral units.

Abstract:
The Umbral Moonshine Conjectures assert that there are infinite-dimensional graded modules, for prescribed finite groups, whose McKay-Thompson series are certain distinguished mock modular forms. Gannon has proved this for the special case involving the largest sporadic simple Mathieu group. Here we establish the existence of the umbral moonshine modules in the remaining 22 cases.

Abstract:
The hypothesis-driven, single-gene analytic approach has dominated molecular neurobiology research and has been very successful. In grant submissions, the US National Institutes of Health demand succinctly defined, closed hypotheses based on expected outcomes. Where does this leave experiments utilizing high-density microarrays, which do not fit this mold? The fact that microarray investigators do not know which genes or pathways will be discovered by their experiments is precisely the strength of microarrays. The ability to examine the expression profile of potentially the entire genome at once, without preconceptions, offers the possibility of completely novel and unexpected insights into entities as complex as the nervous system. But before these insights can be made, the practical problems of experimental design, data analysis, verification, and interpretation need to be addressed.The full potential of microarrays will be realized only when the questions that are asked about a system are sophisticated, rather than seeking simple changes or differences in expression profiles. We need to avoid experiments that generate lists of genes, suitable only for archiving and future data screening. In addition, technical aspects of any experiment require attention; the speed of tissue removal to prevent RNA degradation, extraction of high quality RNA, optimal reverse transcription, amplification, labeling and hybridization with arrays and the use of quality control measures at each step are all critical. The suitability of different array formats also needs to be considered in terms of representation, variability, and sensitivity. Before considering data analysis and verification directly, we will discuss several of the microarray studies of neurobiological interest that have been completed to date. In particular, we focus on those aspects of model choice and experimental design that allow the conclusions of greatest biological importance to be drawn.Carefully designed micr

Abstract:
Theoretical arguments are used to identify the expected effects of a) heterogeneity in exposure to infectious bites; b) heterogeneity in individual's response to the vaccine; and c) waning efficacy on measures of vaccine efficacy from clinical trials for an infection-blocking vaccine.Heterogeneity in exposure and vaccine response leads to a smaller proportion of trial participants becoming infected than one would expect in a homogeneous setting. This causes estimates of vaccine efficacy from clinical trials to be underestimated if transmission heterogeneity is ignored, and overestimated if heterogeneity in vaccine response is ignored. Waning of vaccine efficacy can bias estimates of vaccine efficacy in both directions.Failure to account for heterogeneities in exposure and response, and waning of efficacy in clinical trials can lead to biased estimates of malaria vaccine efficacy. Appropriate methods to reduce these biases need to be used to ensure accurate interpretation and comparability between trial sites of results from the upcoming Phase III clinical trials of RTS, S.Malaria poses a major public health problem with unacceptably high levels of Plasmodium falciparum-associated morbidity and mortality recorded worldwide [1]. In recent years, dramatic declines in both parasite prevalence and disease incidence have been observed in a number of locations across Africa [2-4], likely attributable to the increased access to effective first-line therapy plus roll-out of interventions including long-lasting insecticide treated nets. Whilst these may be considered a success, an effective vaccine would be an important addition to the current suite of anti-malaria interventions. The most promising candidate malaria vaccine under development is RTS, S combined with GlaxoSmithKline's AS01 adjuvant.The principal component of RTS, S is the circumsporozoite antigen, which induces pre-erythrocytic antibodies that prevent sporozoites from infectious mosquito bites from leading to b

Abstract:
In his 1984 Ph.D. thesis, J. Greene defined an analogue of the Euler integral transform for finite field hypergeometric series. Here we consider a special family of matrices which arise naturally in the study of this transform and prove a conjecture of Ono about the decomposition of certain finite field hypergeometric functions into functions of lower dimension.

Abstract:
The pathways that comprise cellular metabolism are highly interconnected, and alterations in individual enzymes can have far-reaching effects. As a result, global profiling methods that measure gene expression are of limited value in predicting how the loss of an individual function will affect the cell. In this work, we employed a new method of global phenotypic profiling to directly define the genes required for the growth of Mycobacterium tuberculosis. A combination of high-density mutagenesis and deep-sequencing was used to characterize the composition of complex mutant libraries exposed to different conditions. This allowed the unambiguous identification of the genes that are essential for Mtb to grow in vitro, and proved to be a significant improvement over previous approaches. To further explore functions that are required for persistence in the host, we defined the pathways necessary for the utilization of cholesterol, a critical carbon source during infection. Few of the genes we identified had previously been implicated in this adaptation by transcriptional profiling, and only a fraction were encoded in the chromosomal region known to encode sterol catabolic functions. These genes comprise an unexpectedly large percentage of those previously shown to be required for bacterial growth in mouse tissue. Thus, this single nutritional change accounts for a significant fraction of the adaption to the host. This work provides the most comprehensive genetic characterization of a sterol catabolic pathway to date, suggests putative roles for uncharacterized virulence genes, and precisely maps genes encoding potential drug targets.

Abstract:
We demonstrate a 5 to 10 fold increase in accumulation levels of the "synaptic" splice variant of human acetylcholinesterase in Nicotiana benthamiana plants expressing the optimized gene as compared to the native human sequence. Both transient expression assays and stable transformants demonstrated conspicuously increased accumulation levels. Importantly, we find that the increase is not a result of increased levels of acetylcholinesterase mRNA, but rather its facilitated translation, possibly due to the reduced energy required to unfold the sequence-optimized mRNA.Our findings demonstrate that codon usage differences may regulate gene expression at different levels and anticipate translational control of acetylcholinesterase gene expression in its native mammalian host as well.Different organisms preferentially use a different subset of the synonymous codons specifying a certain amino acid. In fact, codon usage is emerging as an important regulatory factor, and codon usage bias can be detected not only between organisms [1], but also in the same organism between differentially expressed genes [2], in different tissues [3] and developmental stages [4]. A correlation was found in some cases, most notably among prokaryotes and in some metazoans (e.g. in dipterans and in nematodes), between the codon usage and the abundance of the cognate tRNAs, indicating that in these cases at least codon usage is probably governed by evolutionary selective forces [5-8]. However, "translational selection" may not be the only adaptive process shaping codon usage, which can be biased due to interactions not (directly) involving codon-anticodon interactions such as splice-site recognition [9] and mRNA turnover [10]. Particularly, while the available genome-scale analyses done for several plant species demonstrate that codon bias in plants is adaptive [11,12], heterologous gene expression studies in plants led to a tentative conclusion that translation efficiency of the foreign genes is

Abstract:
Type I interferons (IFN-α and β) induce dynamic host defense mechanisms to inhibit viral infections. It has been recently recognized that the interferon-inducible transmembrane proteins (IFITM) 1, 2 and 3 can block entry of a broad spectrum of RNA viruses. However, no study to date has focused on the role of IFITM proteins in DNA virus restriction. Here, we demonstrate that IFN-α or -β treatment of keratinocytes substantially decreases human papillomavirus 16 (HPV16) infection while robustly inducing IFITM1, 2 and 3 expression. However, IFITM1, 2 and 3 overexpression did not inhibit HPV16 infection; rather, IFITM1 and IFITM3 modestly enhanced HPV16 infection in various cell types including primary keratinocytes. Moreover, IFITM1, 2 and 3 did not inhibit infection by two other DNA viruses, human cytomegalovirus (HCMV) and adenovirus type 5 (Ad5). Taken together, we reveal that the entry of several DNA viruses, including HPV, HCMV, and Ad5 is not affected by IFITM1, 2 and 3 expression. These results imply that HPV, and other DNA viruses, may bypass IFITM restriction during intracellular trafficking.

Abstract:
Mass treatment as a means to reducing P. falciparum malaria transmission was used during the first global malaria eradication campaign and is increasingly being considered for current control programmes. We used a previously developed mathematical transmission model to explore both the short and long-term impact of possible mass treatment strategies in different scenarios of endemic transmission. Mass treatment is predicted to provide a longer-term benefit in areas with lower malaria transmission, with reduced transmission levels for at least 2 years after mass treatment is ended in a scenario where the baseline slide-prevalence is 5%, compared to less than one year in a scenario with baseline slide-prevalence at 50%. However, repeated annual mass treatment at 80% coverage could achieve around 25% reduction in infectious bites in moderate-to-high transmission settings if sustained. Using vector control could reduce transmission to levels at which mass treatment has a longer-term impact. In a limited number of settings (which have isolated transmission in small populations of 1000–10,000 with low-to-medium levels of baseline transmission) we find that five closely spaced rounds of mass treatment combined with vector control could make at least temporary elimination a feasible goal. We also estimate the effects of using gametocytocidal treatments such as primaquine and of restricting treatment to parasite-positive individuals. In conclusion, mass treatment needs to be repeated or combined with other interventions for long-term impact in many endemic settings. The benefits of mass treatment need to be carefully weighed against the risks of increasing drug selection pressure.