Classical Kloosterman sums: representation theory, magic squares, and Ramanujan multigraphs

We study the representation theory of a certain finite group for which Kloosterman sums appear as character values. This leads us to consider a concrete family of commuting hermitian matrices which have Kloosterman sums as eigenvalues. These matrices satisfy a number of "magical" combinatorial properties and they encode various arithmetic properties of Kloosterman sums. These matrices can also be regarded as adjacency matrices for multigraphs which display Ramanujan-like behavior.Comment: 20 page

Honors College_Honors 112 Class Screw this Virus _Essay

Essay by University of Maine student Patrick Fleming for HON 112, featuring COVID-19

Intuitions as Invitations

Recently, there has been a great deal of skepticism about appeals to intuitions in philosophy. Appeals to intuition often get expressed in the form of what ‘we’ believe. Many people take the ‘we’ in this context to refer to what the folk believe. So the claim about what we believe is an empirical claim. And it looks like the support for this claim comes from a biased sample consisting solely of analytic philosophers. In this paper I want to explain a different way appeals to intuition are used in the literature and why it survives such attacks. The basic idea, which comes from Bernard Williams, is that the \u27we\u27 used in many appeals to intuitions is not a referring expression at all. The appeal to intuition is not a claim about what any group of individuals believes. Rather it is an invitation to make a judgment. I argue that when you hear a philosopher say \u27P is what we intuitively believe\u27 the proper response is not \u27who is this \u27we\u27?’ The proper response is to wonder whether one ought to accept P

Hotspots and Coldspots: Household and village-level variation in orphanhood prevalence in rural Malawi

We explore the spatial distribution of orphans in two areas of Malawi. We first review pertinent themes in qualitative data collected in our research sites. Then, using spatial analysis, we show how positive and negative clusters of orphans—which we term orphanhood "hotspots" and "coldspots"—can be found at the village and sub-village levels. In the third and longest section of the paper, and using multilevel analyses with both simple and complex variance structures, we evaluate the relationship between the presence of orphans and a range of individual, household and village-level characteristics, including households' spatial relationship to each other and to other local sites of significance. This series of analyses shows that the most important covariates of orphan presence are the density of settlement, household size, and religious characteristics, with the latter measured simultaneously at both household and village-level. Other characteristics like education, reported mortality levels and HIV infection, are wholly unrelated to orphan prevalence at all analytic levels. Wealth and various spatial characteristics are only marginally associated with orphan prevalence. We conclude by reviewing some difficulties in explaining causal mechanisms underlying these observed relationships, and discussing conceptual, theoretical and programmatic implications.Africa, AIDS/HIV, Malawi, multilevel model, orphan prevalence, orphans, spatial analysis

William Fulford, “The Set,” and The Oxford and Cambridge Magazine

The Oxford and Cambridge Magazine is familiar to Victorian scholars largely because its contributors included William Morris and Edward Burne-Jones (the most famous members of the set that produced the magazine) and because Dante Gabriel Rossetti published several poems there. For the magazine’s first readers, however, its most important feature was not the identity of individual contributors but the fact that it was produced by college students. The magazine was a group project, produced not just by Morris and Burne-Jones but by their whole set. Morris’s and Burne-Jones’s contributions are well-known, and their biographies never fail to mention the magazine as a formative experience. But it could not have been produced were it not for the other members of the set, especially William Fulford, who edited all but the first issue. By focusing on the now-forgotten members of the set, this article reveals the context in which the Oxford and Cambridge Magazine was produced and the “thoughts and language current among the young men” who produced it

The biodegradation of tallow by Trichoderma harzianum rifai RP1

Wastewater, activated sludge and tallow were used as sources o f organisms in enrichment cultures to screen for species capable of degrading the hard fat, tallow. A total of 58 strains were isolated, o f which seven non-filamentous and two filamentous organisms removed greater than 20% of 20g/l tallow from batch cultures. Optimum fat removal of 83% by the strain F2, identified as the fungus Trichoderma harzianum Rifai RP1, was observed in cultures buffered to pH 6, incubated at 25°C, shaking at 130rpm using lg/1 tallow as the sole carbon source with no added surfactant, using an inoculum of one 5-day old 8mm mycelial agar plug. Growth followed Monod kinetics, with a ks of 0.758g/1 and pmax of 1.438 day’1. Glyceride hydrolysis was efficient, but free fatty acids, mainly palmitic, stearic and oleic acids, accumulated in the culture supernatant. Accumulation of intracellular lipid was observed, increasing during incubation to account for 35% - 55% o f biomass. Intracellular lipid was predominantly composed of triglycerides and free fatty acids. No fatty acid preference was evident in this accumulation. In cultures with a mixture o f palmitic, stearic and oleic acids as sole carbon source, up to 97% removal was observed with 0.12g/l of the fatty acid mixture. Oleic acid was assimilated by RP1 more readily than the two saturated fatty acids. Accumulated intracellular lipid accounted for varying proportions o f biomass, from 9% to 47%. Free fatty acids were the dominant lipid class intracellularly, with lower concentrations o f triglycerides. Stearic acid accumulated in the intracellular lipid to a greater extent than palmitic or oleic acids