Non-vanishing of Artin-twisted L-functions of Elliptic Curves

Let E be an elliptic curve and \rho an Artin representation, both defined over the rational numbers. Let p be a prime at which E has good reduction. We prove that there exists an infinite set of Dirichlet characters \chi, ramified only at p, such that the Artin-twisted L-values L(E,\rho \chi,\beta) are non-zero when \beta lies in a specified region in the critical strip (assuming the conjectural continuations and functional equations for these L-functions). The new contribution of our paper is that we may choose our characters to be ramified only at one prime, which may divide the conductor of \rho.Comment: 11 page

The evolution of a visual-to-auditory sensory substitution device using interactive genetic algorithms

Sensory Substitution is a promising technique for mitigating the loss of a sensory modality. Sensory Substitution Devices (SSDs) work by converting information from the impaired sense (e.g. vision) into another, intact sense (e.g. audition). However, there are a potentially infinite number of ways of converting images into sounds and it is important that the conversion takes into account the limits of human perception and other user-related factors (e.g. whether the sounds are pleasant to listen to). The device explored here is termed “polyglot” because it generates a very large set of solutions. Specifically, we adapt a procedure that has been in widespread use in the design of technology but has rarely been used as a tool to explore perception – namely Interactive Genetic Algorithms. In this procedure, a very large range of potential sensory substitution devices can be explored by creating a set of ‘genes’ with different allelic variants (e.g. different ways of translating luminance into loudness). The most successful devices are then ‘bred’ together and we statistically explore the characteristics of the selected-for traits after multiple generations. The aim of the present study is to produce design guidelines for a better SSD. In three experiments we vary the way that the fitness of the device is computed: by asking the user to rate the auditory aesthetics of different devices (Experiment 1), by measuring the ability of participants to match sounds to images (Experiment 2) and the ability to perceptually discriminate between two sounds derived from similar images (Experiment 3). In each case the traits selected for by the genetic algorithm represent the ideal SSD for that task. Taken together, these traits can guide the design of a better SSD

Comment: ‘Knock, Knock: Where is the Evidence for Dangerous Human-Caused Global Warming?’ by Robert M. Carter

Carter (2008) notes that for climate change “sound science [sic] understanding is an essential prerequisite to any meaningful economic analysis”. Unfortunately his paper contains serious and systematic errors and misrepresentations about the causes and potential consequences of climate change, the overall effect of which is to convey an inaccurate and misleading impression of the scientific evidence. Indeed, the overall tone of Carter (2008) is one of a polemic rather than an objective analysis of the facts. An itemisation of all the inaccuracies in Carter (2008) would require a great deal of space, so this paper identifies and corrects some of the most important errors.global warming, human-caused global warming, climate change, economics of climate change, rationalist views on climate change, sceptical views on climate change

Preparing Information Literate Teachers: A Review of the Literature

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Periodic points for good reduction maps on curves

The periodic points of a morphism of good reduction for a smooth projective curve with good reduction over the p-adics form a discrete set. This is used to give an interpretation of the morphic height in terms of asymptotic properties of periodic points, and a morphic analogue of Jensen's formula