Infinitely Many Carmichael Numbers in Arithmetic Progressions

In this paper, we prove that for any $a,M\in \mathbb N$ with $(a,M)=1$, there are infinitely many Carmichael numbers $m$ such that $m\equiv a$ mod $M$Comment: To appear in the Bulletin of the London Mathematical Societ

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

Large-scale computation of pseudospectra using ARPACK and eigs

ARPACK and its MATLAB counterpart, eigs, are software packages that calculate some eigenvalues of a large non-symmetric matrix by Arnoldi iteration with implicit restarts. We show that at a small additional cost, which diminishes relatively as the matrix dimension increases, good estimates of pseudospectra in addition to eigenvalues can be obtained as a by-product. Thus in large-scale eigenvalue calculations it is feasible to obtain routinely not just eigenvalue approximations, but also information as to whether or not the eigenvalues are likely to be physically significant. Examples are presented for matrices with dimension up to 200,000

Chiral Corrections to Baryon Masses Calculated within Lattice QCD

Consideration of the analytic properties of pion-induced baryon self energies leads to new functional forms for the extrapolation of light baryon masses. These functional forms reproduce the leading non-analytic behavior of chiral perturbation theory, the correct non-analytic behavior at the $N \pi$ threshold and the appropriate heavy-quark limit. They involve only three unknown parameters, which may be obtained by fitting lattice QCD data. Recent dynamical fermion results from CP-PACS and UKQCD are extrapolated using these new functional forms. We also use these functions to probe the limit of applicability of chiral perturbation theory.Comment: 4 pages, 2 figures, Contribution to the Proceedings of the 15th Particles and Nuclei International Conference (PANIC 99), Uppsala, Sweden, June 10-16, 199

The Ohio Grain Marketing Legislation of 1982 and 1983

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