Generalized Farey trees, transfer Operators and phase transitions

We consider a family of Markov maps on the unit interval, interpolating between the tent map and the Farey map. The latter map is not uniformly expanding. Each map being composed of two fractional linear transformations, the family generalizes many particular properties which for the case of the Farey map have been successfully exploited in number theory. We analyze the dynamics through the spectral analysis of generalized transfer operators. Application of the thermodynamic formalism to the family reveals first and second order phase transitions and unusual properties like positivity of the interaction function.Comment: 39 pages, 10 figure

The George Eliot Fellowship- 19

When I wrote the last newsletter we had not then had Gabriel Woolf’s prgramme of readings entitled “The Warwichshire Pen”. It was, as always, immensely successful- in its ccontent, its performance (see the Review, p. 50) and also financially. That we make a profit at all is entirely due to the great generosity of those members who sponsor the two performance each year. Without these good friends we would certainly not be able to play at the University of Warwick Arts Centre and we are so grateful for their help and support. “The Warwichshire Pen” is to be repeated in the county on October 8th. When the National Trust is to present it, with Gabriel Woolf, of course, at Coughton Court, near Alcester, and a N.T. leaflet is enclosed for those members within reach. You will see that Gabriel will be presenting another of his recitals (poetry and songs from World War 1) on October 1st. at Berrington Hall, near Leominster. Next year\u27s programme has already been commissioned for April 27th. and 28th.. As this will be Gabriel\u27s 20th. visit to Warwickshire on our behalf, we have invited him to choose his own anthology of poetry and prose in a programme to be called \u27With Great Pleasure\u27…..and we know his pleasure will include a substantial helping of George Eliot. In the next newsletter, I shall be asking for sponsorship again, so if you have some money you don\u27t know what to do with………! Another event which happened after the preparation of the last newsletter was the Seminar of the Alliance of Literary Societies. This, too, was a great success and MS paved the way for the informal Alliance instigated 15 years ago by the George Eliot Fellowship to become a more formal and, we hope, powerful organisation in protecting our literary heritage and being of mutual benefit to the many literary societies who have become members. The Nuneaton Wreath-laying on June 12th. was well supported and we heard John Burton, Chairmanof the Bedworth Society and a very good friend of the Fellowship, appeal for some restraint in the promotion of tourism. Tourists at any price must be avoided if quality and integrity are to be maintained. John\u27s speech will be published in the 1989 Review. We had two guests of honour at the Westminster Abbey Wreath-laying on June 18th. Our principal guest was Jennifer Uglow whose excellent George Eliot was published in the Virago Pioneers series last year. Also in the Abbey was Mrs. Mary Haight, whose husband, Dr. Gordon Haight, had unveiled the memorial stone eight years earlier. Mrs. Uglow very generously offered Mrs. Haight the pleasure of actually placing the chaplet of laurel and white carnations onto the stone; Mrs. Haight was clearly touched by this warm gesture. By an amazing coincidence, Mrs. Uglow had chosen to speak on the very passage also chosen as her reading by Margaret Wolfit! Something similar happened last year; there must be something about Westminster Abbey! Mrs. Uglow\u27s Address will also appear in the 1989 Review

Fast computation of Bernoulli, Tangent and Secant numbers

We consider the computation of Bernoulli, Tangent (zag), and Secant (zig or Euler) numbers. In particular, we give asymptotically fast algorithms for computing the first n such numbers in O(n^2.(log n)^(2+o(1))) bit-operations. We also give very short in-place algorithms for computing the first n Tangent or Secant numbers in O(n^2) integer operations. These algorithms are extremely simple, and fast for moderate values of n. They are faster and use less space than the algorithms of Atkinson (for Tangent and Secant numbers) and Akiyama and Tanigawa (for Bernoulli numbers).Comment: 16 pages. To appear in Computational and Analytical Mathematics (associated with the May 2011 workshop in honour of Jonathan Borwein's 60th birthday). For further information, see http://maths.anu.edu.au/~brent/pub/pub242.htm

Simulating the Cranfield geological carbon sequestration project with high-resolution static models and an accurate equation of state

Bureau of Economic Geolog

CoGeNT Interpretations

Recently, the CoGeNT experiment has reported events in excess of expected background. We analyze dark matter scenarios which can potentially explain this signal. Under the standard case of spin independent scattering with equal couplings to protons and neutrons, we find significant tensions with existing constraints. Consistency with these limits is possible if a large fraction of the putative signal events is coming from an additional source of experimental background. In this case, dark matter recoils cannot be said to explain the excess, but are consistent with it. We also investigate modifications to dark matter scattering that can evade the null experiments. In particular, we explore generalized spin independent couplings to protons and neutrons, spin dependent couplings, momentum dependent scattering, and inelastic interactions. We find that some of these generalizations can explain most of the CoGeNT events without violation of other constraints. Generalized couplings with some momentum dependence, allows further consistency with the DAMA modulation signal, realizing a scenario where both CoGeNT and DAMA signals are coming from dark matter. A model with dark matter interacting and annihilating into a new light boson can realize most of the scenarios considered.Comment: 24 pages, 12 figs, v2: published version, some discussions clarifie

Casimir Effect on the Worldline

We develop a method to compute the Casimir effect for arbitrary geometries. The method is based on the string-inspired worldline approach to quantum field theory and its numerical realization with Monte-Carlo techniques. Concentrating on Casimir forces between rigid bodies induced by a fluctuating scalar field, we test our method with the parallel-plate configuration. For the experimentally relevant sphere-plate configuration, we study curvature effects quantitatively and perform a comparison with the ``proximity force approximation'', which is the standard approximation technique. Sizable curvature effects are found for a distance-to-curvature-radius ratio of a/R >~ 0.02. Our method is embedded in renormalizable quantum field theory with a controlled treatment of the UV divergencies. As a technical by-product, we develop various efficient algorithms for generating closed-loop ensembles with Gaussian distribution.Comment: 27 pages, 10 figures, Sect. 2.1 more self-contained, improved data for Fig. 6, minor corrections, new Refs, version to be published in JHE

Partition functions and double-trace deformations in AdS/CFT

We study the effect of a relevant double-trace deformation on the partition function (and conformal anomaly) of a CFT at large N and its dual picture in AdS. Three complementary previous results are brought into full agreement with each other: bulk and boundary computations, as well as their formal identity. We show the exact equality between the dimensionally regularized partition functions or, equivalently, fluctuational determinants involved. A series of results then follows: (i) equality between the renormalized partition functions for all d; (ii) for all even d, correction to the conformal anomaly; (iii) for even d, the mapping entails a mixing of UV and IR effects on the same side (bulk) of the duality, with no precedent in the leading order computations; and finally, (iv) a subtle relation between overall coefficients, volume renormalization and IR-UV connection. All in all, we get a clean test of the AdS/CFT correspondence beyond the classical SUGRA approximation in the bulk and at subleading O(1) order in the large-N expansion on the boundary.Comment: 18 pages, uses JHEP3.cls. Published JHEP versio

Interactome network analysis identifies multiple caspase-6 interactors involved in the pathogenesis of HD

Caspase-6 (CASP6) has emerged as an important player in Huntington disease (HD), Alzheimer disease (AD) and cerebral ischemia, where it is activated early in the disease process. CASP6 also plays a key role in axonal degeneration, further underscoring the importance of this protease in neurodegenerative pathways. As a protein's function is modulated by its protein-protein interactions we performed a high throughput yeast-2-hybrid (Y2H) screen against ∼17,000 human proteins to gain further insight into the function of CASP6. We identified a high confidence list of 87 potential CASP6 interactors. From this list, 61% are predicted to contain a CASP6 recognition site. Of nine candidate substrates assessed, six are cleaved by CASP6. Proteins that did not contain a predicted CASP6 recognition site were assessed using a LUMIER assay approach and 51% were further validated as interactors by this method. Of note, 54% of the high-confidence interactors identified show alterations in human HD brain at the mRNA level, and there is a significant enrichment for previously validated huntingtin (HTT) interactors. One protein of interest, STK3, a proapoptotic kinase, was validated biochemically to be a CASP6 substrate. Furthermore, our results demonstrate that in striatal cells expressing mutant huntingtin (mHTT) an increase in full length and fragment levels of STK3 are observed. We further show that caspase-3 is not essential for the endogenous cleavage of STK3. Characterization of the interaction network provides important new information regarding key pathways of interactors of CASP6 and highlights potential novel therapeutic targets for HD, AD and cerebral ischemia

Microcraters in aluminum foils exposed by Stardust

We will present preliminary results on the nature and size frequency distribution of microcraters that formed in aluminum foils during the flyby of comet Wild 2 by the Stardust spacecraft

Hard Instances of the Constrained Discrete Logarithm Problem

The discrete logarithm problem (DLP) generalizes to the constrained DLP, where the secret exponent $x$ belongs to a set known to the attacker. The complexity of generic algorithms for solving the constrained DLP depends on the choice of the set. Motivated by cryptographic applications, we study sets with succinct representation for which the constrained DLP is hard. We draw on earlier results due to Erd\"os et al. and Schnorr, develop geometric tools such as generalized Menelaus' theorem for proving lower bounds on the complexity of the constrained DLP, and construct sets with succinct representation with provable non-trivial lower bounds