Computation using Noise-based Logic: Efficient String Verification over a Slow Communication Channel

Utilizing the hyperspace of noise-based logic, we show two string verification methods with low communication complexity. One of them is based on continuum noise-based logic. The other one utilizes noise-based logic with random telegraph signals where a mathematical analysis of the error probability is also given. The last operation can also be interpreted as computing universal hash functions with noise-based logic and using them for string comparison. To find out with 10^-25 error probability that two strings with arbitrary length are different (this value is similar to the error probability of an idealistic gate in today's computer) Alice and Bob need to compare only 83 bits of the noise-based hyperspace.Comment: Accepted for publication in European Journal of Physics B (November 10, 2010

sl(N) Onsager's Algebra and Integrability

We define an $sl(N)$ analog of Onsager's Algebra through a finite set of relations that generalize the Dolan Grady defining relations for the original Onsager's Algebra. This infinite-dimensional Lie Algebra is shown to be isomorphic to a fixed point subalgebra of $sl(N)$ Loop Algebra with respect to a certain involution. As the consequence of the generalized Dolan Grady relations a Hamiltonian linear in the generators of $sl(N)$ Onsager's Algebra is shown to posses an infinite number of mutually commuting integrals of motion

Integrating ecology into macroevolutionary research

On 9 March, over 150 biologists gathered in London for the Centre for Ecology and Evolution spring symposium, ‘Integrating Ecology into Macroevolutionary Research’. The event brought together researchers from London-based institutions alongside others from across the UK, Europe and North America for a day of talks. The meeting highlighted methodological advances and recent analyses of exemplar datasets focusing on the exploration of the role of ecological processes in shaping macroevolutionary patterns

Fermionic solution of the Andrews-Baxter-Forrester model II: proof of Melzer's polynomial identities

We compute the one-dimensional configuration sums of the ABF model using the fermionic technique introduced in part I of this paper. Combined with the results of Andrews, Baxter and Forrester, we find proof of polynomial identities for finitizations of the Virasoro characters $\chi_{b,a}^{(r-1,r)}(q)$ as conjectured by Melzer. In the thermodynamic limit these identities reproduce Rogers--Ramanujan type identities for the unitary minimal Virasoro characters, conjectured by the Stony Brook group. We also present a list of additional Virasoro character identities which follow from our proof of Melzer's identities and application of Bailey's lemma.Comment: 28 pages, Latex, 7 Postscript figure

Study of the Hindrance Effect in Sub-barrier Fusion Reactions

We have measured the fusion cross sections of the 12C(13C, p)24Na reaction through off-line measurement of the beta-decay of 24Na using the beta-gamma coincidence method. Our new measurements in the energy range of Ec.m. = 2.6-3.0 MeV do not show an obvious S-factor maximum but a plateau. Comparison between this work and various models is presented.Comment: 3 pages, 3 figures, Talk at the "10th International Conference on Nucleus-Nucleus Collisions", Beijing, 16-21 August 200

Polynomial Identities, Indices, and Duality for the N=1 Superconformal Model SM(2,4\nu)

We prove polynomial identities for the N=1 superconformal model SM(2,4\nu) which generalize and extend the known Fermi/Bose character identities. Our proof uses the q-trinomial coefficients of Andrews and Baxter on the bosonic side and a recently introduced very general method of producing recursion relations for q-series on the fermionic side. We use these polynomials to demonstrate a dual relation under q \rightarrow q^{-1} between SM(2,4\nu) and M(2\nu-1,4\nu). We also introduce a generalization of the Witten index which is expressible in terms of the Rogers false theta functions.Comment: 41 pages, harvmac, no figures; new identities, proofs and comments added; misprints eliminate

Continued Fractions and Fermionic Representations for Characters of M(p,p') minimal models

We present fermionic sum representations of the characters $\chi^{(p,p')}_{r,s}$ of the minimal $M(p,p')$ models for all relatively prime integers $p'>p$ for some allowed values of $r$ and $s$. Our starting point is binomial (q-binomial) identities derived from a truncation of the state counting equations of the XXZ spin ${1\over 2}$ chain of anisotropy $-\Delta=-\cos(\pi{p\over p'})$. We use the Takahashi-Suzuki method to express the allowed values of $r$ (and $s$) in terms of the continued fraction decomposition of $\{{p'\over p}\}$ (and ${p\over p'}$) where $\{x\}$ stands for the fractional part of $x.$ These values are, in fact, the dimensions of the hermitian irreducible representations of $SU_{q_{-}}(2)$ (and $SU_{q_{+}}(2)$) with $q_{-}=\exp (i \pi \{{p'\over p}\})$ (and $q_{+}=\exp ( i \pi {p\over p'})).$ We also establish the duality relation $M(p,p')\leftrightarrow M(p'-p,p')$ and discuss the action of the Andrews-Bailey transformation in the space of minimal models. Many new identities of the Rogers-Ramanujan type are presented.Comment: Several references, one further explicit result and several discussion remarks adde

The diversification of Heliconius butterflies: what have we learned in 150 years?

Research into Heliconius butterflies has made a significant contribution to evolutionary biology. Here, we review our understanding of the diversification of these butterflies, covering recent advances and a vast foundation of earlier work. Whereas no single group of organisms can be sufficient for understanding life's diversity, after years of intensive study, research into Heliconius has addressed a wide variety of evolutionary questions. We first discuss evidence for widespread gene flow between Heliconius species and what this reveals about the nature of species. We then address the evolution and diversity of warning patterns, both as the target of selection and with respect to their underlying genetic basis. The identification of major genes involved in mimetic shifts, and homology at these loci between distantly related taxa, has revealed a surprising predictability in the genetic basis of evolution. In the final sections, we consider the evolution of warning patterns, and Heliconius diversity more generally, within a broader context of ecological and sexual selection. We consider how different traits and modes of selection can interact and influence the evolution of reproductive isolation.RMM is funded by a Junior Research Fellowship at King’s College, Cambridge. KMK is supported by the Balfour Studentship, University of Cambridge, SHMa by a Research Fellowship at St John's College, Cambridge, and SHMo by a Research Fellowship from the Royal Commission for the Exhibition of 1851. Our work on Heliconius has been additionally supported by the Agence Nationale de la Recherche (France), the Biology and Biotechnology Research Council (UK), the British Ecological Society, the European Research Council, the Natural Environment Research Council (UK), and the Smithsonian Tropical Research Institute.This is the author accepted manuscript. The final version is available from Wiley via http://dx.doi.org/10.1111/jeb.1267

Random Matrix Theory and higher genus integrability: the quantum chiral Potts model

We perform a Random Matrix Theory (RMT) analysis of the quantum four-state chiral Potts chain for different sizes of the chain up to size L=8. Our analysis gives clear evidence of a Gaussian Orthogonal Ensemble statistics, suggesting the existence of a generalized time-reversal invariance. Furthermore a change from the (generic) GOE distribution to a Poisson distribution occurs when the integrability conditions are met. The chiral Potts model is known to correspond to a (star-triangle) integrability associated with curves of genus higher than zero or one. Therefore, the RMT analysis can also be seen as a detector of ``higher genus integrability''.Comment: 23 pages and 10 figure

The Genomic Signature of Crop-Wild Introgression in Maize

The evolutionary significance of hybridization and subsequent introgression has long been appreciated, but evaluation of the genome-wide effects of these phenomena has only recently become possible. Crop-wild study systems represent ideal opportunities to examine evolution through hybridization. For example, maize and the conspecific wild teosinte Zea mays ssp. mexicana, (hereafter, mexicana) are known to hybridize in the fields of highland Mexico. Despite widespread evidence of gene flow, maize and mexicana maintain distinct morphologies and have done so in sympatry for thousands of years. Neither the genomic extent nor the evolutionary importance of introgression between these taxa is understood. In this study we assessed patterns of genome-wide introgression based on 39,029 single nucleotide polymorphisms genotyped in 189 individuals from nine sympatric maize-mexicana populations and reference allopatric populations. While portions of the maize and mexicana genomes were particularly resistant to introgression (notably near known cross-incompatibility and domestication loci), we detected widespread evidence for introgression in both directions of gene flow. Through further characterization of these regions and preliminary growth chamber experiments, we found evidence suggestive of the incorporation of adaptive mexicana alleles into maize during its expansion to the highlands of central Mexico. In contrast, very little evidence was found for adaptive introgression from maize to mexicana. The methods we have applied here can be replicated widely, and such analyses have the potential to greatly informing our understanding of evolution through introgressive hybridization. Crop species, due to their exceptional genomic resources and frequent histories of spread into sympatry with relatives, should be particularly influential in these studies