The Discrete Nonlinear Schr\"odinger equation - 20 Years on

We review work on the Discrete Nonlinear Schr\"odinger (DNLS) equation over the last two decades.Comment: 24 pages, 1 figure, Proceedings of the conference on "Localization and Energy Transfer in Nonlinear Systems", June 17-21, 2002, San Lorenzo de El Escorial, Madrid, Spain; to be published by World Scientifi

Two-dimensional mobile breather scattering in a hexagonal crystal lattice

We describe, for the first time, the full 2D scattering of long-lived breathers in a model hexagonal lattice of atoms. The chosen system, representing an idealized model of mica, combines a Lennard-Jones interatomic potential with an "egg-box" harmonic potential well surface. We investigate the dependence of breather properties on the ratio of the well depths associated to the interaction and on-site potentials. High values of this ratio lead to large spatial displacements in adjacent chains of atoms and thus enhance the two dimensional character of the quasi-one-dimensional breather solutions. This effect is further investigated during breather-breather collisions by following the constrained energy density function in time for a set of randomly excited mobile breather solutions. Certain collisions lead to 60$^\circ$ scattering, and collisions of mobile and stationary breathers can generate a rich variety of states.Comment: 4 pages, 5 figure

Statistical evidence for a helical nascent chain

We investigate the hypothesis that protein folding is a kinetic, non-equilibrium process, in which the structure of the nascent chain is crucial. We compare actual amino acid frequencies in loops, alpha-helices and beta-sheets with the frequencies that would arise in the absence of any amino acid bias for those secondary structures. The novel analysis suggests that while specific amino acids exist to drive the formation of loops and sheets, none stand out as drivers for alpha-helices. This favours the idea that the alpha-helix is the initial structure of most proteins before the folding process begins.UIDB/04326/2020info:eu-repo/semantics/publishedVersio

Nonlinear propagating localized modes in a 2D hexagonal crystal lattice

In this paper we consider a 2D hexagonal crystal lattice model first proposed by Marin, Eilbeck and Russell in 1998. We perform a detailed numerical study of nonlinear propagating localized modes, that is, propagating discrete breathers and kinks. The original model is extended to allow for arbitrary atomic interactions, and to allow atoms to travel out of the unit cell. A new on-site potential is considered with a periodic smooth function with hexagonal symmetry. We are able to confirm the existence of long-lived propagating discrete breathers. Our simulations show that, as they evolve, breathers appear to localize in frequency space, i.e. the energy moves from sidebands to a main frequency band. Our numerical findings contribute to the open question of whether exact moving breather solutions exist in 2D hexagonal layers in physical crystal lattices.Comment: Both this paper and arXiv 1408.6853 discuss similar models with the same on-site potential. This paper has a Lennard-Jones interparticle potential, 1408.6853 has a piecewise polynomial function. The latter favours the existence of long-lived kinks, and much of 1408.6853 is given to a study of these. Both models support long-lived breathers, and the present paper concentrates on such solution

Identities for hyperelliptic P-functions of genus one, two and three in covariant form

We give a covariant treatment of the quadratic differential identities satisfied by the P-functions on the Jacobian of smooth hyperelliptic curves of genera 1, 2 and 3

Discrete solitons in optical BEC lattices. Effects of n-body interactions

In this poster we show some recent results concerning discrete solitons in strong optical lattices, which can be described by the Discrete Nonlinear Schrödinger equation. These results are related to a variation of this equation including saturable nonlinearity terms, a feature throughoutly studied in nonlinear optics. After presenting the derivation of the DNLS equation from the Gross-Pitaevskii equation in the presence of a strong optical lattice, we study the existence of thresholds in the quadratic norm of discrete solitons in the cubic DNLS, cubic-quintic DNLS and photorefractive-DNLS. The second part of the poster is devoted to moving discrete solitons in the photorefractive DNLS equation. In the one hand, we study the existence of radiationless moving discrete solitons; on the other hand, we study the collisions of moving discrete solitons

SBOL Visual: A Graphical Language for Genetic Designs

Synthetic Biology Open Language (SBOL) Visual is a graphical standard for genetic engineering. It consists of symbols representing DNA subsequences, including regulatory elements and DNA assembly features. These symbols can be used to draw illustrations for communication and instruction, and as image assets for computer-aided design. SBOL Visual is a community standard, freely available for personal, academic, and commercial use (Creative Commons CC0 license). We provide prototypical symbol images that have been used in scientific publications and software tools. We encourage users to use and modify them freely, and to join the SBOL Visual community: http://www.sbolstandard.org/visual

Improved annotation of the insect vector of citrus greening disease: Biocuration by a diverse genomics community

The Asian citrus psyllid (Diaphorina citri Kuwayama) is the insect vector of the bacterium Candidatus Liberibacter asiaticus (CLas), the pathogen associated with citrus Huanglongbing (HLB, citrus greening). HLB threatens citrus production worldwide. Suppression or reduction of the insect vector using chemical insecticides has been the primary method to inhibit the spread of citrus greening disease. Accurate structural and functional annotation of the Asian citrus psyllid genome, as well as a clear understanding of the interactions between the insect and CLas, are required for development of new molecular-based HLB control methods. A draft assembly of the D. citri genome has been generated and annotated with automated pipelines. However, knowledge transfer from well-curated reference genomes such as that of Drosophila melanogaster to newly sequenced ones is challenging due to the complexity and diversity of insect genomes. To identify and improve gene models as potential targets for pest control, we manually curated several gene families with a focus on genes that have key functional roles in D. citri biology and CLas interactions. This community effort produced 530 manually curated gene models across developmental, physiological, RNAi regulatory and immunity-related pathways. As previously shown in the pea aphid, RNAi machinery genes putatively involved in the microRNA pathway have been specifically duplicated. A comprehensive transcriptome enabled us to identify a number of gene families that are either missing or misassembled in the draft genome. In order to develop biocuration as a training experience, we included undergraduate and graduate students from multiple institutions, as well as experienced annotators from the insect genomics research community. The resulting gene set (OGS v1.0) combines both automatically predicted and manually curated gene models.Peer reviewedBiochemistry and Molecular BiologyEntomology and Plant Patholog

Recursion Relations on the Power Series Expansion of the Universal Weierstrass Sigma Function (Mathematical structures of integrable systems and their applications)

"Mathematical structures of integrable systems and their applications". September 5-7, 2018. edited by Shinsuke Iwao. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed.The main aim of this paper is an exposition of the theory of Buchstaber and Leykin on the heat equations for the multivariate sigma functions. We treat only the elliptic curve case, but keeping the most general elliptic curve equation, which may be useful for number theoretic applications