On integrability of a (2+1)-dimensional perturbed Kdv equation

A (2+1)-dimensional perturbed KdV equation, recently introduced by W.X. Ma and B. Fuchssteiner, is proven to pass the Painlev\'e test for integrability well, and its 4$\times$4 Lax pair with two spectral parameters is found. The results show that the Painlev\'e classification of coupled KdV equations by A. Karasu should be revised

Psi-series solutions of the cubic H\'{e}non-Heiles system and their convergence

The cubic H\'enon-Heiles system contains parameters, for most values of which, the system is not integrable. In such parameter regimes, the general solution is expressible in formal expansions about arbitrary movable branch points, the so-called psi-series expansions. In this paper, the convergence of known, as well as new, psi-series solutions on real time intervals is proved, thereby establishing that the formal solutions are actual solutions

Coupled KdV equations of Hirota-Satsuma type

It is shown that the system of two coupled Korteweg-de Vries equations passes the Painlev\'e test for integrability in nine distinct cases of its coefficients. The integrability of eight cases is verified by direct construction of Lax pairs, whereas for one case it remains unknown

Is the classical Bukhvostov-Lipatov model integrable? A Painlev\'e analysis

In this work we apply the Weiss, Tabor and Carnevale integrability criterion (Painlev\'e analysis) to the classical version of the two dimensional Bukhvostov-Lipatov model. We are led to the conclusion that the model is not integrable classically, except at a trivial point where the theory can be described in terms of two uncoupled sine-Gordon models

A genome-wide linkage and association scan reveals novel loci for autism

Member of the Autism Genome Project Consortium: Astrid M. VicenteAlthough autism is a highly heritable neurodevelopmental disorder, attempts to identify specific susceptibility genes have thus far met with limited success. Genome-wide association studies using half a million or more markers, particularly those with very large sample sizes achieved through meta-analysis, have shown great success in mapping genes for other complex genetic traits. Consequently, we initiated a linkage and association mapping study using half a million genome-wide single nucleotide polymorphisms (SNPs) in a common set of 1,031 multiplex autism families (1,553 affected offspring). We identified regions of suggestive and significant linkage on chromosomes 6q27 and 20p13, respectively. Initial analysis did not yield genome-wide significant associations; however, genotyping of top hits in additional families revealed an SNP on chromosome 5p15 (between SEMA5A and TAS2R1) that was significantly associated with autism (P = 2 x 10(-7)). We also demonstrated that expression of SEMA5A is reduced in brains from autistic patients, further implicating SEMA5A as an autism susceptibility gene. The linkage regions reported here provide targets for rare variation screening whereas the discovery of a single novel association demonstrates the action of common variants

Analytic and Asymptotic Methods for Nonlinear Singularity Analysis: a Review and Extensions of Tests for the Painlev\'e Property

The integrability (solvability via an associated single-valued linear problem) of a differential equation is closely related to the singularity structure of its solutions. In particular, there is strong evidence that all integrable equations have the Painlev\'e property, that is, all solutions are single-valued around all movable singularities. In this expository article, we review methods for analysing such singularity structure. In particular, we describe well known techniques of nonlinear regular-singular-type analysis, i.e. the Painlev\'e tests for ordinary and partial differential equations. Then we discuss methods of obtaining sufficiency conditions for the Painlev\'e property. Recently, extensions of \textit{irregular} singularity analysis to nonlinear equations have been achieved. Also, new asymptotic limits of differential equations preserving the Painlev\'e property have been found. We discuss these also.Comment: 40 pages in LaTeX2e. To appear in the Proceedings of the CIMPA Summer School on "Nonlinear Systems," Pondicherry, India, January 1996, (eds) B. Grammaticos and K. Tamizhman

Superdiffusion in a Model for Diffusion in a Molecularly Crowded Environment

We present a model for diffusion in a molecularly crowded environment. The model consists of random barriers in percolation network. Random walks in the presence of slowly moving barriers show normal diffusion for long times, but anomalous diffusion at intermediate times. The effective exponents for square distance versus time usually are below one at these intermediate times, but can be also larger than one for high barrier concentrations. Thus we observe sub- as well as super-diffusion in a crowded environment.Comment: 8 pages including 4 figure

Didactic Software for Autistic Children

In this paper we describe the aims and requirements of a project devoted to designing and developing Open Source didactic Software (SW) for children in the autism disorder spectrum, conforming to the Applied Behaviour Analysis (ABA) learning technique. In this context, participatory design with therapists and child?s parents is necessary to ensure a usable product that responds to these children?s special needs and respects education principles and constraints of the ABA methodology

Observation of Target Electron Momentum Effects in Single-Arm M\o ller Polarimetry

In 1992, L.G. Levchuk noted that the asymmetries measured in M\o ller scattering polarimeters could be significantly affected by the intrinsic momenta of the target electrons. This effect is largest in devices with very small acceptance or very high resolution in laboratory scattering angle. We use a high resolution polarimeter in the linac of the polarized SLAC Linear Collider to study this effect. We observe that the inclusion of the effect alters the measured beam polarization by -14% of itself and produces a result that is consistent with measurements from a Compton polarimeter. Additionally, the inclusion of the effect is necessary to correctly simulate the observed shape of the two-body elastic scattering peak.Comment: 29 pages, uuencoded gzip-compressed postscript (351 kb). Uncompressed postscript file (898 kb) available to DECNET users as SLC::USER_DISK_SLC1:[MORRIS]levpre.p

Simultaneous saccharification and fermentation of steam exploded duckweed: Improvement of the ethanol yield by increasing yeast titre

This study investigated the conversion of Lemna minor biomass to bioethanol. The biomass was pre-treated by steam explosion (SE, 210 °C, 10 min) and then subjected to simultaneous saccharification and fermentation (SSF) using CellicÒ CTec 2 (20 U or 0.87 FPU gﰂ1 substrate) cellulase plus b-glucosidase (2 U gﰂ1 substrate) and a yeast inoculum of 10% (v/v or 8.0 ﰀ 107 cells mLﰂ1). At a substrate concentration of 1% (w/v) an ethanol yield of 80% (w/w, theoretical) was achieved. However at a substrate concentration of 20% (w/v), the ethanol yield was lowered to 18.8% (w/w, theoretical). Yields were considerably improved by increasing the yeast titre in the inoculum or preconditioning the yeast on steam exploded liquor. These approaches enhanced the ethanol yield up to 70% (w/w, theoretical) at a substrate concen- tration of 20% (w/v) by metabolising fermentation inhibitors