Open Boundaries for the Nonlinear Schrodinger Equation

We present a new algorithm, the Time Dependent Phase Space Filter (TDPSF) which is used to solve time dependent Nonlinear Schrodinger Equations (NLS). The algorithm consists of solving the NLS on a box with periodic boundary conditions (by any algorithm). Periodically in time we decompose the solution into a family of coherent states. Coherent states which are outgoing are deleted, while those which are not are kept, reducing the problem of reflected (wrapped) waves. Numerical results are given, and rigorous error estimates are described. The TDPSF is compatible with spectral methods for solving the interior problem. The TDPSF also fails gracefully, in the sense that the algorithm notifies the user when the result is incorrect. We are aware of no other method with this capability.Comment: 21 pages, 4 figure

Multi-Behavioral Endpoint Testing Of An 87-Chemical Compound Library In Freshwater Planarians

There is an increased recognition in the field of toxicology of the value of medium-to-high-throughput screening methods using in vitro and alternative animal models. We have previously introduced the asexual freshwater planarian Dugesia japonica as a new alternative animal model and proposed that it is particularly well-suited for the study of developmental neurotoxicology. In this paper, we discuss how we have expanded and automated our screening methodology to allow for fast screening of multiple behavioral endpoints, developmental toxicity, and mortality. Using an 87-compound library provided by the National Toxicology Program (NTP), consisting of known and suspected neurotoxicants, including drugs, flame retardants, industrial chemicals, polycyclic aromatic hydrocarbons (PAHs), pesticides and presumptive negative controls, we further evaluate the benefits and limitations of the system for medium-throughput screening, focusing on the technical aspects of the system. We show that, in the context of this library, planarians are the most sensitive to pesticides with 16/16 compounds causing toxicity and the least sensitive to PAHs, with only 5/17 causing toxicity. Furthermore, while none of the presumptive negative controls were bioactive in adult planarians, 2/5, acetaminophen and acetylsalicylic acid, were bioactive in regenerating worms. Notably, these compounds were previously reported as developmentally toxic in mammalian studies. Through parallel screening of adults and developing animals, planarians are thus a useful model to detect such developmental-specific effects, which was observed for 13 chemicals in this library. We use the data and experience gained from this screen to propose guidelines for best practices when using planarians for toxicology screens

An Efficient Spectral Method for Ordinary Differential Equations with Rational Function Coefficients

We present some relations that allow the efficient approximate inversion of linear differential operators with rational function coefficients. We employ expansions in terms of a large class of orthogonal polynomial families, including all the classical orthogonal polynomials. These families obey a simple three-term recurrence relation for differentiation, which implies that on an appropriately restricted domain the differentiation operator has a unique banded inverse. The inverse is an integration operator for the family, and it is simply the tridiagonal coefficient matrix for the recurrence. Since in these families convolution operators (i.e. matrix representations of multiplication by a function) are banded for polynomials, we are able to obtain a banded representation for linear differential operators with rational coefficients. This leads to a method of solution of initial or boundary value problems that, besides having an operation count that scales linearly with the order of truncation N, is computationally well conditioned. Among the applications considered is the use of rational maps for the resolution of sharp interior layers

Control of a virtual ambulation influences body movement and motion sickness

Drivers typically are less susceptible to motion sickness than passengers. The influence of vehicle control has theoretical implications for the etiology of motion sickness, and has practical implications for the design of virtual environments. In the present study, participants either controlled or did not control a nonvehicular virtual avatar (i.e., an ambulatory character in a console video game). We examined the incidence of motion sickness and patterns of movement of the head and torso as participants either played or watched the game. Motion sickness incidence was lower when controlling the virutal avatar than when watching an avatar that was controlled by someone else. Patterns of head and torso movement differed between particpants who did and did not control the avatar. Indepenently, patterns of movement differed between participants who reported motion sickness and those who did not. The results suggest that motion sickness is influenced by control of stimulus motion, whether that motion arises from a vehicle or from any other source. We consider implications for the design of humancomputer interfaces

A nonstationary form of the range refraction parabolic equation and its application as an artificial boundary condition for the wave equation in a waveguide

The time-dependent form of Tappert's range refraction parabolic equation is derived using Daletskiy-Krein formula form noncommutative analysis and proposed as an artificial boundary condition for the wave equation in a waveguide. The numerical comparison with Higdon's absorbing boundary conditions shows sufficiently good quality of the new boundary condition at low computational cost.Comment: 12 pages, 9 figure

An SMC-like protein binds and regulates Caenorhabditis elegans condensins

Structural Maintenance of Chromosomes (SMC) family proteins participate in multisubunit complexes that govern chromosome structure and dynamics. SMC-containing condensin complexes create chromosome topologies essential for mitosis/meiosis, gene expression, recombination, and repair. Many eukaryotes have two condensin complexes (I and II); C. elegans has three (I, II, and the X-chromosome specialized condensin IDC) and their regulation is poorly understood. Here we identify a novel SMC-like protein, SMCL-1, that binds to C. elegans condensin SMC subunits, and modulates condensin functions. Consistent with a possible role as a negative regulator, loss of SMCL-1 partially rescued the lethal and sterile phenotypes of a hypomorphic condensin mutant, while over-expression of SMCL-1 caused lethality, chromosome mis-segregation, and disruption of condensin IDC localization on X chromosomes. Unlike canonical SMC proteins, SMCL-1 lacks hinge and coil domains, and its ATPase domain lacks conserved amino acids required for ATP hydrolysis, leading to the speculation that it may inhibit condensin ATPase activity. SMCL-1 homologs are apparent only in the subset of Caenorhabditis species in which the condensin I and II subunit SMC-4 duplicated to create the condensin IDC- specific subunit DPY-27, suggesting that SMCL-1 helps this lineage cope with the regulatory challenges imposed by evolution of a third condensin complex. Our findings uncover a new regulator of condensins and highlight how the duplication and divergence of SMC complex components in various lineages has created new proteins with diverse functions in chromosome dynamics