New reductions of integrable matrix PDEs: Sp(m)Sp(m)-invariant systems

We propose a new type of reduction for integrable systems of coupled matrix PDEs; this reduction equates one matrix variable with the transposition of another multiplied by an antisymmetric constant matrix. Via this reduction, we obtain a new integrable system of coupled derivative mKdV equations and a new integrable variant of the massive Thirring model, in addition to the already known systems. We also discuss integrable semi-discretizations of the obtained systems and present new soliton solutions to both continuous and semi-discrete systems. As a by-product, a new integrable semi-discretization of the Manakov model (self-focusing vector NLS equation) is obtained.Comment: 33 pages; (v4) to appear in JMP; This paper states clearly that the elementary function solutions of (a vector/matrix generalization of) the derivative NLS equation can be expressed as the partial $x$-derivatives of elementary functions. Explicit soliton solutions are given in the author's talks at http://poisson.ms.u-tokyo.ac.jp/~tsuchida

Exact Analysis of Soliton Dynamics in Spinor Bose-Einstein Condensates

We propose an integrable model of a multicomponent spinor Bose-Einstein condensate in one dimension, which allows an exact description of the dynamics of bright solitons with spin degrees of freedom. We consider specifically an atomic condensate in the F=1 hyperfine state confined by an optical dipole trap. When the mean-field interaction is attractive (c_0 < 0) and the spin-exchange interaction of a spinor condensate is ferromagnetic (c_2 < 0), we prove that the system possesses a completely integrable point leading to the existence of multiple bright solitons. By applying results from the inverse scattering method, we analyze a collision law for two-soliton solutions and find that the dynamics can be explained in terms of the spin precession.Comment: 4 pages, 2 figure

Complete integrability of derivative nonlinear Schr\"{o}dinger-type equations

We study matrix generalizations of derivative nonlinear Schr\"{o}dinger-type equations, which were shown by Olver and Sokolov to possess a higher symmetry. We prove that two of them are `C-integrable' and the rest of them are `S-integrable' in Calogero's terminology.Comment: 14 pages, LaTeX2e (IOP style), to appear in Inverse Problem

Symmetrically coupled higher-order nonlinear Schroedinger equations: singularity analysis and integrability

The integrability of a system of two symmetrically coupled higher-order nonlinear Schr\"{o}dinger equations with parameter coefficients is tested by means of the singularity analysis. It is proven that the system passes the Painlev\'{e} test for integrability only in ten distinct cases, of which two are new. For one of the new cases, a Lax pair and a multi-field generalization are obtained; for the other one, the equations of the system are uncoupled by a nonlinear transformation.Comment: 12 pages, LaTeX2e, IOP style, final version, to appear in J.Phys.A:Math.Ge

Space biology initiative program definition review. Trade study 1: Automation costs versus crew utilization

A significant emphasis upon automation within the Space Biology Initiative hardware appears justified in order to conserve crew labor and crew training effort. Two generic forms of automation were identified: automation of data and information handling and decision making, and the automation of material handling, transfer, and processing. The use of automatic data acquisition, expert systems, robots, and machine vision will increase the volume of experiments and quality of results. The automation described may also influence efforts to miniaturize and modularize the large array of SBI hardware identified to date. The cost and benefit model developed appears to be a useful guideline for SBI equipment specifiers and designers. Additional refinements would enhance the validity of the model. Two NASA automation pilot programs, 'The Principal Investigator in a Box' and 'Rack Mounted Robots' were investigated and found to be quite appropriate for adaptation to the SBI program. There are other in-house NASA efforts that provide technology that may be appropriate for the SBI program. Important data is believed to exist in advanced medical labs throughout the U.S., Japan, and Europe. The information and data processing in medical analysis equipment is highly automated and future trends reveal continued progress in this area. However, automation of material handling and processing has progressed in a limited manner because the medical labs are not affected by the power and space constraints that Space Station medical equipment is faced with. Therefore, NASA's major emphasis in automation will require a lead effort in the automation of material handling to achieve optimal crew utilization

Integrable discretizations of derivative nonlinear Schroedinger equations

We propose integrable discretizations of derivative nonlinear Schroedinger (DNLS) equations such as the Kaup-Newell equation, the Chen-Lee-Liu equation and the Gerdjikov-Ivanov equation by constructing Lax pairs. The discrete DNLS systems admit the reduction of complex conjugation between two dependent variables and possess bi-Hamiltonian structure. Through transformations of variables and reductions, we obtain novel integrable discretizations of the nonlinear Schroedinger (NLS), modified KdV (mKdV), mixed NLS, matrix NLS, matrix KdV, matrix mKdV, coupled NLS, coupled Hirota, coupled Sasa-Satsuma and Burgers equations. We also discuss integrable discretizations of the sine-Gordon equation, the massive Thirring model and their generalizations.Comment: 24 pages, LaTeX2e (IOP style), final versio

A systematic method for constructing time discretizations of integrable lattice systems: local equations of motion

We propose a new method for discretizing the time variable in integrable lattice systems while maintaining the locality of the equations of motion. The method is based on the zero-curvature (Lax pair) representation and the lowest-order "conservation laws". In contrast to the pioneering work of Ablowitz and Ladik, our method allows the auxiliary dependent variables appearing in the stage of time discretization to be expressed locally in terms of the original dependent variables. The time-discretized lattice systems have the same set of conserved quantities and the same structures of the solutions as the continuous-time lattice systems; only the time evolution of the parameters in the solutions that correspond to the angle variables is discretized. The effectiveness of our method is illustrated using examples such as the Toda lattice, the Volterra lattice, the modified Volterra lattice, the Ablowitz-Ladik lattice (an integrable semi-discrete nonlinear Schroedinger system), and the lattice Heisenberg ferromagnet model. For the Volterra lattice and modified Volterra lattice, we also present their ultradiscrete analogues.Comment: 61 pages; (v2)(v3) many minor correction

Electroencephalographic characteristics of epileptic seizures in preterm neonates

OBJECTIVE: Although seizures are more common in the neonatal period than in any other stage of childhood, those in preterm neonates are still poorly described. The aim of this study was to assess electro-clinical characteristics of seizures occurring before a corrected age of 40 weeks in neonates born prematurely. METHOD: Retrospective analysis of EEG-documented seizures in neonates born prematurely. Seizures in a group of term neonates served as controls. RESULTS: Fifty-six prematurely born and 46 term born neonates were included. Median duration of seizures was 52 s in preterm and 96 s in term neonates. Seizures were focal or multifocal. In least mature neonates, they involved smaller regions of onset and remained localised. With increasing corrected age, propagation became more frequent. The electrographic pattern – maximal frequency of oscillation and the onset pattern also evolved with age. Electro-clinical seizures were observed in 25% of preterm versus 50% of term neonates; almost all electro-clinical seizures involved the central (motor) regions. CONCLUSION: Ictal EEG features undergo changes depending on corrected age. Most seizures are subclinical, thus EEG is essential for diagnosis. SIGNIFICANCE: Relating ictal EEG pattern to corrected age can improve diagnosis and ultimately management