Sensitivity analysis of initial value problems with mixed odes and algebraic equations

An efficient method is described for sensitivity analysis of nonlinear initial value problems, which may include algebraic equations as well as ordinary differential equations.The linearity of the sensitivity equations is utilized to solve them directly via the local Jacobian of the state equations. The method is implemented with the implicit integrator DASSL and is demonstrated on a stiff industrial reaction model.     

Periodic dynamics of coupled cell networks I: rigid patterns of synchrony and phase relations

It has recently been proved by Golubitsky and coworkers that in any network of coupled dynamical systems, the possible 'rigid' patterns of synchrony of hyperbolic equilibria are determined by purely combinatorial properties of the network, known as 'balanced equivalence relations'. A pattern is 'rigid' if it persists under small 'admissible' perturbations of the differential equation — ones that respect the network structure. We discuss a natural generalisation of these ideas to time-periodic states, and motivate two basic conjectures, the Rigid Synchrony Conjecture and the Rigid Phase Conjecture. These conjectures state that for rigid hyperbolic time-periodic patterns, cells with synchronous dynamics must have synchronous input cells, and cells with phase-related dynamics must have input cells that have the same phase relations. We provide evidence supporting the two conjectures, by proving them for a special class of periodic orbits, which we call 'tame', under strong assumptions on the network architecture and the symmetries of the periodic state. The discussion takes place in the formal setting of coupled cell networks. We prove that rigid patterns of synchrony are balanced, together with the analogous result for rigid patterns of phase relations. The assumption on the network architecture simplifies the geometry of admissible vector fields, while tameness rules out patterns with non-trivial local or multilocal symmetry. The main idea is to perturb an admissible vector field in a way that retains sufficient control over the associated perturbed periodic orbit. We present two techniques for constructing these perturbations, both using a general theorem on groupoid-symmetrisation of vector fields, which has independent interest. In particular we introduce a method of 'patching' that makes local changes to an admissible vector field. Having established these results for all-to-all coupled networks and tame periodic orbits we prove more general versions that require these assumptions only on a suitable quotient network. These conditions are weaker and encompass a larger class of networks and periodic orbits. We give an example to show that rigidity cannot be relaxed to hyperbolicity. We also prove, without any technical assumptions, that rigidly synchronous or phase-related cells must be input-isomorphic, a necessary precondition for the two conjectures to hold.     

High Throughput Primer Walking of cDNA Clones

Primer walking of cloned DNA is a standard research tool. It has been used in the past to determine the sequence of individual clones of interest. With the expansion of DNA sequencing capacity the need to be able to walk larger numbers of clones has become necessary. Our laboratory is a mid-sized genomics facility. In conjunction with the Advanced Biomedical Computing Center (ABCC) we have developed methods for automating the primer selection, DNA sequencing, contig assembly and sequence analysis for clones arrayed in microtiter format. This approach has allowed us to walk 475 clones (five microtiter plates) selected from a cDNA library.     

Convection in a concentric annulus with heat generating porous media and a permeable inner boundary

The effects of a permeable inner boundary on the maximum temperature and the convective flows were investigated numerically for a two-dimensional horizontal annulus containing a uniformly heat generating porous media. The time-dependent governing equations were nondimensionalized and put into an explicit finite difference numerical form. The finite difference equations were obtained from truncated Taylor series expansions using a central differencing scheme. Nondimensional temperatures and streamlines were obtained for heat generation rates ranging from 20 to 1,500 W/m³ corresponding to a range of modified Rayleigh numbers of 324 to 24,340 and for several combinations of isothermally heated wall conditions for annuli of radius ratio of 2. It was found that multi-cellular flows occur at the highest Rayleigh numbers investigated.     

The future of behavior therapy.

Predicts the future of behavior therapy, focusing on theoretical development, therapeutic techniques, and empirical research. The importance of cognitive and affective processes in behavior change will attract increasing attention. Already one of the most widely adopted approaches, behavior therapy will be used to treat an expanded range of psychiatric disorders and health problems. Research will focus on comparative outcome studies and provide probes for investigating the nature of specific disorders and the mechanisms of therapeutic change. (PsycINFO Database Record (c) 2010 APA, all rights reserved)