Implicit Taylor methods for stiff stochastic differential equations

In this paper we discuss implicit Taylor methods for stiff Ito stochastic differential equations. Based on the relationship between Ito stochastic integrals and backward stochastic integrals, we introduce three implicit Taylor methods: the implicit Euler-Taylor method with strong order 0.5, the implicit Milstein-Taylor method with strong order 1.0 and the implicit Taylor method with strong order 1.5. The mean-square stability properties of the implicit Euler-Taylor and Milstein-Taylor methods are much better than those of the corresponding semi-implicit Euler and Milstein methods and these two implicit methods can be used to solve stochastic differential equations which are stiff in both the deterministic and the stochastic components. Numerical results are reported to show the convergence properties and the stability properties of these three implicit Taylor methods. The stability analysis and numerical results show that the implicit Euler-Taylor and Milstein-Taylor methods are very promising methods for stiff stochastic differential equations.

Stressor categorization: acute physical and psychological stressors elicit distinctive recruitment patterns in the amygdala and in medullary noradrenergic cell groups

It has been hypothesized that the brain categorizes stressors and utilizes neural response pathways that vary in accordance with the assigned category. If this is true, stressors should elicit patterns of neuronal activation within the brain that are category-specific. Data from previous Immediate-early gene expression mapping studies have hinted that this is the case, but interstudy differences in methodology render conclusions tenuous. In the present study, immunolabelling for the expression of c-fos was used as a marker of neuronal activity elicited in the rat brain by haemorrhage, immune challenge, noise, restraint and forced swim. All stressors elicited c-fos expression in 25-30% of hypothalamic paraventricular nucleus corticotrophin-releasing-factor cells, suggesting that these stimuli were of comparable strength, at least with regard to their ability to activate the hypothalamic-pituitary-ad renal axis. In the amygdala, haemorrhage and immune challenge both elicited c-fos expression in a large number of neurons in the central nucleus of the amygdala, whereas noise, restraint and forced swim primarily elicited recruitment of cells within the medial nucleus of the amygdala. In the medulla, all stressors recruited similar numbers of noradrenergic (A1 and A2) and adrenergic (C1 and C2) cells. However, haemorrhage and immune challenge elicited c-fos expression In subpopulations of A1 and A2 noradrenergic cells that were significantly more rostral than those recruited by noise, restraint or forced swim. The present data support the suggestion that the brain recognizes at least two major categories of stressor, which we have referred to as 'physical' and 'psychological'. Moreover, the present data suggest that the neural activation footprint that is left in the brain by stressors can be used to determine the category to which they have been assigned by the brain.

Categorization and characterization of transcript-confirmed constitutively and alternatively spliced introns and exons from human

By spliced alignment of human DNA and transcript sequence data we constructed a data set of transcript-confirmed exons and introns from 2793 genes, 796 of which (28%) were seen to have multiple isoforms. We find that over one-third of human exons can translate in more than one frame, and that this is highly correlated with G+C content. Introns containing adenosine at donor site position +3 (A3), rather than guanosine (G3), are more common in low G+C regions, while the converse is true in high G+C regions. These two classes of introns are shown to have distinct lengths, consensus sequences and correlations among splice signals, leading to the hypothesis that A3 donor sites are associated with exon definition, and G3 donor sites with intron definition. Minor classes of introns, including GC-AG, U12-type GT-AG, weak, and putative AG-dependant introns are identified and characterized. Cassette exons are more prevalent in low G+C regions, while exon isoforms are more prevalent in high G+C regions. Cassette exon events outnumber other alternative events, while exon isoform events involve truncation twice as often as extension, and occur at acceptor sites twice as often as at donor sites. Alternative splicing is usually associated with weak splice signals, and in a majority of cases, preserves the coding frame. The reported characteristics of constitutive and alternative splice signals, and the hypotheses offered regarding alternative splicing and genome organization, have important implications for experimental research into RNA processing. The 'AltExtron' data sets are available at http://www.bit.uq.edu.au/altExtron/ and http://www.ebi.ac.uk/similar tothanaraj/altExtron/.

Can anticipatory skills be learned through implicit video-based perceptual training?

The aim of this experiment was to determine the effectiveness of two video-based perceptual training approaches designed to improve the anticipatory skills of junior tennis players. Players were assigned equally to an explicit learning group, an implicit learning group, a placebo group or a control group. A progressive temporal occlusion paradigm was used to examine, before and after training, the ability of the players to predict the direction of an opponent's service in an in-vivo on-court setting. The players responded either through hitting a return stroke or making a verbal prediction of stroke direction. Results revealed that the implicit learning group, whose training required them to predict serve speed direction while viewing temporally occluded video footage of the return-of-serve scenario, significantly improved their prediction accuracy after the training intervention. However, this training effect dissipated after a 32 day unfilled retention interval. The explicit learning group, who received instructions about the specific aspects of the pre-contact service kinematics that are informative with respect to service direction, did not demonstrate any significant performance improvements after the intervention. This, together with the absence of any significant improvements for the placebo and control groups, demonstrated that the improvement observed for the implicit learning group was not a consequence of either expectancy or familiarity effects.

A four-stage index 2 Diagonally Implicit Runge-Kutta method

High index Differential Algebraic Equations (DAEs) force standard numerical methods to lower order. Implicit Runge-Kutta methods such as RADAU5 handle high index problems but their fully implicit structure creates significant overhead costs for large problems. Singly Diagonally Implicit Runge-Kutta (SDIRK) methods offer lower costs for integration. This paper derives a four-stage, index 2 Explicit Singly Diagonally Implicit Runge-Kutta (ESDIRK) method. By introducing an explicit first stage, the method achieves second order stage calculations. After deriving and solving appropriate order conditions., numerical examples are used to test the proposed method using fixed and variable step size implementations. (C) 2001 IMACS. Published by Elsevier Science B.V. All rights reserved.

Implicit vector equilibrium problems with applications

Let X and Y be Hausdorff topological vector spaces, K a nonempty, closed, and convex subset of X, C: K--> 2(Y) a point-to-set mapping such that for any x is an element of K, C(x) is a pointed, closed, and convex cone in Y and int C(x) not equal 0. Given a mapping g : K --> K and a vector valued bifunction f : K x K - Y, we consider the implicit vector equilibrium problem (IVEP) of finding x* is an element of K such that f (g(x*), y) is not an element of - int C(x) for all y is an element of K. This problem generalizes the (scalar) implicit equilibrium problem and implicit variational inequality problem. We propose the dual of the implicit vector equilibrium problem (DIVEP) and establish the equivalence between (IVEP) and (DIVEP) under certain assumptions. Also, we give characterizations of the set of solutions for (IVP) in case of nonmonotonicity, weak C-pseudomonotonicity, C-pseudomonotonicity, and strict C-pseudomonotonicity, respectively. Under these assumptions, we conclude that the sets of solutions are nonempty, closed, and convex. Finally, we give some applications of (IVEP) to vector variational inequality problems and vector optimization problems. (C) 2003 Elsevier Science Ltd. All rights reserved.

Explicit/implicit partitioning and a new explicit form of the generalized alpha method

Most finite element packages use the Newmark algorithm for time integration of structural dynamics. Various algorithms have been proposed to better optimize the high frequency dissipation of this algorithm. Hulbert and Chung proposed both implicit and explicit forms of the generalized alpha method. The algorithms optimize high frequency dissipation effectively, and despite recent work on algorithms that possess momentum conserving/energy dissipative properties in a non-linear context, the generalized alpha method remains an efficient way to solve many problems, especially with adaptive timestep control. However, the implicit and explicit algorithms use incompatible parameter sets and cannot be used together in a spatial partition, whereas this can be done for the Newmark algorithm, as Hughes and Liu demonstrated, and for the HHT-alpha algorithm developed from it. The present paper shows that the explicit generalized alpha method can be rewritten so that it becomes compatible with the implicit form. All four algorithmic parameters can be matched between the explicit and implicit forms. An element interface between implicit and explicit partitions can then be used, analogous to that devised by Hughes and Liu to extend the Newmark method. The stability of the explicit/implicit algorithm is examined in a linear context and found to exceed that of the explicit partition. The element partition is significantly less dissipative of intermediate frequencies than one using the HHT-alpha method. The explicit algorithm can also be rewritten so that the discrete equation of motion evaluates forces from displacements and velocities found at the predicted mid-point of a cycle. Copyright (C) 2003 John Wiley Sons, Ltd.

Intra-type migrative scheduling of implicit-deadline sporadic tasks on two- type heterogeneous multiprocessor

Consider the problem of scheduling a set of implicit-deadline sporadic tasks to meet all deadlines on a two-type heterogeneous multiprocessor platform. Each processor is either of type-1 or type-2 with each task having different execution time on each processor type. Jobs can migrate between processors of same type (referred to as intra-type migration) but cannot migrate between processors of different types. We present a new scheduling algorithm namely, LP-Relax(THR) which offers a guarantee that if a task set can be scheduled to meet deadlines by an optimal task assignment scheme that allows intra-type migration then LP-Relax(THR) meets deadlines as well with intra-type migration if given processors 1/THR as fast (referred to as speed competitive ratio) where THR <= 2/3.