Models of brain function predict that the recurrence of a process or state will be reflected in repeated patterns of correlated activity. Previous work on medullary raphe assembly dynamics revealed transient changes in impulse synchrony. This study tested the hypothesis that these variations in synchrony include distributed nonrandom patterns of association. Spike trains were recorded simultane...

Derivatives of a solution of an ODE Cauchy problem can be computed inductively using the Faà di Bruno formula. In this paper, we exhibit a noninductive formula for these derivatives. At the heart of this formula is a combinatorial problem, which is solved in this paper. We also give a more tractable form of the Magnus expansion for the solution of a homogeneous linear ODE.

Neurons in ventromedial medulla, including the nucleus raphe magnus, project to trigeminal nucleus caudalis and, via the dorsolateral funiculus, to spinal dorsal horn. The terminals of this descending system are in loci containing cells responsive to noxious stimuli. Electrical stimulation of nucleus raphe magnus selectively inhibits spinal dorsal horn neurons that respond to noxious stimuli. T...

Many multi-agent systems (MAS) and other kinds of dynamic systems may be modeled as transition systems, in which actions are associated with transitions between different system states. This paper presents an approach to normative systems in this context, in which the permission or prohibition of actions is related to the permission or prohibition of different types of state transitions with re...

Carlos F. Sanz-Navarro,† Per-Olof Åstrand,† De Chen,‡ Magnus Rønning,‡ Adri C. T. van Duin,§ Jonathan E. Mueller,§ and William A. Goddard III§ Department of Chemistry, Norwegian UniVersity of Science and Technology (NTNU), 7491 Trondheim, Norway, Department of Chemical Engineering, Norwegian UniVersity of Science and Technology (NTNU), 7491 Trondheim, Norway, and Materials and Process Simulatio...

The Magnus expansion is a frequently used tool to get approximate analytic solutions of time-dependent linear ordinary differential equations and in particular the Schrödinger equation in quantum mechanics. However, the complexity of the expansion restricts its use in practice only to the first terms. Here we introduce new and more accurate analytic approximations based on the Magnus expansion ...

Idem., St. Bart's Hosp. med. Rep., 1912, 43, 73. Idem., Brit. med. J., 1912, ii, 1367. Idem., Brit. J. Surg., 1914, 2, 17. Idem., The Robert Jones Birthday Volume, Oxford University Press, 1928, p. 127. Idem., J. Bone Jt Surg., 1931, 13, 423. ELMSLE, R. C., FRASER, F. R., DUNHLL, T. P., VICK, R. M., HARRIS, C. F., and DAUPHINEE, J. A., Brit. J. Surg., 1933, 20, 479. ELMsLE, R. C., Lpool med.-ch...

In this paper new integration algorithms for linear diierential equations up to eighth order are obtained. Starting from Magnus expansion, methods based on Cayley transformation and Fer expansion are also built. The structure of the exact solution is retained while the computational cost is reduced compared to similar methods. Their relative performance is tested on some illustrative examples.