Computation of Lyapunov functions for systems with multiple attractors

We present a novel method to compute Lyapunov functions for continuous-time systems with multiple local attractors. In the proposed method one first computes an outer approximation of the local attractors using a graphtheoretic approach. Then a candidate Lyapunov function is computed using a Massera-like construction adapted to multiple local attractors. In the final step this candidate Lyapunov function is interpolated over the simplices of a simplicial complex and, by checking certain inequalities at the vertices of the complex, we can identify the region in which the Lyapunov function is decreasing along system trajectories. The resulting Lyapunov function gives information on the qualitative behavior of the dynamics, including lower bounds on the basins of attraction of the individual local attractors. We develop the theory in detail and present numerical examples demonstrating the applicability of our method

Fractionated Premotor, Motor, and Ankle Dorsiflexion Reaction Times in Hemiplegia

Ten hemiplegic subjects completed 20 rapid dorsiflexions of their afflicted and nonafflicted limbs. Electrodes were attached to the tibialis anterior and the gastrocnemius muscles and electromyograms were recorded for their premotor time, motor time, and simple reaction time during ankle dorsiflexion and plantar flexion of their lower limbs. The fractionated components of reaction time, namely, premotor time and motor time, of both legs were statistically compared. It was found that the premotor time of the subject's stroke-affected limb was significantly slower than the premotor time of the nonaffected limb (control), with no differences between their associated mean motor times. These results supported the hypothesis that a stroke has a deleterious affect upon the central, premotor time processing centers and has no disruptive influence upon the peripheral motor time. Comparing the fractionated components of reaction time (premotor time and motor time), with simple reaction time, the former provided a more sensitive and valid method to detect possible injurious side effects of a stroke upon the brain's neuromotor transmission centers and subcenters, and their peripheral, stimulus, response network

Extraction and implication of path constraints

Abstract. We consider semistructured data as rooted edge-labeled directed graphs, and path inclusion constraints on these graphs. In this paper, we show that we can extract from a finite datum D a finite set Cf(D) of word inclusions, which implies exactly every word inclusion satisfied by D. Then, we give a new decision algorithm for the implication problem of a constraint p � q by a set of constraints pi � ui where p, q, and the pi’s are regular path expressions and the ui’s are non empty paths, improving in this particular case, the more general algorithms of S. Abiteboul and V. Vianu, and Alechina et al. Moreover, in the case of a set of word equalities ui ≡ vi, we give a more efficient decision algorithm for the implication of a word equality u ≡ v, improving the more general algorithm of P. Buneman et al., and we prove that, in this case, the implication problem for non deterministic models or for (complete) deterministic models are equivalent.