Representing narrative and testimonial knowledge in sense-making software for crime analysis.

In the AVERs sense-making tool for crime analysis different types of information are represented in different ways. More precisely, narrative knowledge is represented in an explanatory direction and testimonial knowledge in an indicative direction. This paper shows that this distinction agrees with the preference of potential users and reduces the number of interpretation errors made by them

VLT observations of GRB 990510 and its environment

We present BVRI photometry and spectrophotometry of GRB990510 obtained with the ESO VLT/Antu telescope during the late decline phase. Between days 8 and 29 after the burst, the afterglow faded from R=24.2 to ~26.4. The spectral flux distribution and the light curve support the interpretation of the afterglow as synchrotron emission from a jet. The light curve is consistent with the optical transient alone but an underlying SN with maximum brightness R>27.4 or a galaxy with R>27.6 (3-sigma upper limits) cannot be ruled out. To a 5-sigma detection threshold of R=26.1, no galaxy is found within 6'' of the transient. A very blue V~24.5 extended object which may qualify as a starburst galaxy is located 12'' SE, but at unknown redshift.Comment: 5 pages A&A Latex, accepted for publication in A&A Letter

Dynamically-Coupled Oscillators -- Cooperative Behavior via Dynamical Interaction --

We propose a theoretical framework to study the cooperative behavior of dynamically coupled oscillators (DCOs) that possess dynamical interactions. Then, to understand synchronization phenomena in networks of interneurons which possess inhibitory interactions, we propose a DCO model with dynamics of interactions that tend to cause 180-degree phase lags. Employing an approach developed here, we demonstrate that although our model displays synchronization at high frequencies, it does not exhibit synchronization at low frequencies because this dynamical interaction does not cause a phase lag sufficiently large to cancel the effect of the inhibition. We interpret the disappearance of synchronization in our model with decreasing frequency as describing the breakdown of synchronization in the interneuron network of the CA1 area below the critical frequency of 20 Hz.Comment: 10 pages, 3 figure

Integrate and Fire Neural Networks, Piecewise Contractive Maps and Limit Cycles

We study the global dynamics of integrate and fire neural networks composed of an arbitrary number of identical neurons interacting by inhibition and excitation. We prove that if the interactions are strong enough, then the support of the stable asymptotic dynamics consists of limit cycles. We also find sufficient conditions for the synchronization of networks containing excitatory neurons. The proofs are based on the analysis of the equivalent dynamics of a piecewise continuous Poincar\'e map associated to the system. We show that for strong interactions the Poincar\'e map is piecewise contractive. Using this contraction property, we prove that there exist a countable number of limit cycles attracting all the orbits dropping into the stable subset of the phase space. This result applies not only to the Poincar\'e map under study, but also to a wide class of general n-dimensional piecewise contractive maps.Comment: 46 pages. In this version we added many comments suggested by the referees all along the paper, we changed the introduction and the section containing the conclusions. The final version will appear in Journal of Mathematical Biology of SPRINGER and will be available at http://www.springerlink.com/content/0303-681

Phase Diagram for the Winfree Model of Coupled Nonlinear Oscillators

In 1967 Winfree proposed a mean-field model for the spontaneous synchronization of chorusing crickets, flashing fireflies, circadian pacemaker cells, or other large populations of biological oscillators. Here we give the first bifurcation analysis of the model, for a tractable special case. The system displays rich collective dynamics as a function of the coupling strength and the spread of natural frequencies. Besides incoherence, frequency locking, and oscillator death, there exist novel hybrid solutions that combine two or more of these states. We present the phase diagram and derive several of the stability boundaries analytically.Comment: 4 pages, 4 figure

Pattern selection in a lattice of pulse-coupled oscillators

We study spatio-temporal pattern formation in a ring of N oscillators with inhibitory unidirectional pulselike interactions. The attractors of the dynamics are limit cycles where each oscillator fires once and only once. Since some of these limit cycles lead to the same pattern, we introduce the concept of pattern degeneracy to take it into account. Moreover, we give a qualitative estimation of the volume of the basin of attraction of each pattern by means of some probabilistic arguments and pattern degeneracy, and show how are they modified as we change the value of the coupling strength. In the limit of small coupling, our estimative formula gives a perfect agreement with numerical simulations.Comment: 7 pages, 8 figures. To be published in Physical Review