Synchronous Behavior of Two Coupled Electronic Neurons

We report on experimental studies of synchronization phenomena in a pair of analog electronic neurons (ENs). The ENs were designed to reproduce the observed membrane voltage oscillations of isolated biological neurons from the stomatogastric ganglion of the California spiny lobster Panulirus interruptus. The ENs are simple analog circuits which integrate four dimensional differential equations representing fast and slow subcellular mechanisms that produce the characteristic regular/chaotic spiking-bursting behavior of these cells. In this paper we study their dynamical behavior as we couple them in the same configurations as we have done for their counterpart biological neurons. The interconnections we use for these neural oscillators are both direct electrical connections and excitatory and inhibitory chemical connections: each realized by analog circuitry and suggested by biological examples. We provide here quantitative evidence that the ENs and the biological neurons behave similarly when coupled in the same manner. They each display well defined bifurcations in their mutual synchronization and regularization. We report briefly on an experiment on coupled biological neurons and four dimensional ENs which provides further ground for testing the validity of our numerical and electronic models of individual neural behavior. Our experiments as a whole present interesting new examples of regularization and synchronization in coupled nonlinear oscillators.Comment: 26 pages, 10 figure

Individual, Family and Abuse Characteristics of 700 British Child and Adolescent Sexual Abusers

The individual, family and abuse characteristics of 700 children and young people referred to nine UK services over a nine-year period between 1992 and 2000 as a result of their sexually abusive behaviours were examined. The most common age at referral was 15 years, though a third of all referrals related to children aged 13 or under. Thirty-eight per cent of the sample were identified as learning disabled. Surprisingly high rates of sexual and non-sexual victimisation were present in the backgrounds of the children and young people referred. A wide range of abusive behaviours was perpetrated with just over half of the sample having penetrated or having attempted to penetrate another individual. Victims were usually known to the abuser but in 75 per cent of cases were not related. Fifty-one per cent of the sample abused females only, though 49 per cent had at least one male victim. The implications for policy and practice with children and young people with harmful sexual behaviours are discussed

Neutral carbon in the Egg Nebula (AFGL 2688)

A search for sub-mm C I emission from seven stars that are surrounded by dense molecular gas shells led to the detection, in the case of the "Egg Nebula' (AFGL 2688), of an 0.9 K line implying a C I/CO value greater than 5. The material surrounding this star must be extremely carbon-rich, and it is suggested that the apparently greater extent of the C I emission region may be due to the effects of the galactic UV field on the shell's chemistry, as suggested by Huggins and Glassgold (1982)

Variabilité climatique et statistiques. Etude par simulation de la puissance et de la robustesse de quelques tests utilisés pour vérifier l'homogénéité de chroniques

L'analyse statistique de séries chronologiques de données hydrométéorologiques est un des outils d'identification de variations climatiques. Cette analyse consiste le plus souvent à la mise en œuvre et à l'interprétation de tests statistiques d'homogénéité des séries. Les séries hydrologiques (données de pluie ou de débit) se caractérisent fréquemment par des effectifs faibles, et ne répondent que rarement aux conditions requises par l'application des tests statistiques dont certains sont paramétriques.Nous avons cherché à évaluer, en terme de puissance et de robustesse, le comportement de quelques méthodes statistiques largement employées dans les études de variabilité climatique. Ce travail a été mené dans chaque cas étudié au moyen de procédures de simulations type Monte-Carlo de 100 échantillons de 50 valeurs conformes aux caractéristiques souvent rencontrées dans les séries naturelles. La variabilité simulée est celle d'un changement brutal de la moyenne. Les procédures concernées sont le test de corrélation sur le rang, le test de Pettitt, le test de Buishand, la procédure bayésienne de Lee et Heghinian, et la procédure de segmentation des séries hydrométéorologiques de Hubert et Carbonnel. Des séries artificielles soit stationnaires, soit affectées par une rupture de la moyenne, normales, non-normales, autocorrélées, présentant une tendance linéaire ou un changement brutal de la variance ont été générées.Les conclusions de ce travail doivent être nuancées selon la méthode considérée. D'une manière générale la puissance maximale estimée se situe autour de 50% pour des taux de rupture de la moyenne de l'ordre de 75% de la valeur de l'écart-type. Par ailleurs il apparaît que l'autocorrélation et la présence d'une tendance dans les séries sont les deux caractéristiques qui pénalisent le plus les performances des procédures.Statistical analysis of hydrometeorological time series is often used to identify climatic variations. Most often this analysis consists of applying and interpreting statistical tests of time series homogeneity. Hydrological time series (rainfall and runoff data) are often short and do not always comply with the hypotheses of the statistical methods. Through simulation we have investigated the power and the robustness of some tests which are widely used in the studies dealing with climatic variability. In each case studied, one hundred samples of fifty elements have been generated based on the main characteristics of natural rainfall series. A shift in the mean has been used to represent a possible climatic variation. The procedures used are the rank correlation test, Pettitt's test, Buishand's test, Lee and Heghinian's bayesian procedure, and Hubert and Carbonnel's segmentation procedure for hydrometeorological series.Each simulation of one hundred samples is used to assess the performances of the methods considering a specific characteristic of the series: normality or non-normality, autocorrelation, trend, shift in the variance. First of all, stationary series have been simulated to evaluate the type I error of the tests. Then the series have been simulated with a break in the mean with different levels of amplitude, from 25% to 100% of the standard deviation value. The rank correlation test, Pettitt's test, Buishand's test and the segmentation procedure with a significance level of 1% (significance level of Scheffé's test) reject as heterogeneous less than ten series over one hundred homogeneous simulated series. This result is consistent with the type I error of a statistical test. On the other hand, Lee and Heghinian's bayesian method rejects about 40% of the series. This result means that this latter procedure must only be applied under the hypothesis of heterogeneity. The estimated power of the methods exceeds 40% to 50% when the break in the mean is more than 75% of the standard deviation value.Independent series have been simulated from normal, log-normal and Pearson distributions to compare the performances of the methods requiring normality. The results show that normality has no significant impact on the performances of these methods. However, the simulations do show that the condition of independence of the successive elements of the series is essential to keep performances constant. Otherwise a trend in the series makes the tests inefficient, except for the rank correlation test for which the alternative is a trend. No method seems to be robust against both negative and positive autoregressive dependencies. The procedures requiring a constant variance are robust when the series keep a constant mean, but seem more or less slightly influenced by a break both in the mean and in the standard deviation

The dimension of loop-erased random walk in 3D

We measure the fractal dimension of loop-erased random walk (LERW) in 3 dimensions, and estimate that it is 1.62400 +- 0.00005. LERW is closely related to the uniform spanning tree and the abelian sandpile model. We simulated LERW on both the cubic and face-centered cubic lattices; the corrections to scaling are slightly smaller for the face-centered cubic lattice.Comment: 4 pages, 4 figures. v2 has more data, minor additional change

Noncommutative Induced Gauge Theory

We consider an external gauge potential minimally coupled to a renormalisable scalar theory on 4-dimensional Moyal space and compute in position space the one-loop Yang-Mills-type effective theory generated from the integration over the scalar field. We find that the gauge invariant effective action involves, beyond the expected noncommutative version of the pure Yang-Mills action, additional terms that may be interpreted as the gauge theory counterpart of the harmonic oscillator term, which for the noncommutative $\phi^4$-theory on Moyal space ensures renormalisability. The expression of a possible candidate for a renormalisable action for a gauge theory defined on Moyal space is conjectured and discussed.Comment: 20 pages, 6 figure

Linear connections on matrix geometries

A general definition of a linear connection in noncommutative geometry has been recently proposed. Two examples are given of linear connections in noncommutative geometries which are based on matrix algebras. They both possess a unique metric connection.Comment: 14p, LPTHE-ORSAY 94/9

Scaling Behaviour and Complexity of the Portevin-Le Chatelier Effect

The plastic deformation of dilute alloys is often accompanied by plastic instabilities due to dynamic strain aging and dislocation interaction. The repeated breakaway of dislocations from and their recapture by solute atoms leads to stress serrations and localized strain in the strain controlled tensile tests, known as the Portevin-Le Chatelier (PLC) effect. In this present work, we analyse the stress time series data of the observed PLC effect in the constant strain rate tensile tests on Al-2.5%Mg alloy for a wide range of strain rates at room temperature. The scaling behaviour of the PLC effect was studied using two complementary scaling analysis methods: the finite variance scaling method and the diffusion entropy analysis. From these analyses we could establish that in the entire span of strain rates, PLC effect showed Levy walk property. Moreover, the multiscale entropy analysis is carried out on the stress time series data observed during the PLC effect to quantify the complexity of the distinct spatiotemporal dynamical regimes. It is shown that for the static type C band, the entropy is very low for all the scales compared to the hopping type B and the propagating type A bands. The results are interpreted considering the time and length scales relevant to the effect.Comment: 35 pages, 6 figure

Generalizations of Yang-Mills Theory with Nonlinear Constitutive Equations

We generalize classical Yang-Mills theory by extending nonlinear constitutive equations for Maxwell fields to non-Abelian gauge groups. Such theories may or may not be Lagrangian. We obtain conditions on the constitutive equations specifying the Lagrangian case, of which recently-discussed non-Abelian Born-Infeld theories are particular examples. Some models in our class possess nontrivial Galilean (c goes to infinity) limits; we determine when such limits exist, and obtain them explicitly.Comment: Submitted to the Proceedings of the 3rd Symposium on Quantum Theory and Symmetries (QTS3) 10-14 September 2003. Preprint 9 pages including reference