Attractors in fully asymmetric neural networks

The statistical properties of the length of the cycles and of the weights of the attraction basins in fully asymmetric neural networks (i.e. with completely uncorrelated synapses) are computed in the framework of the annealed approximation which we previously introduced for the study of Kauffman networks. Our results show that this model behaves essentially as a Random Map possessing a reversal symmetry. Comparison with numerical results suggests that the approximation could become exact in the infinite size limit.Comment: 23 pages, 6 figures, Latex, to appear on J. Phys.

Relaxation, closing probabilities and transition from oscillatory to chaotic attractors in asymmetric neural networks

Attractors in asymmetric neural networks with deterministic parallel dynamics were shown to present a "chaotic" regime at symmetry eta < 0.5, where the average length of the cycles increases exponentially with system size, and an oscillatory regime at high symmetry, where the typical length of the cycles is 2. We show, both with analytic arguments and numerically, that there is a sharp transition, at a critical symmetry \e_c=0.33, between a phase where the typical cycles have length 2 and basins of attraction of vanishing weight and a phase where the typical cycles are exponentially long with system size, and the weights of their attraction basins are distributed as in a Random Map with reversal symmetry. The time-scale after which cycles are reached grows exponentially with system size $N$, and the exponent vanishes in the symmetric limit, where $T\propto N^{2/3}$. The transition can be related to the dynamics of the infinite system (where cycles are never reached), using the closing probabilities as a tool. We also study the relaxation of the function $E(t)=-1/N\sum_i |h_i(t)|$, where $h_i$ is the local field experienced by the neuron $i$. In the symmetric system, it plays the role of a Ljapunov function which drives the system towards its minima through steepest descent. This interpretation survives, even if only on the average, also for small asymmetry. This acts like an effective temperature: the larger is the asymmetry, the faster is the relaxation of $E$, and the higher is the asymptotic value reached. $E$ reachs very deep minima in the fixed points of the dynamics, which are reached with vanishing probability, and attains a larger value on the typical attractors, which are cycles of length 2.Comment: 24 pages, 9 figures, accepted on Journal of Physics A: Math. Ge

Transition from regular to complex behaviour in a discrete deterministic asymmetric neural network model

We study the long time behaviour of the transient before the collapse on the periodic attractors of a discrete deterministic asymmetric neural networks model. The system has a finite number of possible states so it is not possible to use the term chaos in the usual sense of sensitive dependence on the initial condition. Nevertheless, at varying the asymmetry parameter, $k$, one observes a transition from ordered motion (i.e. short transients and short periods on the attractors) to a ``complex'' temporal behaviour. This transition takes place for the same value $k_{\rm c}$ at which one has a change for the mean transient length from a power law in the size of the system ($N$) to an exponential law in $N$. The ``complex'' behaviour during the transient shows strong analogies with the chaotic behaviour: decay of temporal correlations, positive Shannon entropy, non-constant Renyi entropies of different orders. Moreover the transition is very similar to that one for the intermittent transition in chaotic systems: scaling law for the Shannon entropy and strong fluctuations of the ``effective Shannon entropy'' along the transient, for $k > k_{\rm c}$.Comment: 18 pages + 6 figures, TeX dialect: Plain TeX + IOP macros (included

On the Stability of the Mean-Field Glass Broken Phase under Non-Hamiltonian Perturbations

We study the dynamics of the SK model modified by a small non-hamiltonian perturbation. We study aging, and we find that on the time scales investigated by our numerical simulations it survives a small perturbation (and is destroyed by a large one). If we assume we are observing a transient behavior the scaling of correlation times versus the asymmetry strength is not compatible with the one expected for the spherical model. We discuss the slow power law decay of observable quantities to equilibrium, and we show that for small perturbations power like decay is preserved. We also discuss the asymptotically large time region on small lattices.Comment: 34 page

The Impact of Global Warming and Anoxia on Marine Benthic Community Dynamics: an Example from the Toarcian (Early Jurassic)

The Pliensbachian-Toarcian (Early Jurassic) fossil record is an archive of natural data of benthic community response to global warming and marine long-term hypoxia and anoxia. In the early Toarcian mean temperatures increased by the same order of magnitude as that predicted for the near future; laminated, organic-rich, black shales were deposited in many shallow water epicontinental basins; and a biotic crisis occurred in the marine realm, with the extinction of approximately 5% of families and 26% of genera. High-resolution quantitative abundance data of benthic invertebrates were collected from the Cleveland Basin (North Yorkshire, UK), and analysed with multivariate statistical methods to detect how the fauna responded to environmental changes during the early Toarcian. Twelve biofacies were identified. Their changes through time closely resemble the pattern of faunal degradation and recovery observed in modern habitats affected by anoxia. All four successional stages of community structure recorded in modern studies are recognised in the fossil data (i.e. Stage III: climax; II: transitional; I: pioneer; 0: highly disturbed). Two main faunal turnover events occurred: (i) at the onset of anoxia, with the extinction of most benthic species and the survival of a few adapted to thrive in low-oxygen conditions (Stages I to 0) and (ii) in the recovery, when newly evolved species colonized the re-oxygenated soft sediments and the path of recovery did not retrace of pattern of ecological degradation (Stages I to II). The ordination of samples coupled with sedimentological and palaeotemperature proxy data indicate that the onset of anoxia and the extinction horizon coincide with both a rise in temperature and sea level. Our study of how faunal associations co-vary with long and short term sea level and temperature changes has implications for predicting the long-term effects of “dead zones” in modern oceans

Cosmopolitan Early Jurassic Marine Gastropods from West-Central Patagonia, Argentina

A new, relatively diverse gastropod fauna is reported from the Chubut province of west−central Patagonia. The gastro− pod association at the “El Córdoba ” fossiliferous locality (Lower Toarcian of Osta Arena Formation) consists of three new species: the eucyclid Amberleya? espinosa sp. nov. and two procerithiids Cryptaulax damboreneae sp. nov. and Cryptaulax nulloi sp. nov. Other members of the association are the ataphrid Striatoconulus sp., discohelicid Colpom− phalus? sp., and an undetermined zygopleurid. Knowledge on Early Jurassic gastropods from South America and other southern continents is reviewed to show that the taxonomic composition of the El Cordoba association strongly resem− bles other gastropod associations of this age (even those from Europe), suggesting a wide distribution of cosmopolita

Upper Toarcian (Lower Jurassic) marine gastropods from the Cleveland Basin, England: systematics, palaeobiogeography and contribution to biotic recovery from the early Toarcian extinction event

Here we describe a new upper Toarcian (Lower Jurassic) marine gastropod fauna from rocks of the Cleveland Basin exposed on the North Yorkshire coast of England. The fossil assemblage consists of 16 species, of which three are new: Katosira ? bicarinata sp. nov., Turritelloidea stepheni sp. nov. and Striactaenonina elegans sp. nov. Four species are described in open nomenclature as Tricarilda ? sp., Jurilda sp., Cylindrobullina sp. and Cossmannina sp. The other species have previously been described: Coelodiscus minutus (Schübler in Zieten), Procerithium quadrilineatum (Römer), Pseudokatosira undulata (Benz in von Zieten), Palaeorissoina aff. acuminata (Gründel), Pietteia unicarinata (Hudleston), Globularia cf. canina (Hudleston), Striactaeonina cf. richterorum Schulbert & Nützel, Striactaenonina aff. tenuistriata (Hudleston) and Sulcoactaeon sedgvici (Phillips). Most of these species are the earliest records of their respective genera and show palaeobiogeographical connections with contemporary gastropod associations from other regions of Europe and South America. The taxonomic composition of the upper Toarcian Cleveland Basin gastropod assemblage differs substantially from the faunas of the upper Pliensbachian and lower Toarcian Tenuicostatum Zone, showing the strong effect of the early Toarcian mass extinction event on the marine gastropod communities in the basin. Only a few gastropod species are shared between the late Toarcian faunas and the much more diverse Aalenian gastropod faunas in the Cleveland Basin, suggesting that there was a facies control on gastropod occurrences at that time. This is also a potential explanation for the taxonomic differences between the late Toarcian gastropod faunas in the Cleveland Basin and those in France, and northern and southern Germany

A silicified Early Triassic marine assemblage from Svalbard

peerreview_statement: The publishing and review policy for this title is described in its Aims & Scope. aims_and_scope_url: http://www.tandfonline.com/action/journalInformation?show=aimsScope&journalCode=tjsp2