The Synthesis of Arbitrary Stable Dynamics in Non-linear Neural Networks II: Feedback and Universality

We wish to construct a realization theory of stable neural networks and use this theory to model the variety of stable dynamics apparent in natural data. Such a theory should have numerous applications to constructing specific artificial neural networks with desired dynamical behavior. The networks used in this theory should have well understood dynamics yet be as diverse as possible to capture natural diversity. In this article, I describe a parameterized family of higher order, gradient-like neural networks which have known arbitrary equilibria with unstable manifolds of known specified dimension. Moreover, any system with hyperbolic dynamics is conjugate to one of these systems in a neighborhood of the equilibrium points. Prior work on how to synthesize attractors using dynamical systems theory, optimization, or direct parametric. fits to known stable systems, is either non-constructive, lacks generality, or has unspecified attracting equilibria. More specifically, We construct a parameterized family of gradient-like neural networks with a simple feedback rule which will generate equilibrium points with a set of unstable manifolds of specified dimension. Strict Lyapunov functions and nested periodic orbits are obtained for these systems and used as a method of synthesis to generate a large family of systems with the same local dynamics. This work is applied to show how one can interpolate finite sets of data, on nested periodic orbits.

Adaptive Resonance Associative Map: A Hierarchical ART System for Fast Stable Associative Learning

This paper introduces a new class of predictive ART architectures, called Adaptive Resonance Associative Map (ARAM) which performs rapid, yet stable heteroassociative learning in real time environment. ARAM can be visualized as two ART modules sharing a single recognition code layer. The unit for recruiting a recognition code is a pattern pair. Code stabilization is ensured by restricting coding to states where resonances are reached in both modules. Simulation results have shown that ARAM is capable of self-stabilizing association of arbitrary pattern pairs of arbitrary complexity appearing in arbitrary sequence by fast learning in real time environment. Due to the symmetrical network structure, associative recall can be performed in both directions.

Trophic role of small cetaceans and seals in Irish waters

Understanding the role of marine mammals in specific ecosystems and their interactions with fisheries involves, inter alia, an understanding of their diet and dietary requirements. In this thesis, the foraging ecology of seven marine mammal species that regularly occur in Irish waters was investigated by reconstructing diet using hard parts from digestive tracts and scats. Of the species examined, two (striped and Atlantic white-sided dolphin) can be considered offshore species or species inhabiting neritic waters, while five others usually inhabit more coastal areas (white-beaked dolphin, harbour porpoise, harbour seal and grey seal); the last species studied was the bottlenose dolphin whose population structure is more complex, with coastal and offshore populations. A total of 13,028 prey items from at least 81 different species (62 fish species, 14 cephalopods, four crustaceans, and a tunicate) were identified. 28% of the fish species were identified using bones other than otoliths, highlighting the importance of using all identifiable structures to reconstruct diet. Individually, each species of marine mammal presented a high diversity of prey taxa, but the locally abundant Trisopterus spp. were found to be the most important prey item for all species, indicating that Trisopterus spp. is probably a key species in understanding the role of these predators in Irish waters. In the coastal marine mammals, other Gadiformes species (haddock, pollack, saithe, whiting) also contributed substantially to the diet; in contrast, in pelagic or less coastal marine mammals, prey was largely comprised of planktivorous fish, such as Atlantic mackerel, horse mackerel, blue whiting, and mesopelagic prey. Striped dolphins and Atlantic white-sided dolphins are offshore small cetaceans foraging in neritic waters. Differences between the diet of striped dolphins collected in drift nets targeting tuna and stranded on Irish coasts showed a complex foraging behaviour; the diet information shows that although this dolphin forages mainly in oceanic waters it may occasionally forage on the continental shelf, feeding on available prey. The Atlantic white-sided dolphin diet showed that this species prefers to feed over the continental edge, where planktivorous fish are abundant. Some resource partitioning was found in bottlenose dolphins in Irish waters consistent with previous genetic and stable isotope analysis studies. Bottlenose dolphins in Irish waters appears to be generalist feeders consuming more than 30 prey species, however most of the diet comprised a few locally abundant species, especially gadoid fish including haddock/pollack/saithe group and Trisopterus spp., but the contribution of Atlantic hake, conger eels and the pelagic planktivorous horse mackerel were also important. Stomach content information suggests that three different feeding behaviours might occur in bottlenose dolphin populations in Irish waters; firstly a coastal behaviour, with animals feeding on prey that mainly inhabit areas close to the coast; secondly an offshore behaviour where dolphins feed on offshore species such as squid or mesopelagic fish; and a third more complex behaviour that involves movements over the continental shelf and close to the shelf edge. The other three coastal marine mammal species (harbour porpoise, harbour seal and grey seal) were found to be feeding on similar prey and competition for food resources among these sympatric species might occur. Both species of seals were found to have a high overlap (more than 80%) in their diet composition, but while grey seals feed on large fish (>110mm), harbour seals feed mostly on smaller fish (<110mm), suggesting some spatial segregation in foraging. Harbour porpoises and grey seals are potentially competing for the same food resource but some differences in prey species were found and some habitat partitioning might occur. Direct interaction (by catch) between dolphins and fisheries was detected in all species. Most of the prey found in the stomach contents from both stranded and by catch dolphins were smaller sizes than those targeted by commercial fisheries. In fact, the total annual food consumption of the species studied was found to be very small (225,160 tonnes) in comparison to fishery landings for the same area (~2 million tonnes). However, marine mammal species might be indirectly interacting with fisheries, removing forage fish. Incorporating the dietary information obtained from the four coastal species, an ECOPATH food web model was established for the Irish Sea, based on data from 2004. Five trophic levels were found, with bottlenose dolphins and grey and harbour seals occurring at the highest trophic level. A comparison with a previous model based on 1973 data suggests that while the overall Irish Sea ecosystem appears to be “maturing”, some indices indicate that the 2004 fishery was less efficient and was targeting fish at higher trophic levels than in 1973, which is reflected in the mean trophic level of the catch. Depletion or substantial decrease of some of the Irish Sea fish stocks has resulted in a significant decline in landings in this area. The integration of diet information in mass-balance models to construct ecosystem food-webs will help to understand the trophic role of these apex predators within the ecosystem.

On stable non supersymmetric vacua at the bottom of cascading theories

We consider a wide class of cascading gauge theories which usually lead to runaway behaviour in the IR, and discuss possible deformations of the superpotential at the bottom of the cascade which stabilize the runaway direction and provide stable non-supersymmetric vacua. The models we find may allow for a weakly coupled supergravity analysis of dynamical supersymmetric breaking in the context of the gauge/string correspondence. © SISSA 2006.

Stable serum levels of anti-Müllerian hormone during the menstrual cycle: A prospective study in normo-ovulatory women

Background: Anti-Müllerian hormone (AMH), secreted by the granulosa cells of preantral and small antral follicles, has been described as a potential marker of the ovarian reserve. The aim of this prospective study is to investigate the variations of AMH during the menstrual cycle in a young selected population of normo-ovulatory women and to analyse the correlation with other cyclic hormones. Methods: Twenty healthy volunteers from 19 to 35 years old, with regular menstrual cycles (26-31 days), normal ovulation (day 10-16), normal hormonal profile and normal body mass index (18-26 kg/m2) were recruited. AMH, inhibin B, LH, FSH, estradiol and progesterone were measured on days 3, 7, 10, 11, 12, 13, 14, 15, 16, 18, 21 and 25 of a spontaneous cycle. Results: AMH serum levels, either expressed by cycleday or aligned according to the ovulation day, did not show any significant variations during the menstrual cycle. Conclusions: No significant fluctuation of the AMH level during the menstrual cycle was observed. Therefore, this hormone is particularly interesting for clinical evaluation of the ovarian reserve as it may be used at any time during the cycle. © The Author 2007.

Stable isotope ratios indicate diet and habitat use in New World monkeys.

This paper demonstrates the use of stable isotope ratios of carbon and nitrogen in animal tissue for indicating aspects of species behavioral strategy. We analyzed hair from individuals representing four species of New World monkeys (Alouatta palliata, the mantled howler; Ateles geoffroyi, the spider monkey; Cebus capucinus, the capuchin; and Brachyteles arachnoides, the woolly-spider monkey or muriqui) for delta 13C and delta 15N using previously developed methods. There are no significant differences in either carbon or nitrogen ratios between sexes, sampling year, or year of analysis. Seasonal differences in delta 13C reached a low level of significance but do not affect general patterns. Variation within species was similar to that recorded previously within single individuals. The omega 13C data show a bimodal distribution with significant difference between the means. The two monkey populations living in an evergreen forest were similar to each other and different from the other two monkey populations that inhabited dry, deciduous forests. This bimodal distribution is independent of any particular species' diet and reflects the level of leaf cover in the two types of forest. The delta 15N data display three significantly different modes. The omnivorous capuchins were most positive reflecting a trophic level offset. The spider monkeys and the muriquis were similar to one another and significantly more positive than the howlers. This distribution among totally herbivorous species correlates with the ingestion of legumes by the howler monkey population. In combination, these data indicate that museum-curated primate material can be analyzed to yield information on forest cover and diet in populations and species lacking behavioral data.

The F4 fimbrial chaperone FaeE is stable as a monomer that does not require self-capping of its pilin-interactive surfaces.

Many Gram-negative bacteria use the chaperone-usher pathway to express adhesive surface structures, such as fimbriae, in order to mediate attachment to host cells. Periplasmic chaperones are required to shuttle fimbrial subunits or pilins through the periplasmic space in an assembly-competent form. The chaperones cap the hydrophobic surface of the pilins through a donor-strand complementation mechanism. FaeE is the periplasmic chaperone required for the assembly of the F4 fimbriae of enterotoxigenic Escherichia coli. The FaeE crystal structure shows a dimer formed by interaction between the pilin-binding interfaces of the two monomers. Dimerization and tetramerization have been observed previously in crystal structures of fimbrial chaperones and have been suggested to serve as a self-capping mechanism that protects the pilin-interactive surfaces in solution in the absence of the pilins. However, thermodynamic and biochemical data show that FaeE occurs as a stable monomer in solution. Other lines of evidence indicate that self-capping of the pilin-interactive interfaces is not a mechanism that is conservedly applied by all periplasmic chaperones, but is rather a case-specific solution to cap aggregation-prone surfaces.

An integrated study (geochemistry, stable oxygen and carbon isotopes, nannofossils, planktonic foraminifera, inoceramid bivalves, ammonites and crinoids) of the Waxahachie Dam Spillway section, north Texas: a possible boundary stratotype for the base of the Campanian Stage

The spillway of Lake Waxahachie, Ellis County (Texas), exposes a > 17 m section of the Hutchins Member of the Austin Chalk Group, un-conformably overlain by Taylor Clay. The Austin sequence was regarded as a potential Global Stratotype Section for the base of the Campanian Stage at the 1995 Brussels meeting on Cretaceous Stage boundaries, with the last occurrence of the crinoid Marsupites testudinarius (von Schlotheim, 1820) as the potential boundary marker. An integrated study of the geochemistry, stable carbon and oxgen isotopes, nannofossils, planktonic foraminifera, inoceramid bivalves, ammonites and crinoids of this section place the last occurrence of M. testudinarius in a matrix of eighteen ancillary biostratigraphic markers, while the boundary can also be recognised on the basis of a delta C-13 excursion that can, in principle, be detected globally in marine sediments. A new forma of the crinoid Marsupites testudinarius is introduced. The Waxahachie section fulfils sufficient geological criteria as to be an excellent candidate GSSP for the base of the Campanian Stage, if problems of ownership and access to the section can be resolved.

A regime shift in the North Sea circa 1988 linked to changes in the North Sea horse mackerel fishery

After 1987, Phytoplankton Colour (a visual estimate of chlorophyll) measured on samples taken by the continuous plankton recorder (CPR) in the North Sea increased substantially, both in level and seasonal extent, compared to earlier years since 1946. Many species of phytoplankton and zooplankton showed marked changes in abundance at about the same time. These events coincided with a large increase in catches of the western stock of the horse mackerel (Trachurus trachurus L.) in the northern North Sea reflecting a northerly expansion of the stock along the shelf edge from the Bay of Biscay to the North Sea after 1987. Using a 3D hydrodynamic model, with input from measured wind parameters, monthly transport of oceanic water into the North Sea has been calculated for the period 1976–1994, integrated for a section from Orkney to Shetland to Norway. A substantial increase in oceanic inflow occurred in the winter months, December to March, from 1988. Higher sea surface temperatures were also measured after 1987 especially in spring and summer months. These biological and physical events may be a response to observed changes in pressure distribution over the North Atlantic. From 1988 onwards, the North Atlantic Oscillation (NAO) index, the pressure difference between Iceland and the Azores, increased to the highest positive level observed in this century. Positive NAO anomalies are associated with stronger and more southerly tracks of the westerly winds and higher temperatures in western Europe. These changing wind distributions may have led to an increase in the northerly advection of water along the western edge of the European shelf and may have assisted the migration of the horse mackerel. This study is possibly a unique demonstration of a correlation between three different trophic levels of a marine ecosystem and hydrographic and atmospheric events at decadal and regional scales. The results emphasise the importance of maintaining into the future long term programmes such as the CPR.