Renormalization of Collective Modes in Large-Scale Neural Dynamics

The bulk of studies of coupled oscillators use, as is appropriate in Physics, a global coupling constant controlling all individual interactions. However, because as the coupling is increased, the number of relevant degrees of freedom also increases, this setting conflates the strength of the coupling with the effective dimensionality of the resulting dynamics. We propose a coupling more appropriate to neural circuitry, where synaptic strengths are under biological, activity-dependent control and where the coupling strength and the dimensionality can be controlled separately. Here we study a set of \(N\rightarrow \infty \) strongly- and nonsymmetrically-coupled, dissipative, powered, rotational dynamical systems, and derive the equations of motion of the reduced system for dimensions 2 and 4. Our setting highlights the statistical structure of the eigenvectors of the connectivity matrix as the fundamental determinant of collective behavior, inheriting from this structure symmetries and singularities absent from the original microscopic dynamics.     

Analytical and numerical studies of noise-induced synchronization of chaotic systems

We study the effect that the injection of a common source of noise has on the trajectories of chaotic systems, addressing some contradictory results present in the literature. We present particular examples of one-dimensional maps and the Lorenz system, both in the chaotic region, and give numerical evidence showing that the addition of a common noise to different trajectories, which start from different initial conditions, leads eventually to their perfect synchronization. When synchronization occurs, the largest Lyapunov exponent becomes negative. For a simple map we are able to show this phenomenon analytically. Finally, we analyze the structural stability of the phenomenon. (c) 2001 American Institute of Physics.     

Chiral symmetry breaking during crystallization: an advection-mediated nonlinear autocatalytic process

When a chiral chemical compound crystallizes from solution or from its melt, stirring often results in the formation of crystals of just one of the two possible enantiomers, while without fluid advection both enantiomers are formed. We demonstrate with simulations of the dynamics of the system that secondary nucleation is a nonlinear autocatalytic phenomenon that can explain these observations. Furthermore, we present theoretical arguments and experimental results that suggest that at the microscale the mechanism of secondary nucleation is whisker crystal growth and dispersion in the fluid flow.     

Pharmacological Extracts and Molecules from Virola Species: Traditional Uses,Phytochemistry, and Biological Activity

Virola is the largest genus of Myristicaceae in America, comprising about 60 species of medium-sized trees geographically spread from Mexico to southern Brazil. The plant species of this genus have been widely used in folk medicine for the treatment of several ailments, such as rheumatic pain, bronchial asthma, tumors in the joints, intestinal worms, halitosis, ulcers, and multiple infections, due to their pharmacological activity. This review presents an updated and comprehensive summary of Virola species, particularly their ethnomedicinal uses, phytochemistry, and biological activity, to support the safe medicinal use of plant extracts and provide guidance for future research. The Virola spp.’s ethnopharmacology, including in the treatment of stomach pain and gastric ulcers, as well as antimicrobial and tryponosomicidal activities, is attributable to the presence of a myriad of phytoconstituents, such as flavonoids, tannins, phenolic acids, lignans, arylalkanones, and sitosterol. Hence, such species yield potential leads or molecular scaffolds for the development of new pharmaceutical formulations, encouraging the elucidation of not-yet-understood action mechanisms and ascertaining their safety for humans.     

Enantioselective synthesis of (s)- and (R)-tolterodine by asymmetric hydrogenation of a coumarin derivative obtained by a Heck reaction

An efficient and short enantioselective synthesis of (S)- and (R)-tolterodine was performed by asymmetric hydrogenation of a coumarin intermediate, easily obtained by a Heck reaction from inexpensive and commercially available starting materials.     

Comparative analysis of the clathrate forms of syndiotactic polystyrene,poly (p-methylstyrene) and poly (m-methylstyrene)

The crystal structures of the clathrate forms of syndiotactic polystyrene (s-PS), poly (p-methylstyrene) (s-PPMS) and poly (m-methylstyrene) (s-PMMS) containing guest molecules having widely different steric hindrance are compared in detail. Common features and differences concerning the packing of the chains, the shape and the dimensions of the cavities and the stability of the forms deprived of the guest molecules are pointed out. A new clathrate form of s-PPMS containing CS₂ is also described.     

Hard photon next-to-leading corrections to two-fermion production in e + e − collisions above the Z 0 peak

A complete next-to-leading order calculation of the initial-state O (α) photonic corrections to hadron and lepton-pair production in e ⁺ e ^?. collisions is presented. The impact of the next-to-leading order corrections on the twofermion cross section and forward-backward asymmetry is studied in detail for several event selections, with special emphasis on hard photon effects at LEP1.5 and LEP2 energies. It is shown that for typical realistic event selections, initial-state next-to-leading order corrections in the soft approximation can be safely extrapolated to energies above the Z ⁰ peak without significant loss of precision.     

“One pot” synthesis of 2,9-disubstituted 8-azaadenines (3,5-disubstituted 7-amino-3H-1,2,3-triazolo[4,5-d]pyrimidines)

A new simple method for the synthesis of title compounds is described starting from malononitrile, benzyl-azide and an aliphatic or aromatic nitrile.     

Population dynamics advected by chaotic flows: A discrete-time map approach

A discrete-time model of reacting evolving fields, transported by a bidimensional chaotic fluid flow, is studied. Our approach is based on the use of a Lagrangian scheme where fluid particles are advected by a two-dimensional symplectic map possibly yielding Lagrangian chaos. Each fluid particle carries concentrations of active substances which evolve according to its own reaction dynamics. This evolution is also modeled in terms of maps. Motivated by the question, of relevance in marine ecology, of how a localized distribution of nutrients or preys affects the spatial structure of predators transported by a fluid flow, we study a specific model in which the population dynamics is given by a logistic map with space-dependent coefficient, and advection is given by the standard map. Fractal and random patterns in the Eulerian spatial concentration of predators are obtained under different conditions. Exploiting the analogies of this coupled-map (advection plus reaction) system with a random map, some features of these patterns are discussed. (c) 2001 American Institute of Physics.