A proof of Perko's conjectures for the Bogdanov-Takens system

The Bogdanov-Takens system has at most one limit cycle and, in the parameter space, it exists between a Hopf and a saddle-loop bifurcation curves. The aim of this paper is to prove the Perko's conjectures about some analytic properties of the saddle-loop bifurcation curve. Moreover, we provide sharp piecewise algebraic upper and lower bounds for this curve

Optimisation of DSF and SOA based phase conjugators by incorporating noise-suppressing fibre gratings

We compare the performance of dispersion-shifted-fibre (DSF) and semiconductor-optical-amplifier (SOA) based phase conjugators for a 10 Gb/s non-return-to-zero system with respect to conversion efficiency, noise figure and distortion. Fibre gratings are used for signal extraction and amplified spontaneous emission (ASE) suppression, allowing closer wavelength spacing and reducing the conjugation noise figure by up to 12 dB. Despite the higher SOA conversion efficiency, both conjugators give similar noise figures with ASE suppression. However, the DSF based conjugator has the advantage of distortion tolerance at higher input power. Introduction: Optical phase conjugation has attracted much recent research attention due to its potential application for group-velocity-dispersion and self-phase-modulation compensation in mid-point spectral inversion (MPSI) systems, and also for coherent wavelength conversion in optical switching and routing. The two most promising optical phase conjugation techniques are four-wave mixing (FWM) in either dispersion-shifted fibre (DSF), or semiconductor optical amplifiers (SOA). A DSF based conjugator requires phase matching close to its zero dispersion wavelength for efficient four-wave mixing. This restricts its wavelength flexibility compared to an SOA based conjugator which offers a much wider conversion bandwidth. Furthermore, the low FWM conversion efficiency in passive DSF seems to make the SOA a preferred phase conjugating medium. However, in a practical communication system, conjugation optical signal-to-noise ratio (SNR) is more important than conversion efficiency. The noise at the conjugate wavelength is usually dominated by the amplified spontaneous emission (ASE) noise from the pump and signal. The reduction of this noise has been demonstrated in an SOA based conjugator (i) by bandpass filtering of the pump and/or signal waves before mixing, and (ii) by the insertion of a notch filter at the conjugate wavelength before the conjugator. In this letter, SOA and DSF based conjugators are compared by investigating the conversion efficiency, noise and eye opening in a 10 Gb/s non-return-to-zero (NRZ) externally-modulated system, using an identical filtering network. We report for the first time the use of fibre gratings for efficient ASE noise filtering and conjugate signal extraction. The performance enhancement using these noise-suppressing gratings is also investigated

From genes to behavior: placing cognitive models in the context of biological pathways.

Connecting neural mechanisms of behavior to their underlying molecular and genetic substrates has important scientific and clinical implications. However, despite rapid growth in our knowledge of the functions and computational properties of neural circuitry underlying behavior in a number of important domains, there has been much less progress in extending this understanding to their molecular and genetic substrates, even in an age marked by exploding availability of genomic data. Here we describe recent advances in analytical strategies that aim to overcome two important challenges associated with studying the complex relationship between genes and behavior: (i) reducing distal behavioral phenotypes to a set of molecular, physiological, and neural processes that render them closer to the actions of genetic forces, and (ii) striking a balance between the competing demands of discovery and interpretability when dealing with genomic data containing up to millions of markers. Our proposed approach involves linking, on one hand, models of neural computations and circuits hypothesized to underlie behavior, and on the other hand, the set of the genes carrying out biochemical processes related to the functioning of these neural systems. In particular, we focus on the specific example of value-based decision-making, and discuss how such a combination allows researchers to leverage existing biological knowledge at both neural and genetic levels to advance our understanding of the neurogenetic mechanisms underlying behavior