Resonance in Periodically Perturbed Hopf Bifurcation

We examine in detail the effect of a periodic perturbation upon a system undergoing a Hopf bifurcation. Particular attention is paid to the case of resonance between the natural Hopf bifurcation frequency and the perturbation frequency. It is shown that for a certain parameter range this Hopf bifurcation is modified by the perturbation to exhibit frequency (phase) pulling and locking, and the nature of this frequency locking is described. In addition, the effect of adding diffusion to the system is discussed, and it is shown that diffusive waves are possible.     

Polarization mode dispersion probability distribution for arbitrary distances

The probability distribution of the differential group delay (DGD) at any fiber length is determined by use of a physically reasonable model of the fiber birefringence. We show that if the fiber correlation length is of the same order as or larger than the beat length, the DGD distribution approaches a Maxwellian in roughly 30 fiber correlation lengths, corresponding to a couple of kilometers in realistic cases. We also find that the probability distribution function of the polarization dispersion vector at the output of the fiber depends on the angle between it and the local birefringence vector on the Poincaré sphere, showing that the DGD remains correlated with the orientation of the local birefringence axes over arbitrarily long distances.     

10-GHz dispersion-managed soliton fiber-optical parametric oscillator using regenerative mode locking

We demonstrate a regeneratively mode-locked fiber-optical parametric oscillator that utilizes intracavity dispersion compensation to generate pulses at a 10-GHz repetition rate in both soliton and nonsoliton regimes. At the threshold pump power the generated pulses are close to fundamental solitons. At higher pump powers we found a significant deviation of the pulses from the sech2 shape. In addition, the use of an ultralow-jitter self-starting pump-pulse source in a regenerative feedback loop allows for a significant reduction of the signal's timing jitter and amplitude noise.     

Applications of importance sampling to polarization mode dispersion

We describe the application of importance sampling to Monte-Carlo simulations of polarization-mode dispersion (PMD) in optical fibers. The method allows rare PMD events to be simulated much more efficiently than with standard Monte-Carlo methods, thus making it possible to assess the effect of PMD on system outage probabilities at realistic bit error ratios.     

Novel isoquinolone PDK1 inhibitors discovered through fragment-based lead discovery

Phosphoinositide-dependent kinase-1 (PDK1) is a critical enzyme in the PI3K/AKT pathway and to the activation of AGC family protein kinases, including S6K, SGK, and PKC. Dysregulation of this pathway plays a key role in cancer cell growth, survival and tumor angiogenesis. As such, inhibitors of PDK1 offer the promise of a new therapeutic modality for cancer treatment. Fragment based drug screening has recently become a viable entry point for hit identification. In this work, NMR spectroscopy fragment screening of PDK1 afforded novel chemotypes as orthogonal starting points from HTS screening hits. Compounds identified as hits by NMR spectroscopy were tested in a biochemical assay, and fragments with activity in both assays were clustered. The Pfizer compound file was mined via substructure and 2D similarity search, and the chemotypes were prioritized by ligand efficiency (LE), SAR mining, chemical attractiveness, and chemical enablement of promising vectors. From this effort, an isoquinolone fragment hit, 5 (IC₅₀ 870 μM, LE = 0.39), was identified as a novel, ligand efficient inhibitor of PDK1 and a suitable scaffold for further optimization. Initially in the absence of crystallographic data, a fragment growing approach efficiently explored four vectors of the isoquinolone scaffold via parallel synthesis to afford a compound with crystallographic data, 16 (IC₅₀ 41.4 μM, LE = 0.33). Subsequent lead optimization efforts provided 24 (IC₅₀ 1.8 μM, LE = 0.42), with greater than fivefold selectivity against other key pathway kinases.     

Anisotropic hinge model for polarization-mode dispersion in installed fibers

We discuss a generalized waveplate hinge model to characterize anisotropic effects associated with the hinge model of polarization-mode dispersion in installed systems. In this model, the action of the hinges is a random time-dependent rotation about a fixed axis. We obtain the probability density function of the differential group delay and the outage probability of an individual wavelength band using a combination of importance sampling and the cross-entropy method, and we then compute the noncompliant capacity ratio by averaging over wavelength bands. The results show that there are significant differences between the outage statistics predicted by isotropic and anisotropic hinge models.     

Slowly Varying Phase Planes and Boundary-Layer Theory

A method is presented that combines phase-plane techniques with the ideas of multiple scale and matched asymptotic expansions to explain the behavior of solutions to second-order, nonlinear, nonautonomous, singular boundary-value problems. It is shown that if one is willing to give up the detailed information provided by a procedure such as matched asymptotic expansions, then complete qualitative information can be obtained by the much simpler method given here. (“Complete” here means that the method provides a way of categorizing all possible solutions of such problems.) In addition, the similarities and differences between the present method and that of Melnikov, which has been useful in the study of dynamical systems, are noted.     

Importance sampling for noise-induced amplitude and timing jitter in soliton transmission systems

We discuss the application of importance-sampling techniques to the numerical simulation of transmission impairments induced by amplified spontaneous emission noise in soliton-based optical transmission systems. The method allows one to concentrate numerical simulations on the noise realizations that are most likely to result in transmission errors, thus leading to increases in speed of several orders of magnitude over standard Monte Carlo methods. We demonstrate the technique by calculating the probability distribution function of amplitude and timing fluctuations.