Random polarization dynamics in a resonant optical medium

Random optical-pulse polarization switching along an active optical medium in the $\Lambda$-configuration with spatially disordered occupation numbers of its lower energy sub-level pair is described using the idealized integrable Maxwell-Bloch model. Analytical results describing the light polarization-switching statistics for the single self-induced transparency pulse are compared with statistics obtained from direct Monte-Carlo numerical simulations.Comment: 7 pages, 3 figure

Contemporary and Future Approaches to Precision Medicine in Inherited Cardiomyopathies: JACC Focus Seminar 3/5

Inherited cardiomyopathies are commonly occurring myocardial disorders that are associated with substantial morbidity and mortality. Clinical management strategies have focused on treatment of heart failure and arrhythmic complications in symptomatic patients according to standardized guidelines. Clinicians are now being urged to implement precision medicine, but what does this involve? Advances in understanding of the genetic underpinnings of inherited cardiomyopathies have brought new possibilities for interventions that are tailored to genes, specific variants, or downstream mechanisms. However, the phenotypic variability that can occur with any given pathogenic variant suggests that factors other than single driver gene mutations are often involved. This is propelling a new imperative to elucidate the nuanced ways in which individual combinations of genetic variation, comorbidities, and lifestyle may influence cardiomyopathy phenotypes. Here, Part 3 of a 5-part precision medicine Focus Seminar series reviews the current status and future opportunities for precision medicine in the inherited cardiomyopathies

Parabolic resonances and instabilities in near-integrable two degrees of freedom Hamiltonian flows

When an integrable two-degrees-of-freedom Hamiltonian system possessing a circle of parabolic fixed points is perturbed, a parabolic resonance occurs. It is proved that its occurrence is generic for one parameter families (co-dimension one phenomenon) of near-integrable, t.d.o. systems. Numerical experiments indicate that the motion near a parabolic resonance exhibits new type of chaotic behavior which includes instabilities in some directions and long trapping times in others. Moreover, in a degenerate case, near a {\it flat parabolic resonance}, large scale instabilities appear. A model arising from an atmospherical study is shown to exhibit flat parabolic resonance. This supplies a simple mechanism for the transport of particles with {\it small} (i.e. atmospherically relevant) initial velocities from the vicinity of the equator to high latitudes. A modification of the model which allows the development of atmospherical jets unfolds the degeneracy, yet traces of the flat instabilities are clearly observed

Arene oxidation with malonoyl peroxides

Malonoyl peroxide 7, prepared in a single step from the commercially available diacid, is an effective reagent for the oxidation of aromatics. Reaction of an arene with peroxide 7 at room temperature leads to the corresponding protected phenol which can be unmasked by aminolysis. An ionic mechanism consistent with the experimental findings and supported by isotopic labeling, Hammett analysis, EPR investigations and reactivity profile studies is proposed

Costs Of Using “Tiny Targets” to Control Glossina fuscipes fuscipes, a Vector of Gambiense Sleeping Sickness in Arua District of Uganda

Introduction To evaluate the relative effectiveness of tsetse control methods, their costs need to be analysed alongside their impact on tsetse populations. Very little has been published on the costs of methods specifically targeting human African trypanosomiasis. Methodology/Principal Findings In northern Uganda, a 250 km2 field trial was undertaken using small (0.5 X 0.25 m) insecticide-treated targets (“tiny targets”). Detailed cost recording accompanied every phase of the work. Costs were calculated for this operation as if managed by the Ugandan vector control services: removing purely research components of the work and applying local salaries. This calculation assumed that all resources are fully used, with no spare capacity. The full cost of the operation was assessed at USD 85.4 per km2, of which USD 55.7 or 65.2% were field costs, made up of three component activities (target deployment: 34.5%, trap monitoring: 10.6% and target maintenance: 20.1%). The remaining USD 29.7 or 34.8% of the costs were for preliminary studies and administration (tsetse surveys: 6.0%, sensitisation of local populations: 18.6% and office support: 10.2%). Targets accounted for only 12.9% of the total cost, other important cost components were labour (24.1%) and transport (34.6%). Discussion Comparison with the updated cost of historical HAT vector control projects and recent estimates indicates that this work represents a major reduction in cost levels. This is attributed not just to the low unit cost of tiny targets but also to the organisation of delivery, using local labour with bicycles or motorcycles. Sensitivity analyses were undertaken, investigating key prices and assumptions. It is believed that these costs are generalizable to other HAT foci, although in more remote areas, with denser vegetation and fewer people, costs would increase, as would be the case for other tsetse control techniques

Chaos around Holographic Regge Trajectories

Using methods of Hamiltonian dynamical systems, we show analytically that a dynamical system connected to the classical spinning string solution holographically dual to the principal Regge trajectory is non-integrable. The Regge trajectories themselves form an integrable island in the total phase space of the dynamical system. Our argument applies to any gravity background dual to confining field theories and we verify it explicitly in various supergravity backgrounds: Klebanov-Strassler, Maldacena-Nunez, Witten QCD and the AdS soliton. Having established non-integrability for this general class of supergravity backgrounds, we show explicitly by direct computation of the Poincare sections and the largest Lyapunov exponent, that such strings have chaotic motion.Comment: 28 pages, 5 figures. V3: Minor changes complying to referee's suggestions. Typos correcte

Nonintegrability of the two-body problem in constant curvature spaces

We consider the reduced two-body problem with the Newton and the oscillator potentials on the sphere ${\bf S}^{2}$ and the hyperbolic plane ${\bf H}^{2}$. For both types of interaction we prove the nonexistence of an additional meromorphic integral for the complexified dynamic systems.Comment: 20 pages, typos correcte

Tuning Nonlinear Mechanical Mode Coupling in GaAs Nanowires Using Cross-Section Morphology Control.

We investigate the nonlinear mechanical properties of GaAs nanowires with anisotropic cross-section. Fundamental and second order flexural modes are studied using laser interferometry with good agreement found between experiment and theory describing the nonlinear response under mechanical excitation. In particular, we demonstrate that the sign of the nonlinear coupling between orthogonal modes is dependent on the cross-section aspect ratio. The findings are of interest for applications such as amplitude to frequency conversion and vectorial force sensing

Solutions for the General, Confluent and Biconfluent Heun equations and their connection with Abel equations

In a recent paper, the canonical forms of a new multi-parameter class of Abel differential equations, so-called AIR, all of whose members can be mapped into Riccati equations, were shown to be related to the differential equations for the hypergeometric 2F1, 1F1 and 0F1 functions. In this paper, a connection between the AIR canonical forms and the Heun General (GHE), Confluent (CHE) and Biconfluent (BHE) equations is presented. This connection fixes the value of one of the Heun parameters, expresses another one in terms of those remaining, and provides closed form solutions in terms of pFq functions for the resulting GHE, CHE and BHE, respectively depending on four, three and two irreducible parameters. This connection also turns evident what is the relation between the Heun parameters such that the solutions admit Liouvillian form, and suggests a mechanism for relating linear equations with N and N-1 singularities through the canonical forms of a non-linear equation of one order less.Comment: Original version submitted to Journal of Physics A: 16 pages, related to math.GM/0002059 and math-ph/0402040. Revised version according to referee's comments: 23 pages. Sign corrected (June/17) in formula (79). Second revised version (July/25): 25 pages. See also http://lie.uwaterloo.ca/odetools.ht