Use of Equivalent Hermitian Hamiltonian for PTPT-Symmetric Sinusoidal Optical Lattices

We show how the band structure and beam dynamics of non-Hermitian $PT$-symmetric sinusoidal optical lattices can be approached from the point of view of the equivalent Hermitian problem, obtained by an analytic continuation in the transverse spatial variable $x$. In this latter problem the eigenvalue equation reduces to the Mathieu equation, whose eigenfunctions and properties have been well studied. That being the case, the beam propagation, which parallels the time-development of the wave-function in quantum mechanics, can be calculated using the equivalent of the method of stationary states. We also discuss a model potential that interpolates between a sinusoidal and periodic square well potential, showing that some of the striking properties of the sinusoidal potential, in particular birefringence, become much less prominent as one goes away from the sinusoidal case.Comment: 11 pages, 8 figure

Longitudinal Profiles of Adaptive Behavior in Fragile X Syndrome

To examine longitudinally the adaptive behavior patterns in fragile X syndrome

Toward Innovative, Cost-Effective, and Systemic Solutions to Improve Outcomes and Well-Being of Military Families Affected by Autism Spectrum Disorder

The burdens faced by military families who have a child with autism are unique. The usual challenges of securing diagnostic, treatment, and educational services are compounded by life circumstances that include the anxieties of war, frequent relocation and separation, and a demand structure that emphasizes mission readiness and service. Recently established military autism-specific health care benefits set the stage for community-viable and cost-effective solutions that can achieve better outcomes for children and greater well-being for families. Here we argue for implementation of evidence-based solutions focused on reducing age of diagnosis and improving access to early intervention, as well as establishment of a tiered menu of services, individualized to the child and family, that fit with the military ethos and system of health care. Absence of this new model of care could compromise the utility and sustainability of the autism-specific benefit

Solitary waves in the Nonlinear Dirac Equation

In the present work, we consider the existence, stability, and dynamics of solitary waves in the nonlinear Dirac equation. We start by introducing the Soler model of self-interacting spinors, and discuss its localized waveforms in one, two, and three spatial dimensions and the equations they satisfy. We present the associated explicit solutions in one dimension and numerically obtain their analogues in higher dimensions. The stability is subsequently discussed from a theoretical perspective and then complemented with numerical computations. Finally, the dynamics of the solutions is explored and compared to its non-relativistic analogue, which is the nonlinear Schr{\"o}dinger equation. A few special topics are also explored, including the discrete variant of the nonlinear Dirac equation and its solitary wave properties, as well as the PT-symmetric variant of the model

Variability in school closure decisions in response to 2009 H1N1: a qualitative systems improvement analysis

<p>Abstract</p> <p>Background</p> <p>School closure was employed as a non-pharmaceutical intervention against pandemic 2009 H1N1, particularly during the first wave. More than 700 schools in the United States were closed. However, closure decisions reflected significant variation in rationales, decision triggers, and authority for closure. This variability presents the opportunity for improved efficiency and decision-making.</p> <p>Methods</p> <p>We identified media reports relating to school closure as a response to 2009 H1N1 by monitoring high-profile sources and searching Lexis-Nexis and Google news alerts, and reviewed reports for key themes. News stories were supplemented by observing conference calls and meetings with health department and school officials, and by discussions with decision-makers and community members.</p> <p>Results</p> <p>There was significant variation in the stated goal of closure decision, including limiting community spread of the virus, protecting particularly vulnerable students, and responding to staff shortages or student absenteeism. Because the goal of closure is relevant to its timing, nature, and duration, unclear rationales for closure can challenge its effectiveness. There was also significant variation in the decision-making authority to close schools in different jurisdictions, which, in some instances, was reflected in open disagreement between school and public health officials. Finally, decision-makers did not appear to expect the level of scientific uncertainty encountered early in the pandemic, and they often expressed significant frustration over changing CDC guidance.</p> <p>Conclusions</p> <p>The use of school closure as a public health response to epidemic disease can be improved by ensuring that officials clarify the goals of closure and tailor closure decisions to those goals. Additionally, authority to close schools should be clarified in advance, and decision-makers should expect to encounter uncertainty disease emergencies unfold and plan accordingly.</p

Do Children with Fragile X Syndrome Show Declines or Plateaus in Adaptive Behavior?

This study explores if children with fragile X syndrome (FXS) show advances, declines, or plateaus in adaptive behavior over time and the relationship of nonverbal cognitive abilities and autistic behavior on these trajectories. Parents of 55 children with FXS completed the Vineland Adaptive Behavior Scales between 3 and 6 times from 2 to 10 years of age. Using raw scores, results indicate that about half of the sample showed advances in adaptive behavior, while the other half showed declines, indicating a regression in skills. Children who were more cognitively advanced and had less autistic behaviors had higher trajectories. Understanding the developmental course of adaptive behavior in FXS has implications for educational planning and intervention, especially for those children showing declines

Strain-induced pseudomagnetic field and Landau levels in photonic structures

Magnetic effects at optical frequencies are notoriously weak. This is evidenced by the fact that the magnetic permeability of nearly all materials is unity in the optical frequency range, and that magneto-optical devices (such as Faraday isolators) must be large in order to allow for a sufficiently strong effect. In graphene, however, it has been shown that inhomogeneous strains can induce 'pseudomagnetic fields' that behave very similarly to real fields. Here, we show experimentally and theoretically that, by properly structuring a dielectric lattice, it is possible to induce a pseudomagnetic field at optical frequencies in a photonic lattice, where the propagation dynamics is equivalent to the evolution of an electronic wavepacket in graphene. To our knowledge, this is the first realization of a pseudomagnetic field in optics. The induced field gives rise to multiple photonic Landau levels (singularities in the density of states) separated by band gaps. We show experimentally and numerically that the gaps between these Landau levels give rise to transverse confinement of the optical modes. The use of strain allows for the exploration of magnetic effects in a non-resonant way that would be otherwise inaccessible in optics. Employing inhomogeneous strain to induce pseudomagnetism suggests the possibility that aperiodic photonic crystal structures can achieve greater field-enhancement and slow-light effects than periodic structures via the high density-of-states at Landau levels. Generalizing these concepts to other systems beyond optics, for example with matter waves in optical potentials, offers new intriguing physics that is fundamentally different from that in purely periodic structures.Comment: 24 pages including supplementary information section, 4 figure

Would school closure for the 2009 H1N1 influenza epidemic have been worth the cost?: a computational simulation of Pennsylvania

<p>Abstract</p> <p>Background</p> <p>During the 2009 H1N1 influenza epidemic, policy makers debated over whether, when, and how long to close schools. While closing schools could have reduced influenza transmission thereby preventing cases, deaths, and health care costs, it may also have incurred substantial costs from increased childcare needs and lost productivity by teachers and other school employees.</p> <p>Methods</p> <p>A combination of agent-based and Monte Carlo economic simulation modeling was used to determine the cost-benefit of closing schools (vs. not closing schools) for different durations (range: 1 to 8 weeks) and symptomatic case incidence triggers (range: 1 to 30) for the state of Pennsylvania during the 2009 H1N1 epidemic. Different scenarios varied the basic reproductive rate (R₀) from 1.2, 1.6, to 2.0 and used case-hospitalization and case-fatality rates from the 2009 epidemic. Additional analyses determined the cost per influenza case averted of implementing school closure.</p> <p>Results</p> <p>For all scenarios explored, closing schools resulted in substantially higher net costs than not closing schools. For R₀= 1.2, 1.6, and 2.0 epidemics, closing schools for 8 weeks would have resulted in median net costs of $21.0 billion (95$8.0 - $45.3 billion). The median cost per influenza case averted would have been$14,185 ($5,423 -$30,565) for R₀= 1.2, $25,253 ($9,501 - $53,461) for R₀= 1.6, and$23,483 ($8,870 -$50,926) for R₀= 2.0.</p> <p>Conclusions</p> <p>Our study suggests that closing schools during the 2009 H1N1 epidemic could have resulted in substantial costs to society as the potential costs of lost productivity and childcare could have far outweighed the cost savings in preventing influenza cases.</p