Fear learning circuitry is biased toward generalization of fear associations in posttraumatic stress disorder.

Fear conditioning is an established model for investigating posttraumatic stress disorder (PTSD). However, symptom triggers may vaguely resemble the initial traumatic event, differing on a variety of sensory and affective dimensions. We extended the fear-conditioning model to assess generalization of conditioned fear on fear processing neurocircuitry in PTSD. Military veterans (n=67) consisting of PTSD (n=32) and trauma-exposed comparison (n=35) groups underwent functional magnetic resonance imaging during fear conditioning to a low fear-expressing face while a neutral face was explicitly unreinforced. Stimuli that varied along a neutral-to-fearful continuum were presented before conditioning to assess baseline responses, and after conditioning to assess experience-dependent changes in neural activity. Compared with trauma-exposed controls, PTSD patients exhibited greater post-study memory distortion of the fear-conditioned stimulus toward the stimulus expressing the highest fear intensity. PTSD patients exhibited biased neural activation toward high-intensity stimuli in fusiform gyrus (P<0.02), insula (P<0.001), primary visual cortex (P<0.05), locus coeruleus (P<0.04), thalamus (P<0.01), and at the trend level in inferior frontal gyrus (P=0.07). All regions except fusiform were moderated by childhood trauma. Amygdala-calcarine (P=0.01) and amygdala-thalamus (P=0.06) functional connectivity selectively increased in PTSD patients for high-intensity stimuli after conditioning. In contrast, amygdala-ventromedial prefrontal cortex (P=0.04) connectivity selectively increased in trauma-exposed controls compared with PTSD patients for low-intensity stimuli after conditioning, representing safety learning. In summary, fear generalization in PTSD is biased toward stimuli with higher emotional intensity than the original conditioned-fear stimulus. Functional brain differences provide a putative neurobiological model for fear generalization whereby PTSD symptoms are triggered by threat cues that merely resemble the index trauma.

Volume, volatility, and leverage: A dynamic analysis

This paper uses dynamic impulse response analysis to investigate the interrelationships among stock price volatility, trading volume, and the leverage effect. Dynamic impulse response analysis is a technique for analyzing the multi-step-ahead characteristics of a nonparametric estimate of the one-step conditional density of a strictly stationary process. The technique is the generalization to a nonlinear process of Sims-style impulse response analysis for linear models. In this paper, we refine the technique and apply it to a long panel of daily observations on the price and trading volume of four stocks actively traded on the NYSE: Boeing, Coca-Cola, IBM, and MMM.

Analytic-domain lens design with proximate ray tracing.

We have developed an alternative approach to optical design which operates in the analytical domain so that an optical designer works directly with rays as analytical functions of system parameters rather than as discretely sampled polylines. This is made possible by a generalization of the proximate ray tracing technique which obtains the analytical dependence of the rays at the image surface (and ray path lengths at the exit pupil) on each system parameter. The resulting method provides an alternative direction from which to approach system optimization and supplies information which is not typically available to the system designer. In addition, we have further expanded the procedure to allow asymmetric systems and arbitrary order of approximation, and have illustrated the performance of the method through three lens design examples.

Transformation optics with photonic band gap media.

We introduce a class of optical media based on adiabatically modulated, dielectric-only, and potentially extremely low-loss, photonic crystals (PC). The media we describe represent a generalization of the eikonal limit of transformation optics (TO). The basis of the concept is the possibility to fit some equal frequency surfaces of certain PCs with elliptic surfaces, allowing them to mimic the dispersion relation of light in anisotropic effective media. PC cloaks and other TO devices operating at visible wavelengths can be constructed from optically transparent substances such as glasses, whose attenuation coefficient can be as small as 10 dB/km, suggesting the TO design methodology can be applied to the development of optical devices not limited by the losses inherent to metal-based, passive metamaterials.

Far-field analysis of axially symmetric three-dimensional directional cloaks.

Axisymmetric radiating and scattering structures whose rotational invariance is broken by non-axisymmetric excitations present an important class of problems in electromagnetics. For such problems, a cylindrical wave decomposition formalism can be used to efficiently obtain numerical solutions to the full-wave frequency-domain problem. Often, the far-field, or Fraunhofer region is of particular interest in scattering cross-section and radiation pattern calculations; yet, it is usually impractical to compute full-wave solutions for this region. Here, we propose a generalization of the Stratton-Chu far-field integral adapted for 2.5D formalism. The integration over a closed, axially symmetric surface is analytically reduced to a line integral on a meridional plane. We benchmark this computational technique by comparing it with analytical Mie solutions for a plasmonic nanoparticle, and apply it to the design of a three-dimensional polarization-insensitive cloak.