Growth rate for the expected value of a generalized random Fibonacci sequence

A random Fibonacci sequence is defined by the relation g_n = | g_{n-1} +/- g_{n-2} |, where the +/- sign is chosen by tossing a balanced coin for each n. We generalize these sequences to the case when the coin is unbalanced (denoting by p the probability of a +), and the recurrence relation is of the form g_n = |\lambda g_{n-1} +/- g_{n-2} |. When \lambda >=2 and 0 < p <= 1, we prove that the expected value of g_n grows exponentially fast. When \lambda = \lambda_k = 2 cos(\pi/k) for some fixed integer k>2, we show that the expected value of g_n grows exponentially fast for p>(2-\lambda_k)/4 and give an algebraic expression for the growth rate. The involved methods extend (and correct) those introduced in a previous paper by the second author

Late-Term Elective Abortion and Susceptibility to Posttraumatic Stress Symptoms

The primary aim of this study was to compare the experience of an early abortion (1st trimester) to a late abortion (2nd and 3rd trimester) relative to Posttraumatic Stress Disorder (PTSD) symptoms after controlling for socio-demographic and personal history variables. Online surveys were completed by 374 women who experienced either a 1st trimester abortion (up to 12 weeks gestation) or a 2nd or 3rd trimester abortion (13 weeks gestation or beyond). Most respondents (81%) were U.S. citizens. Later abortions were associated with higher Intrusion subscale scores and with a greater likelihood of reporting disturbing dreams, reliving of the abortion, and trouble falling asleep. Reporting the pregnancy was desired by one's partner, experiencing pressure to abort, having left the partner prior to the abortion, not disclosing the abortion to the partner, and physical health concerns were more common among women who received later abortions. Social reasons for the abortion were linked with significantly higher PTSD total and subscale scores for the full sample. Women who postpone their abortions may need more active professional intervention before securing an abortion based on the increased risks identified herein. More research with diverse samples employing additional measures of mental illness is needed

Tunable delay lines in silicon photonics: coupled resonators and photonic crystals, a comparison

In this paper, we report a direct comparison between coupled resonator optical waveguides (CROWs) and photonic crystal waveguides (PhCWs), which have both been exploited as tunable delay lines. The two structures were fabricated on the same silicon-on-insulator (SOI) technological platform, with the same fabrication facilities and evaluated under the same signal bit-rate conditions. We compare the frequency- and time-domain response of the two structures; the physical mechanism underlying the tuning of the delay; the main limits induced by loss, dispersion, and structural disorder; and the impact of CROW and PhCW tunable delay lines on the transmission of data stream intensity and phase modulated up to 100 Gb/s. The main result of this study is that, in the considered domain of applications, CROWs and PhCWs behave much more similarly than one would expect. At data rates around 100 Gb/s, CROWs and PhCWs can be placed in competition. Lower data rates, where longer absolute delays are required and propagation loss becomes a critical issue, are the preferred domain of CROWs fabricated with large ring resonators, while at data rates in the terabit range, PhCWs remain the leading technology

Conceptual design study for an advanced cab and visual system, volume 2

The performance, design, construction and testing requirements are defined for developing an advanced cab and visual system. The rotorcraft system integration simulator is composed of the advanced cab and visual system and the rotorcraft system motion generator, and is part of an existing simulation facility. User's applications for the simulator include rotorcraft design development, product improvement, threat assessment, and accident investigation

Fermions and Loops on Graphs. I. Loop Calculus for Determinant

This paper is the first in the series devoted to evaluation of the partition function in statistical models on graphs with loops in terms of the Berezin/fermion integrals. The paper focuses on a representation of the determinant of a square matrix in terms of a finite series, where each term corresponds to a loop on the graph. The representation is based on a fermion version of the Loop Calculus, previously introduced by the authors for graphical models with finite alphabets. Our construction contains two levels. First, we represent the determinant in terms of an integral over anti-commuting Grassman variables, with some reparametrization/gauge freedom hidden in the formulation. Second, we show that a special choice of the gauge, called BP (Bethe-Peierls or Belief Propagation) gauge, yields the desired loop representation. The set of gauge-fixing BP conditions is equivalent to the Gaussian BP equations, discussed in the past as efficient (linear scaling) heuristics for estimating the covariance of a sparse positive matrix.Comment: 11 pages, 1 figure; misprints correcte

Effect of titanium dioxide (TiO₂) nanoparticle coating on the detection performance of microfiber knot resonator sensors for relative humidity measurement

In this study, the sensitivity and the linearity of the un-coated and TiO2-coated microfiber knot resonator (MKR) have been analyzed. The MKR is very sensitive to humidity changes since its refractive index is strongly humidity dependent. As a result, shifts occur in the resonance wavelength and there are also changes in output power. The un-coated MKR showed a sensitivity of 1.3 pm/%RH, in terms of the resonance wavelength, and a sensitivity of 0.0626 dB/%RH for the transmitted output power. The sensitivity increased greatly after the deposition of a porous TiO2 nanoparticle coating on the MKR. The TiO2-coated MKR showed an improved sensitivity of 2.5 pm/%RH, with respect to the resonance wavelength, and 0.0836 dB/%RH for the transmitted output power. This MKR sensor has the potential for use in a variety of humidity sensing applications

A review of size and geometrical factors influencing resonant frequencies in metamaterials

Although metamaterials and so-called left-handed media have originated from theoretical considerations, it is only by their practical fabrication and the measurement of their properties that they have gained credibility and can fulfil the potential of their predicted properties. In this review we consider some of the more generally applicable fabrication methods and changes in geometry as they have progressed, exhibiting resonant frequencies ranging from radio waves to the visible optical region

Variable Waist-Diameter Mach-Zehnder Tapered-Fiber Interferometer as Humidity and Temperature Sensor

In-line single-mode tapered-fiber Mach-Zehnder interferometer (MZI-SMTF) with average waist diameters (davg) of 4.05 and 2.89 μ m have been fabricated, and both the temperature and the humidity sensitivity of the surrounding media have been measured and compared. The humidity and the temperature were measured over the ranges from 0% to 90% and 28 °C to 40 °C, respectively. The stability of the system at 50%RH and 90%RH was investigated, while the temperature of the chamber was maintained at about 28 °C. The humidity and temperature sensitivity resolution values were 0.02 nm/%RH and 0.05 nm/0.1 °C for the MZI-SMTF-1 with an average waist diameter of 4.05 μ m , while they were 0.01 nm/%RH and 0.025 nm/0.1 °C for the MZI-SMTF-2 with an average waist diameter of 2.89 μ m

A Bayesian General Linear Modeling Approach to Cortical Surface fMRI Data Analysis

Cortical surface functional magnetic resonance imaging (cs-fMRI) has recently grown in popularity versus traditional volumetric fMRI. In addition to offering better whole-brain visualization, dimension reduction, removal of extraneous tissue types, and improved alignment of cortical areas across subjects, it is also more compatible with common assumptions of Bayesian spatial models. However, as no spatial Bayesian model has been proposed for cs-fMRI data, most analyses continue to employ the classical general linear model (GLM), a “massive univariate” approach. Here, we propose a spatial Bayesian GLM for cs-fMRI, which employs a class of sophisticated spatial processes to model latent activation fields. We make several advances compared with existing spatial Bayesian models for volumetric fMRI. First, we use integrated nested Laplacian approximations, a highly accurate and efficient Bayesian computation technique, rather than variational Bayes. To identify regions of activation, we utilize an excursions set method based on the joint posterior distribution of the latent fields, rather than the marginal distribution at each location. Finally, we propose the first multi-subject spatial Bayesian modeling approach, which addresses a major gap in the existing literature. The methods are very computationally advantageous and are validated through simulation studies and two task fMRI studies from the Human Connectome Project. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement