Signal restoration for a mass transport problem involving shear dispersion

An inverse problem associated with mass transport down a tube, when the flowing medium has a two-dimensional velocity profile, is examined. The inverse problem of estimation of a temporally varying concentration at one end of a long tube, from the measurement of the cross-sectional average concentration at the opposite end, is solved. It is shown that this inverse problem, which is associated with shear dispersion, is an ill-posed deconvolution problem. Mollification is used to produce a well-conditioned problem

Propagation of transient electromagnetic waves in time-varying media - Direct and inverse scattering problems

Wave propagation of transient electromagnetic waves in time-varying media is considered. The medium, which is assumed to be inhomogeneous and dispersive, lacks invariance under time translations. The spatial variation of the medium is assumed to be in the depth coordinate, i.e., it is stratified. The constitutive relations of the medium is a time integral of a generalized susceptibility kernel and the field. The generalized susceptibility kernel depends on one spatial and two time coordinates. The concept of wave splitting is introduced. The direct and inverse scattering problems are solved by the use of an imbedding or a Green functions approach. The direct and the inverse scattering problems are solved for a homogeneous semi-infinite medium. Explicit algorithms are developed. In this inverse scattering problem, a function depending on two time coordinates is reconstructed. Several numerical computations illustrate the performance of the algorithms

Transient waves in nonstationary media

This paper treats propagation of transient waves in nonstationary media, which has many applications in, for example, electromagnetics and acoustics. The underlying hyperbolic equation is a general, homogeneous, linear, first-order 2×2 system of equations. The coefficients in this system depend on one spatial coordinate and time. Furthermore, memory effects are modeled by integral kernels, which, in addition to the spatial dependence, are functions of two different time coordinates. These integrals generalize the convolution integrals, frequently used as a model for memory effects in the medium. Specifically, the scattering problem for this system of equations is addressed. This problem is solved by a generalization of the wave splitting concept, originally developed for wave propagation in media which are invariant under time translations, and by an imbedding or a Green's functions technique. More explicitly, the imbedding equation for the reflection kernel and the Green's functions (propagator kernels) equations are derived. Special attention is paid to the problem of nonstationary characteristics. A few numerical examples illustrate this problem

Deterministic and stochastic descriptions of gene expression dynamics

A key goal of systems biology is the predictive mathematical description of gene regulatory circuits. Different approaches are used such as deterministic and stochastic models, models that describe cell growth and division explicitly or implicitly etc. Here we consider simple systems of unregulated (constitutive) gene expression and compare different mathematical descriptions systematically to obtain insight into the errors that are introduced by various common approximations such as describing cell growth and division by an effective protein degradation term. In particular, we show that the population average of protein content of a cell exhibits a subtle dependence on the dynamics of growth and division, the specific model for volume growth and the age structure of the population. Nevertheless, the error made by models with implicit cell growth and division is quite small. Furthermore, we compare various models that are partially stochastic to investigate the impact of different sources of (intrinsic) noise. This comparison indicates that different sources of noise (protein synthesis, partitioning in cell division) contribute comparable amounts of noise if protein synthesis is not or only weakly bursty. If protein synthesis is very bursty, the burstiness is the dominant noise source, independent of other details of the model. Finally, we discuss two sources of extrinsic noise: cell-to-cell variations in protein content due to cells being at different stages in the division cycles, which we show to be small (for the protein concentration and, surprisingly, also for the protein copy number per cell) and fluctuations in the growth rate, which can have a significant impact.Comment: 23 pages, 5 figures; Journal of Statistical physics (2012

Absence of Evidence Is Not Evidence of Absence: The Color-Density Relation at Fixed Stellar Mass Persists to z ~ 1

We use data drawn from the DEEP2 Galaxy Redshift Survey to investigate the relationship between local galaxy density, stellar mass, and rest-frame galaxy color. At z ~ 0.9, we find that the shape of the stellar mass function at the high-mass (log (M*/Msun) > 10.1) end depends on the local environment, with high-density regions favoring more massive systems. Accounting for this stellar mass-environment relation (i.e., working at fixed stellar mass), we find a significant color-density relation for galaxies with 10.6 < log(M*/Msun) < 11.1 and 0.75 < z < 0.95. This result is shown to be robust to variations in the sample selection and to extend to even lower masses (down to log(M*/Msun) ~ 10.4). We conclude by discussing our results in comparison to recent works in the literature, which report no significant correlation between galaxy properties and environment at fixed stellar mass for the same redshift and stellar mass domain. The non-detection of environmental dependence found in other data sets is largely attributable to their smaller samples size and lower sampling density, as well as systematic effects such as inaccurate redshifts and biased analysis techniques. Ultimately, our results based on DEEP2 data illustrate that the evolutionary state of a galaxy at z ~ 1 is not exclusively determined by the stellar mass of the galaxy. Instead, we show that local environment appears to play a distinct role in the transformation of galaxy properties at z > 1.Comment: 10 pages, 5 Figures; Accepted for publication in MNRA

Methylphenidate and \u3ci\u3eMemory and Attention Adaptation Training\u3c/i\u3e for persistent cognitive symptoms after traumatic brain injury: a randomized, placebo-controlled trial

The purpose of this multicenter, prospective, randomized, placebo-controlled study was to evaluate and compare the efficacy of two cognitive rehabilitation interventions (Memory and Attention Adaptation Training (MAAT) and Attention Builders Training (ABT)), with and without pharmacologic enhancement (i.e., with methylphenidate (MPH) or placebo), for treating persistent cognitive problems after traumatic brain injury (TBI). Adults with a history of TBI at least four months prior to study enrollment with either objective cognitive deficits or subjective cognitive complaints were randomized to receive MPH or placebo and MAAT or ABT, yielding four treatment combinations: MAAT/MPH (N=17), ABT/MPH (N=19), MAAT/placebo (N=17), and ABT/placebo (N=18). Assessments were conducted pre-treatment (baseline) and after six weeks of treatment (post-treatment). Outcome measures included scores on neuropsychological measures and subjective rating scales. Statistical analyses used linear regression models to predict post-treatment scores for each outcome variable by treatment type, adjusting for relevant covariates. Statistically significant (p\u3c0.05) treatment-related improvements in cognitive functioning were found for word list learning (MAAT/placebo\u3eABT/placebo), nonverbal learning (MAAT/MPH\u3eMAAT/placebo and MAAT/MPH\u3eABT/MPH), and auditory working memory and divided attention (MAAT/MPH\u3eABT/MPH). These results suggest that combined treatment with metacognitive rehabilitation (MAAT) and pharmacotherapy (MPH) can improve aspects of attention, episodic and working memory, and executive functioning after TBI

Spitzer Reveals Hidden Quasar Nuclei in Some Powerful FR II Radio Galaxies

We present a Spitzer mid-infrared survey of 42 Fanaroff-Riley class II radio galaxies and quasars from the 3CRR catalog at redshift z<1. All of the quasars and 45+/-12% of the narrow-line radio galaxies have a mid-IR luminosity of nuLnu(15 micron) > 8E43 erg/s, indicating strong thermal emission from hot dust in the active galactic nucleus. Our results demonstrate the power of Spitzer to unveil dust-obscured quasars. The ratio of mid-IR luminous narrow-line radio galaxies to quasars indicates a mean dust covering fraction of 0.56+/-0.15, assuming relatively isotropic emission. We analyze Spitzer spectra of the 14 mid-IR luminous narrow-line radio galaxies thought to host hidden quasar nuclei. Dust temperatures of 210-660 K are estimated from single-temperature blackbody fits to the low and high-frequency ends of the mid-IR bump. Most of the mid-IR luminous radio galaxies have a 9.7 micron silicate absorption trough with optical depth <0.2, attributed to dust in a molecular torus. Forbidden emission lines from high-ionization oxygen, neon, and sulfur indicate a source of far-UV photons in the hidden nucleus. However, we find that the other 55+/-13% of narrow-line FR II radio galaxies are weak at 15 micron, contrary to single-population unification schemes. Most of these galaxies are also weak at 30 micron. Mid-IR weak radio galaxies may constitute a separate population of nonthermal, jet-dominated sources with low accretion powerComment: 34 pages, 8 figures, ApJ submitte

Methylphenidate and Memory and Attention Adaptation Training for persistent cognitive symptoms after traumatic brain injury: a randomized, placebo-controlled trial

The purpose of this multicenter, prospective, randomized, placebo-controlled study was to evaluate and compare the efficacy of two cognitive rehabilitation interventions (Memory and Attention Adaptation Training (MAAT) and Attention Builders Training (ABT)), with and without pharmacological enhancement (ie, with methylphenidate (MPH) or placebo), for treating persistent cognitive problems after traumatic brain injury (TBI). Adults with a history of TBI at least 4 months before study enrollment with either objective cognitive deficits or subjective cognitive complaints were randomized to receive MPH or placebo and MAAT or ABT, yielding four treatment combinations: MAAT/MPH (N=17), ABT/MPH (N=19), MAAT/placebo (N=17), and ABT/placebo (N=18). Assessments were conducted pre-treatment (baseline) and after 6 weeks of treatment (post treatment). Outcome measures included scores on neuropsychological measures and subjective rating scales. Statistical analyses used linear regression models to predict post-treatment scores for each outcome variable by treatment type, adjusting for relevant covariates. Statistically significant (PABT/placebo), nonverbal learning (MAAT/MPH>MAAT/placebo and MAAT/MPH>ABT/MPH), and auditory working memory and divided attention (MAAT/MPH>ABT/MPH). These results suggest that combined treatment with metacognitive rehabilitation (MAAT) and pharmacotherapy (MPH) can improve aspects of attention, episodic and working memory, and executive functioning after TBI