Entropy rate defined by internal wave scattering in long-range propagation

Author Posting. © Acoustical Society of America, 2015. This article is posted here by permission of Acoustical Society of America for personal use, not for redistribution. The definitive version was published in Journal of the Acoustical Society of America 138 (2015): 1353, doi:10.1121/1.4928617.The reduction of information capacity of the ocean sound channel due to scattering by internal waves is a potential problem for acoustic communication, navigation, and remote sensing over long ranges. In spite of recent progress in research on acoustic signal scattering by random internal waves and the fact that random internal waves are ubiquitous in the world oceans, there is no clear understanding of how these waves influence data communication performance. The entropy decrease resulting from scattering by internal waves is an important measure of information loss. Here a rigorous calculation of the entropy is carried out using second moment transport theory equations with random sound-speed perturbations obeying the Garrett–Munk internal-wave model. It is shown that full-wave rate of entropy is of the same order of magnitude as the Kolmogorov–Sinai entropy and Lyapunov exponents for the relevant ray trajectories. The correspondence between full-wave and ray entropies suggests a correspondence between full-wave scattering and ray chaos near statistical saturation. The relatively small level of entropy rate during propagation through the random internal-wave field shows that scattering by internal waves is likely not an essential limitation for data rate and channel capacity.This work was supported in part by Office of Naval Research grant

On cohesive powers of linear orders

Cohesive powers of computable structures are effective analogs of ultrapowers, where cohesive sets play the role of ultrafilters. Let $\omega$, $\zeta$, and $\eta$ denote the respective order-types of the natural numbers, the integers, and the rationals when thought of as linear orders. We investigate the cohesive powers of computable linear orders, with special emphasis on computable copies of $\omega$. If $\mathcal{L}$ is a computable copy of $\omega$ that is computably isomorphic to the standard presentation of $\omega$, then every cohesive power of $\mathcal{L}$ has order-type $\omega + \zeta\eta$. However, there are computable copies of $\omega$, necessarily not computably isomorphic to the standard presentation, having cohesive powers not elementarily equivalent to $\omega + \zeta\eta$. For example, we show that there is a computable copy of $\omega$ with a cohesive power of order-type $\omega + \eta$. Our most general result is that if $X \subseteq \mathbb{N} \setminus \{0\}$ is either a $\Sigma_2$ set or a $\Pi_2$ set, thought of as a set of finite order-types, then there is a computable copy of $\omega$ with a cohesive power of order-type $\omega + \sigma(X \cup \{\omega + \zeta\eta + \omega^*\})$, where $\sigma(X \cup \{\omega + \zeta\eta + \omega^*\})$ denotes the shuffle of the order-types in $X$ and the order-type $\omega + \zeta\eta + \omega^*$. Furthermore, if $X$ is finite and non-empty, then there is a computable copy of $\omega$ with a cohesive power of order-type $\omega + \sigma(X)$

Associations Between Relocation and Seasonal Depression

Seasonal Affective Disorder (SAD) is a mood disorder that is characterized by depressive symptoms that onset and remit at the same times each year. Whereas few people (about 1%) experience problems severe enough to be labeled SAD, many people (estimates range from 30%-90%) may experience mild to moderate changes in depressive symptoms in response to day length and other seasonal changes. Given that latitude affects the extent to which day length varies seasonally, this study explored the extent to which international college students’ relocation to a new latitude (44.57° N; Corvallis, Oregon) may affect their seasonal depressive symptoms. It was hypothesized that 1) the severity of students’ current depressive symptoms (assessed in winter) would be related to the extent of latitudinal change between their previous residence and Corvallis, and 2) that lifetime histories of seasonal depression would be more prevalent among students from latitudes that are further from the equator. A convenience sample of 50 international students (N = 50, men=33, women=16, unreported=1) age 18 or older with evidence of English proficiency were recruited from an international learning center. Participants were surveyed on acculturative stress, social support, current depressive symptoms, and lifetime seasonal depressive symptoms. Nearly all (98%) participants came from a more southern latitude (mean latitude of origin was 27° N); thus many participants were potentially experiencing a significant latitudinal change, as well as more dramatic changes in day length. Half (49%) of participants reported clinically significant depressive symptoms. Contrary to the hypotheses, latitude change was not associated with severity of current depressive symptoms (r = 0.12). Current depressive symptoms were more related to lower social support (r = -.35, p < .05) and higher acculturative stress (r = .63 p < 0.001). Furthermore, latitude of origin was not related to lifetime history of seasonal depression (r = -.01). Thus, no support was found for the notion that latitude (considered a proxy for the magnitude of seasonal changes in day length) or change in latitude are powerful influences on international students’ depressive symptoms

Multifocal diffractive lens generating several fixed foci at different design wavelengths

We propose a method for designing multifocal diffractive lenses generating prescribed sets of foci with fixed positions at several different wavelengths. The method is based on minimizing the difference between the complex amplitudes of the beams generated by the lens microrelief at the design wavelengths, and the functions of the complex transmission of multifocal lenses calculated for these wavelengths. As an example, a zone plate generating three fixed foci at three different wavelengths was designed, fabricated, and experimentally investigated. The proof-of-concept experimental results confirm the formation of foci with fixed positions at the design wavelengths. The obtained results may find applications in the design and fabrication of novel multifocal contact and intraocular lenses with reduced chromatic effects

Plant 4/1 protein: potential player in intracellular, cell-to-cell and long-distance signaling

Originally isolated as a result of its ability to interact with the movement protein of Tomato spotted wilt virus in a yeast two-hybrid system, the 4/1 protein is proving to be an excellent tool for studying intracellular protein trafficking and intercellular communication. Expression of 4/1 in vivo is tightly regulated, first appearing in the veins of the cotyledon and later in the vasculature of the leaf and stem in association with the xylem parenchyma and phloem parenchyma. Structural studies indicate that 4/1 proteins contain as many as five coiled–coil (CC) domains; indeed, the highest level of sequence identity among 4/1 proteins involves their C-terminal CC domains, suggesting that protein–protein interaction is important for biological function. Recent data predict that the tertiary structure of this C-terminal CC domain is strikingly similar to that of yeast protein She2p; furthermore, like She2p, 4/1 protein exhibits RNA-binding activity, and mutational analysis has shown that the C-terminal CC domain is responsible for RNA binding. The 4/1 protein contains a nuclear export signal. Additional microscopy studies involving leptomycin and computer prediction suggest the presence of a nuclear localization signal as well

Statistics of normal mode amplitudes in an ocean with random sound-speed perturbations : cross-mode coherence and mean intensity

Author Posting. © Acoustical Society of America, 2009. This article is posted here by permission of Acoustical Society of America for personal use, not for redistribution. The definitive version was published in Journal of the Acoustical Society of America 126 (2009): 1026-1035, doi:10.1121/1.3158818.In this paper Creamer's [(1996). J. Acoust. Soc. Am. 99, 2825–2838] transport equation for the mode amplitude coherence matrix resulting from coupled mode propagation through random fields of internal waves is examined in more detail. It is shown that the mode energy equations are approximately independent of the cross mode coherences, and that cross mode coherences and mode energy can evolve over very similar range scales. The decay of cross mode coherence depends on the relative mode phase randomization caused by coupling and adiabatic effects, each of which can be quantified by the theory. This behavior has a dramatic effect on the acoustic field second moments like mean intensity. Comparing estimates of the coherence matrix and mean intensity from Monte Carlo simulation, and the transport equations, good agreement is demonstrated for a 100-Hz deep-water example.This work was supported by the Office of Naval Research and the Naval Undersea Warfare Center’s (NUWC) Under- Sea Warfare (USW) chair at the Naval Postgraduate School