Toward Regional Characterizations of the Oceanic Internal Wavefield

Many major oceanographic internal wave observational programs of the last 4 decades are reanalyzed in order to characterize variability of the deep ocean internal wavefield. The observations are discussed in the context of the universal spectral model proposed by Garrett and Munk. The Garrett and Munk model is a good description of wintertime conditions at Site-D on the continental rise north of the Gulf Stream. Elsewhere and at other times, significant deviations in terms of amplitude, separability of the 2-D vertical wavenumber - frequency spectrum, and departure from the model's functional form are noted. Subtle geographic patterns are apparent in deviations from the high frequency and high vertical wavenumber power laws of the Garrett and Munk spectrum. Moreover, such deviations tend to co-vary: whiter frequency spectra are partnered with redder vertical wavenumber spectra. Attempts are made to interpret the variability in terms of the interplay between generation, propagation and nonlinearity using a statistical radiative balance equation. This process frames major questions for future research with the insight that such integrative studies could constrain both observationally and theoretically based interpretations

Mode doubling and tripling in reaction-diffusion patterns on growing domains: A piece-wise linear model

Reaction-diffusion equations are ubiquitous as models of biological pattern formation. In a recent paper [4] we have shown that incorporation of domain growth in a reaction-diffusion model generates a sequence of quasi-steady patterns and can provide a mechanism for increased reliability of pattern selection. In this paper we analyse the model to examine the transitions between patterns in the sequence. Introducing a piecewise linear approximation we find closed form approximate solutions for steady-state patterns by exploiting a small parameter, the ratio of diffusivities, in a singular perturbation expansion. We consider the existence of these steady-state solutions as a parameter related to the domain length is varied and predict the point at which the solution ceases to exist, which we identify with the onset of transition between patterns for the sequence generated on the growing domain. Applying these results to the model in one spatial dimension we are able to predict the mechanism and timing of transitions between quasi-steady patterns in the sequence. We also highlight a novel sequence behaviour, mode-tripling, which is a consequence of a symmetry in the reaction term of the reaction-diffusion system

Using mathematical models to help understand biological pattern formation

One of the characteristics of biological systems is their ability to produce and sustain spatial and spatio-temporal pattern. Elucidating the underlying mechanisms responsible for this phenomenon has been the goal of much experimental and theoretical research. This paper illustrates this area of research by presenting some of the mathematical models that have been proposed to account for pattern formation in biology and considering their implications.To cite this article: P.K. Maini, C. R. Biologies 327 (2004)

Improved upper bound on root number of linearized polynomials and its application to nonlinearity estimation of Boolean functions

To determine the dimension of null space of any given linearized polynomial is one of vital problems in finite field theory, with concern to design of modern symmetric cryptosystems. But, the known general theory for this task is much far from giving the exact dimension when applied to a specific linearized polynomial. The first contribution of this paper is to give a better general method to get more precise upper bound on the root number of any given linearized polynomial. We anticipate this result would be applied as a useful tool in many research branches of finite field and cryptography. Really we apply this result to get tighter estimations of the lower bounds on the second order nonlinearities of general cubic Boolean functions, which has been being an active research problem during the past decade, with many examples showing great improvements. Furthermore, this paper shows that by studying the distribution of radicals of derivatives of a given Boolean functions one can get a better lower bound of the second-order nonlinearity, through an example of the monomial Boolean function $g_{\mu}=Tr(\mu x^{2^{2r}+2^r+1})$ over any finite field \GF{n}

Cue Combinatorics in Memory Retrieval for Anaphora

Many studies have shown that memory retrieval for real-time language processing relies on a cue-based access mechanism, which allows the cues available at the retrieval site to directly access the target representation in memory. An open question is how different types of cues are combined at retrieval to create a single retrieval probe (“cue combinatorics”). This study addresses this question by testing whether retrieval for antecedent-reflexive dependencies combines cues in a linear (i.e., additive) or nonlinear (i.e., multiplicative) fashion. Results from computational simulations and a reading time experiment show that target items that match all the cues of the reflexive are favored more than target items that mismatch these cues, and that different degrees of mismatches slow reading times in comparable amounts. This profile is consistent with the predictions of a nonlinear cue combination and provides evidence against models in which all cues combine in a linear fashion. A follow-up set of simulations shows that a nonlinear rule also captures previous demonstrations of interference from nontarget items during retrieval for reflexive licensing. Taken together, these results shed new light on how different types of cues combine at the retrieval site and reveal how the method of cue combination impacts the accessibility of linguistic information in memor

STREGA: STRucture and Evolution of the GAlaxy - I : Survey overview and first results

STREGA (STRucture and Evolution of the GAlaxy) is a guaranteed time survey being performed at the VST (the ESO Very Large Telescope Survey Telescope) to map about 150 square degrees in the Galactic halo, in order to constrain the mechanisms of galactic formation and evolution. The survey is built as a 5 yr project, organized in two parts: a core programme to explore the surrounding regions of selected stellar systems and a second complementary part to map the southern portion of the Fornax orbit and extend the observations of the core programme. The adopted stellar tracers are mainly variable stars (RR Lyraes and long-period variables) and main-sequence turn-off stars for which observations in the g, r, i bands are obtained. We present an overview of the survey and some preliminary results for three observing runs that have been completed. For the region centred on ω Cen (37 deg^2), covering about three tidal radii, we also discuss the detected stellar density radial profile and angular distribution, leading to the identification of extratidal cluster stars. We also conclude that the cluster tidal radius is about 1.2 deg, in agreement with values in the literature based on the Wilson model.Peer reviewedFinal Accepted Versio