On the existence of extreme waves and the Stokes conjecture with vorticity

This is a study of singular solutions of the problem of traveling gravity water waves on flows with vorticity. We show that, for a certain class of vorticity functions, a sequence of regular waves converges to an extreme wave with stagnation points at its crests. We also show that, for any vorticity function, the profile of an extreme wave must have either a corner of 120° or a horizontal tangent at any stagnation point about which it is supposed symmetric. Moreover, the profile necessarily has a corner of 120° if the vorticity is nonnegative near the free surface.

Purification and functional characterisation of Rhinocerase, a novel serine protease from the venom of Bitis gabonica rhinoceros

Background: Serine proteases are a major component of viper venoms and are thought to disrupt several distinct elements of the blood coagulation system of envenomed victims. A detailed understanding of the functions of these enzymes is important both for acquiring a fuller understanding of the pathology of envenoming and because these venom proteins have shown potential in treating blood coagulation disorders. Methodology/Principal Findings: In this study a novel, highly abundant serine protease, which we have named rhinocerase, has been isolated and characterised from the venom of Bitis gabonica rhinoceros using liquid phase isoelectric focusing and gel filtration. Like many viper venom serine proteases, this enzyme is glycosylated; the estimated molecular mass of the native enzyme is approximately 36kDa, which reduces to 31kDa after deglycosylation. The partial amino acid sequence shows similarity to other viper venom serine proteases, but is clearly distinct from the sequence of the only other sequenced serine protease from Bitis gabonica. Other viper venom serine proteases have been shown to exert distinct biological effects, and our preliminary functional characterization of rhinocerase suggest it to be multifunctional. It is capable of degrading α and β chains of fibrinogen, dissolving plasma clots and of hydrolysing a kallikrein substrate. Conclusions/Significance: A novel multifunctional viper venom serine protease has been isolated and characterised. The activities of the enzyme are consistent with the known in vivo effects of Bitis gabonica envenoming, including bleeding disorders, clotting disorders and hypotension. This study will form the basis for future research to understand the mechanisms of serine protease action, and examine the potential for rhinocerase to be used clinically to reduce the risk of human haemostatic disorders such as heart attacks and strokes.

A simple column model to explore anticipated problems in variational assimilation of satellite observations

We investigate a simplified form of variational data assimilation in a fully nonlinear framework with the aim of extracting dynamical development information from a sequence of observations over time. Information on the vertical wind profile, w(z ), and profiles of temperature, T (z , t), and total water content, qt (z , t), as functions of height, z , and time, t, are converted to brightness temperatures at a single horizontal location by defining a two-dimensional (vertical and time) variational assimilation testbed. The profiles of T and qt are updated using a vertical advection scheme. A basic cloud scheme is used to obtain the fractional cloud amount and, when combined with the temperature field, this information is converted into a brightness temperature, using a simple radiative transfer scheme. It is shown that our model exhibits realistic behaviour with regard to the prediction of cloud, but the effects of nonlinearity become non-negligible in the variational data assimilation algorithm. A careful analysis of the application of the data assimilation scheme to this nonlinear problem is presented, the salient difficulties are highlighted, and suggestions for further developments are discussed.

The effect of nonlinearity on the variational assimilation of satellite observations using a simple column model

Cloud imagery is not currently used in numerical weather prediction (NWP) to extract the type of dynamical information that experienced forecasters have extracted subjectively for many years. For example, rapidly developing mid-latitude cyclones have characteristic signatures in the cloud imagery that are most fully appreciated from a sequence of images rather than from a single image. The Met Office is currently developing a technique to extract dynamical development information from satellite imagery using their full incremental 4D-Var (four-dimensional variational data assimilation) system. We investigate a simplified form of this technique in a fully nonlinear framework. We convert information on the vertical wind field, w(z), and profiles of temperature, T(z, t), and total water content, qt (z, t), as functions of height, z, and time, t, to a single brightness temperature by defining a 2D (vertical and time) variational assimilation testbed. The profiles of w, T and qt are updated using a simple vertical advection scheme. We define a basic cloud scheme to obtain the fractional cloud amount and, when combined with the temperature field, we convert this information into a brightness temperature, having developed a simple radiative transfer scheme. With the exception of some matrix inversion routines, all our code is developed from scratch. Throughout the development process we test all aspects of our 2D assimilation system, and then run identical twin experiments to try and recover information on the vertical velocity, from a sequence of observations of brightness temperature. This thesis contains a comprehensive description of our nonlinear models and assimilation system, and the first experimental results.

Sequence analysis and distribution of an IS3-like insertion element isolated from Salmonella enteritidis

The nucleotide sequence of a 3 kb region immediately upstream of the sef operon operon of Salmonella enteritidis was determined. A 1230 base pair insertion sequence which shared sequence identity (> 75%) with members of the IS3 family was revealed. This element, designated IS1230, had almost identical (90% identity) terminal inverted repeats to Escherichia coli IS3 but unlike other IS3-like sequences lacked the two characteristic open reading frames which encode the putative transposase. S. enteritidis possessed only one copy of this insertion sequence although Southern hybridisation analysis of restriction digests of genomic DNA revealed another fragment located in a region different from the sef operon which hybridised weakly which suggested the presence of an IS1230 homologue. The distribution of IS1230 and IS1230-like elements was shown to be widespread amongst salmonellas and the patterns of restriction fragments which hybridised differed significantly between Salmonella serotypes and it is suggested that IS1230 has potential for development as a differential diagnostic tool.

Sequence heterogeneity of an mpb70 gene analogue in Mycobacterium kansasii

The protein antigen MPB70 is a major component of culture supernatants of Mycobacterium bovis and Is an active ingredient of bovine PPD used for skin-testing cattle for tuberculosis. we have shown that Mycobacterium kansasii possesses a similar gene that cross-reacts in a PCR test for M. bovis. Single strand conformational polymorphism analysis, and the DNA sequence of the PCR product, shows differences between M. kansasii strains, supporting the suggestion that M. kansasii is not a homogeneous species.

On the solvability of second kind integral equations on the real line

This paper considers general second kind integral equations of the form(in operator form φ − kφ = ψ), where the functions k and ψ are assumed known, with ψ ∈ Y, the space of bounded continuous functions on R, and k such that the mapping s → k(s, · ), from R to L1(R), is bounded and continuous. The function φ ∈ Y is the solution to be determined. Conditions on a set W ⊂ BC(R, L1(R)) are obtained such that a generalised Fredholm alternative holds: If W satisfies these conditions and I − k is injective for all k ∈ W then I − k is also surjective for all k ∈ W and, moreover, the inverse operators (I − k) − 1 on Y are uniformly bounded for k ∈ W. The approximation of the kernel in the integral equation by a sequence (kn) converging in a weak sense to k is also considered and results on stability and convergence are obtained. These general theorems are used to establish results for two special classes of kernels: k(s, t) = κ(s − t)z(t) and k(s, t) = κ(s − t)λ(s − t, t), where κ ∈ L1(R), z ∈ L∞(R), and λ ∈ BC((R\{0}) × R). Kernels of both classes arise in problems of time harmonic wave scattering by unbounded surfaces. The general integral equation results are here applied to prove the existence of a solution for a boundary integral equation formulation of scattering by an infinite rough surface and to consider the stability and convergence of approximation of the rough surface problem by a sequence of diffraction grating problems of increasingly large period.

Discovery of a mammalian splice variant of myostatin that stimulates myogenesis

Myostatin plays a fundamental role in regulating the size of skeletal muscles. To date, only a single myostatin gene and no splice variants have been identified in mammals. Here we describe the splicing of a cryptic intron that removes the coding sequence for the receptor binding moiety of sheep myostatin. The deduced polypeptide sequence of the myostatin splice variant (MSV) contains a 256 amino acid N-terminal domain, which is common to myostatin, and a unique C-terminus of 65 amino acids. Western immunoblotting demonstrated that MSV mRNA is translated into protein, which is present in skeletal muscles. To determine the biological role of MSV, we developed an MSV over-expressing C2C12 myoblast line and showed that it proliferated faster than that of the control line in association with an increased abundance of the CDK2/Cyclin E complex in the nucleus. Recombinant protein made for the novel C-terminus of MSV also stimulated myoblast proliferation and bound to myostatin with high affinity as determined by surface plasmon resonance assay. Therefore, we postulated that MSV functions as a binding protein and antagonist of myostatin. Consistent with our postulate, myostatin protein was co-immunoprecipitated from skeletal muscle extracts with an MSV-specific antibody. MSV over-expression in C2C12 myoblasts blocked myostatin-induced Smad2/3-dependent signaling, thereby confirming that MSV antagonizes the canonical myostatin pathway. Furthermore, MSV over expression increased the abundance of MyoD, Myogenin and MRF4 proteins (P,0.05), which indicates that MSV stimulates myogenesis through the induction of myogenic regulatory factors. To help elucidate a possible role in vivo, we observed that MSV protein was more abundant during early post-natal muscle development, while myostatin remained unchanged, which suggests that MSV may promote the growth of skeletal muscles. We conclude that MSV represents a unique example of intra-genic regulation in which a splice variant directly antagonizes the biological activity of the canonical gene product.

Location and characteristics of the reconnection X line deduced from low-altitude satellite and ground-based observations: 1. Theory

A method for estimating both the Alfvén speed and the field-aligned flow of the magnetosheath at the magnetopause reconnection site is presented. The method employs low-altitude cusp ion observations and requires the identification of a feature in the cusp ion spectra near the low-energy cutoff which will often be present for a low-latitude dayside reconnection site. The appearance of these features in data of limited temporal, energy, and pitch angle resolution is illustrated by using model calculations of cusp ion distribution functions. These are based on the theory of ion acceleration at the dayside magnetopause and allow for the effects on the spectrum of flight times of ions precipitating down newly opened field lines. In addition, the variation of the reconnection rate can be evaluated, and comparison with ground-based observations of the corresponding sequence of transient events allows the field-aligned distance from the ionosphere to the reconnection site to be estimated.

Conditioning and preconditioning of the optimal state estimation problem

Optimal state estimation is a method that requires minimising a weighted, nonlinear, least-squares objective function in order to obtain the best estimate of the current state of a dynamical system. Often the minimisation is non-trivial due to the large scale of the problem, the relative sparsity of the observations and the nonlinearity of the objective function. To simplify the problem the solution is often found via a sequence of linearised objective functions. The condition number of the Hessian of the linearised problem is an important indicator of the convergence rate of the minimisation and the expected accuracy of the solution. In the standard formulation the convergence is slow, indicating an ill-conditioned objective function. A transformation to different variables is often used to ameliorate the conditioning of the Hessian by changing, or preconditioning, the Hessian. There is only sparse information in the literature for describing the causes of ill-conditioning of the optimal state estimation problem and explaining the effect of preconditioning on the condition number. This paper derives descriptive theoretical bounds on the condition number of both the unpreconditioned and preconditioned system in order to better understand the conditioning of the problem. We use these bounds to explain why the standard objective function is often ill-conditioned and why a standard preconditioning reduces the condition number. We also use the bounds on the preconditioned Hessian to understand the main factors that affect the conditioning of the system. We illustrate the results with simple numerical experiments.

THE ROLE OF THE SUPERIOR COLLICULUS IN PREDATORY HUNTING

Combining the results of behavioral, neuronal immediate early gene activation, lesion and neuroanatomical experiments, we have presently investigated the role of the superior colliculus (SC) in predatory hunting. First, we have shown that insect hunting is associated with a characteristic large increase in Fos expression in the lateral part of the intermediate gray layer of the SC (Wig). Next, we have shown that animals with bilateral NMDA lesions of the lateral parts of the SC presented a significant delay in starting to chase the prey and longer periods engaged in other activities than predatory hunting. They also showed a clear deficit to orient themselves toward the moving prey and lost the stereotyped sequence of actions seen for capturing, holding and killing the prey. Our Phaseolus vulgaris-leucoagglutinin analysis revealed that the lateral SCig, besides providing the well-documented descending crossed pathway to premotor sites in brainstem and spinal cord, projects to a number of midbrain and diencephalic sites likely to influence key functions in the context of the predatory behavior, such as general levels of arousal, motivational level to hunt or forage, behavioral planning, appropriate selection of the basal ganglia motor plan to hunt, and motor output of the primary motor cortex. In contrast to the lateral SC lesions, medial SC lesions produced a small deficit in predatory hunting, and compared to what we have seen for the lateral SCig, the medial SCig has a very limited set of projections to thalamic sites related to the control of motor planning or motor output, and provides conspicuous inputs to brainstem sites involved in organizing a wide range of anti-predatory defensive responses. Overall, the present results served to clarify how the different functional domains in the SC may mediate the decision to pursue and hunt a prey or escape from a predator. (C) 2010 IBRO. Published by Elsevier Ltd. All rights reserved.

Exact Search Directions for Optimization of Linear and Nonlinear Models Based on Generalized Orthonormal Functions

A novel technique for selecting the poles of orthonormal basis functions (OBF) in Volterra models of any order is presented. It is well-known that the usual large number of parameters required to describe the Volterra kernels can be significantly reduced by representing each kernel using an appropriate basis of orthonormal functions. Such a representation results in the so-called OBF Volterra model, which has a Wiener structure consisting of a linear dynamic generated by the orthonormal basis followed by a nonlinear static mapping given by the Volterra polynomial series. Aiming at optimizing the poles that fully parameterize the orthonormal bases, the exact gradients of the outputs of the orthonormal filters with respect to their poles are computed analytically by using a back-propagation-through-time technique. The expressions relative to the Kautz basis and to generalized orthonormal bases of functions (GOBF) are addressed; the ones related to the Laguerre basis follow straightforwardly as a particular case. The main innovation here is that the dynamic nature of the OBF filters is fully considered in the gradient computations. These gradients provide exact search directions for optimizing the poles of a given orthonormal basis. Such search directions can, in turn, be used as part of an optimization procedure to locate the minimum of a cost-function that takes into account the error of estimation of the system output. The Levenberg-Marquardt algorithm is adopted here as the optimization procedure. Unlike previous related work, the proposed approach relies solely on input-output data measured from the system to be modeled, i.e., no information about the Volterra kernels is required. Examples are presented to illustrate the application of this approach to the modeling of dynamic systems, including a real magnetic levitation system with nonlinear oscillatory behavior.

Size and power properties of some tests in the Birnbaum-Saunders regression model

The Birnbaum-Saunders distribution has been used quite effectively to model times to failure for materials subject to fatigue and for modeling lifetime data. In this paper we obtain asymptotic expansions, up to order n(-1/2) and under a sequence of Pitman alternatives, for the non-null distribution functions of the likelihood ratio, Wald, score and gradient test statistics in the Birnbaum-Saunders regression model. The asymptotic distributions of all four statistics are obtained for testing a subset of regression parameters and for testing the shape parameter. Monte Carlo simulation is presented in order to compare the finite-sample performance of these tests. We also present two empirical applications. (C) 2010 Elsevier B.V. All rights reserved.

Local power of some tests in exponential family nonlinear models

In this paper we obtain asymptotic expansions up to order n(-1/2) for the nonnull distribution functions of the likelihood ratio, Wald, score and gradient test statistics in exponential family nonlinear models (Cordeiro and Paula, 1989), under a sequence of Pitman alternatives. The asymptotic distributions of all four statistics are obtained for testing a subset of regression parameters and for testing the dispersion parameter, thus generalising the results given in Cordeiro et al. (1994) and Ferrari et al. (1997). We also present Monte Carlo simulations in order to compare the finite-sample performance of these tests. (C) 2010 Elsevier B.V. All rights reserved.

Compositional analysis for an unbiased measure of soil aggregation

Soil aggregation is an index of soil structure measured by mean weight diameter (MWD) or scaling factors often interpreted as fragmentation fractal dimensions (D-f). However, the MWD provides a biased estimate of soil aggregation due to spurious correlations among aggregate-size fractions and scale-dependency. The scale-invariant D-f is based on weak assumptions to allow particle counts and sensitive to the selection of the fractal domain, and may frequently exceed a value of 3, implying that D-f is a biased estimate of aggregation. Aggregation indices based on mass may be computed without bias using compositional analysis techniques. Our objective was to elaborate compositional indices of soil aggregation and to compare them to MWD and D-f using a published dataset describing the effect of 7 cropping systems on aggregation. Six aggregate-size fractions were arranged into a sequence of D-1 balances of building blocks that portray the process of soil aggregation. Isometric log-ratios (ilrs) are scale-invariant and orthogonal log contrasts or balances that possess the Euclidean geometry necessary to compute a distance between any two aggregation states, known as the Aitchison distance (A(x,y)). Close correlations (r>0.98) were observed between MWD, D-f, and the ilr when contrasting large and small aggregate sizes. Several unbiased embedded ilrs can characterize the heterogeneous nature of soil aggregates and be related to soil properties or functions. Soil bulk density and penetrater resistance were closely related to A(x,y) with reference to bare fallow. The A(x,y) is easy to implement as unbiased index of soil aggregation using standard sieving methods and may allow comparisons between studies. (C) 2012 Elsevier B.V. All rights reserved.