Design of delay-tolerant linear dispersion codes

In cooperative communication networks, owing to the nodes' arbitrary geographical locations and individual oscillators, the system is fundamentally asynchronous. This will damage some of the key properties of the space-time codes and can lead to substantial performance degradation. In this paper, we study the design of linear dispersion codes (LDCs) for such asynchronous cooperative communication networks. Firstly, the concept of conventional LDCs is extended to the delay-tolerant version and new design criteria are discussed. Then we propose a new design method to yield delay-tolerant LDCs that reach the optimal Jensen's upper bound on ergodic capacity as well as minimum average pairwise error probability. The proposed design employs stochastic gradient algorithm to approach a local optimum. Moreover, it is improved by using simulated annealing type optimization to increase the likelihood of the global optimum. The proposed method allows for flexible number of nodes, receive antennas, modulated symbols and flexible length of codewords. Simulation results confirm the performance of the newly-proposed delay-tolerant LDCs.

Spectral theory of some non-selfadjoint linear differential operators

We give a characterisation of the spectral properties of linear differential operators with constant coefficients, acting on functions defined on a bounded interval, and determined by general linear boundary conditions. The boundary conditions may be such that the resulting operator is not selfadjoint. We associate the spectral properties of such an operator $S$ with the properties of the solution of a corresponding boundary value problem for the partial differential equation $\partial_t q \pm iSq=0$. Namely, we are able to establish an explicit correspondence between the properties of the family of eigenfunctions of the operator, and in particular whether this family is a basis, and the existence and properties of the unique solution of the associated boundary value problem. When such a unique solution exists, we consider its representation as a complex contour integral that is obtained using a transform method recently proposed by Fokas and one of the authors. The analyticity properties of the integrand in this representation are crucial for studying the spectral theory of the associated operator.

Analysis of the variability of auditory brainstem response components through linear regression

(ABR) is of fundamental importance to the investiga- tion of the auditory system behavior, though its in- terpretation has a subjective nature because of the manual process employed in its study and the clinical experience required for its analysis. When analyzing the ABR, clinicians are often interested in the identi- fication of ABR signal components referred to as Jewett waves. In particular, the detection and study of the time when these waves occur (i.e., the wave la- tency) is a practical tool for the diagnosis of disorders affecting the auditory system. In this context, the aim of this research is to compare ABR manual/visual analysis provided by different examiners. Methods: The ABR data were collected from 10 normal-hearing subjects (5 men and 5 women, from 20 to 52 years). A total of 160 data samples were analyzed and a pair- wise comparison between four distinct examiners was executed. We carried out a statistical study aiming to identify significant differences between assessments provided by the examiners. For this, we used Linear Regression in conjunction with Bootstrap, as a me- thod for evaluating the relation between the responses given by the examiners. Results: The analysis sug- gests agreement among examiners however reveals differences between assessments of the variability of the waves. We quantified the magnitude of the ob- tained wave latency differences and 18% of the inves- tigated waves presented substantial differences (large and moderate) and of these 3.79% were considered not acceptable for the clinical practice. Conclusions: Our results characterize the variability of the manual analysis of ABR data and the necessity of establishing unified standards and protocols for the analysis of these data. These results may also contribute to the validation and development of automatic systems that are employed in the early diagnosis of hearing loss.

On the stability and convergence of the finite section method for integral equation formulations of rough surface scattering

We consider the Dirichlet and Robin boundary value problems for the Helmholtz equation in a non-locally perturbed half-plane, modelling time harmonic acoustic scattering of an incident field by, respectively, sound-soft and impedance infinite rough surfaces.Recently proposed novel boundary integral equation formulations of these problems are discussed. It is usual in practical computations to truncate the infinite rough surface, solving a boundary integral equation on a finite section of the boundary, of length 2A, say. In the case of surfaces of small amplitude and slope we prove the stability and convergence as A→∞ of this approximation procedure. For surfaces of arbitrarily large amplitude and/or surface slope we prove stability and convergence of a modified finite section procedure in which the truncated boundary is ‘flattened’ in finite neighbourhoods of its two endpoints. Copyright © 2001 John Wiley & Sons, Ltd.

Some uniform stability and convergence results for integral equations on the real line and projection methods for their solution

The paper considers second kind equations of the form (abbreviated x=y + K2x) in which and the factor z is bounded but otherwise arbitrary so that equations of Wiener-Hopf type are included as a special case. Conditions on a set are obtained such that a generalized Fredholm alternative is valid: if W satisfies these conditions and I − Kz, is injective for each z ε W then I − Kz is invertible for each z ε W and the operators (I − Kz)−1 are uniformly bounded. As a special case some classical results relating to Wiener-Hopf operators are reproduced. A finite section version of the above equation (with the range of integration reduced to [−a, a]) is considered, as are projection and iterated projection methods for its solution. The operators (where denotes the finite section version of Kz) are shown uniformly bounded (in z and a) for all a sufficiently large. Uniform stability and convergence results, for the projection and iterated projection methods, are obtained. The argument generalizes an idea in collectively compact operator theory. Some new results in this theory are obtained and applied to the analysis of projection methods for the above equation when z is compactly supported and k(s − t) replaced by the general kernel k(s,t). A boundary integral equation of the above type, which models outdoor sound propagation over inhomogeneous level terrain, illustrates the application of the theoretical results developed.

The ocean’s role in setting the mean position of the Inter-Tropical Convergence Zone

Through study of observations and coupled climate simulations, it is argued that the mean position of the Inter-Tropical Convergence Zone (ITCZ) north of the equator is a consequence of a northwards heat transport across the equator by ocean circulation. Observations suggest that the hemispheric net radiative forcing of climate at the top of the atmosphere is almost perfectly symmetric about the equator, and so the total (atmosphere plus ocean) heat transport across the equator is small (order 0.2 PW northwards). Due to the Atlantic ocean’s meridional overturning circulation, however, the ocean carries significantly more heat northwards across the equator (order 0.4 PW) than does the coupled system. There are two primary consequences. First, atmospheric heat transport is southwards across the equator to compensate (0.2 PW southwards), resulting in the ITCZ being displaced north of the equator. Second, the atmosphere, and indeed the ocean, is slightly warmer (by perhaps 2 °C) in the northern hemisphere than in the southern hemisphere. This leads to the northern hemisphere emitting slightly more outgoing longwave radiation than the southern hemisphere by virtue of its relative warmth, supporting the small northward heat transport by the coupled system across the equator. To conclude, the coupled nature of the problem is illustrated through study of atmosphere–ocean–ice simulations in the idealized setting of an aquaplanet, resolving the key processes at work.

Optimal convergence estimates for the trace of the polynomial L2-projection operator on a simplex

In this paper we study convergence of the L2-projection onto the space of polynomials up to degree p on a simplex in Rd, d >= 2. Optimal error estimates are established in the case of Sobolev regularity and illustrated on several numerical examples. The proof is based on the collapsed coordinate transform and the expansion into various polynomial bases involving Jacobi polynomials and their antiderivatives. The results of the present paper generalize corresponding estimates for cubes in Rd from [P. Houston, C. Schwab, E. Süli, Discontinuous hp-finite element methods for advection-diffusion-reaction problems. SIAM J. Numer. Anal. 39 (2002), no. 6, 2133-2163].

A high frequency $hp$ boundary element method for scattering by convex polygons

In this paper we propose and analyze a hybrid $hp$ boundary element method for the solution of problems of high frequency acoustic scattering by sound-soft convex polygons, in which the approximation space is enriched with oscillatory basis functions which efficiently capture the high frequency asymptotics of the solution. We demonstrate, both theoretically and via numerical examples, exponential convergence with respect to the order of the polynomials, moreover providing rigorous error estimates for our approximations to the solution and to the far field pattern, in which the dependence on the frequency of all constants is explicit. Importantly, these estimates prove that, to achieve any desired accuracy in the computation of these quantities, it is sufficient to increase the number of degrees of freedom in proportion to the logarithm of the frequency as the frequency increases, in contrast to the at least linear growth required by conventional methods.

Synthesis of novel hyperbranched polymers featuring oxazoline linear units and their application in fast-drying solvent-borne coating formulations

Novel acid-terminated hyperbranched polymers (HBPs) containing adipic acid and oxazoline monomers derived from oleic and linoleic acid have been synthesized via a bulk polymerization procedure. Branching was achieved as a consequence of an acid-catalyzed opening of the oxazoline ring to produce a trifunctional monomer in situ which delivered branching levels of >45% as determined by 1H and 13C NMR spectroscopy. The HBPs were soluble in common solvents, such as CHCl3, acetone, tetrahydrofuran, dimethylformamide, and dimethyl sulfoxide and were further functionalized by addition of citronellol to afford white-spirit soluble materials that could be used in coating formulations. During end group modification, a reduction in branching levels of the HBPs (down to 12–24%) was observed, predominantly on account of oxazoline ring reformation and trans-esterification processes under the reaction conditions used. In comparison to commercial alkyd resin paint coatings, formulations of the citronellol-functionalized hyperbranched materials blended with a commercial alkyd resin exhibited dramatic decreases of the blend viscosity when the HBP content was increased. The curing characteristics of the HBP/alkyd blend formulations were studied by dynamic mechanical analysis which revealed that the new coatings cured more quickly and produced tougher materials than otherwise identical coatings prepared from only the commercial alkyd resins.

Retrieval characteristics of non-linear sea surface temperature from the Advanced Very High Resolution Radiometer

Criteria are proposed for evaluating sea surface temperature (SST) retrieved from satellite infra-red imagery: bias should be small on regional scales; sensitivity to atmospheric humidity should be small; and sensitivity of retrieved SST to surface temperature should be close to 1 K K−1. Their application is illustrated for non-linear sea surface temperature (NLSST) estimates. 233929 observations from the Advanced Very High Resolution Radiometer (AVHRR) on Metop-A are matched with in situ data and numerical weather prediction (NWP) fields. NLSST coefficients derived from these matches have regional biases from −0.5 to +0.3 K. Using radiative transfer modelling we find that a 10% increase in humidity alone can change the retrieved NLSST by between −0.5 K and +0.1 K. A 1 K increase in SST changes NLSST by <0.5 K in extreme cases. The validity of estimates of sensitivity by radiative transfer modelling is confirmed empirically.

A finite element method for nonlinear elliptic problems

We present a Galerkin method with piecewise polynomial continuous elements for fully nonlinear elliptic equations. A key tool is the discretization proposed in Lakkis and Pryer, 2011, allowing us to work directly on the strong form of a linear PDE. An added benefit to making use of this discretization method is that a recovered (finite element) Hessian is a byproduct of the solution process. We build on the linear method and ultimately construct two different methodologies for the solution of second order fully nonlinear PDEs. Benchmark numerical results illustrate the convergence properties of the scheme for some test problems as well as the Monge–Amp`ere equation and the Pucci equation.

The transient atmospheric response to midlatitude SST anomalies

To study the transient atmospheric response to midlatitude SST anomalies, a three-layer quasigeostrophic (QG) model coupled to a slab oceanic mixed layer in the North Atlantic is used. As diagnosed from a coupled run in perpetual winter conditions, the first two modes of SST variability are linked to the model North Atlantic Oscillation (NAO) and eastern Atlantic pattern (EAP), respectively, the dominant atmospheric modes in the Atlantic sector. The two SST anomaly patterns are then prescribed as fixed anomalous boundary conditions for the model atmosphere, and its transient responses are established from a large ensemble of simulations. In both cases, the tendency of the air–sea heat fluxes to damp the SST anomalies results in an anomalous diabatic heating of the atmosphere that, in turn, forces a baroclinic response, as predicted by linear theory. This initial response rapidly modifies the transient eddy activity and thus the convergence of eddy momentum and heat fluxes. The latter transforms the baroclinic response into a growing barotropic one that resembles the atmospheric mode that had created the SST anomaly in the coupled run and is thus associated with a positive feedback. The total adjustment time is as long as 3–4 months for the NAO-like response and 1–2 months for the EAP-like one. The positive feedback, in both cases, is dependent on the polarity of the SST anomaly, but is stronger in the NAO case, thereby contributing to its predominance at low frequency in the coupled system. However, the feedback is too weak to lead to an instability of the atmospheric modes and primarily results in an increase of their amplitude and persistence and a weakening of the heat flux damping of the SST anomaly.

Further investigations of the quartz optically stimulated luminescence components using linear modulation

The optically stimulated luminescence (OSL) from quartz is known to be the sum of several components with different rates of charge loss, originating from different trap types. The OSL components are clearly distinguished using the linear modulation (LM OSL) technique. A variety of pre-treatment and measurement conditions have been used on sedimentary samples in conjunction with linearly modulated optical stimulation to study in detail the behaviour of the OSL components of quartz. Single aliquots of different quartz samples have been found to contain typically five or six common LM OSL components when stimulated at View the MathML source. The components have been parameterised in terms of thermal stability (i.e. E and s), photoionisation cross-section energy dependence and dose response. The results of studies concerning applications of component-resolved LM OSL measurements on quartz are also presented. These include the detection of partial bleaching in young samples, use of ‘stepped wavelength’ stimulation to observe OSL from single components and attempts to extend the age range of quartz OSL dating.

Linear vs. log-linear unit-root specification: an application of mis-specification encompassing

The objective of this paper is to apply the mis-specification (M-S) encompassing perspective to the problem of choosing between linear and log-linear unit-root models. A simple M-S encompassing test, based on an auxiliary regression stemming from the conditional second moment, is proposed and its empirical size and power are investigated using Monte Carlo simulations. It is shown that by focusing on the conditional process the sampling distributions of the relevant statistics are well behaved under both the null and alternative hypotheses. The proposed M-S encompassing test is illustrated using US total disposable income quarterly data.