Steady periodic water waves with constant vorticity: regularity and local bifurcation

This paper studies periodic traveling gravity waves at the free surface of water in a flow of constant vorticity over a flat bed. Using conformal mappings the free-boundary problem is transformed into a quasilinear pseudodifferential equation for a periodic function of one variable. The new formulation leads to a regularity result and, by use of bifurcation theory, to the existence of waves of small amplitude even in the presence of stagnation points in the flow.

Non-commutative symbolic coding

We give a non-commutative generalization of classical symbolic coding in the presence of a synchronizing word. This is done by a scattering theoretical approach. Classically, the existence of a synchronizing word turns out to be equivalent to asymptotic completeness of the corresponding Markov process. A criterion for asymptotic completeness in general is provided by the regularity of an associated extended transition operator. Commutative and non-commutative examples are analysed.

Representing El Niño in coupled ocean–atmosphere GCMs: the dominant role of the atmospheric component

A systematic modular approach to investigate the respective roles of the ocean and atmosphere in setting El Niño characteristics in coupled general circulation models is presented. Several state-of-the-art coupled models sharing either the same atmosphere or the same ocean are compared. Major results include 1) the dominant role of the atmosphere model in setting El Niño characteristics (periodicity and base amplitude) and errors (regularity) and 2) the considerable improvement of simulated El Niño power spectra—toward lower frequency—when the atmosphere resolution is significantly increased. Likely reasons for such behavior are briefly discussed. It is argued that this new modular strategy represents a generic approach to identifying the source of both coupled mechanisms and model error and will provide a methodology for guiding model improvement.

Improved SOM learning using simulated annealing

Self-Organizing Map (SOM) algorithm has been extensively used for analysis and classification problems. For this kind of problems, datasets become more and more large and it is necessary to speed up the SOM learning. In this paper we present an application of the Simulated Annealing (SA) procedure to the SOM learning algorithm. The goal of the algorithm is to obtain fast learning and better performance in terms of matching of input data and regularity of the obtained map. An advantage of the proposed technique is that it preserves the simplicity of the basic algorithm. Several tests, carried out on different large datasets, demonstrate the effectiveness of the proposed algorithm in comparison with the original SOM and with some of its modification introduced to speed-up the learning.

Exact error estimates and optimal randomized algorithms for integration

Exact error estimates for evaluating multi-dimensional integrals are considered. An estimate is called exact if the rates of convergence for the low- and upper-bound estimate coincide. The algorithm with such an exact rate is called optimal. Such an algorithm has an unimprovable rate of convergence. The problem of existing exact estimates and optimal algorithms is discussed for some functional spaces that define the regularity of the integrand. Important for practical computations data classes are considered: classes of functions with bounded derivatives and Holder type conditions. The aim of the paper is to analyze the performance of two optimal classes of algorithms: deterministic and randomized for computing multidimensional integrals. It is also shown how the smoothness of the integrand can be exploited to construct better randomized algorithms.

What Monte Carlo models can do and cannot do efficiently?

The question "what Monte Carlo models can do and cannot do efficiently" is discussed for some functional spaces that define the regularity of the input data. Data classes important for practical computations are considered: classes of functions with bounded derivatives and Holder type conditions, as well as Korobov-like spaces. Theoretical performance analysis of some algorithms with unimprovable rate of convergence is given. Estimates of computational complexity of two classes of algorithms - deterministic and randomized for both problems - numerical multidimensional integration and calculation of linear functionals of the solution of a class of integral equations are presented. (c) 2007 Elsevier Inc. All rights reserved.

A fast identification algorithm for Box-Cox transformation based radial basis function neural network

In this letter, a Box-Cox transformation-based radial basis function (RBF) neural network is introduced using the RBF neural network to represent the transformed system output. Initially a fixed and moderate sized RBF model base is derived based on a rank revealing orthogonal matrix triangularization (QR decomposition). Then a new fast identification algorithm is introduced using Gauss-Newton algorithm to derive the required Box-Cox transformation, based on a maximum likelihood estimator. The main contribution of this letter is to explore the special structure of the proposed RBF neural network for computational efficiency by utilizing the inverse of matrix block decomposition lemma. Finally, the Box-Cox transformation-based RBF neural network, with good generalization and sparsity, is identified based on the derived optimal Box-Cox transformation and a D-optimality-based orthogonal forward regression algorithm. The proposed algorithm and its efficacy are demonstrated with an illustrative example in comparison with support vector machine regression.

Bernoulli free-boundary problems in strip-like domains and a property of permanent waves on water of finite depth

We study weak solutions for a class of free-boundary problems which includes as a special case the classical problem of travelling gravity waves on water of finite depth. We show that such problems are equivalent to problems in fixed domains and study the regularity of their solutions. We also prove that in very general situations the free boundary is necessarily the graph of a function.

Equivalence of weak formulations of the steady water waves equations

We prove the equivalence of three weak formulations of the steady water waves equations, namely: the velocity formulation, the stream function formulation and the Dubreil-Jacotin formulation, under weak Hölder regularity assumptions on their solutions.

Feedback design for regularizing descriptor systems

This paper surveys numerical techniques for the regularization of descriptor (generalized state-space) systems by proportional and derivative feedback. We review generalizations of controllability and observability to descriptor systems along with definitions of regularity and index in terms of the Weierstraß canonical form. Three condensed forms display the controllability and observability properties of a descriptor system. The condensed forms are obtained through orthogonal equivalence transformations and rank decisions, so they may be computed by numerically stable algorithms. In addition, the condensed forms display whether a descriptor system is regularizable, i.e., when the system pencil can be made to be regular by derivative and/or proportional output feedback, and, if so, what index can be achieved. Also included is a a new characterization of descriptor systems that can be made to be regular with index 1 by proportional and derivative output feedback.

Eigenstructure assignment in descriptor systems

Coordinate free conditions are given for pole assignment by feedback in linear descriptor (singular) systems which guarantee closed-loop regularity. These conditions are shown to be both necessary and sufficient for assignment of the maximum possible number of finite poles. Transformation to special coordinates are not used and the results provide a robust algorithm for the computation of the required feedback.

Algorithms for Robust Pole Assignment in Singular Systems

The solution of the pole assignment problem by feedback in singular systems is parameterized and conditions are given which guarantee the regularity and maximal degree of the closed loop pencil. A robustness measure is defined, and numerical procedures are described for selecting the free parameters in the feedback to give optimal robustness.

Trefftz discontinuous Galerkin methods for acoustic scattering on locally refined meshes

We extend the a priori error analysis of Trefftz-discontinuous Galerkin methods for time-harmonic wave propagation problems developed in previous papers to acoustic scattering problems and locally refined meshes. To this aim, we prove refined regularity and stability results with explicit dependence of the stability constant on the wave number for non convex domains with non connected boundaries. Moreover, we devise a new choice of numerical flux parameters for which we can prove L2-error estimates in the case of locally refined meshes near the scatterer. This is the setting needed to develop a complete hp-convergence analysis.

A spatio-temporal structure-based approach to drought characterisation

Drought characterisation is an intrinsically spatio-temporal problem. A limitation of previous approaches to characterisation is that they discard much of the spatio-temporal information by reducing events to a lower-order subspace. To address this, an explicit 3-dimensional (longitude, latitude, time) structure-based method is described in which drought events are defined by a spatially and temporarily coherent set of points displaying standardised precipitation below a given threshold. Geometric methods can then be used to measure similarity between individual drought structures. Groupings of these similarities provide an alternative to traditional methods for extracting recurrent space-time signals from geophysical data. The explicit consideration of structure encourages the construction of summary statistics which relate to the event geometry. Example measures considered are the event volume, centroid, and aspect ratio. The utility of a 3-dimensional approach is demonstrated by application to the analysis of European droughts (15 °W to 35°E, and 35 °N to 70°N) for the period 1901–2006. Large-scale structure is found to be abundant with 75 events identified lasting for more than 3 months and spanning at least 0.5 × 106 km2. Near-complete dissimilarity is seen between the individual drought structures, and little or no regularity is found in the time evolution of even the most spatially similar drought events. The spatial distribution of the event centroids and the time evolution of the geographic cross-sectional areas strongly suggest that large area, sustained droughts result from the combination of multiple small area (∼106 km2) short duration (∼3 months) events. The small events are not found to occur independently in space. This leads to the hypothesis that local water feedbacks play an important role in the aggregation process.

Endogenous cholinergic tone modulates spontaneous network level neuronal activity in primary cortical cultures grown on multi-electrode arrays

Background Cortical cultures grown long-term on multi-electrode arrays (MEAs) are frequently and extensively used as models of cortical networks in studies of neuronal firing activity, neuropharmacology, toxicology and mechanisms underlying synaptic plasticity. However, in contrast to the predominantly asynchronous neuronal firing activity exhibited by intact cortex, electrophysiological activity of mature cortical cultures is dominated by spontaneous epileptiform-like global burst events which hinders their effective use in network-level studies, particularly for neurally-controlled animat (‘artificial animal’) applications. Thus, the identification of culture features that can be exploited to produce neuronal activity more representative of that seen in vivo could increase the utility and relevance of studies that employ these preparations. Acetylcholine has a recognised neuromodulatory role affecting excitability, rhythmicity, plasticity and information flow in vivo although its endogenous production by cortical cultures and subsequent functional influence upon neuronal excitability remains unknown. Results Consequently, using MEA electrophysiological recording supported by immunohistochemical and RT-qPCR methods, we demonstrate for the first time, the presence of intrinsic cholinergic neurons and significant, endogenous cholinergic tone in cortical cultures with a characterisation of the muscarinic and nicotinic components that underlie modulation of spontaneous neuronal activity. We found that tonic muscarinic ACh receptor (mAChR) activation affects global excitability and burst event regularity in a culture age-dependent manner whilst, in contrast, tonic nicotinic ACh receptor (nAChR) activation can modulate burst duration and the proportion of spikes occurring within bursts in a spatio-temporal fashion. Conclusions We suggest that the presence of significant endogenous cholinergic tone in cortical cultures and the comparability of its modulatory effects to those seen in intact brain tissues support emerging, exploitable commonalities between in vivo and in vitro preparations. We conclude that experimental manipulation of endogenous cholinergic tone could offer a novel opportunity to improve the use of cortical cultures for studies of network-level mechanisms in a manner that remains largely consistent with its functional role.