Global exponential periodicity of a class of neural networks with recent-history distributed delays

In this paper, we propose to study a class of neural networks with recent-history distributed delays. A sufficient condition is derived for the global exponential periodicity of the proposed neural networks, which has the advantage that it assumes neither the differentiability nor monotonicity of the activation function of each neuron nor the symmetry of the feedback matrix or delayed feedback matrix. Our criterion is shown to be valid by applying it to an illustrative system. (c) 2005 Elsevier Ltd. All rights reserved.

Optimal control of a class of discrete–continuous non-linear systems — decomposition and hierarchical structure

A technique is derived for solving a non-linear optimal control problem by iterating on a sequence of simplified problems in linear quadratic form. The technique is designed to achieve the correct solution of the original non-linear optimal control problem in spite of these simplifications. A mixed approach with a discrete performance index and continuous state variable system description is used as the basis of the design, and it is shown how the global problem can be decomposed into local sub-system problems and a co-ordinator within a hierarchical framework. An analysis of the optimality and convergence properties of the algorithm is presented and the effectiveness of the technique is demonstrated using a simulation example with a non-separable performance index.

Guanine specific binding at a DNA junction formed by d[CG(5-BrU)ACG]2 with a topoisomerase poison in the presence of Co2+Ions†,‡

The structure of the duplex d[CG(5-BrU)ACG]2 bound to 9-bromophenazine-4-carboxamide has been solved through MAD phasing at 2.0 Å resolution. It shows an unexpected and previously unreported intercalation cavity stabilized by the drug and novel binding modes of Co2+ ions at certain guanine N7 sites. For the intercalation cavity the terminal cytosine is rotated to pair with the guanine of a symmetry-related duplex to create a pseudo-Holliday junction geometry, with two such cavities linked through the minor groove interactions of the N2/N3 guanine sites at an angle of 40°, creating a quadruplex-like structure. The mode of binding of the drug is shown to be disordered, with the major conformations showing the side chain bound to the N7 position of adjacent guanines. The other end of the duplex exhibits a terminal base fraying in the presence of Co2+ ions linking symmetry-related guanines, causing the helices to intertwine through the minor groove. The stabilization of the structure by the intercalating drug shows that this class of compound may bind to DNA junctions as well as duplex DNA or to strand-nicked DNA (‘hemi-intercalated'), as in the cleavable complex. This suggests a structural basis for the dual poisoning of topoisomerase I and II enzymes by this family of drugs.

Transnational urbanism in Port of Spain: returning middle-class urban elites

Port of Spain, Trinidad offers an ideal context in which to analyze pre-retirement return migration to a Global South urban realm, expanding transnational urban research beyond the conventional focus on Global North metropolitan destinations. In this article, we draw on the transnational narratives of a selected sample of relatively youthful Trinidadians, who have spent many years abroad acquiring education and professional experience, but who have then decided to return in mid-career to the capital region of the island nation of their birth, or of their parent(s). Theoretically, we position these returning professionals as members of a "middling" transnational urban class whose return is at least partly motivated by a desire to "make a difference." Our results contribute to a growing literature that documents the role of transnational middle-class urban elites returning elsewhere in the Carribbean: "middling" transnational urbanism is reshaping key facets of urbanization in the Global South.

Elastic-net prefiltering for two-class classification

A two-stage linear-in-the-parameter model construction algorithm is proposed aimed at noisy two-class classification problems. The purpose of the first stage is to produce a prefiltered signal that is used as the desired output for the second stage which constructs a sparse linear-in-the-parameter classifier. The prefiltering stage is a two-level process aimed at maximizing a model's generalization capability, in which a new elastic-net model identification algorithm using singular value decomposition is employed at the lower level, and then, two regularization parameters are optimized using a particle-swarm-optimization algorithm at the upper level by minimizing the leave-one-out (LOO) misclassification rate. It is shown that the LOO misclassification rate based on the resultant prefiltered signal can be analytically computed without splitting the data set, and the associated computational cost is minimal due to orthogonality. The second stage of sparse classifier construction is based on orthogonal forward regression with the D-optimality algorithm. Extensive simulations of this approach for noisy data sets illustrate the competitiveness of this approach to classification of noisy data problems.

On the spectra and pseudospectra of a class of non-self-adjoint random matrices and operators

In this paper we develop and apply methods for the spectral analysis of non-selfadjoint tridiagonal infinite and finite random matrices, and for the spectral analysis of analogous deterministic matrices which are pseudo-ergodic in the sense of E. B. Davies (Commun. Math. Phys. 216 (2001), 687–704). As a major application to illustrate our methods we focus on the “hopping sign model” introduced by J. Feinberg and A. Zee (Phys. Rev. E 59 (1999), 6433–6443), in which the main objects of study are random tridiagonal matrices which have zeros on the main diagonal and random ±1’s as the other entries. We explore the relationship between spectral sets in the finite and infinite matrix cases, and between the semi-infinite and bi-infinite matrix cases, for example showing that the numerical range and p-norm ε - pseudospectra (ε > 0, p ∈ [1,∞] ) of the random finite matrices converge almost surely to their infinite matrix counterparts, and that the finite matrix spectra are contained in the infinite matrix spectrum Σ. We also propose a sequence of inclusion sets for Σ which we show is convergent to Σ, with the nth element of the sequence computable by calculating smallest singular values of (large numbers of) n×n matrices. We propose similar convergent approximations for the 2-norm ε -pseudospectra of the infinite random matrices, these approximations sandwiching the infinite matrix pseudospectra from above and below.

A high frequency boundary element method for scattering by a class of nonconvex obstacles

In this paper we propose and analyse a hybrid numerical-asymptotic boundary element method for the solution of problems of high frequency acoustic scattering by a class of sound-soft nonconvex polygons. The approximation space is enriched with carefully chosen oscillatory basis functions; these are selected via a study of the high frequency asymptotic behaviour of the solution. We demonstrate via a rigorous error analysis, supported by numerical examples, that to achieve any desired accuracy it is sufficient for the number of degrees of freedom to grow only in proportion to the logarithm of the frequency as the frequency increases, in contrast to the at least linear growth required by conventional methods. This appears to be the first such numerical analysis result for any problem of scattering by a nonconvex obstacle. Our analysis is based on new frequency-explicit bounds on the normal derivative of the solution on the boundary and on its analytic continuation into the complex plane.

Home in British working-class fiction

Offering new readings of working-class writing that focus on the home as a key emotional and material site in writing by working-class authors from the Edwardian period through to the mid-1990s. With close readings of The Ragged Trousered Philanthropists, works by D. H. Lawrence, Ethel Carnie Holdsworth, Ellen Wilkinson, Lewis Grassic Gibbon, Walter Brierley, Alan Sillitoe, John Braine, Nell Dunn, Sam Selvon, Sid Chaplin, Buchi Emecheta, Pat Barker, Jeanette Winterson, James Kelman and many others. The book demonstrates the importance of ideas of home and its narrative representation to the making and expression of class feeling and identity.

Perfective marking in L2 Mandarin: agreement with inherent lexical aspect or the derived Sentential Aspectual class?

This study evaluates the differing claims of the Aspect Hypothesis (Anderson & Shirai 1996) and the Sentential Aspect Hypothesis (Sharma & Deo 2009) for perfective marking by L1 English learners of Mandarin. The AH predicts a narrow focus on inherent lexical aspect (the verb and predicate) in determining the use of the perfective marker le, whilst the SAH suggests that – subject to L1 influence – perfective marking agrees with the final derived aspectual class of the sentence. To test these claims data were collected using a controlled le-insertion task, combined with oral corpus data. The results show that learners’ perfective marking patterns with the sentential aspectual class and not inherent lexical aspect (where these differ), and that overall the sentential aspectual class better predicts learners’ assignment of perfective marking than lexical aspect.

Authenticity and performance of class in British factual TV series

The chapter characterises British ‘Reality TV’ as a hybrid of factual and fictional television genres, as signaled by the more accurate genre designation ‘structured reality’ television. From the 1990s onwards, in order to develop programmes that are attractive to audiences and inexpensive to produce, programme makers have focused on hybrids of dramatic and documentary modes. This chapter argues that many recent Reality TV programmes privilege soap opera’s emphasis on character, storyline and performance. This affects the ways that class authenticity is understood, undermining factual programmes’ usual claim to legitimacy based on reference to a pre-existing reality, and transforming hierarchies that separate highly-valued from low-valued types of programme.

A general Trotter-Kato formula for a class of evolution operators

In this article we prove new results concerning the existence and various properties of an evolution system U(A+B)(t, s)0 <= s <= t <= T generated by the sum -(A(t) + B(t)) of two linear, time-dependent, and generally unbounded operators defined on time-dependent domains in a complex and separable Banach space B. In particular, writing L(B) for the algebra of all linear bounded operators on B, we can express U(A+B)(t, s)0 <= s <= t <= T as the strong limit in C(8) of a product of the holomorphic contraction semigroups generated by -A (t) and - B(t), respectively, thereby proving a product formula of the Trotter-Kato type under very general conditions which allow the domain D(A(t) + B(t)) to evolve with time provided there exists a fixed set D subset of boolean AND(t is an element of)[0,T] D(A(t) + B(t)) everywhere dense in B. We obtain a special case of our formula when B(t) = 0, which, in effect, allows us to reconstruct U(A)(t, s)0 <=(s)<=(t)<=(T) very simply in terms of the semigroup generated by -A(t). We then illustrate our results by considering various examples of nonautonomous parabolic initial-boundary value problems, including one related to the theory of timedependent singular perturbations of self-adjoint operators. We finally mention what we think remains an open problem for the corresponding equations of Schrodinger type in quantum mechanics.

A Trotter-Kato product formula for a class of non-autonomous evolution equations

In this article dedicated to Professor V. Lakshmikantham on the occasion of the celebration of his 84th birthday, we announce new results concerning the existence and various properties of an evolution system UA+B(t, s)(0 <= s <= t <= T) generated by the sum -(A(t)+B(t)) of two linear, time-dependent and generally unbounded operators defined on time-dependent domains in a complex and separable Banach space B. In particular, writing G(B) for the algebra of all linear bounded operators on B, we can express UA+B(t, s)(0 <= s <= t <= T) as the strong limit in L(B) of a product of the holomorphic contraction semigroups generated by -A(t) and -B(t), thereby getting a product formula of the Trotter-Kato type under very general conditions which allow the domain D(A(t)+B(t)) to evolve with time provided there exists a fixed set D subset of boolean AND D-t epsilon[0,D-T](A(t)+B(t)) everywhere dense in B. We then mention several possible applications of our product formula to various classes of non-autonomous parabolic initial-boundary value problems, as well as to evolution problems of Schrodinger type related to the theory of time-dependent singular perturbations of self-adjoint operators in quantum mechanics. We defer all the proofs and all the details of the applications to a separate publication. (C) 2008 Elsevier Ltd. All rights reserved.

SPECTRUM OF SCREENING MASSES FOR SU(2) GAUGE THEORY: UNIVERSALITY CLASS

In this work we study the spectrum of the lowest screening masses for Yang-Mills theories on the lattice. We used the SU(2) gauge group in (3 + 1) dmensions. We adopted the multiple exponential method and the so-called ""variational"" method, in order to detect possible excited states. The calculations were done near the critical temperature of the confinement-deconfinement phase transition. We obtained values for the ratios of the screening masses consistent with predictions from universality arguments. A Monte Carlo evolution of the screening masses in the gauge theory confirms the validity of the predictions.

Wavelet regression with correlated errors on a piecewise Holder class

This paper generalizes the methodology of Cat and Brown [Cai, T., Brown, L.D., 1998. Wavelet shrinkage for nonequispaced samples. The Annals of Statistics 26, 1783-1799] for wavelet shrinkage for nonequispaced samples, but in the presence of correlated stationary Gaussian errors. If the true function is a member of a piecewise Holder class, it is shown that, even for long memory errors, the rate of convergence of the procedure is almost-minimax relative to the independent and identically distributed errors case. (c) 2008 Elsevier B.V. All rights reserved.