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.

N1 enhancement in synesthesia during visual and audio-visual perception in semantic cross-modal conflict situations: an ERP study

Synesthesia entails a special kind of sensory perception, where stimulation in one sensory modality leads to an internally generated perceptual experience of another, not stimulated sensory modality. This phenomenon can be viewed as an abnormal multisensory integration process as here the synesthetic percept is aberrantly fused with the stimulated modality. Indeed, recent synesthesia research has focused on multimodal processing even outside of the specific synesthesia-inducing context and has revealed changed multimodal integration, thus suggesting perceptual alterations at a global level. Here, we focused on audio-visual processing in synesthesia using a semantic classification task in combination with visually or auditory-visually presented animated and in animated objects in an audio-visual congruent and incongruent manner. Fourteen subjects with auditory-visual and/or grapheme-color synesthesia and 14 control subjects participated in the experiment. During presentation of the stimuli, event-related potentials were recorded from 32 electrodes. The analysis of reaction times and error rates revealed no group differences with best performance for audio-visually congruent stimulation indicating the well-known multimodal facilitation effect. We found enhanced amplitude of the N1 component over occipital electrode sites for synesthetes compared to controls. The differences occurred irrespective of the experimental condition and therefore suggest a global influence on early sensory processing in synesthetes.

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.

Adaptive B-spline neural network based nonlinear equalization for high-order QAM systems with nonlinear transmit high power amplifier

High bandwidth-efficiency quadrature amplitude modulation (QAM) signaling widely adopted in high-rate communication systems suffers from a drawback of high peak-toaverage power ratio, which may cause the nonlinear saturation of the high power amplifier (HPA) at transmitter. Thus, practical high-throughput QAM communication systems exhibit nonlinear and dispersive channel characteristics that must be modeled as a Hammerstein channel. Standard linear equalization becomes inadequate for such Hammerstein communication systems. In this paper, we advocate an adaptive B-Spline neural network based nonlinear equalizer. Specifically, during the training phase, an efficient alternating least squares (LS) scheme is employed to estimate the parameters of the Hammerstein channel, including both the channel impulse response (CIR) coefficients and the parameters of the B-spline neural network that models the HPA’s nonlinearity. In addition, another B-spline neural network is used to model the inversion of the nonlinear HPA, and the parameters of this inverting B-spline model can easily be estimated using the standard LS algorithm based on the pseudo training data obtained as a natural byproduct of the Hammerstein channel identification. Nonlinear equalisation of the Hammerstein channel is then accomplished by the linear equalization based on the estimated CIR as well as the inverse B-spline neural network model. Furthermore, during the data communication phase, the decision-directed LS channel estimation is adopted to track the time-varying CIR. Extensive simulation results demonstrate the effectiveness of our proposed B-Spline neural network based nonlinear equalization scheme.

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.

Local solvability for a class of evolution equations

Motivated by the celebrated example of Y. Kannai of a linear partial differential operator which is hypoelliptic but not locally solvable, we consider it class of evolution operators with real-analytic coefficients and study their local solvability both in L(2) and in the weak sense. In order to do so we are led to propose a generalization of the Nirenberg-Treves condition (psi) which is suitable to our study. (C) 2009 Published by Elsevier Inc.

d-Koszul algebras, 2-d-determined algebras and 2-d-Koszul algebras

The relationship between an algebra and its associated monomial algebra is investigated when at least one of the algebras is d-Koszul It is shown that an algebra which has a reduced Grobnerbasis that is composed of homogeneous elements of degree d is d-Koszul if and only if its associated monomial algebra is d-Koszul The class of 2-d-determined algebras and the class 2-d-Koszul algebras are introduced In particular it is shown that 2-d-determined monomial algebras are 2-d-Koszul algebras and the structure of the ideal of relations of such an algebra is completely determined (C) 2010 Elsevier B V All rights reserved

Twisted conjugacy classes in symplectic groups, mapping class groups and braid groups (with an appendix written jointly with Francois Dahmani)

We prove that the symplectic group Sp(2n, Z) and the mapping class group Mod(S) of a compact surface S satisfy the R(infinity) property. We also show that B(n)(S), the full braid group on n-strings of a surface S, satisfies the R(infinity) property in the cases where S is either the compact disk D, or the sphere S(2). This means that for any automorphism phi of G, where G is one of the above groups, the number of twisted phi-conjugacy classes is infinite.

Filmljudets funktioner i krigsfilm : En audio-visuell analys av Apocalypse Now och Saving Private Ryan

I denna uppsats har filmljudet i krigsfilmerna Apocalypse Now och Saving Private Ryan undersökts. Detta har gjorts för att försöka bidra med ökad förståelse för filmljudets användningsområde och funktioner, främst för filmerna i fråga, men även för krigsfilm rent generellt. Filmljud i denna kontext omfattar allt det ljud som finns i film, men utesluter dock all ickediegetisk musik. Båda filmerna har undersökts genom en audio-visuell analys. En sådan analys görs genom att detaljgranska båda filmernas ljud- och bildinnehåll var för sig, för att slutligen undersöka samma filmsekvens som helhet då ljudet och bilden satts ihop igen. Den audio-visuella analysmetod som nyttjats i uppsatsen är Michel Chions metod, Masking. De 30 minuter film som analyserades placerades sedan i olika filmljudzoner, där respektive filmljudzons ljudinnehåll bland annat visade vilka främsta huvudfunktioner somfilmljudet hade i dessa filmer. Dessa funktioner är till för att bibehålla åskådarens fokus och intresse, att skapa närhet till rollkaraktärerna, samt att tillföra en hög känsla av realism och närvaro. Intentionerna med filmljudet verkade vara att flytta åskådaren in i filmens verklighet, att låta åskådaren bli ett med filmen. Att återspegla denna känsla av realism, närvaro, fokus samt intresse, visade sig också vara de intentioner som funnits redan i de båda filmernas förproduktionsstadier. Detta bevisar att de lyckats åstadkomma det de eftersträvat. Men om filmljudet använts på samma sätt eller innehar samma funktioner i krigsfilm rent genrellt går inte att säga.I have for this bachelor’s thesis examined the movie sound of the classic warfare movies Apocalypse Now and Saving Private Ryan. This is an attempt to contribute to a more profound comprehension of the appliance and importance of movie sound. In this context movie sound implies all kinds of sounds within the movies, accept from non-diegetic music. These two movies have been examined by an audio-visual analysis. It's done by auditing the sound and picture content separately, and then combined to audit the same sequence as a whole. Michel Chion, which is the founder of this analysis, calls this method Masking. The sound in this 30 minute sequence was then divided into different zones, where every zone represented a certain main function. These functions are provided to create a stronger connection to the characters, sustain the viewers interest and bring a sense of realism and presence. It seems though the intention with the movies sound is to bring the viewers to the scene in hand, and let it become their reality. To mirror this sense of realism, presence, focus and interest, proves to be the intention from an early stage of the production. This bachelor’s thesis demonstrates a success in their endeavours. Although it can’t confirm whether the movie sound have been utilized in the same manner or if they posess the same functions to warefare movies in general.