Computing Zeros of Analytic Functions in the Complex Plane without using Derivatives

A new approach to evaluating all multiple complex roots of analytical function f(z) confined to the specified rectangular domain of complex plane has been developed and implemented in Fortran code. Generally f (z), despite being holomorphic function, does not have a closed analytical form thereby inhibiting explicit evaluation of its derivatives. The latter constraint poses a major challenge to implementation of the robust numerical algorithm. This work is at the instrumental level and provides an enabling tool for solving a broad class of eigenvalue problems and polynomial approximations.

Discordant quantitative detection of putative biomarkers in nodal micrometastases of colorectal cancer: biological and clinical implications

Aims: Nodal expression of the carcinoembryonic antigen ( CEA), cytokeratin 20 ( CK20), and guanylyl cyclase C ( GCC) genes was measured in tandem in patients with colorectal cancer ( CRC) to assess whether there would be sufficient agreement between these markers in their ability to detect micrometastasis to qualify one of them as a universal marker, and whether frozen and paraffin wax embedded tissues would yield similar results.

Portfolio of Compositions investigating ensemble improvisation, distributed and real-time scoring, and multi-nodal input and output

This output is a collection of compositions which explore issues of ensemble improvisation, ensemble management and orchestration, real-time and distributed scoring, multi-nodal inputs and outputs, and animated and graphic notation. Compositions include: Activities I; tutti, duet, trio, solo, quartet; Lewitt Notations I; Webwork I; and Sometimes I feel the space between people (voices) in terms of tempos. These compositions are presented in computer animated scores which are synchronized through the network and subject to real-time modification and control. They can be performed by ensembles distributed over large physical spaces connected by the network. The scores for these compositions include software which displays the animations to the performers, software to structure and disseminate score events, and triggering software that allows the control of a performance to be distributed. Scores can also include live electronics which are coordinated with graphic events.

Zeros and Os:Silence, Absence and Erasure in an Intercultural O-thello

The performative function of sound and music has received little attention in performance theory and criticism and certainly much less so in studies of intercultural theatre. Such an absence is noteworthy particularly since interculturalism is an appropriative Western theatrical form that absorbs Eastern sources to re-create the targeted Western mise en scene. Consequently, a careful consideration of the employment of sound and music are imperative for sound and music form the vertebrae of Asian traditional performance practices. In acoustemological and ethnomusicological studies, sound and music demarcate cultural boundaries and locate cultures by an auditory (dis)recognition. In the light of this need for a more considered understanding of the performative function of sound and music in intercultural performance, this paper seeks to examine the soundscapes of an intercultural production of Shakespeare’s Othello – Desdemona. Directed by Singaporean Ong Keng Sen, Desdemona was a re-scripting of Shakespeare’s text and a self-conscious performance an identity politics. Staged with a multi-ethnic, multi-national cast, Desdemona employed various Asian performance traditions such as Sanskrit Kutiyattam, Myanmarese puppetry, and Korean p’ansori to create the intercultural spectacle. The spectacle was not only a visual aesthetic but an aural one as well. By examining the soundscapes of fractured silences and eruptive cultural sounds the paper hopes to establish the ways in which Desdemona performs absences and erasures of ‘Asia’ in a simultaneous act of performing an Asian Shakespeare.

An analysis of wind curtailment and constraint at a nodal level

Many countries have set challenging wind power targets to achieve by 2020. This paper implements a realistic analysis of curtailment and constraint of wind energy at a nodal level using a unit commitment and economic dispatch model of the Irish Single Electricity Market in 2020. The key findings show that significant reduction in curtailment can be achieved when the system non-synchronous penetration limit increases from 65% to 75%. For the period analyzed, this results in a decreased total generation cost and a reduction in the dispatch-down of wind. However, some nodes experience significant dispatch-down of wind, which can be in the order of 40%. This work illustrates the importance of implementing analysis at a nodal level for the purpose of power system planning.

An exactly solvable four transition point model

Heavy particle collisions, in particular low-energy ion-atom collisions, are amenable to semiclassical JWKB phase integral analysis in the complex plane of the internuclear separation. Analytic continuation in this plane requires due attention to the Stokes phenomenon which parametrizes the physical mechanisms of curve crossing, non-crossing, the hybrid Nikitin model, rotational coupling and predissociation. Complex transition points represent adiabatic degeneracies. In the case of two or more such points, the Stokes constants may only be completely determined by resort to the so-called comparison- equation method involving, in particular, parabolic cylinder functions or Whittaker functions and their strong-coupling asymptotics. In particular, the Nikitin model is a two transition-point one-double-pole problem in each half-plane corresponding to either ingoing or outgoing waves. When the four transition points are closely clustered, new techniques are required to determine Stokes constants. However, such investigations remain incomplete, A model problem is therefore solved exactly for scattering along a one-dimensional z-axis. The energy eigenvalue is b(2)-a(2) and the potential comprises -z(2)/2 (parabolic) and -a(2) + b(2)/2z(2) (centrifugal/centripetal) components. The square of the wavenumber has in the complex z-plane, four zeros each a transition point at z = +/-a +/- ib and has a double pole at z = 0. In cases (a) and (b), a and b are real and unitarity obtains. In case (a) the reflection and transition coefficients are parametrized by exponentials when a(2) + b(2) > 1/2. In case (b) they are parametrized by trigonometrics when a(2) + b(2) <1/2 and total reflection is achievable. In case (c) a and b are complex and in general unitarity is not achieved due to loss of flux to a continuum (O'Rourke and Crothers, 1992 Proc. R. Sec. 438 1). Nevertheless, case (c) coefficients reduce to (a) or (b) under appropriate limiting conditions. Setting z = ht, with h a real constant, an attempt is made to model a two-state collision problem modelled by a pair of coupled first-order impact parameter equations and an appropriate (T) over tilde-tau relation, where (T) over tilde is the Stueckelberg variable and tau is the reduced or scaled time. The attempt fails because (T) over tilde is an odd function of tau, which is unphysical in a real collision problem. However, it is pointed out that by applying the Kummer exponential model to each half-plane (O'Rourke and Crothers 1994 J. Phys. B: At. Mel. Opt. Phys. 27 2497) the current model is in effect extended to a collision problem with four transition points and a double pole in each half-plane. Moreover, the attempt in itself is not a complete failure since it is shown that the result is a perfect diabatic inelastic collision for a traceless Hamiltonian matrix, or at least when both diagonal elements are odd and the off-diagonal elements equal and even.

B-type supergiants in the Small Magellanic Cloud: rotational velocities and implications for evolutionary models

High-resolution spectra for 24 SMC and Galactic B-type supergiants have been analysed to estimate the contributions of both macroturbulence and rotation to the broadening of their metal lines. Two different methodologies are considered, viz. goodness-of-fit comparisons between observed and theoretical line profiles and identifying zeros in the Fourier transforms of the observed profiles. The advantages and limitations of the two methods are briefly discussed with the latter techniques being adopted for estimating projected rotational velocities ( v sin i) but the former being used to estimate macroturbulent velocities. The projected rotational velocity estimates range from approximately 20 to 60 kms(-1), apart from one SMC supergiant, Sk 191, with a v sin i similar or equal to 90 km s(-1). Apart from Sk 191, the distribution of projected rotational velocities as a function of spectral type are similar in both our Galactic and SMC samples with larger values being found at earlier spectral types. There is marginal evidence for the projected rotational velocities in the SMC being higher than those in the Galactic targets but any differences are only of the order of 5 - 10 km s(-1), whilst evolutionary models predict differences in this effective temperature range of typically 20 to 70 km s(-1). The combined sample is consistent with a linear variation of projected rotational velocity with effective temperature, which would imply rotational velocities for supergiants of 70 kms(-1) at an effective temperature of 28 000 K ( approximately B0 spectral type) decreasing to 32 km s(-1) at 12 000 K (B8 spectral type). For all targets, the macroturbulent broadening would appear to be consistent with a Gaussian distribution ( although other distributions cannot be discounted) with an 1/e half-width varying from approximately 20 km s(-1) at B8 to 60 km s(-1) at B0 spectral types.

Fixed-node diffusion Monte Carlo computations for closed-shell jellium spheres

Fixed-node diffusion Monte Carlo computations are used to determine the ground state energy and electron density for jellium spheres with up to N = 106 electrons and background densities corresponding to the electron gas parameter 1 less than or equal to r(s)less than or equal to5.62. We analyze the density and size dependence of the surface energy, and we extrapolate our data to the thermodynamic limit. The results agree well with the predictions of density functional computations using the local density approximation. In the case of N = 20, we extend our computation to higher densities and identify a transition between atomic- and jelliumlike nodal structures occurring at the background density corresponding to r(s)=0.13. In this case the local density approximation is unable to reproduce the changes in the correlation energy due to the discontinuous transition in the ground state nodal structure. We discuss the relevance of our results for nonlocal approximations to density functional theory.

Efficient analysis, design, and filter applications of EBG waveguide with periodic resonant loads

An efficient analysis and design of an electromagnetic-bandgap (EBG) waveguide with resonant loads is presented. Equivalent-circuit analysis is employed to demonstrate the differences between EBG waveguides with resonant and nonresonant loadings. As a result of the resonance, transmission zeros at finite frequencies emerge. The concept is demonstrated in E-plane waveguides. A generic fast and efficient formulation is presented, which starts from the generalized scattering matrix of the unit cell and derives the dispersion properties of the infinite structure. Both real and imaginary parts of the propagation constant are derived and discussed. The Floquet wavelength and impedance are also presented. The theoretical results are validated by comparison with simulations of a finite structure and experimental results. The application of the proposed EBG waveguide in the suppression of the spurious passband of a conventional E-plane filter is presented by experiment.

Compact ridge waveguide filter with parallel and series-coupled resonators

A novel 3rd-order compact E-plane ridge waveguide filter is presented. Miniaturization is achieved upon introducing a configuration of parallel-coupled E-plane ridge waveguide resonators. Furthermore, the proposed filter allows for transmission zeros at finite frequencies. Fabrication simplicity and mass producibility of standard E-plane filters is maintained. The numerical and experimental results are presented to validate the proposed configuration. A miniaturisation factor of 2 and very sharp upper cutoff are achieved. 2005 Wiley Periodicals, Inc.

MSGR-based Low Latency Complex Matrix Inversion Architecture

This paper presents a matrix inversion architecture based on the novel Modified Squared Givens Rotations (MSGR) algorithm, which extends the original SGR method to complex valued data, and also corrects erroneous results in the original SGR method when zeros occur on the diagonal of the matrix either initially or during processing. The MSGR algorithm also avoids complex dividers in the matrix inversion, thus minimising the complexity of potential real-time implementations. A systolic array architecture is implemented and FPGA synthesis results indicate a high-throughput low-latency complex matrix inversion solution. © 2008 IEEE.

The last meal of the Late Ordovician mollusc ‘Helminthochiton’ thraivensis Reed, 1911, from the Lady Burn Starfish Beds, southwest Scotland.

An exceptional specimen of the Late Ordovician mollusc ‘Helminthochiton’ thraivensis Reed, from the Katian of the Lady Burn Starfish Beds, southwest Scotland, preserves gut contents that include nine pelmatozoan ossicles. These are interpreted as including two nodal and five intermodal columnals, and two radice ossicles from the attachment structure. The stem was cyclocyclic and heteromorphic, possibly N212. Radice ossicles were wider than the height of nodals, so radice scars must have encroached onto the latera of adjacent pluricolumnals. These features were compared with the 26 known pelmatozoan taxa from the Lady Burn Starfish Beds. Paracrinoids (one species) and glyptocystitid rhombiferans (six species) were discounted as prey because of their cemented attachment, and incorrect columnal morphology and lack of attachment, respectively. Of 19 species of crinoids, eight are discounted in which the column is pentagonal, tetragonal or unknown. Of the remaining eleven species, only the monobathrid camerate Macrostylocrinus cirrifer Ramsbottom satisfies all criteria for identification of the prey, including heteromorphy and radice scars encroaching adjacent internodals.

Intrinsic variability in the detection of micrometastases in lymph nodes for re-staging of colorectal cancer: effect of individual markers and tissue samples

In this study, we investigated whether (a) carcinoembryonic antigen (CEA), cytokeratin-20 (CK-20) and guanylyl cyclase C (GCC) are clinically useful markers for the molecular detection of submicroscopic metastases in colorectal cancer (CRC) and (b) whether overexpression of CEA, CK-20 and GCC can be reliably detected in formalin-fixed, paraffin-embedded tissues as well as frozen lymph nodes. We studied 175 frozen lymph nodes and 158 formalin-fixed, paraffin-embedded lymph nodes from 28 cases of CRC. CEA or CK-20 or GCC-specific polymerase chain reaction (PCR) was carried out on mRNA transcripts extracted from the nodal tissues. Ten out of I I Dukes' B CRC cases had detectable CEA and CK-20 while 6 out of 11 Dukes' B CRC cases had detectable GCC. In general, the difference of re-staged cases when comparing frozen and paraffin-embedded samples was marked; the only statistically significant correlation between frozen and paraffin tissue was for the CEA marker. Our results indicated a high incidence (>50%) of detecting micrometastases in histologically-negative lymph nodes at the molecular level. (C) 2003 Elsevier Science Ltd. All rights reserved.