Spectrum of a Feinberg-Zee random hopping matrix

This paper provides a new proof of a theorem of Chandler-Wilde, Chonchaiya, and Lindner that the spectra of a certain class of infinite, random, tridiagonal matrices contain the unit disc almost surely. It also obtains an analogous result for a more general class of random matrices whose spectra contain a hole around the origin. The presence of the hole forces substantial changes to the analysis.

Numerical computation of an analytic singular value decomposition of a matrix valued function

This paper extends the singular value decomposition to a path of matricesE(t). An analytic singular value decomposition of a path of matricesE(t) is an analytic path of factorizationsE(t)=X(t)S(t)Y(t) T whereX(t) andY(t) are orthogonal andS(t) is diagonal. To maintain differentiability the diagonal entries ofS(t) are allowed to be either positive or negative and to appear in any order. This paper investigates existence and uniqueness of analytic SVD's and develops an algorithm for computing them. We show that a real analytic pathE(t) always admits a real analytic SVD, a full-rank, smooth pathE(t) with distinct singular values admits a smooth SVD. We derive a differential equation for the left factor, develop Euler-like and extrapolated Euler-like numerical methods for approximating an analytic SVD and prove that the Euler-like method converges.

Robust eigenstructure assignment in quadratic matrix polynomials: nonsingular case

Feedback design for a second-order control system leads to an eigenstructure assignment problem for a quadratic matrix polynomial. It is desirable that the feedback controller not only assigns specified eigenvalues to the second-order closed loop system but also that the system is robust, or insensitive to perturbations. We derive here new sensitivity measures, or condition numbers, for the eigenvalues of the quadratic matrix polynomial and define a measure of the robustness of the corresponding system. We then show that the robustness of the quadratic inverse eigenvalue problem can be achieved by solving a generalized linear eigenvalue assignment problem subject to structured perturbations. Numerically reliable methods for solving the structured generalized linear problem are developed that take advantage of the special properties of the system in order to minimize the computational work required. In this part of the work we treat the case where the leading coefficient matrix in the quadratic polynomial is nonsingular, which ensures that the polynomial is regular. In a second part, we will examine the case where the open loop matrix polynomial is not necessarily regular.

Fast median calculation method

The ever increasing demand for high image quality requires fast and efficient methods for noise reduction. The best-known order-statistics filter is the median filter. A method is presented to calculate the median on a set of N W-bit integers in W/B time steps. Blocks containing B-bit slices are used to find B-bits of the median; using a novel quantum-like representation allowing the median to be computed in an accelerated manner compared to the best-known method (W time steps). The general method allows a variety of designs to be synthesised systematically. A further novel architecture to calculate the median for a moving set of N integers is also discussed.

A matrix iteration for dynamic network summaries

We propose a new algorithm for summarizing properties of large-scale time-evolving networks. This type of data, recording connections that come and go over time, is being generated in many modern applications, including telecommunications and on-line human social behavior. The algorithm computes a dynamic measure of how well pairs of nodes can communicate by taking account of routes through the network that respect the arrow of time. We take the conventional approach of downweighting for length (messages become corrupted as they are passed along) and add the novel feature of downweighting for age (messages go out of date). This allows us to generalize widely used Katz-style centrality measures that have proved popular in network science to the case of dynamic networks sampled at non-uniform points in time. We illustrate the new approach on synthetic and real data.

A note on the Fredholm properties of Toeplitz operators on weighted Bergman spaces with matrix-valued symbols

We characterize the essential spectra of Toeplitz operators Ta on weighted Bergman spaces with matrix-valued symbols; in particular we deal with two classes of symbols, the Douglas algebra C+H∞ and the Zhu class Q := L∞ ∩VMO∂ . In addition, for symbols in C+H∞ , we derive a formula for the index of Ta in terms of its symbol a in the scalar-valued case, while in the matrix-valued case we indicate that the standard reduction to the scalar-valued case fails to work analogously to the Hardy space case. Mathematics subject classification (2010): 47B35,

Importance of oceanic resolution and mean state on the extra-tropical response to El Niño in a matrix of coupled models

The extra-tropical response to El Niño in configurations of a coupled model with increased horizontal resolution in the oceanic component is shown to be more realistic than in configurations with a low resolution oceanic component. This general conclusion is independent of the atmospheric resolution. Resolving small-scale processes in the ocean produces a more realistic oceanic mean state, with a reduced cold tongue bias, which in turn allows the atmospheric model component to be forced more realistically. A realistic atmospheric basic state is critical in order to represent Rossby wave propagation in response to El Niño, and hence the extra-tropical response to El Niño. Through the use of high and low resolution configurations of the forced atmospheric-only model component we show that, in isolation, atmospheric resolution does not significantly affect the simulation of the extra-tropical response to El Niño. It is demonstrated, through perturbations to the SST forcing of the atmospheric model component, that biases in the climatological SST field typical of coupled model configurations with low oceanic resolution can account for the erroneous atmospheric basic state seen in these coupled model configurations. These results highlight the importance of resolving small-scale oceanic processes in producing a realistic large-scale mean climate in coupled models, and suggest that it might may be possible to “squeeze out” valuable extra performance from coupled models through increases to oceanic resolution alone.

Direct observation of membrane insertion by enveloped virus matrix proteins by phosphate displacement

Enveloped virus release is driven by poorly understood proteins that are functional analogs of the coat protein assemblies that mediate intracellular vesicle trafficking. We used differential electron density mapping to detect membrane integration by membrane-bending proteins from five virus families. This demonstrates that virus matrix proteins replace an unexpectedly large portion of the lipid content of the inner membrane face, a generalized feature likely to play a role in reshaping cellular membranes.

Daidzein, R-(+)equol and S-(-)equol inhibit the invasion of MDA-MB-231 breast cancer cells potentially via the down-regulation of matrix metalloproteinase-2

PURPOSE: Soy isoflavones may inhibit tumor cell invasion and metastasis via their effects on matrix metalloproteinases (MMPs) and their tissue inhibitors (TIMPs). The current study investigates the effects of daidzein, R- and S-equol on the invasion of MDA-MB-231 human breast cancer cells and the effects of these compounds on MMP/TIMP expression at the mRNA level. METHODS: The anti-invasive effects of daidzein, R- and S-equol (0, 2.5, 10, 50 μM) on MDA-MB-231 cells were determined using the Matrigel invasion assay following 48-h exposure. Effects on MMP-2, MMP-9, TIMP-1 and TIMP-2 expression were assessed using real-time PCR. Chiral HPLC analysis was used to determine intracellular concentrations of R- and S-equol. RESULTS: The invasive capacity of MDA-MB-231 cells was significantly reduced (by approximately 50-60 %) following treatment with 50 μM daidzein, R- or S-equol. Anti-invasive effects were also observed with R-equol at 2.5 and 10 μM though overall equipotent effects were induced by all compounds. Inhibition of invasion induced by all three compounds at 50 μM was associated with the down-regulation of MMP-2, while none of the compounds tested significantly affected the expression levels of MMP-9, TIMP-1 or TIMP-2 at this concentration. Following exposure to media containing 50 μM R- or S-equol for 48-h intracellular concentrations of R- and S-equol were 4.38 ± 1.17 and 3.22 ± 0.47 nM, respectively. CONCLUSION: Daidzein, R- and S-equol inhibit the invasion of MDA-MB-231 human breast cancer cells in part via the down-regulation of MMP-2 expression, with equipotent effects observed for the parent isoflavone daidzein and the equol enantiomers.

Software-based study of a non-sorting method for median calculation on a set of integer numbers

This paper presents a software-based study of a hardware-based non-sorting median calculation method on a set of integer numbers. The method divides the binary representation of each integer element in the set into bit slices in order to find the element located in the middle position. The method exhibits a linear complexity order and our analysis shows that the best performance in execution time is obtained when slices of 4-bit in size are used for 8-bit and 16-bit integers, in mostly any data set size. Results suggest that software implementation of bit slice method for median calculation outperforms sorting-based methods with increasing improvement for larger data set size. For data set sizes of N > 5, our simulations show an improvement of at least 40%.

Median architecture by accumulative parallel counters

The time to process each of W/B processing blocks of a median calculation method on a set of N W-bit integers is improved here by a factor of three compared to the literature. Parallelism uncovered in blocks containing B-bit slices are exploited by independent accumulative parallel counters so that the median is calculated faster than any known previous method for any N, W values. The improvements to the method are discussed in the context of calculating the median for a moving set of N integers for which a pipelined architecture is developed. An extra benefit of smaller area for the architecture is also reported.

Introducing matrix management within a children's services setting - personal reflections

This article reflects on the introduction of ‘matrix management’ arrangements for an Educational Psychology Service (EPS) within a Children’s Service Directorate of a Local Authority (LA). It seeks to demonstrate critical self-awareness, consider relevant literature with a view to bringing insights to processes and outcomes, and offers recommendations regarding the use of matrix management. The report arises from an East Midland’s LA initiative: ALICSE − Advanced Leadership in an Integrated Children’s Service Environment. Through a literature review and personal reflection, the authors consider the following: possible tensions within the development of matrix management arrangements; whether matrix management is a prerequisite within complex organizational systems; and whether competing professional cultures may contribute barriers to creating complementary and collegiate working. The authors briefly consider some research paradigms, notably ethnographic approaches, soft systems methodology, activity theory and appreciative inquiry. These provide an analytic framework for the project and inform this iterative process of collaborative inquiry. Whilst these models help illuminate otherwise hidden processes, none have been implemented following full research methodologies, reflecting the messy reality of local authority working within dynamic organizational structures and shrinking budgets. Nevertheless, this article offers an honest reflection of organizational change within a children’s services environment.

Pipelined median architecture

The core processing step of the noise reduction median filter technique is to find the median within a window of integers. A four-step procedure method to compute the running median of the last N W-bit stream of integers showing area and time benefits is proposed. The method slices integers into groups of B-bit using a pipeline of W/B blocks. From the method, an architecture is developed giving a designer the flexibility to exchange area gains for faster frequency of operation, or vice versa, by adjusting N, W and B parameter values. Gains in area of around 40%, or in frequency of operation of around 20%, are clearly observed by FPGA circuit implementations compared to latest methods in the literature.