A scalarization technique for computing the power and exponential moments of gaussian random matrices

We consider the problems of computing the power and exponential moments EXs and EetX of square Gaussian random matrices X=A+BWC for positive integer s and real t, where W is a standard normal random vector and A, B, C are appropriately dimensioned constant matrices. We solve the problems by a matrix product scalarization technique and interpret the solutions in system-theoretic terms. The results of the paper are applicable to Bayesian prediction in multivariate autoregressive time series and mean-reverting diffusion processes.

Mathematical modelling and optimal multivariable control of chemical processes

This work reports the developnent of a mathenatical model and distributed, multi variable computer-control for a pilot plant double-effect climbing-film evaporator. A distributed-parameter model of the plant has been developed and the time-domain model transformed into the Laplace domain. The model has been further transformed into an integral domain conforming to an algebraic ring of polynomials, to eliminate the transcendental terms which arise in the Laplace domain due to the distributed nature of the plant model. This has made possible the application of linear control theories to a set of linear-partial differential equations. The models obtained have well tracked the experimental results of the plant. A distributed-computer network has been interfaced with the plant to implement digital controllers in a hierarchical structure. A modern rnultivariable Wiener-Hopf controller has been applled to the plant model. The application has revealed a limitation condition that the plant matrix should be positive-definite along the infinite frequency axis. A new multi variable control theory has emerged fram this study, which avoids the above limitation. The controller has the structure of the modern Wiener-Hopf controller, but with a unique feature enabling a designer to specify the closed-loop poles in advance and to shape the sensitivity matrix as required. In this way, the method treats directly the interaction problems found in the chemical processes with good tracking and regulation performances. Though the ability of the analytical design methods to determine once and for all whether a given set of specifications can be met is one of its chief advantages over the conventional trial-and-error design procedures. However, one disadvantage that offsets to some degree the enormous advantages is the relatively complicated algebra that must be employed in working out all but the simplest problem. Mathematical algorithms and computer software have been developed to treat some of the mathematical operations defined over the integral domain, such as matrix fraction description, spectral factorization, the Bezout identity, and the general manipulation of polynomial matrices. Hence, the design problems of Wiener-Hopf type of controllers and other similar algebraic design methods can be easily solved.

A semi-oriented radial measure for measuring the efficiency of decision making units with negative data, using DEA

Data Envelopment Analysis (DEA) is a nonparametric method for measuring the efficiency of a set of decision making units such as firms or public sector agencies, first introduced into the operational research and management science literature by Charnes, Cooper, and Rhodes (CCR) [Charnes, A., Cooper, W.W., Rhodes, E., 1978. Measuring the efficiency of decision making units. European Journal of Operational Research 2, 429–444]. The original DEA models were applicable only to technologies characterized by positive inputs/outputs. In subsequent literature there have been various approaches to enable DEA to deal with negative data. In this paper, we propose a semi-oriented radial measure, which permits the presence of variables which can take both negative and positive values. The model is applied to data on a notional effluent processing system to compare the results with those yielded by two alternative methods for dealing with negative data in DEA: The modified slacks-based model suggested by Sharp et al. [Sharp, J.A., Liu, W.B., Meng, W., 2006. A modified slacks-based measure model for data envelopment analysis with ‘natural’ negative outputs and inputs. Journal of Operational Research Society 57 (11) 1–6] and the range directional model developed by Portela et al. [Portela, M.C.A.S., Thanassoulis, E., Simpson, G., 2004. A directional distance approach to deal with negative data in DEA: An application to bank branches. Journal of Operational Research Society 55 (10) 1111–1121]. A further example explores the advantages of using the new model.

A study of potential serum markers for a diagnosis of gram-positive and gram-negative bacterial sepsis

Sepsis continues to be a major cause of morbidity and mortality as it can readily lead tosevere sepsis, septic shock, multiple organ failure and death. The onset can be rapid and difficult to define clinically. Despite the numerous candidate markers proposed in the literature, to date a serum marker for sepsis has not been found. The aim of this study was to assay the serum of clinically diagnosed patients with eithera Gram-negative or Gram- positive bacterial sepsis for elevated levels of nine potentialmarkers of sepsis, using commercially produced enzyme linked immunosorbent assays(ELISA). The purpose was to find a test marker for sepsis that would be helpful toclinicians in cases of uncertain sepsis and consequently expose false positive BC'scaused by skin or environmental contaminants. Nine test markers were assayed including IL-6, IL-I 0, ILI2, TNF-α, lipopolysaccharide binding protein, procalcitonin, sE-selectin, sICAM -1 and a potential differential marker for Gram-positive sepsis- anti-lipid S antibody. A total of 445 patients were enrolled into this study from the Queen Elizabeth Hospital and Selly Oak Hospital (Birmingham). The results showed that all the markers were elevated in patients with sepsis and that patients with a Gram-negative sepsis consistently produced higher median/range serum levels than those with a Gram-positive sepsis. No single marker was able to identify all the septic patients. Combining two markers caused the sensitivities and specificities for a diagnosis of sepsis to increase to within a 90% to 100% range. By a process of elimination the markers that survived into the last phase were IL-6 with sICAM -1, and anti-lipid S IgG assays Defining cut-off levels for a diagnosis of sepsis became problematic and a semi-blind trial was devised to test the markers in the absence of both clinical details and positive blood cultures. Patients with pyrexia of unknown origin and negative BC were included in this phase (4). The results showed that IL-6 with sICAM-l are authentic markers of sepsis. There was 82% agreement between the test marker diagnosis and the clinical diagnosis for sepsis in patients with a Gram-positive BC and 78% agreement in cases of Gram-negative Be. In the PUO group the test markers identified 12 cases of sepsis and the clinical diagnosis 15. The markers were shown to differentiate between early sepsis and sepsis, inflammatory responses and infection. Anti-lipid S with IL-6 proved be a sensitive marker for Gram-positive infections/sepsis.

Some Computational Aspects of the Consistent Mass Finite Element Method for a (semi-)periodic Eigenvalue Problem

We consider a model eigenvalue problem (EVP) in 1D, with periodic or semi–periodic boundary conditions (BCs). The discretization of this type of EVP by consistent mass finite element methods (FEMs) leads to the generalized matrix EVP Kc = λ M c, where K and M are real, symmetric matrices, with a certain (skew–)circulant structure. In this paper we fix our attention to the use of a quadratic FE–mesh. Explicit expressions for the eigenvalues of the resulting algebraic EVP are established. This leads to an explicit form for the approximation error in terms of the mesh parameter, which confirms the theoretical error estimates, obtained in [2].

A Representation of Binary Matrices

Христина Костадинова, Красимир Йорджев - В статията се обсъжда представянето на произволна бинарна матрица с помощта на последователност от цели неотрицателни числа. Разгледани са някои предимства и недостатъци на това представяне като алтернатива на стандартното, общоприето представяне чрез двумерен масив. Показано е, че представянето на бинарните матрици с помощта на наредени n-торки от естествени числа води до по-бързи алгоритми и до съществена икономия на оперативна памет. Използуван е апарата на обектно-ориентираното програмиране със синтаксиса и семантиката на езика C++.

Global Waves with Non-Positive Energy in General Relativity

2000 Mathematics Subject Classification: 35Lxx, 35Pxx, 81Uxx, 83Cxx.

The Direct and Inverse Spectral Problems for some Banded Matrices

2000 Mathematics Subject Classification: 15A29.

Extended principal component analysis and its applications to image analysis

The objectives of this research are to analyze and develop a modified Principal Component Analysis (PCA) and to develop a two-dimensional PCA with applications in image processing. PCA is a classical multivariate technique where its mathematical treatment is purely based on the eigensystem of positive-definite symmetric matrices. Its main function is to statistically transform a set of correlated variables to a new set of uncorrelated variables over $\IR\sp{n}$ by retaining most of the variations present in the original variables.^ The variances of the Principal Components (PCs) obtained from the modified PCA form a correlation matrix of the original variables. The decomposition of this correlation matrix into a diagonal matrix produces a set of orthonormal basis that can be used to linearly transform the given PCs. It is this linear transformation that reproduces the original variables. The two-dimensional PCA can be devised as a two successive of one-dimensional PCA. It can be shown that, for an $m\times n$ matrix, the PCs obtained from the two-dimensional PCA are the singular values of that matrix.^ In this research, several applications for image analysis based on PCA are developed, i.e., edge detection, feature extraction, and multi-resolution PCA decomposition and reconstruction. ^

Environmental analysis of polar herbicides in complex organic-rich matrices by high performance liquid chromatography atmospheric pressure ionization mass spectrometry (HPLC-API-MS)

A comprehensive forensic investigation of sensitive ecosystems in the Everglades Area is presented. Assessing the background levels of contamination in these ecosystems represents a vital resource to build up forensic evidence required to enforce future environmental crimes within the studied areas. This investigation presents the development and validation of a fractionation and isolation method for two families of herbicides commonly applied in the vicinity of the study area, including phenoxy acids like 2,4-D, MCPA, and silvex; as well as the most common triazine-based herbicides like atrazine, prometyne, simazine and related metabolites like DIA and DEA. Accelerated solvent extraction (ASE) and solid phase extraction (SPE) were used to isolate the analytes from abiotic matrices containing large amounts of organic material. Atmospheric-pressure ionization (API) with electrospray ionization in negative mode (ESP-), and Chemical Ionization in the positive mode (APCI+) were used to perform the characterization of the herbicides of interest.

Source apportionment of PM2.5 in Cork Harbour, Ireland using a combination of single particle mass spectrometry and quantitative semi-continuous measurements

An aerosol time-of-flight mass spectrometer (ATOFMS) was deployed for the measurement of the size resolved chemical composition of single particles at a site in Cork Harbour, Ireland for three weeks in August 2008. The ATOFMS was co-located with a suite of semi-continuous instrumentation for the measurement of particle number, elemental carbon (EC), organic carbon (OC), sulfate and particulate matter smaller than 2.5 μm in diameter (PM2.5). The temporality of the ambient ATOFMS particle classes was subsequently used in conjunction with the semi-continuous measurements to apportion PM2.5 mass using positive matrix factorisation. The synergy of the single particle classification procedure and positive matrix factorisation allowed for the identification of six factors, corresponding to vehicular traffic, marine, long-range transport, various combustion, domestic solid fuel combustion and shipping traffic with estimated contributions to the measured PM2.5 mass of 23%, 14%, 13%, 11%, 5% and 1.5% respectively. Shipping traffic was found to contribute 18% of the measured particle number (20–600 nm mobility diameter), and thus may have important implications for human health considering the size and composition of ship exhaust particles. The positive matrix factorisation procedure enabled a more refined interpretation of the single particle results by providing source contributions to PM2.5 mass, while the single particle data enabled the identification of additional factors not possible with typical semi-continuous measurements, including local shipping traffic.

Dispositifs optoélectroniques à base de semi-conducteurs organiques en couches minces

Les petites molécules de type p à bandes interdites étroites sont de plus en plus perçues comme des remplaçantes possibles aux polymères semi-conducteurs actuellement utilisés conjointement avec des dérivés de fullerènes de type n, dans les cellules photovoltaïques organiques (OPV). Par contre, ces petites molécules tendent à cristalliser facilement lors de leur application en couches minces et forment difficilement des films homogènes appropriés. Des dispositifs OPV de type hétérojonction de masse ont été réalisés en ajoutant différentes espèces de polymères semi-conducteurs ou isolants, agissant comme matrices permettant de rectifier les inhomogénéités des films actifs et d’augmenter les performances des cellules photovoltaïques. Des polymères aux masses molaires spécifiques ont été synthétisés par réaction de Wittig en contrôlant précisément les ratios molaires des monomères et de la base utilisée. L’effet de la variation des masses molaires en fonction des morphologies de films minces obtenus et des performances des diodes organiques électroluminescentes reliées, a également été étudié. La microscopie électronique en transmission (MET) ou à balayage (MEB) a été employée en complément de la microscopie à force atomique (AFM) pour suivre l’évolution de la morphologie des films organiques minces. Une nouvelle méthode rapide de préparation des films pour l’imagerie MET sur substrats de silicium est également présentée et comparée à d’autres méthodes d’extraction. Motivé par le prix élevé et la rareté des métaux utilisés dans les substrats d’oxyde d’indium dopé à l’étain (ITO), le développement d’une nouvelle méthode de recyclage eco-responsable des substrats utilisés dans ces études est également présenté.

Non-invasive diagnosis of pediatric tuberculosis

Thesis (Master's)--University of Washington, 2016-08

Growing Well-beings: the Positive Experience of Care Farms

Objectives: Care farms enable people who are in some way vulnerable to engage with agricultural places and farming activities. This study investigates how this impacts on the health and well-being of service users and explores associated processes and outcomes. Design: A mixed methods design was adopted that allowed for the integration of quantitative measurements of change with qualitative descriptions of this change. A pragmatic approach provided sufficient flexibility to support the investigation of complex contexts. Methods: A total of 216 service users completed an initial questionnaire, and 137 (63%) of this number provided comparative data in a follow-up questionnaire. Questionnaires contained multiple choice and open-ended questions alongside standardized health and well-being measures requiring Likert-format responses. Semi-structured interviews with 33 service users allowed personal experiences to be detailed. Results: Statistical analysis of well-being measure scores identified significant positive relationships with the length of time people had been attending the care farm. Questionnaire and interview data presented health benefits as being enabled by the farm environment, the positive experience as supporting personal development, and associated social interactions as becoming increasingly influential as time progressed. Conclusions: The health and well-being outcomes that result from participating at a care farm influence multiple elements of the human condition and apply amongst vulnerable people with a wide range of personal needs. Care farms have access to a potentially unique range of resources that can support many service users in becoming happier and healthier individuals.

Critical magnetic elds in superconducting systems with semi-metallic bands

In this work, we study the Zeeman splitting effects in the parallel magnetic field versus temperature phase diagram of two-dimensional superconductors with one graphene-like band and the orbital effects of perpendicular magnetic fields in isotropic two-dimensional semi-metallic superconductors. We show that when parallel magnetic fields are applied to graphene and as the intraband interaction decreases to a critical value, the width of the metastability region present in the phase diagram decreases, vanishing completely at that critical value. In the case of two-band superconductors with one graphene-like band, a new critical interaction, associated primarily with the graphene-like band, is required in order for a second metastability region to be present in the phase diagram. For intermediate values of this interaction, a low-temperature first-order transition line bifurcates at an intermediate temperature into a first-order transition between superconducting phases and a second-order transition line between the normal and the superconducting states. In our study on the upper critical fields in generic semi-metallic superconductors, we find that the pair propagator decays faster than that of a superconductor with a metallic band. As result, the zero field band gap equation does not have solution for weak intraband interactions, meaning that there is a critical intraband interaction value in order for a superconducting phase to be present in semi-metallic superconductors. Finally, we show that the out-of-plane critical magnetic field versus temperature phase diagram displays a positive curvature, contrasting with the parabolic-like behaviour typical of metallic superconductors.