Parallel Hybrid Monte Carlo Algorithms for Matrix Computations

In this paper we consider hybrid (fast stochastic approximation and deterministic refinement) algorithms for Matrix Inversion (MI) and Solving Systems of Linear Equations (SLAE). Monte Carlo methods are used for the stochastic approximation, since it is known that they are very efficient in finding a quick rough approximation of the element or a row of the inverse matrix or finding a component of the solution vector. We show how the stochastic approximation of the MI can be combined with a deterministic refinement procedure to obtain MI with the required precision and further solve the SLAE using MI. We employ a splitting A = D – C of a given non-singular matrix A, where D is a diagonal dominant matrix and matrix C is a diagonal matrix. In our algorithm for solving SLAE and MI different choices of D can be considered in order to control the norm of matrix T = D –1C, of the resulting SLAE and to minimize the number of the Markov Chains required to reach given precision. Further we run the algorithms on a mini-Grid and investigate their efficiency depending on the granularity. Corresponding experimental results are presented.

Domínios de potências fracionárias de operadores matriciais segundo Lasiecka-Triggiani

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Maximum principle, mean value operators and quasi boundedness in non-euclidean settings

This work deals with some classes of linear second order partial differential operators with non-negative characteristic form and underlying non- Euclidean structures. These structures are determined by families of locally Lipschitz-continuous vector fields in RN, generating metric spaces of Carnot- Carath´eodory type. The Carnot-Carath´eodory metric related to a family {Xj}j=1,...,m is the control distance obtained by minimizing the time needed to go from two points along piecewise trajectories of vector fields. We are mainly interested in the causes in which a Sobolev-type inequality holds with respect to the X-gradient, and/or the X-control distance is Doubling with respect to the Lebesgue measure in RN. This study is divided into three parts (each corresponding to a chapter), and the subject of each one is a class of operators that includes the class of the subsequent one. In the first chapter, after recalling “X-ellipticity” and related concepts introduced by Kogoj and Lanconelli in [KL00], we show a Maximum Principle for linear second order differential operators for which we only assume a Sobolev-type inequality together with a lower terms summability. Adding some crucial hypotheses on measure and on vector fields (Doubling property and Poincar´e inequality), we will be able to obtain some Liouville-type results. This chapter is based on the paper [GL03] by Guti´errez and Lanconelli. In the second chapter we treat some ultraparabolic equations on Lie groups. In this case RN is the support of a Lie group, and moreover we require that vector fields satisfy left invariance. After recalling some results of Cinti [Cin07] about this class of operators and associated potential theory, we prove a scalar convexity for mean-value operators of L-subharmonic functions, where L is our differential operator. In the third chapter we prove a necessary and sufficient condition of regularity, for boundary points, for Dirichlet problem on an open subset of RN related to sub-Laplacian. On a Carnot group we give the essential background for this type of operator, and introduce the notion of “quasi-boundedness”. Then we show the strict relationship between this notion, the fundamental solution of the given operator, and the regularity of the boundary points.

In vivo biochemical 7.0 Tesla magnetic resonance: preliminary results of dGEMRIC, zonal T2, and T2* mapping of articular cartilage

INTRODUCTION: Ultra-high-field whole-body systems (7.0 T) have a high potential for future human in vivo magnetic resonance imaging (MRI). In musculoskeletal MRI, biochemical imaging of articular cartilage may benefit, in particular. Delayed gadolinium-enhanced MRI of cartilage (dGEMRIC) and T2 mapping have shown potential at 3.0 T. Although dGEMRIC, allows the determination of the glycosaminoglycan content of articular cartilage, T2 mapping is a promising tool for the evaluation of water and collagen content. In addition, the evaluation of zonal variation, based on tissue anisotropy, provides an indicator of the nature of cartilage ie, hyaline or hyaline-like articular cartilage.Thus, the aim of our study was to show the feasibility of in vivo dGEMRIC, and T2 and T2* relaxation measurements, at 7.0 T MRI; and to evaluate the potential of T2 and T2* measurements in an initial patient study after matrix-associated autologous chondrocyte transplantation (MACT) in the knee. MATERIALS AND METHODS: MRI was performed on a whole-body 7.0 T MR scanner using a dedicated circular polarization knee coil. The protocol consisted of an inversion recovery sequence for dGEMRIC, a multiecho spin-echo sequence for standard T2 mapping, a gradient-echo sequence for T2* mapping and a morphologic PD SPACE sequence. Twelve healthy volunteers (mean age, 26.7 +/- 3.4 years) and 4 patients (mean age, 38.0 +/- 14.0 years) were enrolled 29.5 +/- 15.1 months after MACT. For dGEMRIC, 5 healthy volunteers (mean age, 32.4 +/- 11.2 years) were included. T1 maps were calculated using a nonlinear, 2-parameter, least squares fit analysis. Using a region-of-interest analysis, mean cartilage relaxation rate was determined as T1 (0) for precontrast measurements and T1 (Gd) for postcontrast gadopentate dimeglumine [Gd-DTPA(2-)] measurements. T2 and T2* maps were obtained using a pixelwise, monoexponential, non-negative least squares fit analysis; region-of-interest analysis was carried out for deep and superficial cartilage aspects. Statistical evaluation was performed by analyses of variance. RESULTS: Mean T1 (dGEMRIC) values for healthy volunteers showed slightly different results for femoral [T1 (0): 1259 +/- 277 ms; T1 (Gd): 683 +/- 141 ms] compared with tibial cartilage [T1 (0): 1093 +/- 281 ms; T1 (Gd): 769 +/- 150 ms]. Global mean T2 relaxation for healthy volunteers showed comparable results for femoral (T2: 56.3 +/- 15.2 ms; T2*: 19.7 +/- 6.4 ms) and patellar (T2: 54.6 +/- 13.0 ms; T2*: 19.6 +/- 5.2 ms) cartilage, but lower values for tibial cartilage (T2: 43.6 +/- 8.5 ms; T2*: 16.6 +/- 5.6 ms). All healthy cartilage sites showed a significant increase from deep to superficial cartilage (P < 0.001). Within healthy cartilage sites in MACT patients, adequate values could be found for T2 (56.6 +/- 13.2 ms) and T2* (18.6 +/- 5.3 ms), which also showed a significant stratification. Within cartilage repair tissue, global mean values showed no difference, with 55.9 +/- 4.9 ms for T2 and 16.2 +/- 6.3 ms for T2*. However, zonal assessment showed only a slight and not significant increase from deep to superficial cartilage (T2: P = 0.174; T2*: P = 0.150). CONCLUSION: In vivo T1 dGEMRIC assessment in healthy cartilage, and T2 and T2* mapping in healthy and reparative articular cartilage, seems to be possible at 7.0 T MRI. For T2 and T2*, zonal variation of articular cartilage could also be evaluated at 7.0 T. This zonal assessment of deep and superficial cartilage aspects shows promising results for the differentiation of healthy and affected articular cartilage. In future studies, optimized protocol selection, and sophisticated coil technology, together with increased signal at ultra-high-field MRI, may lead to advanced biochemical cartilage imaging.

(Table 1) Concentration of organohalogenated compounds in clean and contaminated hair of polar bears (Ursus maritimus) from East Greenland

In this pilot study, we report on levels of persistent organohalogenated contaminants (OHCs) in hair of polar bears (Ursus maritimus) from East Greenland sampled between 1999 and 2001. To our knowledge, this is the first study on the validation of polar bear hair as a non-invasive matrix representative of concentrations and profiles in internal organs and blood plasma. Because of low sample weights (13-140 mg), only major bioaccumulative OHCs were detected above the limit of quantification: five polychlorinated biphenyl (PCB) congeners (CB 99, 138, 153, 170 and 180), one polybrominated diphenyl ether (PBDE) congener (BDE 47), oxychlordane, trans-nonachlor and ß-hexachlorocyclohexane. The PCB profile in hair was similar to that of internal tissues (i.e. adipose, liver, brain and blood), with CB 153 and 180 as the major congeners in all matrices. A gender difference was found for concentrations in hair relative to concentrations in internal tissues. Females (n = 6) were found to display negative correlations, while males (n = 5) showed positive correlations, although p-values were not found significant. These negative correlations in females may reflect seasonal OHC mobilisation from periphery adipose tissue due to, for example, lactation and fasting. The lack of significance in most correlations may be due to small sample sizes and seasonal variability of concentrations in soft tissues. Further research with larger sample weights and sizes is therefore necessary to draw more definitive conclusions on the usefulness of hair for biomonitoring OHCs in polar bears and other fur mammals.

3D Frangi-based lung vessel enhancement filter penalizing airways

This paper describes a fully automatic simultaneous lung vessel and airway enhancement filter. The approach consists of a Frangi-based multiscale vessel enhancement filtering specifically designed for lung vessel and airway detection, where arteries and veins have high contrast with respect to the lung parenchyma, and airway walls are hollow tubular structures with a non negative response using the classical Frangi's filter. The features extracted from the Hessian matrix are used to detect centerlines and approximate walls of airways, decreasing the filter response in those areas by applying a penalty function to the vesselness measure. We validate the segmentation method in 20 CT scans with different pathological states within the VESSEL12 challenge framework. Results indicate that our approach obtains good results, decreasing the number of false positives in airway walls.

Negative data in DEA:a directional distance approach applied to bank branches

This paper is drawn from the use of data envelopment analysis (DEA) in helping a Portuguese bank to manage the performance of its branches. The bank wanted to set targets for the branches on such variables as growth in number of clients, growth in funds deposited and so on. Such variables can take positive and negative values but apart from some exceptions, traditional DEA models have hitherto been restricted to non-negative data. We report on the development of a model to handle unrestricted data in a DEA framework and illustrate the use of this model on data from the bank concerned.

A modified semi-oriented radial measure for target setting with negative data

Over the last few years Data Envelopment Analysis (DEA) has been gaining increasing popularity as a tool for measuring efficiency and productivity of Decision Making Units (DMUs). Conventional DEA models assume non-negative inputs and outputs. However, in many real applications, some inputs and/or outputs can take negative values. Recently, Emrouznejad et al. [6] introduced a Semi-Oriented Radial Measure (SORM) for modelling DEA with negative data. This paper points out some issues in target setting with SORM models and introduces a modified SORM approach. An empirical study in bank sector demonstrates the applicability of the proposed model. © 2014 Elsevier Ltd. All rights reserved.

N–Dimensional Orthogonal Tile Sizing Problem

AMS subject classification: 68Q22, 90C90

Density of Polynomials in the L^2 Space on the Real and the Imaginary Axes and in a Sobolev Space

2000 Mathematics Subject Classification: 41A10, 30E10, 41A65.

Characterization of urban aerosol in Cork city (Ireland) using aerosol mass spectrometry

Ambient wintertime background urban aerosol in Cork city, Ireland, was characterized using aerosol mass spectrometry. During the three-week measurement study in 2009, 93% of the ca. 1 350 000 single particles characterized by an Aerosol Time-of-Flight Mass Spectrometer (TSI ATOFMS) were classified into five organic-rich particle types, internally mixed to different proportions with elemental carbon (EC), sulphate and nitrate, while the remaining 7% was predominantly inorganic in nature. Non-refractory PM1 aerosol was characterized using a High Resolution Time-of-Flight Aerosol Mass Spectrometer (Aerodyne HR-ToF-AMS) and was also found to comprise organic aerosol as the most abundant species (62 %), followed by nitrate (15 %), sulphate (9 %) and ammonium (9 %), and chloride (5 %). Positive matrix factorization (PMF) was applied to the HR-ToF-AMS organic matrix, and a five-factor solution was found to describe the variance in the data well. Specifically, "hydrocarbon-like" organic aerosol (HOA) comprised 20% of the mass, "low-volatility" oxygenated organic aerosol (LV-OOA) comprised 18 %, "biomass burning" organic aerosol (BBOA) comprised 23 %, non-wood solid-fuel combustion "peat and coal" organic aerosol (PCOA) comprised 21 %, and finally a species type characterized by primary m/z peaks at 41 and 55, similar to previously reported "cooking" organic aerosol (COA), but possessing different diurnal variations to what would be expected for cooking activities, contributed 18 %. Correlations between the different particle types obtained by the two aerosol mass spectrometers are also discussed. Despite wood, coal and peat being minor fuel types used for domestic space heating in urban areas, their relatively low combustion efficiencies result in a significant contribution to PM1 aerosol mass (44% and 28% of the total organic aerosol mass and non-refractory total PM1, respectively).Ambient wintertime background urban aerosol in Cork city, Ireland, was characterized using aerosol mass spectrometry. During the three-week measurement study in 2009, 93% of the ca. 1 350 000 single particles characterized by an Aerosol Time-of-Flight Mass Spectrometer (TSI ATOFMS) were classified into five organic-rich particle types, internally mixed to different proportions with elemental carbon (EC), sulphate and nitrate, while the remaining 7% was predominantly inorganic in nature. Non-refractory PM1 aerosol was characterized using a High Resolution Time-of-Flight Aerosol Mass Spectrometer (Aerodyne HR-ToF-AMS) and was also found to comprise organic aerosol as the most abundant species (62 %), followed by nitrate (15 %), sulphate (9 %) and ammonium (9 %), and chloride (5 %). Positive matrix factorization (PMF) was applied to the HR-ToF-AMS organic matrix, and a five-factor solution was found to describe the variance in the data well. Specifically, "hydrocarbon-like" organic aerosol (HOA) comprised 20% of the mass, "low-volatility" oxygenated organic aerosol (LV-OOA) comprised 18 %, "biomass burning" organic aerosol (BBOA) comprised 23 %, non-wood solid-fuel combustion "peat and coal" organic aerosol (PCOA) comprised 21 %, and finally a species type characterized by primary m/z peaks at 41 and 55, similar to previously reported "cooking" organic aerosol (COA), but possessing different diurnal variations to what would be expected for cooking activities, contributed 18 %. Correlations between the different particle types obtained by the two aerosol mass spectrometers are also discussed. Despite wood, coal and peat being minor fuel types used for domestic space heating in urban areas, their relatively low combustion efficiencies result in a significant contribution to PM1 aerosol mass (44% and 28% of the total organic aerosol mass and non-refractory total PM1, respectively).

Methods for Imputing Missing Values and Synthesizing Confidential Values for Continuous and Magnitude Data

Abstract

Continuous variable is one of the major data types collected by the survey organizations. It can be incomplete such that the data collectors need to fill in the missingness. Or, it can contain sensitive information which needs protection from re-identification. One of the approaches to protect continuous microdata is to sum them up according to different cells of features. In this thesis, I represents novel methods of multiple imputation (MI) that can be applied to impute missing values and synthesize confidential values for continuous and magnitude data.

The first method is for limiting the disclosure risk of the continuous microdata whose marginal sums are fixed. The motivation for developing such a method comes from the magnitude tables of non-negative integer values in economic surveys. I present approaches based on a mixture of Poisson distributions to describe the multivariate distribution so that the marginals of the synthetic data are guaranteed to sum to the original totals. At the same time, I present methods for assessing disclosure risks in releasing such synthetic magnitude microdata. The illustration on a survey of manufacturing establishments shows that the disclosure risks are low while the information loss is acceptable.

The second method is for releasing synthetic continuous micro data by a nonstandard MI method. Traditionally, MI fits a model on the confidential values and then generates multiple synthetic datasets from this model. Its disclosure risk tends to be high, especially when the original data contain extreme values. I present a nonstandard MI approach conditioned on the protective intervals. Its basic idea is to estimate the model parameters from these intervals rather than the confidential values. The encouraging results of simple simulation studies suggest the potential of this new approach in limiting the posterior disclosure risk.

The third method is for imputing missing values in continuous and categorical variables. It is extended from a hierarchically coupled mixture model with local dependence. However, the new method separates the variables into non-focused (e.g., almost-fully-observed) and focused (e.g., missing-a-lot) ones. The sub-model structure of focused variables is more complex than that of non-focused ones. At the same time, their cluster indicators are linked together by tensor factorization and the focused continuous variables depend locally on non-focused values. The model properties suggest that moving the strongly associated non-focused variables to the side of focused ones can help to improve estimation accuracy, which is examined by several simulation studies. And this method is applied to data from the American Community Survey.

Long-term chemical characterization of aerosols at CVAO from 2007 to 2011

The first long-term aerosol sampling and chemical characterization results from measurements at the Cape Verde Atmospheric Observatory (CVAO) on the island of São Vicente are presented and are discussed with respect to air mass origin and seasonal trends. In total 671 samples were collected using a high-volume PM10 sampler on quartz fiber filters from January 2007 to December 2011. The samples were analyzed for their aerosol chemical composition, including their ionic and organic constituents. Back trajectory analyses showed that the aerosol at CVAO was strongly influenced by emissions from Europe and Africa, with the latter often responsible for high mineral dust loading. Sea salt and mineral dust dominated the aerosol mass and made up in total about 80% of the aerosol mass. The 5-year PM10 mean was 47.1 ± 55.5 µg/m**2, while the mineral dust and sea salt means were 27.9 ± 48.7 and 11.1 ± 5.5 µg/m**2, respectively. Non-sea-salt (nss) sulfate made up 62% of the total sulfate and originated from both long-range transport from Africa or Europe and marine sources. Strong seasonal variation was observed for the aerosol components. While nitrate showed no clear seasonal variation with an annual mean of 1.1 ± 0.6 µg/m**3, the aerosol mass, OC (organic carbon) and EC (elemental carbon), showed strong winter maxima due to strong influence of African air mass inflow. Additionally during summer, elevated concentrations of OM were observed originating from marine emissions. A summer maximum was observed for non-sea-salt sulfate and was connected to periods when air mass inflow was predominantly of marine origin, indicating that marine biogenic emissions were a significant source. Ammonium showed a distinct maximum in spring and coincided with ocean surface water chlorophyll a concentrations. Good correlations were also observed between nss-sulfate and oxalate during the summer and winter seasons, indicating a likely photochemical in-cloud processing of the marine and anthropogenic precursors of these species. High temporal variability was observed in both chloride and bromide depletion, differing significantly within the seasons, air mass history and Saharan dust concentration. Chloride (bromide) depletion varied from 8.8 ± 8.5% (62 ± 42%) in Saharan-dust-dominated air mass to 30 ± 12% (87 ± 11%) in polluted Europe air masses. During summer, bromide depletion often reached 100% in marine as well as in polluted continental samples. In addition to the influence of the aerosol acidic components, photochemistry was one of the main drivers of halogenide depletion during the summer; while during dust events, displacement reaction with nitric acid was found to be the dominant mechanism. Positive matrix factorization (PMF) analysis identified three major aerosol sources: sea salt, aged sea salt and long-range transport. The ionic budget was dominated by the first two of these factors, while the long-range transport factor could only account for about 14% of the total observed ionic mass.

Sources of carbonaceous aerosol in the Amazon basin

The quantification of sources of carbonaceous aerosol is important to understand their atmospheric concentrations and regulating processes and to study possible effects on climate and air quality, in addition to develop mitigation strategies. In the framework of the European Integrated Project on Aerosol Cloud Climate Interactions (EUCAARI) fine (D(p) < 2.5 mu m) and coarse (2.5 mu m < Dp < 10 mu m) aerosol particles were sampled from February to June (wet season) and from August to September (dry season) 2008 in the central Amazon basin. The mass of fine particles averaged 2.4 mu g m(-3) during the wet season and 4.2 mu g m(-3) during the dry season. The average coarse aerosol mass concentration during wet and dry periods was 7.9 and 7.6 mu g m(-3), respectively. The overall chemical composition of fine and coarse mass did not show any seasonality with the largest fraction of fine and coarse aerosol mass explained by organic carbon (OC); the average OC to mass ratio was 0.4 and 0.6 in fine and coarse aerosol modes, respectively. The mass absorbing cross section of soot was determined by comparison of elemental carbon and light absorption coefficient measurements and it was equal to 4.7 m(2) g(-1) at 637 nm. Carbon aerosol sources were identified by Positive Matrix Factorization (PMF) analysis of thermograms: 44% of fine total carbon mass was assigned to biomass burning, 43% to secondary organic aerosol (SOA), and 13% to volatile species that are difficult to apportion. In the coarse mode, primary biogenic aerosol particles (PBAP) dominated the carbonaceous aerosol mass. The results confirmed the importance of PBAP in forested areas. The source apportionment results were employed to evaluate the ability of global chemistry transport models to simulate carbonaceous aerosol sources in a regional tropical background site. The comparison showed an overestimation of elemental carbon (EC) by the TM5 model during the dry season and OC both during the dry and wet periods. The overestimation was likely due to the overestimation of biomass burning emission inventories and SOA production over tropical areas.

On quantum integrability of the Landau-Lifshitz model

We investigate the quantum integrability of the Landau-Lifshitz (LL) model and solve the long-standing problem of finding the local quantum Hamiltonian for the arbitrary n-particle sector. The particular difficulty of the LL model quantization, which arises due to the ill-defined operator product, is dealt with by simultaneously regularizing the operator product and constructing the self-adjoint extensions of a very particular structure. The diagonalizibility difficulties of the Hamiltonian of the LL model, due to the highly singular nature of the quantum-mechanical Hamiltonian, are also resolved in our method for the arbitrary n-particle sector. We explicitly demonstrate the consistency of our construction with the quantum inverse scattering method due to Sklyanin [Lett. Math. Phys. 15, 357 (1988)] and give a prescription to systematically construct the general solution, which explains and generalizes the puzzling results of Sklyanin for the particular two-particle sector case. Moreover, we demonstrate the S-matrix factorization and show that it is a consequence of the discontinuity conditions on the functions involved in the construction of the self-adjoint extensions.