Weighted geometric mean of large-scale matrices: numerical analysis and algorithms

Computing the weighted geometric mean of large sparse matrices is an operation that tends to become rapidly intractable, when the size of the matrices involved grows. However, if we are not interested in the computation of the matrix function itself, but just in that of its product times a vector, the problem turns simpler and there is a chance to solve it even when the matrix mean would actually be impossible to compute. Our interest is motivated by the fact that this calculation has some practical applications, related to the preconditioning of some operators arising in domain decomposition of elliptic problems. In this thesis, we explore how such a computation can be efficiently performed. First, we exploit the properties of the weighted geometric mean and find several equivalent ways to express it through real powers of a matrix. Hence, we focus our attention on matrix powers and examine how well-known techniques can be adapted to the solution of the problem at hand. In particular, we consider two broad families of approaches for the computation of f(A) v, namely quadrature formulae and Krylov subspace methods, and generalize them to the pencil case f(A\B) v. Finally, we provide an extensive experimental evaluation of the proposed algorithms and also try to assess how convergence speed and execution time are influenced by some characteristics of the input matrices. Our results suggest that a few elements have some bearing on the performance and that, although there is no best choice in general, knowing the conditioning and the sparsity of the arguments beforehand can considerably help in choosing the best strategy to tackle the problem.

Analisi di morfologie carsiche o crio-carsiche in relazione alla mobilizzazione di fluidi nella regione di Arabia Terra, Marte.

This thesis tries to interpret the origin and evolution of karst-like forms present in Arabia Terra, a region of Mars that develops in the equatorial zone of the planet. The work has been carried out specifically in the craters Crommelin (4o 91’ N-10o 51’ E), 12000088 (3o 48’ N-1o 30’ E), NE 12000088 (4° 20’ N-2° 50’ E), C "2" (3° 54’ N-1° W), and in their surrounding areas. These craters contain layered deposits characterized by a high albedo and on which erosion is very pronounced. The area containing the craters is a plateau that has the same characteristics of albedo and texture. The preliminary morphological study has made use of instrumentation such as the Mars Reconnaissance Orbiter (MRO), in particular HiRISE images (High Resolution Imaging Science Experiment), CTX (Context Camera) and CRISM (Compact Reconnaissance Imaging Spectrometers for Mars). A regional geomorphological map has been drawn up containing the main morphotypes, and detailed geomorphological maps were prepared for different karst-like morphologies. The analysis of spectral data collected from CRISM instrumentation has allowed to identify the footprint of sulphate minerals in the external area. Data were collected for morphometric negative forms (karst-like) and positive forms (mud volcanoes, dikes and pingos). For the analysis of the relief forms DTMs (Digital Terrain Models) produced by the union of stereographic CTX couples or HiRISE were used. From the analysis of high-resolution images morphological footprints similar to periglacial environments have been identified, including the presence of patterned ground and polygonal cracks found all over the area of investigation, and relief structures similar to pingos present in the crater C "2". These observations allow us to imagine a geological past with a cold climate at the equator able to freeze the few fluids present in the Martian arid terrain. The development of karst-like landforms, on the other hand, can be attributed to a subsequent improval of the weather conditions that led to a normal climate regime for the equatorial areas, resulting in the degradation of the permafrost. The melt waters have thus allowed the partial dissolution of the sulphate layers. The karst-like forms look rather fresh suggesting them to be not that old.

Atorvastatin attenuates hepatic fibrosis in rats after bile duct ligation via decreased turnover of hepatic stellate cells

Activation of hepatic stellate cells (HSC) and transdifferentiation to myofibroblasts following liver injury is the main culprit for hepatic fibrosis. Myofibroblasts show increased proliferation, migration, contraction, and production of extracellular matrix (ECM). In vitro, HMG-CoA reductase inhibitors (statins) inhibit proliferation and induce apoptosis of myofibroblastic HSC. To investigate the antifibrotic effects of atorvastatin in vivo we used bile duct ligated rats (BDL).

Geochemical Modeling and Analysis of the Frac Water Used in the Hydraulic Fracturing of the Marcellus Formation, Pennsylvania

The hydraulic fracturing of the Marcellus Formation creates a byproduct known as frac water. Five frac water samples were collected in Bradford County, PA. Inorganic chemical analysis, field parameters analysis, alkalinity titrations, total dissolved solids(TDS), total suspended solids (TSS), biological oxygen demand (BOD), and chemical oxygen demand (COD) were conducted on each sample to characterize frac water. A database of frac water chemistry results from across the state of Pennsylvania from multiple sources was compiled in order to provide the public and research communitywith an accurate characterization of frac water. Four geochemical models were created to model the reactions between frac water and the Marcellus Formation, Purcell Limestone, and the oil field brines presumed present in the formations. The average concentrations of chloride and TDS in the five frac water samples were 1.1 �± 0.5 x 105 mg/L (5.5X average seawater) and 140,000 mg/L (4X average seawater). BOD values for frac water immediately upon flow back were over 10X greater than the BOD of typical wastewater, but decreased into the range of typical wastewater after a short period of time. The COD of frac water decreases dramatically with an increase in elapsed time from flow back, but remain considerably higher than typicalwastewater. Different alkalinity calculation methods produced a range of alkalinity values for frac water: this result is most likely due to high concentrations of aliphatic acid anions present in the samples. Laboratory analyses indicate that the frac watercomposition is quite variable depending on the companies from which the water was collected, the geology of the local area, and number of fracturing jobs in which the frac water was used, but will require more treatment than typical wastewater regardless of theprecise composition of each sample. The geochemical models created suggest that the presence of organic complexes in an oil field brine and Marcellus Formation aid in the dissolution of ions such as bariumand strontium into the solution. Although equilibration reactions between the Marcellus Formation and the slickwater account for some of the final frac water composition, the predominant control of frac water composition appears to be the ratio of the mixture between the oil field brine and slickwater. The high concentration of barium in the frac water is likely due to the abundance of barite nodules in the Purcell Limestone, and the lack of sulfate in the frac water samples is due to the reducing, anoxic conditions in the earth's subsurface that allow for the degassing of H2S(g).

Genetic determinants of alcoholic liver disease

Alcoholic liver disease (ALD) accounts for the majority of chronic liver disease in Western countries. The spectrum of ALD includes steatosis with or without fibrosis in virtually all individuals with an alcohol consumption of >80 g/day, alcoholic steatohepatitis of variable severity in 10-35% and liver cirrhosis in approximately 15% of patients. Once cirrhosis is established, there is an annual risk for hepatocellular carcinoma of 1-2%. Environmental factors such as drinking patterns, coexisting liver disease, obesity, diet composition and comedication may modify the natural course of ALD. Twin studies have revealed a substantial contribution of genetic factors to the evolution of ALD, as demonstrated by a threefold higher disease concordance between monozygotic twins and dizygotic twins. With genotyping becoming widely available, a large number of genetic case-control studies evaluating candidate gene variants coding for proteins involved in the degradation of alcohol, mediating antioxidant defence, the evolution and counteraction of necroinflammation and formation and degradation of extracellular matrix have been published with largely unconfirmed, impeached or even disproved associations. Recently, whole genome analyses of large numbers of genetic variants in several chronic liver diseases including gallstone disease, primary sclerosing cholangitis and non-alcoholic fatty liver disease (NAFLD) have identified novel yet unconsidered candidate genes. Regarding the latter, a sequence variation within the gene coding for patatin-like phospholipase encoding 3 (PNPLA3, rs738409) was found to modulate steatosis, necroinflammation and fibrosis in NAFLD. Subsequently, the same variant was repeatedly confirmed as the first robust genetic risk factor for progressive ALD.

A Stable Niche Assumption-Free Test of Ecological Divergence

Understanding the impact of geological events on diversification processes is central to evolutionary ecology. The recent amalgamation between ecological niche models (ENMs) and phylogenetic analyses has been used to estimate historical ranges of modern lineages by projecting current ecological niches of organisms onto paleoclimatic reconstructions. A critical assumption underlying this approach is that niches are stable over time. Using Notophthalmus viridescens (eastern newt), in which four ecologically diverged subspecies are recognized, we introduce an analytical framework free from the niche stability assumption to examine how refugial retreat and subsequent postglacial expansion have affected intraspecific ecological divergence. We found that the current subspecies designation was not congruent with the phylogenetic lineages. Thus, we examined ecological niche overlap between the refugial and modern populations, in both subspecies and lineage, by creating ENMs independently for modern and estimated last glacial maximum (LGM) newt populations, extracting bioclimate variables by randomly generated points, and conducting principal component analyses. Our analyses consistently showed that when tested as a hypothesis, rather than used as an assumption, the niches of N. viridescens lineages have been unstable since the LGM (both subspecies and lineages). There was greater ecological niche differentiation among the subspecies than the modern phylogenetic lineages, suggesting that the subspecies, rather than the phylogenetic lineages, is the unit of the current ecological divergence. The present study found little evidence that the LGM refugial retreat caused the currently observed ecological divergence and suggests that ecological divergence has occurred during postglacial expansion to the current distribution ranges.

The role of genetic polymorphisms in alcoholic liver disease

Chronic alcohol consumption is a major cause of liver cirrhosis which, however, develops in only a minority of heavy drinkers. Evidence from twin studies indicates that genetic factors account for at least 50% of individual susceptibility. The contribution of genetic factors to the development of diseases may be investigated either by means of animal experiments, through linkage studies in families of affected patients, or population based case-control studies. With regard to the latter, single nucleotide polymorphisms of genes involved in the degradation of alcohol, antioxidant defense, necroinflammation, and formation and degradation of extracellular matrix are attractive candidates for studying genotype-phenotype associations. However, many associations in early studies were found to be spurious and could not be confirmed in stringently designed investigations. Therefore, future genotype-phenotype studies in alcoholic liver disease should meet certain requirements in order to avoid pure chance observations due to a lack of power, false functional interpretation, and insufficient statistical evaluation.

Gelatinase B [matrix metalloproteinase (MMP)-9] and collagenases (MMP-8/-13) are upregulated in cerebrospinal fluid during aseptic and bacterial meningitis in children

We investigated the protein expression of gelatinases [matrix metalloproteinase (MMP)-2 and -9] and collagenases (MMP-8 and -13) in cerebrospinal fluid (CSF) from patients with bacterial (BM, n = 17) and aseptic (AM, n = 14) meningitis. In both, MMP-8 and -9 were increased in 100% of patients, whereas MMP-13 was detectable in 53% and 82% respectively. Three patients with clinical signs of meningitis, without CSF pleocytosis, scored positive for all three MMPs. MMP-8 appeared in two isoforms, granulocyte-type [polymorphonuclear cell (PMN)] and fibroblast/macrophage (F/M) MMP-8. Analysis of kinetic changes from serial lumbar punctures showed that these MMPs are independently regulated, and correlate only partly with CSF cytosis or levels of the endogenous inhibitor, tissue inhibitor of matrix metalloproteinase-1. In vitro, T cells, peripheral blood mononuclear cells (PBMCs) and granulocytes (PMN) release MMP-8 and -9, whereas MMP-13 could be found only in the former two cell types. Using models of exogenous (n-formyl-Met-Leu-Phe, T cell receptor cross-linking) and host-derived stimuli (interleukin-2), the kinetics and the release of the MMP-8, -9 and -13 showed strong variation between these immune cells and suggest release from preformed stocks. In addition, MMP-9 is also synthesized de novo in PBMCs and T cells. In conclusion, invading immune cells contribute only partially to MMPs in CSF during meningitis, and parenchymal cells are an equally relevant source. In this context, in patients with clinical signs of meningitis, but without CSF pleocytosis, MMPs seem to be a highly sensitive marker for intrathecal inflammation. The present data support the concept that broad-spectrum enzyme inhibition targeting gelatinases and collagenases is a potential strategy for adjunctive therapy in infectious meningitis.

Erosive tooth wear - a multifactorial condition of growing concern and increasing knowledge

Dental erosion is often described solely as a surface phenomenon, unlike caries where it has been established that the destructive effects involve both the surface and the subsurface region. However, besides removal and softening of the surface, erosion may show dissolution of mineral underneath the surface. There is some evidence that the presence of this condition is growing steadily. Hence, erosive tooth wear is becoming increasingly significant in the management of the long-term health of the dentition. What is considered as an acceptable amount of wear is dependent on the anticipated lifespan of the dentition and, therefore, is different for deciduous compared to permanent teeth. However, erosive damage to the permanent teeth occurring in childhood may compromise the growing child's dentition for their entire lifetime and may require repeated and increasingly complex and expensive restoration. Therefore, it is important that diagnosis of the tooth wear process in children and adults is made early and adequate preventive measures are undertaken. These measures can only be initiated when the risk factors are known and interactions between them are present. A scheme is proposed which allows the possible risk factors and their relation to each other to be examined.

A BAYESIAN HIERARCHICAL MODEL FOR CONSTRAINED DISTRIBUTED LAG FUNCTIONS: ESTIMATING THE TIME COURSE OF HOSPITALIZATION ASSOCIATED WITH AIR POLLUTION EXPOSURE

Numerous time series studies have provided strong evidence of an association between increased levels of ambient air pollution and increased levels of hospital admissions, typically at 0, 1, or 2 days after an air pollution episode. An important research aim is to extend existing statistical models so that a more detailed understanding of the time course of hospitalization after exposure to air pollution can be obtained. Information about this time course, combined with prior knowledge about biological mechanisms, could provide the basis for hypotheses concerning the mechanism by which air pollution causes disease. Previous studies have identified two important methodological questions: (1) How can we estimate the shape of the distributed lag between increased air pollution exposure and increased mortality or morbidity? and (2) How should we estimate the cumulative population health risk from short-term exposure to air pollution? Distributed lag models are appropriate tools for estimating air pollution health effects that may be spread over several days. However, estimation for distributed lag models in air pollution and health applications is hampered by the substantial noise in the data and the inherently weak signal that is the target of investigation. We introduce an hierarchical Bayesian distributed lag model that incorporates prior information about the time course of pollution effects and combines information across multiple locations. The model has a connection to penalized spline smoothing using a special type of penalty matrix. We apply the model to estimating the distributed lag between exposure to particulate matter air pollution and hospitalization for cardiovascular and respiratory disease using data from a large United States air pollution and hospitalization database of Medicare enrollees in 94 counties covering the years 1999-2002.

Origin of renal myofibroblasts in the model of unilateral ureter obstruction in the rat

Tubulo-interstitial fibrosis is a constant feature of chronic renal failure and it is suspected to contribute importantly to the deterioration of renal function. In the fibrotic kidney there exists, besides normal fibroblasts, a large population of myofibroblasts, which are supposedly responsible for the increased production of intercellular matrix. It has been proposed that myofibroblasts in chronic renal failure originate from the transformation of tubular cells via epithelial-mesenchymal transition (EMT) or from infiltration by bone marrow-derived precursors. Little attention has been paid to the possibility of a transformation of resident fibroblasts into myofibroblasts in renal fibrosis. Therefore we examined the fate of resident fibroblasts in the initial phase of renal fibrosis in the classical model of unilateral ureter obstruction (UUO) in the rat. Rats were perfusion-fixed on days 1, 2, 3 and 4 after ligature of the right ureter. Starting from 1 day of UUO an increasing expression of alpha-smooth muscle actin (alphaSMA) in resident fibroblasts was revealed by immunofluorescence and confirmed by the observation of bundles of microfilaments and webs of intermediate filaments in the electron microscope. Inversely, there was a decreased expression of 5'-nucleotidase (5'NT), a marker of renal cortical fibroblasts. The RER became more voluminous, suggesting an increased synthesis of matrix. Intercellular junctions, a characteristic feature of myofibroblasts, became more frequent. The mitotic activity in fibroblasts was strongly increased. Renal tubules underwent severe regressive changes but the cells retained their epithelial characteristics and there was no sign of EMT. In conclusion, after ureter ligature, resident peritubular fibroblasts proliferated and they showed progressive alterations, suggesting a transformation in myofibroblasts. Thus the resident fibroblasts likely play a central role in fibrosis in that model.

Extracts of Lindera obtusiloba induce antifibrotic effects in hepatic stellate cells via suppression of a TGF-beta-mediated profibrotic gene expression pattern

Liver fibrosis is characterized by high expression of the key profibrogenic cytokine transforming growth factor (TGF)-beta and the natural tissue inhibitor of metalloproteinases (TIMP)-1, leading to substantial accumulation of extracellular matrix. Liver fibrosis originates from various chronic liver diseases, such as chronic viral hepatitis that, to date, cannot be treated sufficiently. Thus, novel therapeutics, for example, those derived from Oriental medicine, have gained growing attention. In Korea, extracts prepared from Lindera obtusiloba are used for centuries for treatment of inflammation, improvement of blood circulation and prevention of liver damage, but experimental evidence of their efficacy is lacking. We studied direct antifibrotic effects in activated hepatic stellate cells (HSCs), the main target cell in the fibrotic liver. L. obtusiloba extract (135 mug/ml) reduced the de novo DNA synthesis of activated rat and human HSCs by about 90%, which was not accompanied by cytotoxicity of HSC, primary hepatocytes and HepG2 cells, pointing to induction of cellular quiescence. As determined by quantitative polymerase chain reaction, simultaneous treatment of HSCs with TGF-beta and L. obtusiloba extract resulted in reduction of TIMP-1 expression to baseline level, disruption of the autocrine loop of TGF-beta autoinduction and increased expression of fibrolytic matrix metalloproteinase (MMP)-3. In addition, L. obtusiloba reduced gelatinolytic activity of HSC by interfering with profibrogenic MMP-2 activity. Since L. obtusiloba extract prevented intracellular oxidative stress experimentally induced by tert-butylhydroperoxide, we concluded that the direct antifibrotic effect of L. obtusiloba extract might be mediated by antioxidant activity. Thus, L. obtusiloba, traditionally used in Oriental medicine, may complement treatment of chronic liver disease.

Geology and Ore Deposits of the Golden Era and Goldfinch Mines, Argenta Mining District, Montana.

This report includes the results of geological investigation of a small area in the northern part of the Argenta mining district. Approximately two square miles were mapped. The underground working of the three mines only were accessible: the Goldfinch. Golden Era, and Mayday mines.

Geology and Ore Deposits of the Clinton Mining District

This report includes the results of geological investigation of the Clinton Mining District and the Hidden Treasure Mine.The Clinton Mining District is an unorganized mining dis­trict situated in the Garnet Range two and one-half miles northeast of the town of Clinton, Montana, which is on the Northern Pacific Railway and the Chicago, Milwaukee, St. Paul, and Pacific Railroad seventeen miles east of the city of Missoula. The district is in the same range of mountains as the Gar­net Mining District and the drainage from the district covered is to the south into the Hell Gate or Clarks Fork of the Colum­bia River. The main stream is known as Trail creek, which runs in a southerly direction from the area studied.