Potential Analysis for Hypoelliptic Second Order PDEs with Nonnegative Characteristic Form

In this Thesis we consider a class of second order partial differential operators with non-negative characteristic form and with smooth coefficients. Main assumptions on the relevant operators are hypoellipticity and existence of a well-behaved global fundamental solution. We first make a deep analysis of the L-Green function for arbitrary open sets and of its applications to the Representation Theorems of Riesz-type for L-subharmonic and L-superharmonic functions. Then, we prove an Inverse Mean value Theorem characterizing the superlevel sets of the fundamental solution by means of L-harmonic functions. Furthermore, we establish a Lebesgue-type result showing the role of the mean-integal operator in solving the homogeneus Dirichlet problem related to L in the Perron-Wiener sense. Finally, we compare Perron-Wiener and weak variational solutions of the homogeneous Dirichlet problem, under specific hypothesis on the boundary datum.

Characterization of a dual-energy X-ray absorptiometry system for soft tissues assessment and their correlations with metabolic state

Il crescente utilizzo di sistemi di analisi high-throughput per lo studio dello stato fisiologico e metabolico del corpo, ha evidenziato che una corretta alimentazione e una buona forma fisica siano fattori chiave per la salute. L'aumento dell'età media della popolazione evidenzia l'importanza delle strategie di contrasto delle patologie legate all'invecchiamento. Una dieta sana è il primo mezzo di prevenzione per molte patologie, pertanto capire come il cibo influisce sul corpo umano è di fondamentale importanza. In questo lavoro di tesi abbiamo affrontato la caratterizzazione dei sistemi di imaging radiografico Dual-energy X-ray Absorptiometry (DXA). Dopo aver stabilito una metodologia adatta per l'elaborazione di dati DXA su un gruppo di soggetti sani non obesi, la PCA ha evidenziato alcune proprietà emergenti dall'interpretazione delle componenti principali in termini delle variabili di composizione corporea restituite dalla DXA. Le prime componenti sono associabili ad indici macroscopici di descrizione corporea (come BMI e WHR). Queste componenti sono sorprendentemente stabili al variare dello status dei soggetti in età, sesso e nazionalità. Dati di analisi metabolica, ottenuti tramite Magnetic Resonance Spectroscopy (MRS) su campioni di urina, sono disponibili per circa mille anziani (provenienti da cinque paesi europei) di età compresa tra i 65 ed i 79 anni, non affetti da patologie gravi. I dati di composizione corporea sono altresì presenti per questi soggetti. L'algoritmo di Non-negative Matrix Factorization (NMF) è stato utilizzato per esprimere gli spettri MRS come combinazione di fattori di base interpretabili come singoli metaboliti. I fattori trovati sono stabili, quindi spettri metabolici di soggetti sono composti dallo stesso pattern di metaboliti indipendentemente dalla nazionalità. Attraverso un'analisi a singolo cieco sono stati trovati alti valori di correlazione tra le variabili di composizione corporea e lo stato metabolico dei soggetti. Ciò suggerisce la possibilità di derivare la composizione corporea dei soggetti a partire dal loro stato metabolico.

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.

T2 mapping in the knee after microfracture at 3.0 T: correlation of global T2 values and clinical outcome - preliminary results

OBJECTIVE: The aim of our study was to correlate global T2 values of microfracture repair tissue (RT) with clinical outcome in the knee joint. METHODS: We assessed 24 patients treated with microfracture in the knee joint. Magnetic resonance (MR) examinations were performed on a 3T MR unit, T2 relaxation times were obtained with a multi-echo spin-echo technique. T2 maps were obtained using a pixel wise, mono-exponential non-negative least squares fit analysis. Slices covering the cartilage RT were selected and region of interest analysis was done. An individual T2 index was calculated with global mean T2 of the RT and global mean T2 of normal, hyaline cartilage. The Lysholm score and the International Knee Documentation Committee (IKDC) knee evaluation forms were used for the assessment of clinical outcome. Bivariate correlation analysis and a paired, two tailed t test were used for statistics. RESULTS: Global T2 values of the RT [mean 49.8ms, standards deviation (SD) 7.5] differed significantly (P<0.001) from global T2 values of normal, hyaline cartilage (mean 58.5ms, SD 7.0). The T2 index ranged from 61.3 to 101.5. We found the T2 index to correlate with outcome of the Lysholm score (r(s)=0.641, P<0.001) and the IKDC subjective knee evaluation form (r(s)=0.549, P=0.005), whereas there was no correlation with the IKDC knee form (r(s)=-0.284, P=0.179). CONCLUSION: These findings indicate that T2 mapping is sensitive to assess RT function and provides additional information to morphologic MRI in the monitoring of microfracture.

An Evaluation of Effective Fiber in Beef Feedlot Finishing Diets

A study was designed to collect a database of Iowa feedlot rations for determination of effective neutral detergent fiber (NDF) in complete diets from fiber analysis and particle size determination of individual feed ingredients and compare this with particle size determination of mixed wet rations. Seventy-one beef finishing total mixed rations were collected by ISU Extension Beef Field Specialists across Iowa. Producers were asked to complete a form assessing the acidosis risk associated with each ration. The average NDF of these diets was 25.9%. Of the total mixed rations 1.33 % remained in the top tray (>.75 in.), 47.27 % remained in the middle tray (>.31 in.), and 50.88 % was smaller than the .31 in screen. The effective NDF (eNDF) calculated from the eNDF of the ingredients averaged 10.56%. Estimated eNDF from total diet NDF and the percentage of the total diet in the top and middle trays averaged 12.47%. The calculated eNDF from non-grain sources alone averaged 3.6%. The percentage of digestive deads was weakly related to the percentage of the ration in the bottom tray (r=.19), the percentage in the top tray (r=- .46) and the effective NDF of the ration (r=-.23). The percentage of bloat was related to the total NDF of the diet (r=.28) and the effective fiber from non-grain sources (r=-.23). The number of off-feed incidences was related to the dry matter of the ration (r=.38), the apparent eNDF (r=-.28) and the percentage of ration in the bottom tray (r=.24). This study confirms that there is some relationship between effective NDF of the diet, effective NDF from non-grain sources or diet particle size; and acidosis indicators. These relationships are weak, however, indicating that other factors such as feedbunk management, feed processing, feed presentation and feed mixing likely also play a role in the incidence of acidosis in feedlot cattle.

Intercomparison of C-14 Analysis of Carbonaceous Aerosols: Exercise 2009

Radiocarbon analysis of the carbonaceous aerosol allows an apportionment of fossil and non-fossil sources of airborne particulate matter (PM). A chemical separation of total carbon (TC) into its subfractions organic carbon (OC) and elemental carbon (EC) refines this powerful technique, as OC and EC originate from different sources and undergo different processes in the atmosphere. Although C-14 analysis of TC, EC, and OC has recently gained increasing attention, interlaboratory quality assurance measures have largely been missing, especially for the isolation of EC and OC. In this work, we present results from an intercomparison of 9 laboratories for C-14 analysis of carbonaceous aerosol samples on quartz fiber filters. Two ambient PM samples and 1 reference material (RM 8785) were provided with representative filter blanks. All laboratories performed C-14 determinations of TC and a subset of isolated EC and OC for isotopic measurement. In general, C-14 measurements of TC and OC agreed acceptably well between the laboratories, i.e. for TC within 0.015-0.025 (FC)-C-14 for the ambient filters and within 0.041 (FC)-C-14 for RM 8785. Due to inhomogeneous filter loading, RM 8785 demonstrated only limited applicability as a reference material for C-14 analysis of carbonaceous aerosols. C-14 analysis of EC revealed a large deviation between the laboratories of 28-79 as a consequence of different separation techniques. This result indicates a need for further discussion on optimal methods of EC isolation for C-14 analysis and a second stage of this intercomparison.

From Similes to Allegory: The Deconstruction of Chariot Imagery in Early Buddhist Texts, Analyzed with Cognitive Metaphor Theory

The presentation will start by unfolding the various layers of chariot imagery in early Indian sources, namely, chariots as vehicles of gods such as the sun (sūrya), i.e. as symbol of cosmic stability; chariots as symbols of royal power and social prestige e.g. of Brahmins; and, finally, chariots as metaphors for the “person”, the “mind” and the “way to liberation” (e.g., Kaṭ.-Up. III.3; Maitr.-Up. II. 6). In Buddhist and non-Buddhist sources, chariots are in certain aspects used as a metaphor for the (old) human body (e.g., Caraka-S., Vi.3.37-38; D II.100; D II.107); apart from that, there is, of course, mention of the “real” use of chariots in sports, cults, journey, and combat. The most prominent example of the Buddhist use of chariot imagery is its application as a model for the person (S I.134 f.; Milindapañha, ed. Trenckner, 26), i.e., for highlighting the “non-substantial self”. There are, however, other significant examples of the usage of chariot imagery in early Buddhist texts. Of special interest are those cases in which chariot metaphors were applied in order to explain how the ‘self’ may proceed on the way to salvation – with ‘mindfulness’ or the ‘self’ as charioteer, with ‘wisdom’ and ‘confidence’ as horses etc. (e.g. S I. 33; S V.7; Dhp 94; or the Nārada-Jātaka, No. 545, verses 181-190). One might be tempted to say that these instances reaffirm the traditional soteriology of a substantial “progressing soul”. Taking conceptual metaphor analysis as a tool, I will, in contrast, argue that there is a special Buddhist use of this metaphor. Indeed, at first sight, it seems to presuppose a non-Buddhist understanding (the “self” as charioteer; the chariot as vehicle to liberation, etc.). Yet, it will be argued that in these cases the chariot imagery is no longer fully “functional”. The Buddhist usage may, therefore, best be described as a final allegorical phase of the chariot-imagery, which results in a thorough deconstruction of the “chariot” itself.

Gravitational wave background from Standard Model physics: qualitative features

Because of physical processes ranging from microscopic particle collisions to macroscopic hydrodynamic fluctuations, any plasma in thermal equilibrium emits gravitational waves. For the largest wavelengths the emission rate is proportional to the shear viscosity of the plasma. In the Standard Model at 0T > 16 GeV, the shear viscosity is dominated by the most weakly interacting particles, right-handed leptons, and is relatively large. We estimate the order of magnitude of the corresponding spectrum of gravitational waves. Even though at small frequencies (corresponding to the sub-Hz range relevant for planned observatories such as eLISA) this background is tiny compared with that from non-equilibrium sources, the total energy carried by the high-frequency part of the spectrum is non-negligible if the production continues for a long time. We suggest that this may constrain (weakly) the highest temperature of the radiation epoch. Observing the high-frequency part directly sets a very ambitious goal for future generations of GHz-range detectors.

Continued fractions built from convex sets and convex functions

In a partially ordered semigroup with the duality (or polarity) transform, it is pos- sible to define a generalisation of continued fractions. General sufficient conditions for convergence of continued fractions are provided. Two particular applications concern the cases of convex sets with the Minkowski addition and the polarity transform and the family of non-negative convex functions with the Legendre–Fenchel and Artstein-Avidan–Milman transforms.

An empirical model to estimate the demand for primary care in urban settings

Objective. To measure the demand for primary care and its associated factors by building and estimating a demand model of primary care in urban settings.^ Data source. Secondary data from 2005 California Health Interview Survey (CHIS 2005), a population-based random-digit dial telephone survey, conducted by the UCLA Center for Health Policy Research in collaboration with the California Department of Health Services, and the Public Health Institute between July 2005 and April 2006.^ Study design. A literature review was done to specify the demand model by identifying relevant predictors and indicators. CHIS 2005 data was utilized for demand estimation.^ Analytical methods. The probit regression was used to estimate the use/non-use equation and the negative binomial regression was applied to the utilization equation with the non-negative integer dependent variable.^ Results. The model included two equations in which the use/non-use equation explained the probability of making a doctor visit in the past twelve months, and the utilization equation estimated the demand for primary conditional on at least one visit. Among independent variables, wage rate and income did not affect the primary care demand whereas age had a negative effect on demand. People with college and graduate educational level were associated with 1.03 (p < 0.05) and 1.58 (p < 0.01) more visits, respectively, compared to those with no formal education. Insurance was significantly and positively related to the demand for primary care (p < 0.01). Need for care variables exhibited positive effects on demand (p < 0.01). Existence of chronic disease was associated with 0.63 more visits, disability status was associated with 1.05 more visits, and people with poor health status had 4.24 more visits than those with excellent health status. ^ Conclusions. The average probability of visiting doctors in the past twelve months was 85% and the average number of visits was 3.45. The study emphasized the importance of need variables in explaining healthcare utilization, as well as the impact of insurance, employment and education on demand. The two-equation model of decision-making, and the probit and negative binomial regression methods, was a useful approach to demand estimation for primary care in urban settings.^

An evaluation of the Cypress Creek watershed for inorganic chemical load as it flows into Lake Houston

Background. The Cypress Creek is one of the main tributaries of Lake Houston, which provides drinking water to 21.4 million customers. Furthermore, the watershed is being utilized for contact and non-contact recreation, such as canoeing, swimming, hiking trail, and picnics. Water along the creek is impacted by numerous wastewater outfalls from both point and non-point sources. As the creek flows into Lake Houston, it carries both organic and inorganic contaminants that may affect the drinking water quality of this important water source reservoir. Objective. This study was carried out to evaluate the inorganic chemical load of the water in Cypress Creek along its entire length, from the headwaters in Waller County and up to the drainage into Lake Houston. The purpose was to determine whether there are hazardous concentrations of metals in the water and what would be the likely sources. Method. Samples were collected at 29 sites along the creek and analyzed for 29 metals, 17 of which were on the Environmental Protection Agency priority pollution list. Public access sites primarily at bridges were used for sample collection. Samples were transported on ice to the University Of Texas School Of Public Health laboratory, spiked with 2 ml HNO3 kept overnight in the refrigerator, and the following day transported to the EPA laboratory for analysis. Analysis was done by EPA Method 200.7-ICP, Method 200.8ICP/MS and Method 245.1-CVAAS. Results. Metals were present above the detection limits at 65% of sites. Concentrations of aluminum, iron, sodium, potassium, magnesium, and calcium, were particularly high at all sites. Aluminum, sodium, and iron concentrations greatly exceeded the EPA secondary drinking water standards at all sites. ^ Conclusion. The recreational water along Cypress Creek is impacted by wastewater from both permitted and non-permitted outfalls, which deposit inorganic substances into the water. Although a number of inorganic contaminants were present in the water, toxic metals regulated by the EPA were mostly below the recommended limits. However, high concentrations of aluminum, sodium, and iron in the Cypress Creek bring forward the issue of unauthorized discharges of salt water from mining, as well as industrial and domestic wastewater.^

Mathematical analysis of a model of chemotaxis arising from morphogenesis

We consider non-negative solution of a chemotaxis system with non constant chemotaxis sensitivity function X. This system appears as a limit case of a model formorphogenesis proposed by Bollenbach et al. (Phys. Rev. E. 75, 2007).Under suitable boundary conditions, modeling the presence of a morphogen source at x=0, we prove the existence of a global and bounded weak solution using an approximation by problems where diffusion is introduced in the ordinary differential equation. Moreover,we prove the convergence of the solution to the unique steady state provided that ? is small and ? is large enough. Numerical simulations both illustrate these results and give rise to further conjectures on the solution behavior that go beyond the rigorously proved statements.

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.

Reduction of critical mass in a chemotaxis system by external application of a chemoattractant

In this paper we study non-negative radially symmetric solutions of a parabolic-elliptic Keller-Segel system. The system describes the chemotactic movement of cells under the additional circumstance that an external application of a chemo attractant at a distinguished point is introduced.

Study of PM10 and PM2.5 levels in three European cities: Analysis of intra and inter urban variations

In the present paper, 1-year PM10 and PM 2.5 data from roadside and urban background monitoring stations in Athens (Greece), Madrid (Spain) and London (UK) are analysed in relation to other air pollutants (NO,NO2,NOx,CO,O3 and SO2)and several meteorological parameters (wind velocity, temperature, relative humidity, precipitation, solar radiation and atmospheric pressure), in order to investigate the sources and factors affecting particulate pollution in large European cities. Principal component and regression analyses are therefore used to quantify the contribution of both combustion and non-combustion sources to the PM10 and PM 2.5 levels observed. The analysis reveals that the EU legislated PM 10 and PM2.5 limit values are frequently breached, forming a potential public health hazard in the areas studied. The seasonal variability patterns of particulates varies among cities and sites, with Athens and Madrid presenting higher PM10 concentrations during the warm period and suggesting the larger relative contribution of secondary and natural particles during hot and dry days. It is estimated that the contribution of non-combustion sources varies substantially among cities, sites and seasons and ranges between 38-67% and 40-62% in London, 26-50% and 20-62% in Athens, and 31-58% and 33-68% in Madrid, for both PM10 and PM 2.5. Higher contributions from non-combustion sources are found at urban background sites in all three cities, whereas in the traffic sites the seasonal differences are smaller. In addition, the non-combustion fraction of both particle metrics is higher during the warm season at all sites. On the whole, the analysis provides evidence of the substantial impact of non-combustion sources on local air quality in all three cities. While vehicular exhaust emissions carry a large part of the risk posed on human health by particle exposure, it is most likely that mitigation measures designed for their reduction will have a major effect only at traffic sites and additional measures will be necessary for the control of background levels. However, efforts in mitigation strategies should always focus on optimal health effects.