Some Inverse Problems in Analysis and Geometry

Thesis (Ph.D.)--University of Washington, 2016-08

Geographical Distribution Of The Association Between El Niño South Oscillation And Dengue Fever In The Americas: A Continental Analysis Using Geographical Information System-based Techniques.

El Niño South Oscillation (ENSO) is one climatic phenomenon related to the inter-annual variability of global meteorological patterns influencing sea surface temperature and rainfall variability. It influences human health indirectly through extreme temperature and moisture conditions that may accelerate the spread of some vector-borne viral diseases, like dengue fever (DF). This work examines the spatial distribution of association between ENSO and DF in the countries of the Americas during 1995-2004, which includes the 1997-1998 El Niño, one of the most important climatic events of 20(th) century. Data regarding the South Oscillation index (SOI), indicating El Niño-La Niña activity, were obtained from Australian Bureau of Meteorology. The annual DF incidence (AIy) by country was computed using Pan-American Health Association data. SOI and AIy values were standardised as deviations from the mean and plotted in bars-line graphics. The regression coefficient values between SOI and AIy (rSOI,AI) were calculated and spatially interpolated by an inverse distance weighted algorithm. The results indicate that among the five years registering high number of cases (1998, 2002, 2001, 2003 and 1997), four had El Niño activity. In the southern hemisphere, the annual spatial weighted mean centre of epidemics moved southward, from 6° 31' S in 1995 to 21° 12' S in 1999 and the rSOI,AI values were negative in Cuba, Belize, Guyana and Costa Rica, indicating a synchrony between higher DF incidence rates and a higher El Niño activity. The rSOI,AI map allows visualisation of a graded surface with higher values of ENSO-DF associations for Mexico, Central America, northern Caribbean islands and the extreme north-northwest of South America.

Multivariate analysis of the effects of soil parameters and environmental factors on the flavonoid content of leaves of Passiflora incarnata L., Passifloraceae

The aim of the present study was to evaluate the effect of soil characteristics (pH, macro- and micro-nutrients), environmental factors (temperature, humidity, period of the year and time of day of collection) and meteorological conditions (rain, sun, cloud and cloud/rain) on the flavonoid content of leaves of Passiflora incarnata L., Passifloraceae. The total flavonoid contents of leaf samples harvested from plants cultivated or collected under different conditions were quantified by high-performance liquid chromatography with ultraviolet detection (HPLC-UV/PAD). Chemometric treatment of the data by principal component (PCA) and hierarchic cluster analyses (HCA) showed that the samples did not present a specific classification in relation to the environmental and soil variables studied, and that the environmental variables were not significant in describing the data set. However, the levels of the elements Fe, B and Cu present in the soil showed an inverse correlation with the total flavonoid contents of the leaves of P. incarnata.

Inverse aerodynamic design applications using the MGM hybrid formulation

The well-known modified Garabedian-Mcfadden (MGM) method is an attractive alternative for aerodynamic inverse design, for its simplicity and effectiveness (P. Garabedian and G. Mcfadden, Design of supercritical swept wings, AIAA J. 20(3) (1982), 289-291; J.B. Malone, J. Vadyak, and L.N. Sankar, Inverse aerodynamic design method for aircraft components, J. Aircraft 24(2) (1987), 8-9; Santos, A hybrid optimization method for aerodynamic design of lifting surfaces, PhD Thesis, Georgia Institute of Technology, 1993). Owing to these characteristics, the method has been the subject of several authors over the years (G.S. Dulikravich and D.P. Baker, Aerodynamic shape inverse design using a Fourier series method, in AIAA paper 99-0185, AIAA Aerospace Sciences Meeting, Reno, NV, January 1999; D.H. Silva and L.N. Sankar, An inverse method for the design of transonic wings, in 1992 Aerospace Design Conference, No. 92-1025 in proceedings, AIAA, Irvine, CA, February 1992, 1-11; W. Bartelheimer, An Improved Integral Equation Method for the Design of Transonic Airfoils and Wings, AIAA Inc., 1995). More recently, a hybrid formulation and a multi-point algorithm were developed on the basis of the original MGM. This article discusses applications of those latest developments for airfoil and wing design. The test cases focus on wing-body aerodynamic interference and shock wave removal applications. The DLR-F6 geometry is picked as the baseline for the analysis.

The generalized inverse Weibull distribution

The inverse Weibull distribution has the ability to model failure rates which are quite common in reliability and biological studies. A three-parameter generalized inverse Weibull distribution with decreasing and unimodal failure rate is introduced and studied. We provide a comprehensive treatment of the mathematical properties of the new distribution including expressions for the moment generating function and the rth generalized moment. The mixture model of two generalized inverse Weibull distributions is investigated. The identifiability property of the mixture model is demonstrated. For the first time, we propose a location-scale regression model based on the log-generalized inverse Weibull distribution for modeling lifetime data. In addition, we develop some diagnostic tools for sensitivity analysis. Two applications of real data are given to illustrate the potentiality of the proposed regression model.

Cloning, characterization and functional analysis of a 1-FEH cDNA from Vernonia herbacea (Vell.) Rusby

Variations in the inulin contents have been detected in rhizophores of Vernonia herbacea during the phenological cycle. These variations indicate the occurrence of active inulin synthesis and depolymerization throughout the cycle and a role for this carbohydrate as a reserve compound. 1-Fructan exohydrolase (1-FEH) is the enzyme responsible for inulin depolymerization, and its activity has been detected in rhizophores of sprouting plants. Defoliation and low temperature are enhancer conditions of this 1-FEH activity. The aim of the present work was the cloning of this enzyme. Rhizophores were collected from plants induced to sprout, followed by storage at 5C. A full length 1-FEH cDNA sequence was obtained by PCR and inverse PCR techniques, and expressed in Pichia pastoris. Cold storage enhances FEH gene expression. Vh1-FEH was shown to be a functional 1-FEH, hydrolyzing predominantly -2,1 linkages, sharing high identity with chicory FEH sequences, and its activity was inhibited by 81 in the presence of 10 mM sucrose. In V. herbacea, low temperature and sucrose play a role in the control of fructan degradation. This is the first study concerning the cloning and functional analysis of a 1-FEH cDNA of a native species from the Brazilian Cerrado. Results will contribute to understanding the role of fructans in the establishment of a very successful fructan flora of the Brazilian Cerrado, subjected to water limitation and low temperature during winter.

Kinetic analysis of vascular marker distribution in perfused rat livers after regeneration following partial hepatectomy

Background/Aims: Liver clearance models are based on information (or assumptions) on solute distribution kinetics within the microvasculatory system, The aim was to study albumin distribution kinetics in regenerated livers and in livers of normal adult rats, Methods: A novel mathematical model was used to evaluate the distribution space and the transit time dispersion of albumin in livers following regeneration after a two-thirds hepatectomy compared to livers of normal adult rats. Outflow curves of albumin measured after bolus injection in single-pass perfused rat livers were analyzed by correcting for the influence of catheters and fitting a long-tailed function to the data. Results: The curves were well described by the proposed model. The distribution volume and the transit time dispersion of albumin observed in the partial hepatectomy group were not significantly different from livers of normal adult rats. Conclusions: These findings suggest that the distribution space and the transit time dispersion of albumin (CV2) is relatively constant irrespective of the presence of rapid and extensive repair. This invariance of CV2 implies, as a first approximation, a similar degree of intrasinusoidal mixing, The finding that a sum of two (instead of one) inverse Gaussian densities is an appropriate empirical function to describe the outflow curve of vascular indicators has consequences for an improved prediction of hepatic solute extraction.

Commentary: Using the convection-dispersion model and transit time density functions in the analysis of organ distribution kinetics

The convection-dispersion model and its extended form have been used to describe solute disposition in organs and to predict hepatic availabilities. A range of empirical transit-time density functions has also been used for a similar purpose. The use of the dispersion model with mixed boundary conditions and transit-time density functions has been queried recently by Hisaka and Sugiyanaa in this journal. We suggest that, consistent with soil science and chemical engineering literature, the mixed boundary conditions are appropriate providing concentrations are defined in terms of flux to ensure continuity at the boundaries and mass balance. It is suggested that the use of the inverse Gaussian or other functions as empirical transit-time densities is independent of any boundary condition consideration. The mixed boundary condition solutions of the convection-dispersion model are the easiest to use when linear kinetics applies. In contrast, the closed conditions are easier to apply in a numerical analysis of nonlinear disposition of solutes in organs. We therefore argue that the use of hepatic elimination models should be based on pragmatic considerations, giving emphasis to using the simplest or easiest solution that will give a sufficiently accurate prediction of hepatic pharmacokinetics for a particular application. (C) 2000 Wiley-Liss Inc. and the American Pharmaceutical Association J Pharm Sci 89:1579-1586, 2000.

Body mass index and risk of head and neck cancer in a pooled analysis of case-control studies in the International Head and Neck Cancer Epidemiology (INHANCE) Consortium

Methods We pooled data from 17 case-control studies including 12 716 cases and the 17 438 controls. Odds ratios (ORs) and 95% confidence intervals (CIs) were estimated for associations between body mass index (BMI) at different ages and HNC risk, adjusted for age, sex, centre, race, education, tobacco smoking and alcohol consumption. Results Adjusted ORs (95% CIs) were elevated for people with BMI at reference (date of diagnosis for cases and date of selection for controls) < 18.5 kg/m(2) (2.13, 1.75-2.58) and reduced for BMI > 25.0-30.0 kg/m(2) (0.52, 0.44-0.60) and BMI >= 30 kg/m(2) (0.43, 0.33-0.57), compared with BMI > 18.5-25.0 kg/m(2). These associations did not differ by age, sex, tumour site or control source. Although the increased risk among people with BMI < 18.5 kg/m(2) was not modified by tobacco smoking or alcohol drinking, the inverse association for people with BMI > 25 kg/m(2) was present only in smokers and drinkers. Conclusions In our large pooled analysis, leanness was associated with increased HNC risk regardless of smoking and drinking status, although reverse causality cannot be excluded. The reduced risk among overweight or obese people may indicate body size is a modifier of the risk associated with smoking and drinking. Further clarification may be provided by analyses of prospective cohort and mechanistic studies.

Cytogenetic and molecular analysis of MLL rearrangements in acute lymphoblastic leukaemia survivors

The successful treatment of paediatric malignancies by multimodal therapy has improved outcomes for children with cancer, especially those with acute lymphoblastic leukaemia (ALL). Second malignant neoplasms, however, represent a serious complication after treatment. Depending on dosage, 2-12% of patients treated with topoisomerase II inhibitors and/or alkylating agents develop treatment-related acute myeloid leukaemia characterized by translocations at 11q23. Our goal was to study MLL rearrangements in peripheral lymphocytes using cytogenetic and molecular methods in order to evaluate the late effects of cancer therapy in patients previously treated for childhood ALL. Chromosomal rearrangements at 11q23 were analysed in cytogenetic preparations from 49 long-term ALL survivors and 49 control individuals. Patients were subdivided depending on the inclusion or omission of topoisomerase II inhibitors (VP-16 and/or VM-26) in their treatment protocol. The statistical analysis showed significant (P = 0.007) differences between the frequency of translocations observed for the groups of patients and controls. These differences were also significant (P = 0.006) when the groups of patients (independent of the inclusion of topoisomerase II inhibitors) and controls were compared (P = 0.006). The frequencies of extra signals, however, did not differ between groups of patients and controls. Several MLL translocations were detected and identified by inverse polymerase chain reaction, followed by cloning and sequencing. Thirty-five patients (81%) presented putative translocations; among those, 91% corresponded with t(4;11) (q21;q23), while the other 9% corresponded with t(11;X), t(8;11)(q23;q23) and t(11;16). Our results indicate an increase in MLL aberrations in childhood ALL survivors years after completion of therapy. The higher frequency in this cohort might be associated with therapy using anti-tumoural drugs, independent of the inclusion of topoisomerase II inhibitors. Even though the biological significance of these rearrangements needs further investigation, they demonstrate a degree of genome instability, indicating the relevance of cytogenetic and molecular studies during the follow-up of patients in complete clinical remission.

Comparison of inverse planning systems based on biological or physical factors: Pinnacle®, Corvus® and Monaco®

Radiotherapy (RT) is one of the most important approaches in the treatment of cancer and its performance can be improved in three different ways: through the optimization of the dose distribution, by the use of different irradiation techniques or through the study of radiobiological initiatives. The first is purely physical because is related to the physical dose distributiuon. The others are purely radiobiological because they increase the differential effect between the tumour and the health tissues. The Treatment Planning Systems (TPS) are used in RT to create dose distributions with the purpose to maximize the tumoral control and minimize the complications in the healthy tissues. The inverse planning uses dose optimization techniques that satisfy the criteria specified by the user, regarding the target and the organs at risk (OAR’s). The dose optimization is possible through the analysis of dose-volume histograms (DVH) and with the use of computed tomography, magnetic resonance and other digital image techniques.

Uncertainty propagation in inverse reliability-based design of composite structures

An approach for the analysis of uncertainty propagation in reliability-based design optimization of composite laminate structures is presented. Using the Uniform Design Method (UDM), a set of design points is generated over a domain centered on the mean reference values of the random variables. A methodology based on inverse optimal design of composite structures to achieve a specified reliability level is proposed, and the corresponding maximum load is outlined as a function of ply angle. Using the generated UDM design points as input/output patterns, an Artificial Neural Network (ANN) is developed based on an evolutionary learning process. Then, a Monte Carlo simulation using ANN development is performed to simulate the behavior of the critical Tsai number, structural reliability index, and their relative sensitivities as a function of the ply angle of laminates. The results are generated for uniformly distributed random variables on a domain centered on mean values. The statistical analysis of the results enables the study of the variability of the reliability index and its sensitivity relative to the ply angle. Numerical examples showing the utility of the approach for robust design of angle-ply laminates are presented.

Spatial neighborhood matrix computation: Inverse distance weighted versus binary contiguity

Paper presented at Geo-Spatial Crossroad GI_Forum, Salzburg, Austria.