Data driven regularization models of non-linear ill-posed inverse problems in imaging

Imaging technologies are widely used in application fields such as natural sciences, engineering, medicine, and life sciences. A broad class of imaging problems reduces to solve ill-posed inverse problems (IPs). Traditional strategies to solve these ill-posed IPs rely on variational regularization methods, which are based on minimization of suitable energies, and make use of knowledge about the image formation model (forward operator) and prior knowledge on the solution, but lack in incorporating knowledge directly from data. On the other hand, the more recent learned approaches can easily learn the intricate statistics of images depending on a large set of data, but do not have a systematic method for incorporating prior knowledge about the image formation model. The main purpose of this thesis is to discuss data-driven image reconstruction methods which combine the benefits of these two different reconstruction strategies for the solution of highly nonlinear ill-posed inverse problems. Mathematical formulation and numerical approaches for image IPs, including linear as well as strongly nonlinear problems are described. More specifically we address the Electrical impedance Tomography (EIT) reconstruction problem by unrolling the regularized Gauss-Newton method and integrating the regularization learned by a data-adaptive neural network. Furthermore we investigate the solution of non-linear ill-posed IPs introducing a deep-PnP framework that integrates the graph convolutional denoiser into the proximal Gauss-Newton method with a practical application to the EIT, a recently introduced promising imaging technique. Efficient algorithms are then applied to the solution of the limited electrods problem in EIT, combining compressive sensing techniques and deep learning strategies. Finally, a transformer-based neural network architecture is adapted to restore the noisy solution of the Computed Tomography problem recovered using the filtered back-projection method.

Non-linear modelling of microwave devices embedding nano-ferroelectric materials for real-time reconfigurable transmitarray

In this thesis work a nonlinear model for Interdigitated Capacitors (IDCs) based on ferroelectric materials, is proposed. Through the properties of materials such as Hafnium-Zirconium Oxide (HfZrO2), it is possible to realize tunable radiofrequency (RF) circuits. In particular, the model proposed in this thesis describes the use of an IDC, realized on a High-Resistivity silicon substrate, as a phase shifter for beam-steering applications. The model is obtained starting from already present experimental measurements, through which it is possible to identify a circuit model. The model is tested for both low power values and other power values using Harmonic Balance simulations, which show an excellent convergence of the model up to 40 dBm of input power. Furthermore, an array composed by two patches operating both at 2.55 GHz, which exploits the tunable properties of the HfZrO-based IDC is proposed. At 0dBm the model shows a 47° phase shift with polarization -1 V and 1 V which leads to a 11° steering of the main lobe of the array.

Synthetic generation of amyloid PET images by non-linear dimensionality reduction inversion

Privacy issues and data scarcity in PET field call for efficient methods to expand datasets via synthetic generation of new data that cannot be traced back to real patients and that are also realistic. In this thesis, machine learning techniques were applied to 1001 amyloid-beta PET images, which had undergone a diagnosis of Alzheimer’s disease: the evaluations were 540 positive, 457 negative and 4 unknown. Isomap algorithm was used as a manifold learning method to reduce the dimensions of the PET dataset; a numerical scale-free interpolation method was applied to invert the dimensionality reduction map. The interpolant was tested on the PET images via LOOCV, where the removed images were compared with the reconstructed ones with the mean SSIM index (MSSIM = 0.76 ± 0.06). The effectiveness of this measure is questioned, since it indicated slightly higher performance for a method of comparison using PCA (MSSIM = 0.79 ± 0.06), which gave clearly poor quality reconstructed images with respect to those recovered by the numerical inverse mapping. Ten synthetic PET images were generated and, after having been mixed with ten originals, were sent to a team of clinicians for the visual assessment of their realism; no significant agreements were found either between clinicians and the true image labels or among the clinicians, meaning that original and synthetic images were indistinguishable. The future perspective of this thesis points to the improvement of the amyloid-beta PET research field by increasing available data, overcoming the constraints of data acquisition and privacy issues. Potential improvements can be achieved via refinements of the manifold learning and the inverse mapping stages during the PET image analysis, by exploring different combinations in the choice of algorithm parameters and by applying other non-linear dimensionality reduction algorithms. A final prospect of this work is the search for new methods to assess image reconstruction quality.

Mortes evitáveis em menores de um ano, Brasil, 1997 a 2006: contribuições para a avaliação de desempenho do Sistema Único de Saúde

Os óbitos de menores de um ano foram classificados em causas evitáveis, mal definidas e não evitáveis empregando a Lista Brasileira de Mortes Evitáveis, entre 1997-2006. Foram calculados tendências dos coeficientes de mortalidade infantil por causas de morte e se usou regressão não linear para avaliação de tendência. As causas evitáveis e as causas mal definidas apresentaram significativa redução (p < 0,001). As causas reduzíveis de mortalidade apresentaram redução de 37%. A mortalidade por causas reduzíveis por adequada atenção ao parto declinou em 27,7%; adequada atenção ao recém-nascido, 42,5%; e por adequada atenção à gestação cresceu 28,3%. Concluiu-se que os serviços de saúde contribuíram para a redução da mortalidade infantil. O declínio das causas mal definidas de morte indica ampliação do acesso aos serviços de saúde. O aumento do acesso e atenção ao parto e aos cuidados com recém-nascido contribuíram para a redução de óbitos infantis. O aumento da mortalidade por adequada atenção à gestação revela a necessidade de aprimoramento da atenção pré-natal.

Relative dispersions of intra-albumin transit times across rat and elasmobranch perfused livers, and implications for intra- and inter-species scaling of hepatic clearance using microsomal data

It is recognized that vascular dispersion in the liver is a determinant of high first-pass extraction of solutes by that organ. Such dispersion is also required for translation of in-vitro microsomal activity into in-vivo predictions of hepatic extraction for any solute. We therefore investigated the relative dispersion of albumin transit times (CV2) in the livers of adult and weanling rats and in elasmobranch livers. The mean and normalized variance of the hepatic transit time distribution of albumin was estimated using parametric non-linear regression (with a correction for catheter influence) after an impulse (bolus) input of labelled albumin into a single-pass liver perfusion. The mean +/- s.e. of CV2 for albumin determined in each of the liver groups were 0.85 +/- 0.20 (n = 12), 1.48 +/- 0.33 (n = 7) and 0.90 +/- 0.18 (n = 4) for the livers of adult and weanling rats and elasmobranch livers, respectively. These CV2 are comparable with that reported previously for the dog and suggest that the CV2 Of the liver is of a similar order of magnitude irrespective of the age and morphological development of the species. It might, therefore, be justified, in the absence of other information, to predict the hepatic clearances and availabilities of highly extracted solutes by scaling within and between species livers using hepatic elimination models such as the dispersion model with a CV2 of approximately unity.

Application of the Williams-Landel-Ferry model to the viscosity-temperature relationship of Australian honeys

The rheological behaviour of nine unprocessed Australian honeys was investigated for the applicability of the Williams-Landel-Ferry (WLF) model. The viscosity of the honeys was obtained over a range of shear rates (0.01-40 s(-1)) from 2degrees to 40 degreesC, and all the honeys exhibited Newtonian behaviour with viscosity reducing as the temperature was increased. The honeys with high moisture were of lower viscosity, The glass transition temperatures of the honeys, as measured with a differential scanning calorimeter (DSC), ranged from -40degrees to -46 degreesC, and four models (WLF. Arrhenius, Vogel-Tammann-Fulcher (VTF), and power-law) were investigated to describe the temperature dependence of the viscosity. The WLF was the most suitable and the correlation coefficient averaged 0.999 +/- 0.0013 as against 0.996 +/- 0.0042 for the Arrhenius model while the mean relative deviation modulus was 0-12% for the WLF model and 10-40% for the Arrhenius one. With the universal values for the WLF constants, the temperature dependence of the viscosity was badly predicted. From non-linear regression analysis, the constants of the WLF models for the honeys were obtained (C-1 = 13.7-21.1: C-2 = 55.9-118.7) and are different from the universal values. These WLF constants will be valuable for adequate modeling of the rheology of the honeys, and they can be used to assess the temperature sensitivity of the honeys. (C) 2002 Elsevier Science Ltd. All rights reserved.

Cytogenetic response to imatinib in chronic myeloid leukaemia patients: concentration dependency and associated influences under field-conditions

Introduction: Imatinib, a first-line drug for chronic myeloid leukaemia (CML), has been increasingly proposed for therapeutic drug monitoring (TDM), as trough concentrations >=1000 ng/ml (Cmin) have been associated with improved molecular and complete cytogenetic response (CCyR). The pharmacological monitoring project of EUTOS (European Treatment and Outcome Study) was launched to validate retrospectively the correlation between Cmin and response in a large population of patients followed by central TDM in Bordeaux.¦Methods: 1898 CML patients with first TDM 0-9 years after imatinib initiation, providing cytogenetic data along with demographic and comedication (37%) information, were included. Individual Cmin, estimated by non-linear regression (NONMEM), was adjusted to initial standard dose (400 mg/day) and stratified at 1000 ng/ml. Kaplan-Meier estimates of overall cumulative CCyR rates (stratified by sex, age, comedication and Cmin) were compared using asymptotic logrank k-sample test for interval-censored data. Differences in Cmin were assessed by Wilcoxon test.¦Results: There were no significant differences in overall cumulative CCyR rates between Cmin strata, sex and comedication with P-glycoprotein inhibitors/inducers or CYP3A4 inhibitors (p >0.05). Lower rates were observed in 113 young patients <30 years (p = 0.037; 1-year rates: 43% vs 60% in older patients), as well as in 29 patients with CYP3A4 inducers (p = 0.001, 1-year rates: 40% vs 66% without). Higher rates were observed in 108 patients on organic-cation-transporter-1 (hOCT-1) inhibitors (p = 0.034, 1-year rates: 83% vs 56% without). Considering 1-year CCyR rates, a trend towards better response for Cmin above 1000 ng/ml was observed: 64% (95%CI: 60-69%) vs 59% (95%CI: 56-61%). Median Cmin (400 mg/day) was significantly reduced in male patients (732 vs 899ng/ml, p <0.001), young patients <30 years (734 vs 802 ng/ml, p = 0.037) and under CYP3A4 inducers (758 vs 859 ng/ml, p = 0.022). Under hOCT-1 inhibitors, Cmin was increased (939 vs 827 ng/ml, p = 0.038).¦Conclusion: Based on observational TDM data, the impact of imatinib Cmin >1000 ng/ml on CCyR was not salient. Young CML patients (<30 years) and patients taking CYP3A4 inducers probably need close monitoring and possibly higher imatinib doses, due to lower Cmin along with lower CCyR rates. Patients taking hOCT-1 inhibitors seem in contrast to have improved CCyR response rates. The precise role for imatinib TDM remains to be established prospectively.

Reconsolidation of the soil surface after tillage discontinuity, with and without cultivation, related to erosion and its prediction with RUSLE

Site-specific regression coefficient values are essential for erosion prediction with empirical models. With the objective to investigate the surface-soilconsolidation factor, Cf, linked to the RUSLE's prior-land-use subfactor, PLU, an erosion experiment using simulated rainfall on a 0.075 m m-1 slope, sandy loam Paleudult soil, was conducted at the Agriculture Experimental Station of the Federal University of Rio Grande do Sul (EEA/UFRGS), in Eldorado do Sul, State of Rio Grande do Sul, Brazil. Firstly, a row-cropped area was excluded from cultivation (March 1995), the existing crop residue removed from the field, and the soil kept clean-tilled the rest of the year (to get a degraded soil condition for the intended purpose of this research). The soil was then conventional-tilled for the last time (except for a standard plot which was kept continuously cleantilled for comparison purposes), in January 1996, and the following treatments were established and evaluated for soil reconsolidation and soil erosion until May 1998, on duplicated 3.5 x 11.0 m erosion plots: (a) fresh-tilled soil, continuously in clean-tilled fallow (unit plot); (b) reconsolidating soil without cultivation; and (c) reconsolidating soil with cultivation (a crop sequence of three corn- and two black oats cycles, continuously in no-till, removing the crop residues after each harvest for rainfall application and redistributing them on the site after that). Simulated rainfall was applied with a Swanson's type, rotating-boom rainfall simulator, at 63.5 mm h-1 intensity and 90 min duration, six times during the two-and-half years of experimental period (at the beginning of the study and after each crop harvest, with the soil in the unit plot being retilled before each rainfall test). The soil-surface-consolidation factor, Cf, was calculated by dividing soil loss values from the reconsolidating soil treatments by the average value from the fresh-tilled soil treatment (unit plot). Non-linear regression was used to fit the Cf = e b.t model through the calculated Cf-data, where t is time in days since last tillage. Values for b were -0.0020 for the reconsolidating soil without cultivation and -0.0031 for the one with cultivation, yielding Cf-values equal to 0.16 and 0.06, respectively, after two-and-half years of tillage discontinuation, compared to 1.0 for fresh-tilled soil. These estimated Cf-values correspond, respectively, to soil loss reductions of 84 and 94 %, in relation to soil loss from the fresh-tilled soil, showing that the soil surface reconsolidated intenser with cultivation than without it. Two distinct treatmentinherent soil surface conditions probably influenced the rapid decay-rate of Cf values in this study, but, as a matter of a fact, they were part of the real environmental field conditions. Cf-factor curves presented in this paper are therefore useful for predicting erosion with RUSLE, but their application is restricted to situations where both soil type and particular soil surface condition are similar to the ones investigate in this study.

Surface and subsurface decomposition of a desiccated grass pasture biomass related to erosion and its prediction with RUSLE

Erosion is deleterious because it reduces the soil's productivity capacity for growing crops and causes sedimentation and water pollution problems. Surface and buried crop residue, as well as live and dead plant roots, play an important role in erosion control. An efficient way to assess the effectiveness of such materials in erosion reduction is by means of decomposition constants as used within the Revised Universal Soil Loss Equation - RUSLE's prior-land-use subfactor - PLU. This was investigated using simulated rainfall on a 0.12 m m-1 slope, sandy loam Paleudult soil, at the Agriculture Experimental Station of the Federal University of Rio Grande do Sul, in Eldorado do Sul, State of Rio Grande do Sul, Brazil. The study area had been covered by native grass pasture for about fifteen years. By the middle of March 1996, the sod was mechanically mowed and the crop residue removed from the field. Late in April 1996, the sod was chemically desiccated with herbicide and, about one month later, the following treatments were established and evaluated for sod biomass decomposition and soil erosion, from June 1996 to May 1998, on duplicated 3.5 x 11.0 m erosion plots: (a) and (b) soil without tillage, with surface residue and dead roots; (c) soil without tillage, with dead roots only; (d) soil tilled conventionally every two-and-half months, with dead roots plus incorporated residue; and (e) soil tilled conventionally every six months, with dead roots plus incorporated residue. Simulated rainfall was applied with a rotating-boom rainfall simulator, at an intensity of 63.5 mm h-1 for 90 min, eight to nine times during the experimental period (about every two-and-half months). Surface and subsurface sod biomass amounts were measured before each rainfall test along with the erosion measurements of runoff rate, sediment concentration in runoff, soil loss rate, and total soil loss. Non-linear regression analysis was performed using an exponential and a power model. Surface sod biomass decomposition was better depicted by the exponential model, while subsurface sod biomass was by the power model. Subsurface sod biomass decomposed faster and more than surface sod biomass, with dead roots in untilled soil without residue on the surface decomposing more than dead roots in untilled soil with surface residue. Tillage type and frequency did not appreciably influence subsurface sod biomass decomposition. Soil loss rates increased greatly with both surface sod biomass decomposition and decomposition of subsurface sod biomass in the conventionally tilled soil, but they were minimally affected by subsurface sod biomass decomposition in the untilled soil. Runoff rates were little affected by the studied treatments. Dead roots plus incorporated residues were effective in reducing erosion in the conventionally tilled soil, while consolidation of the soil surface was important in no-till. The residual effect of the turned soil on erosion diminished gradually with time and ceased after two years.

Macronutrient uptake, accumulation and export by the irrigated 'vitória' pineapple plant

The nutritional state of the pineapple plant has a large effect on plant growth, on fruit production, and fruit quality. The aim of this study was to assess the uptake, accumulation, and export of nutrients by the irrigated 'Vitória' pineapple plant during and at the end of its development. A randomized block statistical design with four replications was used. The treatments were defined by different times of plant collection: at 270, 330, 390, 450, 510, 570, 690, 750, and 810 days after planting (DAP). The collected plants were separated into the following components: leaves, stem, roots, fruit, and slips for determination of fresh and dry matter weight at 65 ºC. After drying, the plant components were ground for characterization of the composition and content of nutrients taken up and exported by the pineapple plant. The results were subjected to analysis of variance, and non-linear regression models were fitted for the significant differences identified by the F test (p<0.01). The leaves and the stem were the plant components that showed the greatest accumulation of nutrients. For production of 72 t ha-1 of fruit, the macronutrient accumulation in the 'Vitória' pineapple exhibited the following decreasing order: K > N > S > Ca > Mg > P, which corresponded to 898, 452, 134, 129, 126, and 107 kg ha-1, respectively, of total accumulation. The export of macronutrients by the pineapple fruit was in the following decreasing order: K > N > S > Ca > P > Mg, which was equivalent to 18, 17, 11, 8, 8, and 5 %, respectively, of the total accumulated by the pineapple. The 'Vitória' pineapple plant exported 78 kg ha-1 of N, 8 kg ha-1 of P, 164 kg ha-1 of K, 14 kg ha-1 of S, 10 kg ha-1 of Ca, and 6 kg ha-1 of Mg by the fruit. The nutrient content exported by the fruits represent important components of nutrient extraction from the soil, which need to be restored, while the nutrients contained in the leaves, stems and roots can be incorporated in the soil within a program of recycling of crop residues.

Estimating the time since discharge of spent cartridges: a logical approach fro interpreting the evidence

Estimating the time since discharge of a spent cartridge or a firearm can be useful in criminal situa-tions involving firearms. The analysis of volatile gunshot residue remaining after shooting using solid-phase microextraction (SPME) followed by gas chromatography (GC) was proposed to meet this objective. However, current interpretative models suffer from several conceptual drawbacks which render them inadequate to assess the evidential value of a given measurement. This paper aims to fill this gap by proposing a logical approach based on the assessment of likelihood ratios. A probabilistic model was thus developed and applied to a hypothetical scenario where alternative hy-potheses about the discharge time of a spent cartridge found on a crime scene were forwarded. In order to estimate the parameters required to implement this solution, a non-linear regression model was proposed and applied to real published data. The proposed approach proved to be a valuable method for interpreting aging-related data.

Quantitative modelling of transcription factor binding sites

Abstract One of the most important issues in molecular biology is to understand regulatory mechanisms that control gene expression. Gene expression is often regulated by proteins, called transcription factors which bind to short (5 to 20 base pairs),degenerate segments of DNA. Experimental efforts towards understanding the sequence specificity of transcription factors is laborious and expensive, but can be substantially accelerated with the use of computational predictions. This thesis describes the use of algorithms and resources for transcriptionfactor binding site analysis in addressing quantitative modelling, where probabilitic models are built to represent binding properties of a transcription factor and can be used to find new functional binding sites in genomes. Initially, an open-access database(HTPSELEX) was created, holding high quality binding sequences for two eukaryotic families of transcription factors namely CTF/NF1 and LEFT/TCF. The binding sequences were elucidated using a recently described experimental procedure called HTP-SELEX, that allows generation of large number (> 1000) of binding sites using mass sequencing technology. For each HTP-SELEX experiments we also provide accurate primary experimental information about the protein material used, details of the wet lab protocol, an archive of sequencing trace files, and assembled clone sequences of binding sequences. The database also offers reasonably large SELEX libraries obtained with conventional low-throughput protocols.The database is available at http://wwwisrec.isb-sib.ch/htpselex/ and and ftp://ftp.isrec.isb-sib.ch/pub/databases/htpselex. The Expectation-Maximisation(EM) algorithm is one the frequently used methods to estimate probabilistic models to represent the sequence specificity of transcription factors. We present computer simulations in order to estimate the precision of EM estimated models as a function of data set parameters(like length of initial sequences, number of initial sequences, percentage of nonbinding sequences). We observed a remarkable robustness of the EM algorithm with regard to length of training sequences and the degree of contamination. The HTPSELEX database and the benchmarked results of the EM algorithm formed part of the foundation for the subsequent project, where a statistical framework called hidden Markov model has been developed to represent sequence specificity of the transcription factors CTF/NF1 and LEF1/TCF using the HTP-SELEX experiment data. The hidden Markov model framework is capable of both predicting and classifying CTF/NF1 and LEF1/TCF binding sites. A covariance analysis of the binding sites revealed non-independent base preferences at different nucleotide positions, providing insight into the binding mechanism. We next tested the LEF1/TCF model by computing binding scores for a set of LEF1/TCF binding sequences for which relative affinities were determined experimentally using non-linear regression. The predicted and experimentally determined binding affinities were in good correlation.

Effect of competitive situation and price on diffusion of mobile communications

Työn päätavoitteena oli selvittää hinnan ja kilpailutilanteen vaikutusta matkaviestinnän diffuusioon. Työn empiirinen osuus tarkasteli matkapuhelinliittymien hinnan vaikutusta liittymien diffuusioon sekä sitä, miten alan kilpailu on vaikuttanut matkaviestinnän hintatasoon. Työssä analysoitiin myös matkaviestinnän kilpailutilannetta Suomen markkinoilla. Tutkimuksen empiirinen aineisto kerättiin toissijaisista lähteistä, esimerkiksi EMC-tietokannasta. Tutkimus oli luonteeltaan kvantitatiivinen.Empiirisessä osassa käytetyt mallit oli muodostettu aikaisempien tutkimuksien perusteella. Regressioanalyysiä käytettiin arvioitaessa hinnan vaikutusta diffuusionopeuteen ja mahdollisten omaksujien määrään. Regressioanalyysissä sovellettiin ei-lineaarista mallia.Tutkimustulokset osoittivat, että tasaisesti laskevilla matkapuhelinliittymien sekä matkapuhelimien hinnoilla ei ole merkittävää vaikutusta matkaviestinnän diffuusioon. Myöskään kilpailutilanne ei ole vaikuttanut paljon matkaviestinnän yleiseen hintatasoon. Työn tulosten perusteella voitiin antaa myös muutamia toimenpide-ehdotuksia jatkotutkimuksia varten.

O ajuste de funções matemáticas a dados experimentais

The least square method is analyzed. The basic aspects of the method are discussed. Emphasis is given in procedures that allow a simple memorization of the basic equations associated with the linear and non linear least square method, polinomial regression and multilinear method.

Analysis of patterns in mining time series using Qlucore

Raw measurement data does not always immediately convey useful information, but applying mathematical statistical analysis tools into measurement data can improve the situation. Data analysis can offer benefits like acquiring meaningful insight from the dataset, basing critical decisions on the findings, and ruling out human bias through proper statistical treatment. In this thesis we analyze data from an industrial mineral processing plant with the aim of studying the possibility of forecasting the quality of the final product, given by one variable, with a model based on the other variables. For the study mathematical tools like Qlucore Omics Explorer (QOE) and Sparse Bayesian regression (SB) are used. Later on, linear regression is used to build a model based on a subset of variables that seem to have most significant weights in the SB model. The results obtained from QOE show that the variable representing the desired final product does not correlate with other variables. For SB and linear regression, the results show that both SB and linear regression models built on 1-day averaged data seriously underestimate the variance of true data, whereas the two models built on 1-month averaged data are reliable and able to explain a larger proportion of variability in the available data, making them suitable for prediction purposes. However, it is concluded that no single model can fit well the whole available dataset and therefore, it is proposed for future work to make piecewise non linear regression models if the same available dataset is used, or the plant to provide another dataset that should be collected in a more systematic fashion than the present data for further analysis.