Use of direct and iterative solvers for estimation of SNP effects in genome-wide selection

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

ITERATIVE NUMERICAL-SOLUTION OF SCATTERING PROBLEMS

An iterative Neumann series method, employing a real auxiliary scattering integral equation, is used to calculate scattering lengths and phase shifts for the atomic Yukawa and exponential potentials. For these potentials the original Neumann series diverges. The present iterative method yields results that are far better, in convergence, stability and precision, than other momentum space methods. Accurate result is obtained in both cases with an estimated error of about 1 in 10(10) after some 8-10 iterations.

Application of an iterative method and an evolutionary algorithm in fuzzy optimization

This work develops two approaches based on the fuzzy set theory to solve a class of fuzzy mathematical optimization problems with uncertainties in the objective function and in the set of constraints. The first approach is an adaptation of an iterative method that obtains cut levels and later maximizes the membership function of fuzzy decision making using the bound search method. The second one is a metaheuristic approach that adapts a standard genetic algorithm to use fuzzy numbers. Both approaches use a decision criterion called satisfaction level that reaches the best solution in the uncertain environment. Selected examples from the literature are presented to compare and to validate the efficiency of the methods addressed, emphasizing the fuzzy optimization problem in some import-export companies in the south of Spain. © 2012 Brazilian Operations Research Society.

Mixed finite-element methods for elliptic convection-dominated problems arising in semiconductor physics

In this work we develop and analyze an adaptive numerical scheme for simulating a class of macroscopic semiconductor models. At first the numerical modelling of semiconductors is reviewed in order to classify the Energy-Transport models for semiconductors that are later simulated in 2D. In this class of models the flow of charged particles, that are negatively charged electrons and so-called holes, which are quasi-particles of positive charge, as well as their energy distributions are described by a coupled system of nonlinear partial differential equations. A considerable difficulty in simulating these convection-dominated equations is posed by the nonlinear coupling as well as due to the fact that the local phenomena such as "hot electron effects" are only partially assessable through the given data. The primary variables that are used in the simulations are the particle density and the particle energy density. The user of these simulations is mostly interested in the current flow through parts of the domain boundary - the contacts. The numerical method considered here utilizes mixed finite-elements as trial functions for the discrete solution. The continuous discretization of the normal fluxes is the most important property of this discretization from the users perspective. It will be proven that under certain assumptions on the triangulation the particle density remains positive in the iterative solution algorithm. Connected to this result an a priori error estimate for the discrete solution of linear convection-diffusion equations is derived. The local charge transport phenomena will be resolved by an adaptive algorithm, which is based on a posteriori error estimators. At that stage a comparison of different estimations is performed. Additionally a method to effectively estimate the error in local quantities derived from the solution, so-called "functional outputs", is developed by transferring the dual weighted residual method to mixed finite elements. For a model problem we present how this method can deliver promising results even when standard error estimator fail completely to reduce the error in an iterative mesh refinement process.

Refined Estimation of Earthquake Source Parameters: Methods, Applications and Scaling Relationships

The objective of this work of thesis is the refined estimations of source parameters. To such a purpose we used two different approaches, one in the frequency domain and the other in the time domain. In frequency domain, we analyzed the P- and S-wave displacement spectra to estimate spectral parameters, that is corner frequencies and low frequency spectral amplitudes. We used a parametric modeling approach which is combined with a multi-step, non-linear inversion strategy and includes the correction for attenuation and site effects. The iterative multi-step procedure was applied to about 700 microearthquakes in the moment range 1011-1014 N•m and recorded at the dense, wide-dynamic range, seismic networks operating in Southern Apennines (Italy). The analysis of the source parameters is often complicated when we are not able to model the propagation accurately. In this case the empirical Green function approach is a very useful tool to study the seismic source properties. In fact the Empirical Green Functions (EGFs) consent to represent the contribution of propagation and site effects to signal without using approximate velocity models. An EGF is a recorded three-component set of time-histories of a small earthquake whose source mechanism and propagation path are similar to those of the master event. Thus, in time domain, the deconvolution method of Vallée (2004) was applied to calculate the source time functions (RSTFs) and to accurately estimate source size and rupture velocity. This technique was applied to 1) large event, that is Mw=6.3 2009 L’Aquila mainshock (Central Italy), 2) moderate events, that is cluster of earthquakes of 2009 L’Aquila sequence with moment magnitude ranging between 3 and 5.6, 3) small event, i.e. Mw=2.9 Laviano mainshock (Southern Italy).

Coarse-graining methods and polymer dynamics

This thesis studies molecular dynamics simulations on two levels of resolution: the detailed level of atomistic simulations, where the motion of explicit atoms in a many-particle system is considered, and the coarse-grained level, where the motion of superatoms composed of up to 10 atoms is modeled. While atomistic models are capable of describing material specific effects on small scales, the time and length scales they can cover are limited due to their computational costs. Polymer systems are typically characterized by effects on a broad range of length and time scales. Therefore it is often impossible to atomistically simulate processes, which determine macroscopic properties in polymer systems. Coarse-grained (CG) simulations extend the range of accessible time and length scales by three to four orders of magnitude. However, no standardized coarse-graining procedure has been established yet. Following the ideas of structure-based coarse-graining, a coarse-grained model for polystyrene is presented. Structure-based methods parameterize CG models to reproduce static properties of atomistic melts such as radial distribution functions between superatoms or other probability distributions for coarse-grained degrees of freedom. Two enhancements of the coarse-graining methodology are suggested. Correlations between local degrees of freedom are implicitly taken into account by additional potentials acting between neighboring superatoms in the polymer chain. This improves the reproduction of local chain conformations and allows the study of different tacticities of polystyrene. It also gives better control of the chain stiffness, which agrees perfectly with the atomistic model, and leads to a reproduction of experimental results for overall chain dimensions, such as the characteristic ratio, for all different tacticities. The second new aspect is the computationally cheap development of nonbonded CG potentials based on the sampling of pairs of oligomers in vacuum. Static properties of polymer melts are obtained as predictions of the CG model in contrast to other structure-based CG models, which are iteratively refined to reproduce reference melt structures. The dynamics of simulations at the two levels of resolution are compared. The time scales of dynamical processes in atomistic and coarse-grained simulations can be connected by a time scaling factor, which depends on several specific system properties as molecular weight, density, temperature, and other components in mixtures. In this thesis the influence of molecular weight in systems of oligomers and the situation in two-component mixtures is studied. For a system of small additives in a melt of long polymer chains the temperature dependence of the additive diffusion is predicted and compared to experiments.

Decomposition Methods and Network Design Problems

Decomposition based approaches are recalled from primal and dual point of view. The possibility of building partially disaggregated reduced master problems is investigated. This extends the idea of aggregated-versus-disaggregated formulation to a gradual choice of alternative level of aggregation. Partial aggregation is applied to the linear multicommodity minimum cost flow problem. The possibility of having only partially aggregated bundles opens a wide range of alternatives with different trade-offs between the number of iterations and the required computation for solving it. This trade-off is explored for several sets of instances and the results are compared with the ones obtained by directly solving the natural node-arc formulation. An iterative solution process to the route assignment problem is proposed, based on the well-known Frank Wolfe algorithm. In order to provide a first feasible solution to the Frank Wolfe algorithm, a linear multicommodity min-cost flow problem is solved to optimality by using the decomposition techniques mentioned above. Solutions of this problem are useful for network orientation and design, especially in relation with public transportation systems as the Personal Rapid Transit. A single-commodity robust network design problem is addressed. In this, an undirected graph with edge costs is given together with a discrete set of balance matrices, representing different supply/demand scenarios. The goal is to determine the minimum cost installation of capacities on the edges such that the flow exchange is feasible for every scenario. A set of new instances that are computationally hard for the natural flow formulation are solved by means of a new heuristic algorithm. Finally, an efficient decomposition-based heuristic approach for a large scale stochastic unit commitment problem is presented. The addressed real-world stochastic problem employs at its core a deterministic unit commitment planning model developed by the California Independent System Operator (ISO).

Towards the 3D attenuation imaging of active volcanoes: methods and tests on real and simulated data

The purpose of my PhD thesis has been to face the issue of retrieving a three dimensional attenuation model in volcanic areas. To this purpose, I first elaborated a robust strategy for the analysis of seismic data. This was done by performing several synthetic tests to assess the applicability of spectral ratio method to our purposes. The results of the tests allowed us to conclude that: 1) spectral ratio method gives reliable differential attenuation (dt*) measurements in smooth velocity models; 2) short signal time window has to be chosen to perform spectral analysis; 3) the frequency range over which to compute spectral ratios greatly affects dt* measurements. Furthermore, a refined approach for the application of spectral ratio method has been developed and tested. Through this procedure, the effects caused by heterogeneities of propagation medium on the seismic signals may be removed. The tested data analysis technique was applied to the real active seismic SERAPIS database. It provided a dataset of dt* measurements which was used to obtain a three dimensional attenuation model of the shallowest part of Campi Flegrei caldera. Then, a linearized, iterative, damped attenuation tomography technique has been tested and applied to the selected dataset. The tomography, with a resolution of 0.5 km in the horizontal directions and 0.25 km in the vertical direction, allowed to image important features in the off-shore part of Campi Flegrei caldera. High QP bodies are immersed in a high attenuation body (Qp=30). The latter is well correlated with low Vp and high Vp/Vs values and it is interpreted as a saturated marine and volcanic sediments layer. High Qp anomalies, instead, are interpreted as the effects either of cooled lava bodies or of a CO2 reservoir. A pseudo-circular high Qp anomaly was detected and interpreted as the buried rim of NYT caldera.

Squared Extrapolation Methods (SQUAREM): A New Class of Simple and Efficient Numerical Schemes for Accelerating the Convergence of the EM Algorithm

We derive a new class of iterative schemes for accelerating the convergence of the EM algorithm, by exploiting the connection between fixed point iterations and extrapolation methods. First, we present a general formulation of one-step iterative schemes, which are obtained by cycling with the extrapolation methods. We, then square the one-step schemes to obtain the new class of methods, which we call SQUAREM. Squaring a one-step iterative scheme is simply applying it twice within each cycle of the extrapolation method. Here we focus on the first order or rank-one extrapolation methods for two reasons, (1) simplicity, and (2) computational efficiency. In particular, we study two first order extrapolation methods, the reduced rank extrapolation (RRE1) and minimal polynomial extrapolation (MPE1). The convergence of the new schemes, both one-step and squared, is non-monotonic with respect to the residual norm. The first order one-step and SQUAREM schemes are linearly convergent, like the EM algorithm but they have a faster rate of convergence. We demonstrate, through five different examples, the effectiveness of the first order SQUAREM schemes, SqRRE1 and SqMPE1, in accelerating the EM algorithm. The SQUAREM schemes are also shown to be vastly superior to their one-step counterparts, RRE1 and MPE1, in terms of computational efficiency. The proposed extrapolation schemes can fail due to the numerical problems of stagnation and near breakdown. We have developed a new hybrid iterative scheme that combines the RRE1 and MPE1 schemes in such a manner that it overcomes both stagnation and near breakdown. The squared first order hybrid scheme, SqHyb1, emerges as the iterative scheme of choice based on our numerical experiments. It combines the fast convergence of the SqMPE1, while avoiding near breakdowns, with the stability of SqRRE1, while avoiding stagnations. The SQUAREM methods can be incorporated very easily into an existing EM algorithm. They only require the basic EM step for their implementation and do not require any other auxiliary quantities such as the complete data log likelihood, and its gradient or hessian. They are an attractive option in problems with a very large number of parameters, and in problems where the statistical model is complex, the EM algorithm is slow and each EM step is computationally demanding.

MODEL UPDATING AND STRUCTURAL HEALTH MONITORING OF HORIZONTAL AXIS WIND TURBINES VIA ADVANCED SPINNING FINITE ELEMENTS AND STOCHASTIC SUBSPACE IDENTIFICATION METHODS

Wind energy has been one of the most growing sectors of the nation’s renewable energy portfolio for the past decade, and the same tendency is being projected for the upcoming years given the aggressive governmental policies for the reduction of fossil fuel dependency. Great technological expectation and outstanding commercial penetration has shown the so called Horizontal Axis Wind Turbines (HAWT) technologies. Given its great acceptance, size evolution of wind turbines over time has increased exponentially. However, safety and economical concerns have emerged as a result of the newly design tendencies for massive scale wind turbine structures presenting high slenderness ratios and complex shapes, typically located in remote areas (e.g. offshore wind farms). In this regard, safety operation requires not only having first-hand information regarding actual structural dynamic conditions under aerodynamic action, but also a deep understanding of the environmental factors in which these multibody rotating structures operate. Given the cyclo-stochastic patterns of the wind loading exerting pressure on a HAWT, a probabilistic framework is appropriate to characterize the risk of failure in terms of resistance and serviceability conditions, at any given time. Furthermore, sources of uncertainty such as material imperfections, buffeting and flutter, aeroelastic damping, gyroscopic effects, turbulence, among others, have pleaded for the use of a more sophisticated mathematical framework that could properly handle all these sources of indetermination. The attainable modeling complexity that arises as a result of these characterizations demands a data-driven experimental validation methodology to calibrate and corroborate the model. For this aim, System Identification (SI) techniques offer a spectrum of well-established numerical methods appropriated for stationary, deterministic, and data-driven numerical schemes, capable of predicting actual dynamic states (eigenrealizations) of traditional time-invariant dynamic systems. As a consequence, it is proposed a modified data-driven SI metric based on the so called Subspace Realization Theory, now adapted for stochastic non-stationary and timevarying systems, as is the case of HAWT’s complex aerodynamics. Simultaneously, this investigation explores the characterization of the turbine loading and response envelopes for critical failure modes of the structural components the wind turbine is made of. In the long run, both aerodynamic framework (theoretical model) and system identification (experimental model) will be merged in a numerical engine formulated as a search algorithm for model updating, also known as Adaptive Simulated Annealing (ASA) process. This iterative engine is based on a set of function minimizations computed by a metric called Modal Assurance Criterion (MAC). In summary, the Thesis is composed of four major parts: (1) development of an analytical aerodynamic framework that predicts interacted wind-structure stochastic loads on wind turbine components; (2) development of a novel tapered-swept-corved Spinning Finite Element (SFE) that includes dampedgyroscopic effects and axial-flexural-torsional coupling; (3) a novel data-driven structural health monitoring (SHM) algorithm via stochastic subspace identification methods; and (4) a numerical search (optimization) engine based on ASA and MAC capable of updating the SFE aerodynamic model.

Dose Reduction in Standard Head CT: First Results from a New Scanner Using Iterative Reconstruction and a New Detector Type in Comparison with Two Previous Generations of Multi-slice CT

PURPOSE Computed tomography (CT) accounts for more than half of the total radiation exposure from medical procedures, which makes dose reduction in CT an effective means of reducing radiation exposure. We analysed the dose reduction that can be achieved with a new CT scanner [Somatom Edge (E)] that incorporates new developments in hardware (detector) and software (iterative reconstruction). METHODS We compared weighted volume CT dose index (CTDIvol) and dose length product (DLP) values of 25 consecutive patients studied with non-enhanced standard brain CT with the new scanner and with two previous models each, a 64-slice 64-row multi-detector CT (MDCT) scanner with 64 rows (S64) and a 16-slice 16-row MDCT scanner with 16 rows (S16). We analysed signal-to-noise and contrast-to-noise ratios in images from the three scanners and performed a quality rating by three neuroradiologists to analyse whether dose reduction techniques still yield sufficient diagnostic quality. RESULTS CTDIVol of scanner E was 41.5 and 36.4 % less than the values of scanners S16 and S64, respectively; the DLP values were 40 and 38.3 % less. All differences were statistically significant (p < 0.0001). Signal-to-noise and contrast-to-noise ratios were best in S64; these differences also reached statistical significance. Image analysis, however, showed "non-inferiority" of scanner E regarding image quality. CONCLUSIONS The first experience with the new scanner shows that new dose reduction techniques allow for up to 40 % dose reduction while still maintaining image quality at a diagnostically usable level.

Coronary artery stents: influence of adaptive statistical iterative reconstruction on image quality using 64-HDCT

OBJECTIVE: The assessment of coronary stents with present-generation 64-detector row computed tomography (HDCT) scanners is limited by image noise and blooming artefacts. We evaluated the performance of adaptive statistical iterative reconstruction (ASIR) for noise reduction in coronary stent imaging with HDCT. METHODS AND RESULTS: In 50 stents of 28 patients (mean age 64 ± 10 years) undergoing coronary CT angiography (CCTA) on an HDCT scanner the mean in-stent luminal diameter, stent length, image quality, in-stent contrast attenuation, and image noise were assessed. Studies were reconstructed using filtered back projection (FBP) and ASIR-FBP composites. ASIR resulted in reduced image noise vs. FBP (P < 0.0001). Two readers graded the CCTA stent image quality on a 4-point Likert scale and determined the proportion of interpretable stent segments. The best image quality for all clinical images was obtained with 40 and 60% ASIR with significantly larger luminal area visualization compared with FBP (+42.1 ± 5.4% with 100% ASIR vs. FBP alone; P < 0.0001) while the stent length was decreased (-4.7 ± 0.9%,

Impact of a 4th generation iterative reconstruction technique on image quality in low-dose computed tomography of the chest in immunocompromised patients

PURPOSE To determine the image quality of an iterative reconstruction (IR) technique in low-dose MDCT (LDCT) of the chest of immunocompromised patients in an intraindividual comparison to filtered back projection (FBP) and to evaluate the dose reduction capability. MATERIALS AND METHODS 30 chest LDCT scans were performed in immunocompromised patients (Brilliance iCT; 20-40 mAs; mean CTDIvol: 1.7 mGy). The raw data were reconstructed using FBP and the IR technique (iDose4™, Philips, Best, The Netherlands) set to seven iteration levels. 30 routine-dose MDCT (RDCT) reconstructed with FBP served as controls (mean exposure: 116 mAs; mean CDTIvol: 7.6 mGy). Three blinded radiologists scored subjective image quality and lesion conspicuity. Quantitative parameters including CT attenuation and objective image noise (OIN) were determined. RESULTS In LDCT high iDose4™ levels lead to a significant decrease in OIN (FBP vs. iDose7: subscapular muscle 139.4 vs. 40.6 HU). The high iDose4™ levels provided significant improvements in image quality and artifact and noise reduction compared to LDCT FBP images. The conspicuity of subtle lesions was limited in LDCT FBP images. It significantly improved with high iDose4™ levels (> iDose4). LDCT with iDose4™ level 6 was determined to be of equivalent image quality as RDCT with FBP. CONCLUSION iDose4™ substantially improves image quality and lesion conspicuity and reduces noise in low-dose chest CT. Compared to RDCT, high iDose4™ levels provide equivalent image quality in LDCT, hence suggesting a potential dose reduction of almost 80%.

Reducing CT radiation dose with iterative reconstruction algorithms: the influence of scan and reconstruction parameters on image quality and CTDIvol

OBJECTIVES In this phantom CT study, we investigated whether images reconstructed using filtered back projection (FBP) and iterative reconstruction (IR) with reduced tube voltage and current have equivalent quality. We evaluated the effects of different acquisition and reconstruction parameter settings on image quality and radiation doses. Additionally, patient CT studies were evaluated to confirm our phantom results. METHODS Helical and axial 256 multi-slice computed tomography scans of the phantom (Catphan(®)) were performed with varying tube voltages (80-140kV) and currents (30-200mAs). 198 phantom data sets were reconstructed applying FBP and IR with increasing iterations, and soft and sharp kernels. Further, 25 chest and abdomen CT scans, performed with high and low exposure per patient, were reconstructed with IR and FBP. Two independent observers evaluated image quality and radiation doses of both phantom and patient scans. RESULTS In phantom scans, noise reduction was significantly improved using IR with increasing iterations, independent from tissue, scan-mode, tube-voltage, current, and kernel. IR did not affect high-contrast resolution. Low-contrast resolution was also not negatively affected, but improved in scans with doses <5mGy, although object detectability generally decreased with the lowering of exposure. At comparable image quality levels, CTDIvol was reduced by 26-50% using IR. In patients, applying IR vs. FBP resulted in good to excellent image quality, while tube voltage and current settings could be significantly decreased. CONCLUSIONS Our phantom experiments demonstrate that image quality levels of FBP reconstructions can also be achieved at lower tube voltages and tube currents when applying IR. Our findings could be confirmed in patients revealing the potential of IR to significantly reduce CT radiation doses.

Feasible Dose Reduction in Routine Chest Computed Tomography Maintaining Constant Image Quality Using the Last Three Scanner Generations: From Filtered Back Projection to Sinogram-affirmed Iterative Reconstruction and Impact of the Novel Fully Integrated Detector Design Minimizing Electronic Noise

OBJECTIVE The aim of the present study was to evaluate a dose reduction in contrast-enhanced chest computed tomography (CT) by comparing the three latest generations of Siemens CT scanners used in clinical practice. We analyzed the amount of radiation used with filtered back projection (FBP) and an iterative reconstruction (IR) algorithm to yield the same image quality. Furthermore, the influence on the radiation dose of the most recent integrated circuit detector (ICD; Stellar detector, Siemens Healthcare, Erlangen, Germany) was investigated. MATERIALS AND METHODS 136 Patients were included. Scan parameters were set to a thorax routine: SOMATOM Sensation 64 (FBP), SOMATOM Definition Flash (IR), and SOMATOM Definition Edge (ICD and IR). Tube current was set constantly to the reference level of 100 mA automated tube current modulation using reference milliamperes. Care kV was used on the Flash and Edge scanner, while tube potential was individually selected between 100 and 140 kVp by the medical technologists at the SOMATOM Sensation. Quality assessment was performed on soft-tissue kernel reconstruction. Dose was represented by the dose length product. RESULTS Dose-length product (DLP) with FBP for the average chest CT was 308 mGy*cm ± 99.6. In contrast, the DLP for the chest CT with IR algorithm was 196.8 mGy*cm ± 68.8 (P = 0.0001). Further decline in dose can be noted with IR and the ICD: DLP: 166.4 mGy*cm ± 54.5 (P = 0.033). The dose reduction compared to FBP was 36.1% with IR and 45.6% with IR/ICD. Signal-to-noise ratio (SNR) was favorable in the aorta, bone, and soft tissue for IR/ICD in combination compared to FBP (the P values ranged from 0.003 to 0.048). Overall contrast-to-noise ratio (CNR) improved with declining DLP. CONCLUSION The most recent technical developments, namely IR in combination with integrated circuit detectors, can significantly lower radiation dose in chest CT examinations.