Solution of the Least Squares Method problem of pairwise comparison matrices

The aim of the paper is to present a new global optimization method for determining all the optima of the Least Squares Method (LSM) problem of pairwise comparison matrices. Such matrices are used, e.g., in the Analytic Hierarchy Process (AHP). Unlike some other distance minimizing methods, LSM is usually hard to solve because of the corresponding nonlinear and non-convex objective function. It is found that the optimization problem can be reduced to solve a system of polynomial equations. Homotopy method is applied which is an efficient technique for solving nonlinear systems. The paper ends by two numerical example having multiple global and local minima.

Rigid and non-rigid point-based medical image registration

The primary goal of this dissertation is to develop point-based rigid and non-rigid image registration methods that have better accuracy than existing methods. We first present point-based PoIRe, which provides the framework for point-based global rigid registrations. It allows a choice of different search strategies including (a) branch-and-bound, (b) probabilistic hill-climbing, and (c) a novel hybrid method that takes advantage of the best characteristics of the other two methods. We use a robust similarity measure that is insensitive to noise, which is often introduced during feature extraction. We show the robustness of PoIRe using it to register images obtained with an electronic portal imaging device (EPID), which have large amounts of scatter and low contrast. To evaluate PoIRe we used (a) simulated images and (b) images with fiducial markers; PoIRe was extensively tested with 2D EPID images and images generated by 3D Computer Tomography (CT) and Magnetic Resonance (MR) images. PoIRe was also evaluated using benchmark data sets from the blind retrospective evaluation project (RIRE). We show that PoIRe is better than existing methods such as Iterative Closest Point (ICP) and methods based on mutual information. We also present a novel point-based local non-rigid shape registration algorithm. We extend the robust similarity measure used in PoIRe to non-rigid registrations adapting it to a free form deformation (FFD) model and making it robust to local minima, which is a drawback common to existing non-rigid point-based methods. For non-rigid registrations we show that it performs better than existing methods and that is less sensitive to starting conditions. We test our non-rigid registration method using available benchmark data sets for shape registration. Finally, we also explore the extraction of features invariant to changes in perspective and illumination, and explore how they can help improve the accuracy of multi-modal registration. For multimodal registration of EPID-DRR images we present a method based on a local descriptor defined by a vector of complex responses to a circular Gabor filter.

Rigid and Non-rigid Point-based Medical Image Registration

The primary goal of this dissertation is to develop point-based rigid and non-rigid image registration methods that have better accuracy than existing methods. We first present point-based PoIRe, which provides the framework for point-based global rigid registrations. It allows a choice of different search strategies including (a) branch-and-bound, (b) probabilistic hill-climbing, and (c) a novel hybrid method that takes advantage of the best characteristics of the other two methods. We use a robust similarity measure that is insensitive to noise, which is often introduced during feature extraction. We show the robustness of PoIRe using it to register images obtained with an electronic portal imaging device (EPID), which have large amounts of scatter and low contrast. To evaluate PoIRe we used (a) simulated images and (b) images with fiducial markers; PoIRe was extensively tested with 2D EPID images and images generated by 3D Computer Tomography (CT) and Magnetic Resonance (MR) images. PoIRe was also evaluated using benchmark data sets from the blind retrospective evaluation project (RIRE). We show that PoIRe is better than existing methods such as Iterative Closest Point (ICP) and methods based on mutual information. We also present a novel point-based local non-rigid shape registration algorithm. We extend the robust similarity measure used in PoIRe to non-rigid registrations adapting it to a free form deformation (FFD) model and making it robust to local minima, which is a drawback common to existing non-rigid point-based methods. For non-rigid registrations we show that it performs better than existing methods and that is less sensitive to starting conditions. We test our non-rigid registration method using available benchmark data sets for shape registration. Finally, we also explore the extraction of features invariant to changes in perspective and illumination, and explore how they can help improve the accuracy of multi-modal registration. For multimodal registration of EPID-DRR images we present a method based on a local descriptor defined by a vector of complex responses to a circular Gabor filter.

Cascade artificial neural networks technique for solving ellipsometry problems

Ellipsometry is a well known optical technique used for the characterization of reflective surfaces in study and films between two media. It is based on measuring the change in the state of polarization that occurs as a beam of polarized light is reflected from or transmitted through the film. Measuring this change can be used to calculate parameters of a single layer film such as the thickness and the refractive index. However, extracting these parameters of interest requires significant numerical processing due to the noninvertible equations. Typically, this is done using least squares solving methods which are slow and adversely affected by local minima in the solvable surface. This thesis describes the development and implementation of a new technique using only Artificial Neural Networks (ANN) to calculate thin film parameters. The new method offers a speed in the orders of magnitude faster than preceding methods and convergence to local minima is completely eliminated.

Dissolved Zinc in the Southern Ocean measured on water bottle samples during POLARSTERN cruise ANT-XXIV/3

The distribution of dissolved zinc (Zn) was investigated in the Atlantic sector of the Southern Ocean in the austral autumn of 2008 as part of the IPY GEOTRACES expedition ZERO & DRAKE. Research focused on transects across the major frontal systems along the Zero Meridian and across the Drake Passage. There was a strong gradient in surface zinc concentrations observed across the Antarctic Polar Front along both transects and high zinc levels were found in surface waters throughout the Southern Ocean. Vertical profiles for dissolved Zinc showed the presence of local minima and maxima in the upper 200 m consistent with significant uptake by phytoplankton and release by zooplankton grazing, respectively. Highest deep water zinc concentrations were found in the centre of the Weddell Gyre associated with Central Intermediate Water (CIW), a water mass which is depleted in O2, elevated in CO2 and is regionally a CFC minimum. Our data suggests that the remineralization of sinking particles is a key control on the distribution of Zn in the Southern Ocean. Disappearance ratios of zinc to phosphate (Zn:P) in the upper water column increased southwards along both transects and based on laboratory studies they suggest slower growth rates of phytoplankton due to iron or light limitation. Zinc and silicate were strongly correlated throughout the study region but the disappearance ratio (Zn:Si) was relatively uniform overall except for the region close to the ice edge on the Zero Meridian.

Estratificação de solos em camadas horizontais utilizando evolução diferencial

This work's objective is the development of a methodology to represent an unknown soil through a stratified horizontal multilayer soil model, from which the engineer may carry out eletrical grounding projects with high precision. The methodology uses the experimental electrical apparent resistivity curve, obtained through measurements on the ground, using a 4-wire earth ground resistance tester kit, along with calculations involving the measured resistance. This curve is then compared with the theoretical electrical apparent resistivity curve, obtained through calculations over a horizontally strati ed soil, whose parameters are conjectured. This soil model parameters, such as the number of layers, in addition to the resistivity and the thickness of each layer, are optimized by Differential Evolution method, with enhanced performance through parallel computing, in order to both apparent resistivity curves get close enough, and it is possible to represent the unknown soil through the multilayer horizontal soil model fitted with optimized parameters. In order to assist the Differential Evolution method, in case of a stagnation during an arbitrary amount of generations, an optimization process unstuck methodology is proposed, to expand the search space and test new combinations, allowing the algorithm to nd a better solution and/or leave the local minima. It is further proposed an error improvement methodology, in order to smooth the error peaks between the apparent resistivity curves, by giving opportunities for other more uniform solutions to excel, in order to improve the whole algorithm precision, minimizing the maximum error. Methodologies to verify the polynomial approximation of the soil characteristic function and the theoretical apparent resistivity calculations are also proposed by including middle points among the approximated ones in the verification. Finally, a statistical evaluation prodecure is presented, in order to enable the classication of soil samples. The soil stratification methodology is used in a control group, formed by horizontally stratified soils. By using statistical inference, one may calculate the amount of soils that, within an error margin, does not follow the horizontal multilayer model.

MULTI-BAND BOSE HUBBARD MODELS AND EFFECTIVE THREE-BODY INTERACTIONS

Experiments with ultracold atoms in optical lattice have become a versatile testing ground to study diverse quantum many-body Hamiltonians. A single-band Bose-Hubbard (BH) Hamiltonian was first proposed to describe these systems in 1998 and its associated quantum phase-transition was subsequently observed in 2002. Over the years, there has been a rapid progress in experimental realizations of more complex lattice geometries, leading to more exotic BH Hamiltonians with contributions from excited bands, and modified tunneling and interaction energies. There has also been interesting theoretical insights and experimental studies on “un- conventional” Bose-Einstein condensates in optical lattices and predictions of rich orbital physics in higher bands. In this thesis, I present our results on several multi- band BH models and emergent quantum phenomena. In particular, I study optical lattices with two local minima per unit cell and show that the low energy states of a multi-band BH Hamiltonian with only pairwise interactions is equivalent to an effec- tive single-band Hamiltonian with strong three-body interactions. I also propose a second method to create three-body interactions in ultracold gases of bosonic atoms in a optical lattice. In this case, this is achieved by a careful cancellation of two contributions in the pair-wise interaction between the atoms, one proportional to the zero-energy scattering length and a second proportional to the effective range. I subsequently study the physics of Bose-Einstein condensation in the second band of a double-well 2D lattice and show that the collision aided decay rate of the con- densate to the ground band is smaller than the tunneling rate between neighboring unit cells. Finally, I propose a numerical method using the discrete variable repre- sentation for constructing real-valued Wannier functions localized in a unit cell for optical lattices. The developed numerical method is general and can be applied to a wide array of optical lattice geometries in one, two or three dimensions.

DNA polymorphism and local variation in base-pair orientation: a theoretical rationale

Basepair stacking calculations have been carried out to understand the conformational polymorphism of DNA and its sequence dependence. The recently developed self-consistent parameter set, which is specially suitable for describing irregular DNA structures, has been used to describe the geometry of a basepair doublet. While for basepairs without any propeller, the favourable stacking patterns do not appear to have very strong features, much more noticeable sequence dependent stacking patterns emerge once a propeller is applied to the basepairs. The absolute minima for most sequences occurs for a doublet geometry close to the B-DNA fibre models. Hence in the B-DNA region, no strong sequence dependent features are found, but the range of doublet geometries observed in the crystal structures generally lie within the low energy contours, obtained from stacking energy calculations. The doublet geometry corresponding to the A-DNA fibre model is not energetically favourable for the purine-pyrimidine sequences, which prefer small roll angle values when the slide has a large negative value as in A-DNA. However positive roll with large negative slide is allowed for GG, GA, AG and the pyrimidine-purine steps. This is consistent with the observed geometries of various steps in A-DNA crystals. Thus the general features of the basepair doublets predicted from these theoretical studies agree very well with the results from crystal structure analysis. However, since most sequences show an overall preference for B-type doublet geometry, the B --> A transition for random sequence DNA cannot be explained on the basis of basepair stacking interactions.

Time scales for transitions between free-energy minima of a dense hard-sphere system

Time scales associated with activated transitions between glassy metastable states of a free-energy functional appropriate for a dense hard-sphere system are calculated by using a new Monte Carlo method for the local density variables. In particular, we calculate the time the system, initially placed in a shallow glassy minimum of the free-energy, spends in the neighborhood of this minimum before making a transition to the basin of attraction of another free-energy minimum. This time scale is found to increase as the average density is increased. We find a crossover density near which this time scale increases very sharply and becomes longer than the longest times accessible in our simulation. This time scale does not show any evidence of increasing with sample size

Electron concentration dependence of exciton localization and freeze-out at local potential fluctuations in InN films

InN films with electron concentration ranging from n similar to 10(17) to 10(20) cm(-3) grown by metal-organic chemical vapor deposition (MOCVD) and molecular beam epitaxy (MBE) were investigated by variable-temperature photoluminescence and absorption measurements. The energy positions of absorption edge as well as photoluminescence peak of these InN samples with electron concentration above 10(18) cm(-3) show a distinct S-shape temperature dependence. With a model of potential fluctuations caused by electron-impurity interactions, the behavior can be quantitatively explained in terms of exciton freeze-out in local potential minima at sufficiently low temperatures, followed by thermal redistribution of the localized excitons when the band gap shrinks with increasing temperature. The exciton localization energy sigma (loc) is found to follow the n (5/12) power relation, which testifies to the observed strong localization effects in InN with high electron concentrations.

Plasma structure within poleward-moving cusp/cleft auroral transients: EISCAT Svalbard radar observations and an explanation in terms of large local time extent of events

We report high-resolution observations of the southward-IMF cusp/cleft ionosphere made on December 16th 1998 by the EISCAT (European incoherent scatter) Svalbard radar (ESR), and compare them with observations of dayside auroral luminosity, as seen at a wavelength of 630 nm by a meridian scanning photometer at Ny Alesund, and of plasma flows, as seen by the CUTLASS (co-operative UK twin location auroral sounding system) Finland HF radar. The optical data reveal a series of poleward-moving transient red-line (630 nm) enhancements, events that have been associated with bursts in the rate of magnetopause reconnection generating new open flux. The combined observations at this time have strong similarities to predictions of the effects of soft electron precipitation modulated by pulsed reconnection, as made by Davis and Lockwood (1996); however, the effects of rapid zonal flow in the ionosphere, caused by the magnetic curvature force on the newly opened field lines, are found to be a significant additional factor. In particular, it is shown how enhanced plasma loss rates induced by the rapid convection can explain two outstanding anomalies of the 630 nm transients, namely how minima in luminosity form between the poleward-moving events and how events can re-brighten as they move poleward. The observations show how cusp/cleft aurora and transient poleward-moving auroral forms appear in the ESR data and the conditions which cause enhanced 630 nm emission in the transients: they are an important first step in enabling the ESR to identify these features away from the winter solstice when supporting auroral observations are not available.

Local luminous infrared galaxies. I. Spatially resolved observations with the Spitzer infrared spectrograph

We present results from the Spitzer Infrared Spectrograph spectral mapping observations of 15 local luminous infrared galaxies (LIRGs). In this paper, we investigate the spatial variations of the mid-IR emission which includes fine structure lines, molecular hydrogen lines, polycyclic aromatic features (PAHs), continuum emission, and the 9.7 μm silicate feature. We also compare the nuclear and integrated spectra. We find that the star formation takes place in extended regions (several kpc) as probed by the PAH emission, as well as the [Ne II]12.81 μm and [Ne III]15.56 μm emissions. The behavior of the integrated PAH emission and 9.7 μm silicate feature is similar to that of local starburst galaxies. We also find that the minima of the [Ne III]15.56 μm/[Ne II]12.81 μm ratio tends to be located at the nuclei and its value is lower than that of H II regions in our LIRGs and nearby galaxies. It is likely that increased densities in the nuclei of LIRGs are responsible for the smaller nuclear [Ne III]15.56 μm/[Ne II]12.81 μm ratios. This includes the possibility that some of the most massive stars in the nuclei are still embedded in ultracompact H II regions. In a large fraction of our sample, the 11.3 μm PAH emission appears more extended than the dust 5.5 μm continuum emission. We find a dependency of the 11.3 μm PAH/7.7 μm PAH and [Ne II]12.81 μm/11.3 μm PAH ratios with the age of the stellar populations. Smaller and larger ratios, respectively, indicate recent star formation. The estimated warm (300 K local starbursts, and Seyfert galaxies. Finally we find that the [Ne II]12.81 μm velocity fields for most of the LIRGs in our sample are compatible with a rotating disk at ~kpc scales, and they are in a good agreement with Hα velocity fields.