I dagens samhälle finns alla möjliga sorters sjukdomar - alltifrån den vanliga säsongsinfluensan till mer allvarliga infektioner och kroniska sjukdomar som cancer och Alzheimers. Därför finns även ett stort intresse för att kunna ställa rätt diagnos samt söka möjliga behandlingar och att bota dessa sjukdomar. Ett sätt att göra detta på är genom att använda biomarkörer, IgG (Immunoglobulin G) är en biomarkör som visat sig vara passande i detta syfte. Vid användning av MALDI-TOF-MS (Matrix Assisted Laser Desorption/Ionization - Time of Flight - Mass Spectrometry) krävs dock anrikning av glykopeptiderna för att exakta resultat ska erhållas. Genom att utnyttja de starka hydrofila interaktionerna mellan glykanerna, som inte finns hos icke-glykopeptider, kan de glykosylerade peptiderna bli anrikade för att högre intensitet ska erhållas i spektrat. Därav, är syftet med detta kandidatexamensarbete att undersöka huruvida SpheriCals® kalibreringsstandarder är passande i syftet att möjliggöra- samt förbättra användandet av biomarkörer i diagnostik och andra medicinska appliceringar där prov analyseras med MALDI-TOF-MS. Hittills har andra peptidbaserade kalibranter använts och det är därför önskvärt att jämföra dessa med SpheriCal® för att se om den sistnämnda genererar mer exakta mätningar. Det första steget var glykosylering för att få glykopeptider från IgG. Därefter genomfördes experiment med både interna och externa kalibreringsmetoder för naturliga, renade samt till viss del nedbrutna peptider och mänskliga prover från friska individer samt från patienter med COVID-19. Dessa experiment genomfördes i olika matriser, mer exakt i DHB (2,4-dihydroxibensoesyra) och HCCA (α-cyano-4-hydroxikanelsyra) En sammanfattning av resultaten visar att SpheriCal®-kalibranter möjliggör mätningar med hög noggrannhet och små fel för uppmätt m/z (massa mot laddning) för både intern och extern kalibrering vid analys av IgG glykopeptider. Vid extern kalibrering gav SpheriCal®-APH mätningar med väsentligt högre exakthet än för kalibrering med mer traditionellt använt PCS i både HCCA och DHB. / Our world is full of all different kinds of diseases - everything from the regular flu to more severe infections and chronic illnesses such as cancer and Alzheimer's disease. It is therefore of interest to be able to establish a diagnosis, and thus search possible treatments and cures. One way to do this is by using biomarkers and IgG (Immunoglobulin G) has shown to be suited as one. When using MALDI-TOF-MS (Matrix Assisted Laser Desorption/Ionization -Time of Flight - Mass Spectrometry), enrichment of the glycopeptides is required to provide an accurate analysis. Hence, by utilizing the strong hydrophilic interactions of glycans, which do not exist in non-glycopeptides, the glycosylated peptides can be enriched to achieve higher intensity in the spectra. That is why the aim of this bachelor’s degree project is to investigate if SpheriCal® calibrant standards are appropriate for the purpose of enabling and bettering the use of biomarkers in diagnostics and other medical areas when analyzing samples with MALDI-TOF-MS. Until now, other peptide-based calibrants have been used. Therefore, it has been desirable to compare the two to showcase whether SpheriCal® generates more accurate measurements. An initial step was glycosylation in order to obtain glycopeptides of IgG. Following that, tests were carried out with both internal- as well as external calibration methods with natural, purified and partly digested peptides and human samples of healthy- and COVID-19 infected patients. Furthermore, different matrices were tested, more specifically, DHB (2,5-dihydroxybenzoic acid) and HCCA (α-Cyano-4-hydroxycinnamic acid). To conclude the results, they showed that SpheriCal® calibrants generate high accuracy with small m/z (mass to charge) errors, for both internal- as well as external calibration methods, when analyzing IgG glycopeptides. For external calibration, SpheriCal®-APH showed significantly higher mass accuracy than conventionally used PCS in both HCCA and DHB.

[pt] O objetivo deste trabalho é estudar uma certa classe de polígonos espaciais e provar teoremas a respeito do número mínimo de achatamentos que tais polígonos necessariamente possuem. Para tal, investigamos polígonos esféricos que não estão contidos em nenhum hemisfério fechado e deduzimos, entre vários resultados, que sob certas hipóteses tais polígonos esféricos possuem uma cota inferior não-trivial para o número de inflexões esféricas. / [en] The aim of this work is to study a certain class of spatial polygons and prove theorems on the minimal number of flattenings that such polygons must have. In order to do this, we investigate spherical polygons which are not contained in any closed hemisphere and deduce, among many results, that under certain hypotheses such spherical polygons have a nontrivial lower bound on the number of spherical inflections.

O objetivo deste trabalho é estudar aproximação na esfera por uma soma com pesos de harmônicos esféricos. Apresentamos condições necessárias e suficientes sobre os pesos para garantir a convergência, tanto no caso contínuo quanto no caso Lp. Analisamos a ordem de convergência dos processos aproximatórios usando um módulo de suavidade esférico relacionado à derivada forte de Laplace-Beltrami. Incluímos provas para vários resultados sobre a derivada forte de Laplace-Beltrami, já que não conseguimos encontrá-las na literatura / The subject of this work is to study approximation on the sphere by weighted sums of spherical harmonics. We present necessary and sufficient conditions on the weights for convergence in both, the continuous and the Lp cases. We analyse the convergence rates of the approximation processes using a modulus of smoothness related to the strong Laplace- Beltrami derivative. We include proofs for several results related to such a derivative, since we were unable to find them in the literature

O objetivo deste trabalho é estudar aproximação na esfera por uma soma com pesos de harmônicos esféricos. Apresentamos condições necessárias e suficientes sobre os pesos para garantir a convergência, tanto no caso contínuo quanto no caso Lp. Analisamos a ordem de convergência dos processos aproximatórios usando um módulo de suavidade esférico relacionado à derivada forte de Laplace-Beltrami. Incluímos provas para vários resultados sobre a derivada forte de Laplace-Beltrami, já que não conseguimos encontrá-las na literatura / The subject of this work is to study approximation on the sphere by weighted sums of spherical harmonics. We present necessary and sufficient conditions on the weights for convergence in both, the continuous and the Lp cases. We analyse the convergence rates of the approximation processes using a modulus of smoothness related to the strong Laplace- Beltrami derivative. We include proofs for several results related to such a derivative, since we were unable to find them in the literature

This thesis addresses a number of problems in computer vision, image processing, and geometry processing, and presents novel solutions to these problems. The overarching theme of the techniques presented here is a multi-scale approach, leveraging mathematical tools to represent images and surfaces at different scales, and methods that can be adapted from one type of domain (eg., the plane) to another (eg., the sphere). The main problem addressed in this thesis is known as stereo reconstruction: reconstructing the geometry of a scene or object from two or more images of that scene. We develop novel algorithms to do this, which work for both planar and spherical images. By developing a novel way to formulate the notion of disparity for spherical images, we are able effectively adapt our algorithms from planar to spherical images. Our stereo reconstruction algorithm is based on a novel application of distance transforms to multi-scale matching. We use matching information aggregated over multiple scales, and enforce consistency between these scales using distance transforms. We then show how multiple spherical disparity maps can be efficiently and robustly fused using visibility and other geometric constraints. We then show how the reconstructed point clouds can be used to synthesize a realistic sequence of novel views, images from points of view not captured in the input images, in real-time. Along the way to this result, we address some related problems. For example, multi-scale features can be detected in spherical images by convolving those images with a filterbank, generating an overcomplete spherical wavelet representation of the image from which the multiscale features can be extracted. Convolution of spherical images is much more efficient in the spherical harmonic domain than in the spatial domain. Thus, we develop a GPU implementation for fast spherical harmonic transforms and frequency domain convolutions of spherical images. This tool can also be used to detect multi-scale features on geometric surfaces. When we have a point cloud of a surface of a particular class of object, whether generated by stereo reconstruction or by some other modality, we can use statistics and machine learning to more robustly estimate the surface. If we have at our disposal a database of surfaces of a particular type of object, such as the human face, we can compute statistics over this database to constrain the possible shape a new surface of this type can take. We show how a statistical spherical wavelet shape prior can be used to efficiently and robustly reconstruct a face shape from noisy point cloud data, including stereo data.

This thesis addresses a number of problems in computer vision, image processing, and geometry processing, and presents novel solutions to these problems. The overarching theme of the techniques presented here is a multi-scale approach, leveraging mathematical tools to represent images and surfaces at different scales, and methods that can be adapted from one type of domain (eg., the plane) to another (eg., the sphere). The main problem addressed in this thesis is known as stereo reconstruction: reconstructing the geometry of a scene or object from two or more images of that scene. We develop novel algorithms to do this, which work for both planar and spherical images. By developing a novel way to formulate the notion of disparity for spherical images, we are able effectively adapt our algorithms from planar to spherical images. Our stereo reconstruction algorithm is based on a novel application of distance transforms to multi-scale matching. We use matching information aggregated over multiple scales, and enforce consistency between these scales using distance transforms. We then show how multiple spherical disparity maps can be efficiently and robustly fused using visibility and other geometric constraints. We then show how the reconstructed point clouds can be used to synthesize a realistic sequence of novel views, images from points of view not captured in the input images, in real-time. Along the way to this result, we address some related problems. For example, multi-scale features can be detected in spherical images by convolving those images with a filterbank, generating an overcomplete spherical wavelet representation of the image from which the multiscale features can be extracted. Convolution of spherical images is much more efficient in the spherical harmonic domain than in the spatial domain. Thus, we develop a GPU implementation for fast spherical harmonic transforms and frequency domain convolutions of spherical images. This tool can also be used to detect multi-scale features on geometric surfaces. When we have a point cloud of a surface of a particular class of object, whether generated by stereo reconstruction or by some other modality, we can use statistics and machine learning to more robustly estimate the surface. If we have at our disposal a database of surfaces of a particular type of object, such as the human face, we can compute statistics over this database to constrain the possible shape a new surface of this type can take. We show how a statistical spherical wavelet shape prior can be used to efficiently and robustly reconstruct a face shape from noisy point cloud data, including stereo data.

Nuclear reactor design requires the calculation of integral core parameters and power and radiation profiles. These physical parameters are obtained by the solution of the linear neutron transport equation over the geometry of the reactor. In order to represent the fine structure of the nuclear core a very small geometrical mesh size should be used, but the computational capacity available these days is still not enough to solve these transport problems in the time range (hours-days) that would make the method useful as a design tool. This problem is traditionally solved by the solution of simple, smaller problems in specific parts of the core and then use a procedure known as homogenization to create average material properties and solve the full problem with a wider mesh size. The iterative multi-level solution procedure is inspired in this multi-stage approach, solving the problem at fuel-pin (cell) level, fuel assembly and nodal levels. The nested geometrical structure of the finite element representation of a reactor can be used to create a set of restriction/prolongation operators to connect the solution in the different levels. The procedure is to iterate between the levels, solving for the error in the coarse level using as source the restricted residual of the solution in the finer level. This way, the complete problem is only solved in the coarsest level and in the other levels only a pair of restriction/interpolation operations and a relaxation is required. In this work, a multigrid solver is developed for the in-moment equation of the spherical harmonics, finite element formulation of the second order transport equation. This solver is implemented as a subroutine in the code EVENT. Numerical tests are provided as a standalone diffusion solver and as part of a block Jacobi transport solver.

Στην παρούσα εργασία μελετήθηκε η δυναμική συμπεριφορά μιας τυπικής σφαιρικής δεξαμενής για την εφαρμογή διάφορων συστημάτων σεισμικής προστασίας. Πέντε διαφορετικά συστήματα σεισμικής προστασίας εξετάζονται:Οι αποσβεστήρες ιξώδους απόσβεσης, οι αποσβεστήρες τριβής και οι μη-λυγίζοντες μεταλλικοί σύνδεσμοι που η λειτουργία τους βασίζεται στην κατανάλωση σεισμικής ενέργειας, και τα ελαστομερή εφέδρανα υψηλής απόσβεσης και αυτά με πυρήνα μολύβδου που η λειτουργία τους βασίζεται στην απομόνωση της βάσης της δεξαμενής. Η αριθμητική ανάλυση έγινε με την χρήση ενός λεπτομερούς μοντέλου πεπερασμένων στοιχείων που προσομοιώνει την ακριβή γεωμετρία της σφαιρικής δεξαμενής, την επίδραση του φαινομένου αλληλεπίδρασης υγρού-δεξαμενής για ενδεικτικά ποσοστά πλήρωσης, την αλληλεπίδραση εδάφους-δεξαμενής και την μη-γραμμική συμπεριφορά των συστημάτων σεισμικής προστασίας. Παρουσιάζονται αποτελέσματα της τέμνουσας δύναμης βάσης, της κατακόρυφης μετατόπισης της ελεύθερης επιφάνειας του περιεχόμενου υγρού και οριζόντιες μετατοπίσεις χαρακτηριστικών σημείων της δεξαμενής, για καθε περίπτωση συστήματος σεισμικής προστασίας υπό σεισμική διέγερση, και συγκρίνονται με τα αντίστοιχα που προκύπτουν για την σφαιρική δεξαμενή με τους συμβατούς χιαστούς συνδέσμους. / Various seismic protection systems are used to study numerically the dynamic behavior of a typical spherical liquid storage tank. Five different anti-seismic devices are investigated; nonlinear viscous dampers, buckling restrained braces and friction devices based on the passive energy dissipation technique and lead core and high damping rubber bearings based on base isolation technique. The numerical analysis is performed by means of a detailed finite element model, taking into account the exact geometry of the steel tank, the fluid-structure interaction effects for an arbitrary level of filling, the soil-structure interaction as well as the non-linearities introduced by either the dissipative bracing systems. Representative results for base shear forces, vertical displacements of the fluid content and displacements at characteristic locations of the spherical tank are presented and compared to those corresponding to a tank with a conventional bracing system.

Thesis (Ph. D.)--Harvard University, 1977. / Includes bibliographical references (p. 285-319).

Submitted by (lucia.rodrigues@ufrpe.br) on 2017-03-29T14:39:03Z No. of bitstreams: 1 Tetsuo Usui.pdf: 2577747 bytes, checksum: 9114b8620e50bf459a5b0f41ed172e08 (MD5) / Made available in DSpace on 2017-03-29T14:39:03Z (GMT). No. of bitstreams: 1 Tetsuo Usui.pdf: 2577747 bytes, checksum: 9114b8620e50bf459a5b0f41ed172e08 (MD5) Previous issue date: 2014-08-25 / This work aims to establish a connection among Mathematics with Geography and Astronomy. In this perspective it aims to encompass an interdisciplinary approach in understanding the geographical concepts of the globe, as well as the concepts inherent in the celestial sphere underlying the theoretical foundations of Euclidean Geometry, in order to present a logical and deductive structure of Geometry and Trigonometry in that sphere. This work complements the existing gap between the subjects of Geography and Mathematics in High School because it gives Mathematical supports to the lines (parallels and meridians) and geographic coordinates. Being therefore useful for undergraduate Mathematics students, the same way that teachers of Mathematics and Geography from High School and Elementary Education. Moreover, it also contemplates the sky watchers who wish to have a look at Astronomy from a point of view of Greek antiquity, since the study of Spherical Trigonometry was totally linked to the celestial study. / O presente trabalho tem como objetivo principal estabelecer uma conexão da Matemática com a Geografia e a Astronomia. Nesta perspectiva visa contemplar uma abordagem interdisciplinar na compreensão dos conceitos geográficos do globo terrestre, assim como, dos conceitos inerentes à esfera celeste acoplados na fundamentação teórica de Geometria Euclidiana, a fim de apresentar uma estrutura lógica e dedutiva da geometria e da trigonometria na esfera. O trabalho complementa a lacuna existente entre as disciplinas de Geografia e Matemática do Ensino Médio, pois fundamenta matematicamente, as linhas (paralelos e meridianos) e coordenadas geográficas. Sendo, portanto, útil para alunos de Graduação de Licenciatura em Matemática, da mesma forma que aos professores de Matemática e Geografia do Ensino Médio e Fundamental. Além disso, também contempla aos observadores do céu que queiram olhar a astronomia de um ponto de vista da antiguidade grega, pois o estudo da trigonometria esférica estava totalmente vinculado ao estudo celestial.