Life on Earth is strongly related to the Sun, which makes it a vital star to study and understand. To improve our knowledge of the way the Sun works, many satellites have been launched into space to monitor the Sun‟s activities where the one of main focus is the effect of these activities on the Earth‟s climate; PICARD is one such satellite. Due to the noise associated with SODISM images, the clarity of these images and the appearance of solar features are affected. Image denoising and enhancement are the main techniques to improve the visual appearance of SODISM images. Affective de-noising algorithm methods depend on a proper detecting of noise present in the image. The aim is to identify which type of noise is present in the image. To reach this point, supervised machine-learning (ML) classifier is used to classify the type of noise present in the image. Furthermore, this work introduces a novel technique developed to enhance the quality of SODISM images. In this thesis, the Modified Undecimated Discrete Wavelet Transform (M-UDWT) technique is used to de-noise and enhance the quality of SODISM images. The proposed method is robust and effectively improves the quality of SODISM images, and produces more precise information and clear feature are brought out. In addition, the non wavelet enhancement is developed as well in this thesis. The results of this algorithm is discussed. The new methods are also assessed using two different methods: subjective (by human observation) and objective (by calculation)

Deep neural networks have been a leading research topic within the machine learning field for the past few years. The introduction of graphical processing units (GPUs) and hardware advances made possible the training of deep neural networks. Previously the training procedure was impossible due to the huge amount of training samples required. The new trained introduced architectures have outperformed the classical methods in different classification and regression problems. With the introduction of 5G technology, related to low-latency and online applications, the research on decreasing the computational cost of deep learning architectures while maintaining state-of-art performance has gained huge interest. This thesis focuses on the use of Self Size-estimating Feedforward Network (SSFN), a feedforward multilayer network. SSFN presents low complexity on the training procedure due to a random matrix instance used in its weights. Its weight matrices are trained using a layer-wise convex optimization approach (a supervised training) combined with a random matrix instance (an unsupervised training). The use of deterministic transforms is explored to replace random matrix instances on the SSFN weight matrices. The use of deterministic transforms automatically reduces the computational complexity, as its structure allows to compute them by fast algorithms. Several deterministic transforms such as discrete cosine transform, Hadamard transform and wavelet transform, among others, are investigated. To this end, two methods based on features’ statistical parameters are developed. The proposed methods are implemented on each layer to decide the deterministic transform to use. The effectiveness of the proposed approach is illustrated by SSFN for object classification tasks using several benchmark datasets. The results show a proper performance, similar to the original SSFN, and also consistency across the different datasets. Therefore, the possibility of introducing deterministic transformations in machine learning research is demonstrated. / Under de senaste åren har djupa neurala nätverk varit det huvudsakliga forskningsområdet inom maskininlärning. Införandet av grafiska processorenheter (GPU:er) och hårdvaruutveckling möjliggjorde träning av djupa neurala nätverk. Tidigare var träningsförfarandet omöjligt på grund av den enorma mängd datapunkter som krävs. De nya tränade arkitekturerna har överträffat de klassiska metoderna i olika klassificerings- och regressionsproblem. Med introduktionen av 5G-teknik, som hör samman med låg fördröjning och onlineapplikationer, har forskning om att minska beräkningskostnaderna för djupinlärningsarkitekturer utan att tappa prestandan, fått ökat intresset. Denna avhandling fokuserar på användningen av Self Size Estimating Feedforward Network (SSFN), ett feedforward multilayer-nätverk. SSFN har låg komplexitet i träningsproceduren på grund av en slumpmässig matrisinstans som används i dess vikter. Dess viktmatriser tränas med hjälp av en lagervis konvex optimeringsstrategi (en övervakad träning) i kombination med en slumpmässig matrisinstans (en oövervakad träning). Användningen av deterministiska transformationer undersöks för att ersätta slumpmässiga matrisinstanser på SSFN-viktmatriserna. Användningen av deterministiska transformationer ger automatiskt en minskning av beräkningskomplexiteten, eftersom dess struktur gör det möjligt att beräkna dem med snabba algoritmer. Flera deterministiska transformationer som diskret cosinustransformation, Hadamardtransformation och wavelettransformation undersöks bland andra. För detta ändamål utvecklas två metoder som baseras på statistiska parametrar i indatans olika dimensioner. De föreslagna metoderna implementeras på varje lager för att bestämma den deterministiska transform som ska användas. Effektiviteten av det föreslagna tillvägagångssättet illustreras med SSFN för objektklassificering med hjälp av flera dataset. Resultatet visar ett korrekt beteende, likt den ursprungliga SSFN, och konsistenta resultat över de olika dataseten. Därmed demonstreras möjligheten att införa deterministiska transformationer i maskininlärningsforskning.

The research focuses on analysis and subsurface imaging of siliciclastics rocks on steam-affected 3D poststack seismic data, merged from different vintages, from the Temblor Formation in the Coalinga heavy oil reservoir in the San Joaquin basin, California. The objective was identification, delineation, and demarcation of reservoir heterogeneities by seismostratigraphic and seismogeomorphic analysis. The proximity of the San Andreas Transforms greatly controlled basin evolution and caused substantial reservoir heterogeneity by changing the depositional environment from shallow marine to near-shore fluvial. Moreover, two unconformities dissect the reservoir interval. The seismic dataset exhibits erratic, distorted reflection strengths and amplitudes caused by steam-injection-aided production. A petrophysical analysis based on Gassmann fluid substitution suggests a 27% P-wave velocity decrease in steam-saturated intervals. Seismic to well log ties were problematic and vexing due to the resulting statics, wavelet changes, and line mismatches. Mapping and flattening on a deeper horizon, however, allowed mapping of the internal unconformities and well ties which were crucial for seismostratigraphic sequence identification. Visualization of seismic attributes brought out stratification patterns and two distinct, laterally and vertically extensive, porous, and interconnected facies tracts interpreted as incised valley fills and tidal-to-subtidal deposits as evidenced by bright, steam related amplitudes. Seismic attribute analysis, Geobody Visualization and Interpretation, and structure and isochron maps brought out two prominent channel-systems, recut and restacked in the central part of the area. These deposits were identified on seismic data and correlated to high-gamma coarsening-upward sands on logs and cores. The deeper one, shifting towards SSE with depth, lies between the Base Temblor and Buttonbed unconformities both in the southwestern and northwestern parts of the study area and is scattered in the western-central portion. The shallower one originates in southwestern corner below the Top Temblor unconformity shifts towards ESE-SE with depth, and runs nearly parallel to the Top Temblor unconformity. It cuts across the Valv unconformity in central part creating a channel incision, and follows the Buttonbed unconformity towards the north. The investigation segmented the reservoir into channels, non-channel bearing, and unconformity-bounded subunits which will allow the operator to improve steam injection and optimize placement of oil producing infill wells. / Ph. D.

Long Range (LoRa) has become a key enabler technology for low power wide area networks. However, due to its ALOHA-based medium access scheme, LoRa has to cope with collisions that limit the capacity and network scalability. Collisions between randomly overlapped signals modulated with different spreading factors (SFs) result in inter-SF interference, which increases the packet loss likelihood when signal-to-interference ratio (SIR) is low. This issue cannot be resolved by channel coding since the probability of error distance is not concentrated around the adjacent symbol. In this paper, we analytically model this interference, and propose an interference cancellation method based on the idea of segmentation of the received signal. This scheme has three steps. First, the SF of the interference signal is identified, then the equivalent data symbol and complex amplitude of the interference are estimated. Finally, the estimated interference signal is subtracted from the received signal before demodulation. Unlike conventional serial interference cancellation (SIC), this scheme can directly estimate and reconstruct the non-aligned inter-SF interference without synchronization. Simulation results show that the proposed method can significantly reduce the symbol error rate (SER) under low SIR compared with the conventional demodulation. Moreover, it also shows high robustness to fractional sample timing offset (STO) and carrier frequency offset (CFO) of interference. The presented results clearly show the effectiveness of the proposed method in terms of the SER performance.

<p dir="ltr">We present first order asymptotic estimates for the divisor function problem, the set of lists (restricted number of divisors) problem, and a generalization of the overpartition problem. In particular, we prove Kotesovec's conjecture for A294363 from the OEIS and also extend his conjecture to a full asymptotic treatment by providing an estimate in terms of elementary functions for the EGF coefficients directly rather than the log of the coefficients. We also provide asymptotic estimates for generalizations of the set of lists and overpartition problem, while making comparisons to any existing Kotesovec conjectures. We perform the asymptotic analysis via Mellin transforms, residue analysis, and the saddle point method. These families of generating functions have potential application to families of randomly generated partitions in which ordered subsets of a partition that exceed a certain fixed size may be one of two different objects and to overpartitions with potential heading labels.</p>

Numerické metody inverzní Laplaceovy transformace (NILT) se staly důležitou částí numerické sady nástrojů praktikujících a výzkumných pracovníků v mnoha vědeckých a inženýrských oborech, zejména v aplikované elektrotechnice. Techniky NILT zejména pomáhají při získávání výsledků simulací v časové oblasti v různých aplikacích. Příkladem jsou řešení obyčejných diferenciálních rovnic, které se objevují např. při analýze obvodů se soustředěnými parametry, nebo řešení parciálních diferenciálních rovnic objevujících se v systémech s rozprostřenými parametry, např. při zkoumání problematiky integrity signálů. Obecně platí, že většina dostupných 1D NILT metod je velmi specifická, tj. funguje dobře na několika typech funkcí a tudíž na omezeném počtu aplikací; Cílem této práce je podrobně se věnovat těmto numerickým metodám, vývoji univerzálních metod NILT a jejich rozšíření na multidimenzionální NILT, které mohou pokrývat širokou oblast aplikací a mohly by poskytnout praktický mechanism pro efektivnější způsob analýzy a simulace v časové oblasti. Myšlenky výzkumu jsou prezentovány v rámci diskusí nad širokou škálou případových studií a aplikací; Například metody NILT se používají při řešení přenosových vedení, včetně vícevodičových, a dokonce i při řešení slabě nelinárních obvodů při použití NILT více proměnných. Pomocí metody NILT mohou být s výhodou uvažovány parametry prvků závislé na kmitočtu a prvky necelistvých řádů v jejich příslušných modelech mohou být zahrnuty velmi přesným a jednoduchým způsobem.

Cette thèse étudie la gestion et la couverture du risque en s’appuyant sur la Value-at-Risk (VaR) et la Value-at-Risk Conditionnelle (CVaR), comme mesures de risque. La première partie propose un modèle d’évolution de prix que nous confrontons à des données réelles issues de la bourse de Paris (Euronext PARIS). Notre modèle prend en compte les probabilités d’occurrence des pertes extrêmes et les changements de régimes observés sur les données. Notre approche consiste à détecter les différentes périodes de chaque régime par la construction d’une chaîne de Markov cachée et à estimer la queue de distribution de chaque régime par des lois puissances. Nous montrons empiriquement que ces dernières sont plus adaptées que les lois normales et les lois stables. L’estimation de la VaR est validée par plusieurs backtests et comparée aux résultats d’autres modèles classiques sur une base de 56 actifs boursiers. Dans la deuxième partie, nous supposons que les prix boursiers sont modélisés par des exponentielles de processus de Lévy. Dans un premier temps, nous développons une méthode numérique pour le calcul de la VaR et la CVaR cumulatives. Ce problème est résolu en utilisant la formalisation de Rockafellar et Uryasev, que nous évaluons numériquement par inversion de Fourier. Dans un deuxième temps, nous nous intéressons à la minimisation du risque de couverture des options européennes, sous une contrainte budgétaire sur le capital initial. En mesurant ce risque par la CVaR, nous établissons une équivalence entre ce problème et un problème de type Neyman-Pearson, pour lequel nous proposons une approximation numérique s’appuyant sur la relaxation de la contrainte / This thesis studies the risk management and hedging, based on the Value-at-Risk (VaR) and the Conditional Value-at-Risk (CVaR) as risk measures. The first part offers a stocks return model that we test in real data from NSYE Euronext. Our model takes into account the probability of occurrence of extreme losses and the regime switching observed in the data. Our approach is to detect the different periods of each regime by constructing a hidden Markov chain and estimate the tail of each regime distribution by power laws. We empirically show that powers laws are more suitable than Gaussian law and stable laws. The estimated VaR is validated by several backtests and compared to other conventional models results on a basis of 56 stock market assets. In the second part, we assume that stock prices are modeled by exponentials of a Lévy process. First, we develop a numerical method to compute the cumulative VaR and CVaR. This problem is solved by using the formalization of Rockafellar and Uryasev, which we numerically evaluate by Fourier inversion techniques. Secondly, we are interested in minimizing the hedging risk of European options under a budget constraint on the initial capital. By measuring this risk by CVaR, we establish an equivalence between this problem and a problem of Neyman-Pearson type, for which we propose a numerical approximation based on the constraint relaxation

Σκοπός της διδακτορικής διατριβής είναι η ανάπτυξη κατάλληλων μεθόδων ψηφιακής επεξεργασίας εικόνας και αναγνώρισης προτύπων με τις οποίες θα προσδιορίζονται βιομετρικές και διαγνωστικές παράμετροι μέσω της αλληλεπίδρασης φωτονίων στο ορατό και υπέρυθρο φάσμα. Πιο συγκεκριμένα επιλύεται ένα αντίστροφο πρόβλημα σκέδασης ΗΜ ακτινοβολίας από ένα ανθρώπινο, υγιές και απαραμόρφωτο ερυθρό αιμοσφαίριο. Παρουσιάζονται μέθοδοι εκτίμησης και αναγνώρισης των γεωμετρικών χαρακτηριστικών απαραμόρφωτων υγιών ερυθρών αιμοσφαιρίων με χρήση εικόνων που προσομοιώνουν φαινόμενα σκέδασης ηλεκτρομαγνητικής ακτινοβολίας που διέρχεται από προσανατολισμένα ερυθρά αιμοσφαίρια. Η διαδικασία της ανάκτησης της πληροφορίας περιλαμβάνει, εξαγωγή χαρακτηριστικών με χρήση δισδιάστατων μετασχηματισμών, κανονικοποίηση των χαρακτηριστικών και την χρήση νευρωνικών δικτύων για την εκτίμηση των γεωμετρικών ιδιοτήτων του ερυθροκυττάρου. Παράλληλα σχεδιάστηκε και αξιολογήθηκε σύστημα αναγνώρισης των γεωμετρικών χαρακτηριστικών των ερυθρών αιμοσφαιρίων. Οι εικόνες σκέδασης δημιουργήθηκαν προσομοιώνοντας το πρόβλημα εμπρόσθιας σκέδασης ενός επίπεδου ηλεκτρομαγνητικού (ΗΜ) κύματος, χρησιμοποιώντας την μέθοδο των συνοριακών στοιχείων, λαμβάνοντας υπόψη τόσο την αξονοσυμμετρική γεωμετρία του ερυθροκυττάρου όσο και τις μη αξονοσυμμετρικές οριακές συνθήκες του προβλήματος. Η επίλυση του εν λόγω προβλήματος πραγματοποιήθηκε στα 632.8 nm και εν συνεχεία επεκτάθηκε σε 12 διακριτά ίσου βήματος μήκη κύματος από 432.8 nm έως 1032.8 nm. Επίσης, προτάθηκε μία νέα πειραματική διάταξη για την απόκτηση πολλαπλών εικόνων σκέδασης και την εκτίμηση των γεωμετρικών χαρακτηριστικών των ερυθρών αιμοσφαιρίων, αποτελούμενη από μία πολυχρωματική πηγή φωτός (Led) και πολλαπλά χρωματικά φίλτρα. Επίσης κατασκευάστηκε μέθοδος επίλυσης του σημαντικού προβλήματος εύρεσης της περιεκτικότητας του διαλύματος σε ερυθρά αιμοσφαίρια διαφορετικών μεγεθών στην περίπτωση απόκτησης πολλαπλών εικόνων σκέδασης από διαφορετικές φωτοδιόδους και πολλαπλά χρωματικά φίλτρα. Στα πειράματα αξιολόγησης της μεθόδου που προτείνεται με εικόνες προσομοίωσης δείχνεται ότι είναι ικανή η εύρεση της αναλογίας των ερυθρών αιμοσφαιρίων με πολύ μεγάλη ακρίβεια ακόμα και στη περίπτωση όπου στις εικόνες έχει προστεθεί λευκός κανονικός θόρυβος. Η βασική μεθοδολογία που παρουσιάζεται στην παρούσα δια-τριβή μπορεί να χρησιμοποιηθεί για την αναγνώριση παθολογικών αιμοσφαιρίων ή να χρησιμοποιηθεί στην αναγνώριση μικροσωματιδίων σε υγρά ή αέρια. / The aim of this PhD thesis is the development of digital image processing and pattern recognition methods to estimate biometric and diagnostic parameters using scattering phenomena in the visible and infrared spectrum. More concretely, several reverse scattering problems of EM radiation from a human, healthy and undistorted Red Blood Cell (RBC) is solved. Methods of estimation and recognition of geometrical characteristics of healthy and undistorted RBCs using simulating images are presented. The information retrieval process includes, features extraction using two-dimensional integral transforms, features normalization, and Neural Networks for estimation of three major RBC geometrical proper-ties. Using the same features set, a recognition system of the geometric characteristics of RBCs was developed and evaluated. The scattering images were created simulating the forward scattering problem of a plane electromagnetic wave using the Boundary Element Method, taking into account both axisymmetric geometry of the scatterer and the non-axisymmetric boundary conditions of the problem. Initially, the problem is solved at 632.8 nm and consequently the same problem was solved at 12 different wavelengths, from 432.8 to 1032.8 nm equally spaced. Also, a new device for acquisition of scattering images from RBCs-flow, consisting of a multi-color light source (Led) was proposed, for RBC size estimation and recognition. Finally, a system for the estimation of different RBCs concentration was developed when scattering images acquired using multiple scattering images acquired from multiple Leds and color filters. The system was evaluated using additive white regular noise.

Ce mémoire est consacré à des résultats d'analyse harmonique réelle dans des cadres géométriques discrets (graphes) ou continus (groupes de Lie).Soit $\Gamma$ un graphe (ensemble de sommets et d'arêtes) muni d'un laplacien discret $\Delta=I-P$, où $P$ est un opérateur de Markov.Sous des hypothèses géométriques convenables sur $\Gamma$, nous montrons la continuité $L^p$ de fonctionnelles de Littlewood-Paley fractionnaires. Nous introduisons des espaces de Hardy $H^1$ de fonctions et de $1$-formes différentielles sur $\Gamma$, dont nous donnons plusieurs caractérisations, en supposant seulement la propriété de doublement pour le volume des boules de $\Gamma$. Nous en déduisons la continuité de la transformée de Riesz sur $H^1$. En supposant de plus des estimations supérieures ponctuelles (gaussiennes ou sous-gaussiennes) sur les itérées du noyau de l'opérateur $P$, nous obtenons aussi la continuité de la transformée de Riesz sur $L^p$ pour $1<p<2$.Nous considérons également l'espace de Besov $B^{p,q}_\alpha(G)$ sur un groupe de Lie unimodulaire $G$ muni d'un sous-laplacien $\Delta$. En utilisant des estimations du noyau de la chaleur associé à $\Delta$, nous donnons plusieurs caractérisations des espaces de Besov, et montrons une propriété d'algèbre pour $B^{p,q}_\alpha(G) \cap L^\infty(G)$, pour $\alpha>0$, $1\leq p\leq+\infty$ et $1\leq q\leq +\infty$. Les résultats sont valables en croissance polynomiale ou exponentielle du volume des boules. / This thesis is devoted to results in real harmonic analysis in discrete (graphs) or continuous (Lie groups) geometric contexts.Let $\Gamma$ be a graph (a set of vertices and edges) equipped with a discrete laplacian $\Delta=I-P$, where $P$ is a Markov operator.Under suitable geometric assumptions on $\Gamma$, we show the $L^p$ boundedness of fractional Littlewood-Paley functionals. We introduce $H^1$ Hardy spaces of functions and of $1$-differential forms on $\Gamma$, giving several characterizations of these spaces, only assuming the doubling property for the volumes of balls in $\Gamma$. As a consequence, we derive the $H^1$ boundedness of the Riesz transform. Assuming furthermore pointwise upper bounds for the kernel (Gaussian of subgaussian upper bounds) on the iterates of the kernel of $P$, we also establish the $L^p$ boundedness of the Riesz transform for $1<p<2$.We also consider the Besov space $B^{p,q}_\alpha(G)$ on a unimodular Lie group $G$ equipped with a sublaplacian $\Delta$.Using estimates of the heat kernel associated with $\Delta$, we give several characterizations of Besov spaces, and show an algebra property for $B^{p,q}_\alpha(G) \cap L^\infty(G)$ for $\alpha>0$, $1\leq p\leq+\infty$ and $1\leq q\leq +\infty$.These results hold for polynomial as well as for exponential volume growth of balls.

Cognitive radio is a technology that aims to maximize the current usage of the licensed frequency spectrum. Cognitive radio aims to provide services for license-exempt users by making use of dynamic spectrum access (DSA) and opportunistic spectrum sharing strategies (OSS). Cognitive radios are defined as intelligent wireless devices capable of adapting their communication parameters in order to operate within underutilized bands while avoiding causing interference to licensed users. An underused band of frequencies in a specific location or time is known as a spectrum hole. Therefore, in order to locate spectrum holes, reliable spectrum sensing algorithms are crucial to facilitate the evolution of cognitive radio networks. Since a large and growing body of literature has mainly focused into the conventional time domain (TD) energy detector, throughout this thesis the problem of spectrum sensing is investigated within the context of a frequency domain (FD) approach. The purpose of this study is to investigate detection based on methods of nonparametric power spectrum estimation. The considered methods are the periodogram, Bartlett's method, Welch overlapped segments averaging (WOSA) and the Multitaper estimator (MTE). Another major motivation is that the MTE is strongly recommended for the application of cognitive radios. This study aims to derive the detector performance measures for each case. Another aim is to investigate and highlight the main differences between the TD and the FD approaches. The performance is addressed for independent and identically distributed (i.i.d.) Rayleigh channels and the general Rician and Nakagami fading channels. For each of the investigated detectors, the analytical models are obtained by studying the characteristics of the Hermitian quadratic form representation of the decision statistic and the matrix of the Hermitian form is identified. The results of the study have revealed the high accuracy of the derived mathematical models. Moreover, it is found that the TD detector differs from the FD detector in a number of aspects. One principal and generalized conclusion is that all the investigated FD methods provide a reduced probability of false alarm when compared with the TD detector. Also, for the case of periodogram, the probability of sensing errors is independent of the length of observations, whereas in time domain the probability of false alarm is increased when the sample size increases. The probability of false alarm is further reduced when diversity reception is employed. Furthermore, compared to the periodogram, both Bartlett method and Welch method provide better performance in terms of lower probability of false alarm but an increased probability of detection for a given probability of false alarm. Also, the performance of both Bartlett's method and WOSA is sensitive to the number of segments, whereas WOSA is also sensitive to the overlapping factor. Finally, the performance of the MTE is dependent on the number of employed discrete prolate spheroidal (Slepian) sequences, and the MTE outperforms the periodogram, Bartlett's method and WOSA, as it provides the minimal probability of false alarm.