Digital options, the basic building blocks for valuing complex financial assets, they play an important role in options valuation and hedging. We survey the digital options pricing formula under diffusion processes and jump-diffusion processes. Since the existent first-touch digital options pricing formulas with jump-diffusion processes are all in their Laplace transform of the option value. To inverse the Laplace transforms is critical when doing options valuation. Therefore, we adopt a phase-type jump-diffusion model which is developed by Chen, Lee and Sheu [2007] as our main model, and use FFT inversion to get the first-touch digital option price under (2,2)-factor exponential jump-diffusion processes.

Thesis (M.S.)--Brigham Young University. Dept. of Mechanical Engineering, 2003. / Includes bibliographical references (p. 105-107).

As the demand for higher and more sophisticated security solutions has dramatically increased, a trustworthy and a more intelligent authentication technology has to takeover. That is biometric authentication. Although biometrics provides promising solutions, it is still a pattern recognition and artificial intelligence grand challenge. More importantly, biometric data in itself are vulnerable and requires comprehensive protection that ensures their security at every stage of the authentication procedure including the processing stage. Without this protection biometric authentication cannot replace traditional authentication methods. This protection however cannot be accomplished using conventional cryptographic methods due to the nature of biometric data, its usage and inherited dynamical changes. The new protection method has to transform the biometric data into a secure domain where original information cannot be reversed or retrieved. This secure domain has also to be suitable for accurate authentication performance. In addition, due to the permanence characteristic of the biometric data and the limited number of valid biometrics for each individual, the transform has to be able to generate multiple versions of the same original biometric trait. This to facilitate the replacement and the cancellation of any compromised transformed template with a newer one without compromising the security of the system. Hence the name of the transform that is best known as cancellable biometric. Two cancellable face biometric transforms have been designed, implemented and analysed in this thesis, the Polynomial and Co-occurrence Mapping (PCoM) and the Randomised Radon Signatures (RRS). The PCoM transform is based on high-order polynomial function mappings and co-occurrence matrices derived from the face images. The secure template is formed by the Hadamard product of the generated metrics. A mathematical framework of the two-dimensional Principal Component Analysis (2DPCA) recognition is established for accuracy performance evaluation and analysis. The RRS transform is based on the Radon Transform (RT) and the random projection. The Radon Signature is generated from the parametric Radon domain of the face and mixed with the random projection of the original face image. The transform relies on the extracted signatures and the Johnson-Lindenstrauss lemma for high accuracy performance. The Fisher Discriminant Analysis (FDA) is used for evaluating the accuracy performance of the transformed templates. Each of the transforms has its own security analysis besides a comprehensive security analysis for both. This comprehensive analysis is based on a conventional measure for the Exhaustive Search Attack (ESA) and a new derived measure based on the lower-bound guessing entropy for Smart Statistical Attack (SSA). This entropy measure is shown to be greater than the Shannon lower-bound of the guessing entropy for the transformed templates. This shows that the transforms provide greater security while the ESA analysis demonstrates immunity against brute force attacks. In terms of authentication performance, both transforms have either maintained or improved the accuracy of authentication. The PCoM has maintained the recognition rates for the CMU Advance Multimedia Processing Lab (AMP) and the CMU Pose, Illumination & Expression (PIE) databases at 98.35% and 90.13% respectively while improving the rate for the Olivetti Research Ltd (ORL) database to 97%. The transform has achieved a maximum recognition performance improvement of 4%. Meanwhile, the RRS transform has obtained an outstanding performance by achieving zero error rates for the ORL and PIE databases while improving the rate for the AMP by 37.50%. In addition, the transform has significantly enhanced the genuine and impostor distributions separations by 263.73%, 24.94% and 256.83% for the ORL, AMP and PIE databases while the overlap of these distributions have been completely eliminated for the ORL and PIE databases.

Οι ολοκληρωτικοί μετασχηματισμοί είναι ένα από τα πιο σημαντικά εργαλεία των μαθηματικών. Για σχεδόν πάνω από δυο αιώνες, οι ολοκληρωτικοί μετασχηματισμοί χρησιμοποιούνται επιτυχώς για την επίλυση πολλών προβλημάτων στα εφαρμοσμένα μαθηματικά, τη μαθηματική φυσική και τις επιστήμες των μηχανικών. Η βασική λογική τους είναι να μετασχηματιστεί ένα δύσκολο πρόβλημα σε ένα πιο απλό, να λυθεί και μετά, χρησιμοποιώντας τον αντίστροφο μετασχηματισμό, να βρεθεί η λύση του αρχικού προβλήματος. Οι ολοκληρωτικοί μετασχηματισμοί χρησιμοποιούνται για την επίλυση συνήθων διαφορικών εξισώσεων (Σ.Δ.Ε), διαφορικών εξισώσεων με μερικές παραγώγους (Μ.Δ.Ε), ολοκληρωτικών εξισώσεων όπως επίσης και στον υπολογισμό ολοκληρωμάτων. Στην παρούσα διπλωματική εργασία παρουσιάζουμε πέντε ολοκληρωτικούς μετασχηματισμούς: τον μετασχηματισμό Laplace, Fourier, Hankel, Hilbert και Stieltjes και αφού παρουσιάσουμε κάποια ιστορικά στοιχεία και τις ιδιότητές του για τον κάθε ένα ξεχωριστά, εν συνεχεία, δίνουμε διάφορα παραδείγματα εφαρμογής τους σε διάφορους τομείς των θετικών επιστημών, τόσο σε κλασικά προβλήματα όσο και σε προβλήματα που έχουν ‘αντληθεί’ από ερευνητικές εργασίες. / Integral transforms are one of the most significant tools at the disposal of mathematicians around the world. For almost two centuries now, integral transforms have been successfully deployed in various domains such as applied mathematics, physics and engineering. The main logic behind integral transforms is the transformation of a complicated problem into a much simpler one, the solution of the simpler version, and finally the application of the inverse transform in order to obtain the solution of the initial "complicated" one. Integral transforms are mainly used for solving ordinary differential equations (ODE), partial differential equations (PDE) and integral equations. However, they are also used in the computation of improper integrals. In the current Thesis, five major integral transforms will be presented, namely, Laplace, Fourier, Hankel, Hilbert and Stieltjes. Initially we will start by providing the historical background as well as the properties of each one of these integral transforms. We will then continue by discussing some practical examples of how these integral transforms may be applied in sciences – not just for solving widely discussed and known problems, but also for problems that have emerged from recent research studies.

Thesis (Ph. D.)--University of Washington, 2007. / Vita. Includes bibliographical references (p. 51-56).

Thesis (Ph. D.)--University of Washington, 2004. / Vita. Includes bibliographical references (p. 61-63).

Thesis (Ph. D.)--West Virginia University, 2006. / Title from document title page. Document formatted into pages; contains xiv, 85 p. : ill. Includes abstract. Includes bibliographical references (p. 83-85).

Stereo vision is a means of obtaining three-dimensional information by considering the same scene from two different positions. Stereo correspondence has long been and will continue to be the active research topic in computer vision. The requirement of dense disparity map output is great demand motivated by modern applications of stereo such as three-dimensional high-resolution object reconstruction and view synthesis, which require disparity estimates in all image regions. Stereo correspondence algorithms usually require significant computation. The challenges are computational economy, accuracy and robustness. While a large number of algorithms for stereo matching have been developed, there still leaves the space for improvement especially when a new mathematical tool such as wavelet analysis becomes mature. The aim of the thesis is to investigate the stereo matching approach using wavelet transform with a view to producing efficient and dense disparity map outputs. After the shift invariance property of various wavelet transforms is identified, the main contributions of the thesis are made in developing and evaluating two wavelet approaches (the dyadic wavelet transform and complex wavelet transform) for solving the standard correspondence problem. This comprises an analysis of the applicability of dyadic wavelet transform to disparity map computation, the definition of a waveletbased similarity measure for matching, the combination of matching results from different scales based on the detectable minimum disparity at each scale and the application of complex wavelet transform to stereo matching. The matching method using the dyadic wavelet transform is through SSD correlation comparison and is in particular detailed. A new measure using wavelet coefficients is defined for similarity comparison. The approach applying a dual tree of complex wavelet transform to stereo matching is formulated through phase information. A multiscale matching scheme is applied for both the matching methods. Imaging testing has been made with various synthesised and real image pairs. Experimental results with a variety of stereo image pairs exhibit a good agreement with ground truth data, where available, and are qualitatively similar to published results for other stereo matching approaches. Comparative results show that the dyadic wavelet transform-based matching method is superior in most cases to the other approaches considered.

Submitted by Aelson Maciera (aelsoncm@terra.com.br) on 2017-09-15T17:48:02Z No. of bitstreams: 1 DissBKLP.pdf: 732641 bytes, checksum: 8bdc1dafdeedf7c70d07335608bfe4ee (MD5) / Approved for entry into archive by Ronildo Prado (bco.producao.intelectual@gmail.com) on 2018-01-31T17:13:55Z (GMT) No. of bitstreams: 1 DissBKLP.pdf: 732641 bytes, checksum: 8bdc1dafdeedf7c70d07335608bfe4ee (MD5) / Approved for entry into archive by Ronildo Prado (bco.producao.intelectual@gmail.com) on 2018-01-31T17:14:10Z (GMT) No. of bitstreams: 1 DissBKLP.pdf: 732641 bytes, checksum: 8bdc1dafdeedf7c70d07335608bfe4ee (MD5) / Made available in DSpace on 2018-01-31T17:20:30Z (GMT). No. of bitstreams: 1 DissBKLP.pdf: 732641 bytes, checksum: 8bdc1dafdeedf7c70d07335608bfe4ee (MD5) Previous issue date: 2017-07-19 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / We study the Tjurina transforms of determinantal singularities and its properties. / Estudamos as transformadas de Tjurina de singularidades determinantais apresentada em [20], e algumas de suas propriedades.

Neste trabalho é descrito um software denominado Scanc implementado no ambiente Windows, para a identificação de formas circulares em imagens digitais do tipo BMP. Dois métodos foram implementados para esse fim: a Transformada de Hough e Template Matching. Incluídos neste software encontram-se recursos para detecção de bordas e binarização da imagem, entre outros. O software tem aplicação nas mais diversas áreas, que requeiram a identificação de formas circulares. / The present work describes a software named Scanc, developed for circular pattern identification in digital bitmap images (BMP). Scanc was developed for Microsoft Windows environment and it takes advantage of two methods: Hough Transform and Template Matching. Image tools such as border detection and binarization are also available among other resources. The software finds several applications wherever circular forms identification is requered.