Xi-Cheng Lou ... [et al.]. / Bibliography: leaf 14. / "October, 1983." / Air Force Office of Scientific Research Contract AFOSR-82-0258 Natural Sciences and Engineering Research Council of Canada Grant A-1240

First published in the Bulletin of the American Mathematical Society in Vol.79, 1973, published by the American Mathematical Society

by John L. Wyatt, Jr., William M. Siebert, Han-Ngee Tan. / "October, 1982." / Bibliography: p. 16-17. / National Science Foundation Grant No. ECS 800 6878

Το παρών έγγραφο παρουσιάζει μεθόδους για την τρισδιάστατη αναδημιουργία μιας άκαμπτης σκηνής ή αντικειμένου από δυο εικόνες. Δυο εικόνες μιας σκηνής σχετίζονται με την επιπολική γεωμετρία, η οποία μπορεί να περιγραφεί από μια 3x3 μήτρα η οποία καλείται θεμελιώδης μήτρα. Αρχικά, περιγράφεται ένας αλγόριθμος για την εύρεση αντιστοιχιών σημείων στις δυο εικόνες και στη συνέχεια μέθοδοι για την εκτίμηση της θεμελιώδους μήτρας από τις αντιστοιχίες αυτές. Μια προβολική αναδημιουργία της σκηνής λαμβάνεται από τη θεμελιώδη μήτρα, η οποία στην συνέχεια μπορεί να αναβαθμιστεί σε μια συσχετισμένη και τέλος σε μια μετρική αναδημιουργία χρησιμοποιώντας πρόσθετες πληροφορίες από την σκηνή. Επιπλέον, παρουσιάζεται μια εναλλακτική προσέγγιση, στην οποία εφαρμόζουμε μια μέθοδο αυτοβαθμονόμησης των καμερών από τις οποίες λήφθησαν οι εικόνες χωρίς τη χρήση ενός ειδικού αντικειμένου βαθμονόμησης και χωρίς καμία υπόθεση όσον αφορά τις παραμέτρους τους. Έπειτα, λαμβάνεται μια μετρική αναδημιουργία, η οποία στις περισότερες εφαρμογές είναι το ζητούμενο, μέσω της ουσιώδους μήτρας που είναι η αντίστοιχη της θεμελιώδους στην περίπτωση όπου οι εσωτερικές παράμετροι των καμερών είναι γνωστές. Τέλος, περιγράφονται διάφορες μέθοδοι με τις οποίες μπορούμε να υπολογίσουμε τη δομή της σκηνής, που αποτελεί το τελικό στάδιο της αναδημιουργίας. Σημειώνουμε ότι μεγαλύτερη έμφαση έχει δοθεί σε μεθόδους οι οποίες είναι ανθεκτικές στο θόρυβο, δεδομένης της παρουσίας του κατά τη λήψη των εικόνων, ώστε η λαμβανόμενη αναδημιουργία να είναι αξιόπιστη και ικανοποιητικής ακρίβειας. / This paper describes methods for the 3d reconstruction of a scene from two images. The epipolic geometry of two images can be described by a 3x3 matric, called the funtamental matrix. Firstly, an algorithm is described that finds corresponding points in thw two images and then thiw corresponding points are used for the estimation of the funtamemtal matrix. A prolective reconstruction of a scene is obtained from the funtamental matrix. This reconstruction will then be upgraided to an affine one, and finally to a metric, using additional information from the scene. Finally, we describe a number of methods for the triangulation of the scene. We denote that because of the noise in the data, we have emphasise at robust methods

In this thesis I will deal with the comparison of Plato´s vision of the ideal state presented in his work Constitution to negative utopias in the 20th century. I will seek common invariants occuring in all presented works by using method of structural analysis formulated by Claude Lévi-Strauss. The subjects of my analysis are books Constitution, We, Brave New World, 1984 and movies Metropolis, Matrix and Equilibrium. In the end I will present my hypothesis that there is another invariant fact that all negative utopias are based on raising the economic character of a man in order to maximize effect of his work. This is done by suppression and destruction of John Dewey´s concept of an experience.

We choose a generator G of the derived category of coherent sheaves on a smooth curve X of genus g which corresponds to a choice of g distinguished points P1, . . . , Pg on X. We compute the Hochschild cohomology of the algebra B = Ext (G,G) in certain internal degrees relevant to extending the associative algebra structure on B to an A1-structure, which demonstrates that A1-structures on B are finitely determined for curves of arbitrary genus. When the curve is taken over C and g = 1, we amend an explicit A1-structure on B computed by Polishchuk so that the higher products m6 and m8 become Hochschild cocycles. We use the cohomology classes of m6 and m8 to recover the j-invariant of the curve. When g 2, we use Massey products in Db(X) to show that in the A1-structure on B, m3 is homotopic to 0 if and only if X is hyperelliptic and P1, . . . , Pg are chosen to be Weierstrass points. iv

Orientador: Marcos Benevuto Jardim / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-06T14:41:30Z (GMT). No. of bitstreams: 1 Mendes_RicardoAugustoEmmanuel_M.pdf: 1229319 bytes, checksum: 7d65aa46096004844b3768b2c49bbd0a (MD5) Previous issue date: 2006 / Resumot: A presente tese está dividida em duas partes. Na primeira parte apresentamos as principais idéias e ferramentas da Teoria Geométrica dos lnvariantes, que tem como objetivo definir precisamente e resolver o seguinte problema: Em que circunstâncias é possível dar uma estrutura de variedade algébrica ao quociente de uma variedade algébrica pela ação de um grupo (também algébrico)? Um dos resultados mais importantes diz que é possível construir um quociente se nos restringirmos a um aberto denso (dos chamados pontos semiestáveis) da variedade original. E o principal motivo pelo qual esse é um bom resultado é que há um critério numérico (de Hilbert-Mumford) que nos permite verificar se um dado ponto é ou não (semi- )estável. A Teoria Geométrica dos lnvariantes tem aplicações amplas em muitas áreas, principalmente nos problemas de moduli. A segunda parte desta tese trata justamente de uma tal aplicação: a construção e estudo dos espaços de moduli de representações de quivers. Quivers são nada mais que grafos orientados, e uma representação consiste em associar a cada vértice um espaço vetorial e a cada flecha um mapa linear. Este assunto é interessante tanto por ser uma generalização direta de problemas clássicos de álgebra linear quanto pela ligação com a teoria de módulos sobre álgebras associativas de dimensão finita sobre um corpo / Abstract: This thesis is divided into two parts. ln the first part we present the main ideas and tools of Geometric lnvariant Theory, which is concerned with the following problem: ls it possible to give an algebraic structure to the quotient of an algebraic variety by the action of an algebraic group? Qne of the most important results says that an algebraic quotient exists if we restrict the space to a dense open subset of the original variety (the so-called semi-stable points). The main reason why this is a good result is that there is a numerical criterion (due to Hilbert and Mumford) to decide whether a given point is (semi- )stable. Geometric lnvariant Theory has applications to many areas, especially to moduli problems. The second part of this thesis shows one such application: we construct the moduli space of representations of a quiver. Quivers are just directed graphs, and a representation consists of associating to each vertex a vector space and to each arrow a linear map between the spaces associated to the initial and final vertices of that arrow. There are two reasons why this is an interesting subject: it is a natural generalization of classical linear algebra problems; and it is connected to the study of modules over a finite dimensional algebra over a field / Mestrado / Algebra / Mestre em Matemática

This thesis examines several problems related to singly-constrained Monotropic Network Flow Problems. In the first part, a linear time algorithm that reduces the solution of a monotropic network flow problem with an additional linear equality constraint to the solution of lower dimensional subproblems is presented. Of the subproblems, at most one is a singly-constrained monotropic network flow problem while the others are unconstrained. If none of the subproblems is constrained, the algorithm provides a linear-time transformation of constrained to unconstrained monotropic network flow problems. Extensions to nonlinear and inequality constraints are given. In the second part the qualitative theory of sensitivity analysis for Unconstrained Minimum-Cost Flow Problems presented by Granot and Veinott [GV85] is extended to Minimum-Cost Flow Problems with one additional linear constraint. The departure from the unconstrained network structure is shown to have a profound effect on computational issues. Two natural extensions of the "less-dependent-on" partial ordering of the arcs given in [GV85] are presented. One is decidable in linear time while the other yields more information but is NP-complete in general. The Ripple Theorem gives upper bounds on the absolute value of optimal-flow variations as a function of variations in the problem parameter. Moreover, it shows how changes may "ripple down" throughout the network, decreasing in magnitude as one gets "further away" from the arc whose parameter initiated the change. The Theory of Substitutes and Complements presents necessary and sufficient conditions for optimal-flow changes to consistently have the same (or the opposite) sign in two given arcs. The complexity of determining Substitutes and Complements is shown to be NP-complete in general. However, for all intractable problems, families of cases arise from easily recognizable graph structures and can be computed in linear time. The Monotonicity Theory links the changes in the value of the parameters to the change in the optimal arc-flows. Bounds on the rates of changes are discussed. We further provide a number of practical situations where our theory may apply. We discuss some Multi-Period Multi-Product Inventory-Production models that can be formulated as nonlinear parametric network flow problems with one additional linear constraint. We then apply our theory to help decision makers understand qualitatively how to respond to changes in the environment such as machine breakdown, strike or variations in inventory carrying costs without additional computation. In a second example, we show how a Cash-Flow Management model can be formulated as a nonlinear parametric network flow problem with one additional linear constraint. The theory is then recommended as a method by which a decision maker could understand qualitatively how to respond to changes in the environment such as variations in interest rates, taxes or asset prices without any additional computation. / Business, Sauder School of / Graduate

No description available.

Safety concerns have been keeping autonomous vehicles off the roads for decades, although the main drivers for introducing some autonomy are to increase safety, reduce congestion, and greenhouse gas emissions. Safety is a vast topic that includes the safety of the system alone, known as string stability, and the safety of the system on public roads. This thesis provides experimental validation of the string stability of the Assume-Guarantee approach. This approach suggests that each agent models the interactions with neighbors as bounded disturbances while simultaneously self-imposing symmetric magnitude bounds. Two main controllers were tested in an indoor lab set-up: decentralized platooning and decentralized cooperative adaptive cruise controllers. First, we tested three versions of the platooning controller whose objective is to maintain a constant spacing. They differ in the assumptions and guarantees. We observed a robust performance with relaxed bounds and some violations as the bounds become tighter and tighter. Second, we modified and transformed the platoon model into cooperative adaptive cruise control (CACC). Unlike the platoon controller, the cooperative adaptive cruise controller keeps the time gap constant. Two experiments were conducted at different velocities to evaluate the limitation of the controller. The results show a stable and smooth performance.