Doctor of Philosophy (PhD) / In this work, we investigate methods for computing explicitly with homomorphisms (and particularly endomorphisms) of Jacobian varieties of algebraic curves. Our principal tool is the theory of correspondences, in which homomorphisms of Jacobians are represented by divisors on products of curves. We give families of hyperelliptic curves of genus three, five, six, seven, ten and fifteen whose Jacobians have explicit isogenies (given in terms of correspondences) to other hyperelliptic Jacobians. We describe several families of hyperelliptic curves whose Jacobians have complex or real multiplication; we use correspondences to make the complex and real multiplication explicit, in the form of efficiently computable maps on ideal class representatives. These explicit endomorphisms may be used for efficient integer multiplication on hyperelliptic Jacobians, extending Gallant--Lambert--Vanstone fast multiplication techniques from elliptic curves to higher dimensional Jacobians. We then describe Richelot isogenies for curves of genus two; in contrast to classical treatments of these isogenies, we consider all the Richelot isogenies from a given Jacobian simultaneously. The inter-relationship of Richelot isogenies may be used to deduce information about the endomorphism ring structure of Jacobian surfaces; we conclude with a brief exploration of these techniques.

<p>This thesis looks into how one could use Hierarchal Temporal Memory (HTM) networks to generate models that could be used as trading algorithms. The thesis begins with a brief introduction to algorithmic trading and commonly used concepts when developing trading algorithms. The thesis then proceeds to explain what an HTM is and how it works. To explore whether an HTM could be used to generate models that could be used as trading algorithms, the thesis conducts a series of experiments. The goal of the experiments is to iteratively optimize the settings for an HTM and try to generate a model that when used as a trading algorithm would have more profitable trades than losing trades. The setup of the experiments is to train an HTM to predict if it is a good time to buy some shares in a security and hold them for a fixed time before selling them again. A fair amount of the models generated during the experiments was profitable on data the model have never seen before, therefore the author concludes that it is possible to train an HTM so it can be used as a profitable trading algorithm.</p>

A novel algorithm for the simplified tele-operation of mobile-manipulator systems is presented. The algorithm allows for unified, intuitive, and coordinated control of mobile manipulators, systems comprised of a robotic arm mounted on a mobile base. Unlike other approaches, the mobile-manipulator system is modeled and controlled as two separate entities rather than as a whole. The algorithm consists of thee states. In the rst state a 6-DOF (degree-of-freedom) joystick is used to freely control the manipulator's position and orientation. The second state occurs when the manipulator approaches a singular configuration, a con guration where the arm instantaneously loses a DOF of motion capability. This state causes the mobile base to proceed in such a way as to keep the end-effector moving in its last direction of motion. This is done through the use of a constrained optimization routine. The third state is triggered by the user: once the end-effector is in the desired position, the mobile base and manipulator both move with respect to one another keeping the end-effector stationary and placing the manipulator into an ideal configuration. The proposed algorithm avoids the problems of algorithmic singularities and simplifies the control approach. The algorithm has been implemented on the Jasper Mobile-Manipulator System. Test results show that the developed algorithm is effective at moving the system in an intuitive manner.

A low-energy current-mode algorithmic pipelined ADC targeted for use in distributed sensor networks is presented. The individual nodes combine sensing, computation and communications into an extremely small volume. The nodes operate with very low duty cycle due to limited energy. Ideally these sensor networks will be massive in size and dense in order to promote redundancy. In addition the networks will be collectively intelligent and adaptive. To achieve these goals, distributed sensor networks will require very small,inexpensive nodes that run for long periods of time on very little energy. One component of such network nodes is an A/D converter. An ADC acts as a crucial interface between the sensed environment and the sensor network as a whole. The work presented here focuses on moderate resolution, and moderate speed, but ultra-low-power ADCs. The 6 bit current-mode algorithmic pipelined ADC reported here consumes 8 pJ/bit samples at 0.65V supply and 130 kS/s. The current was chosen as the information carrying quantity instead of voltage as it is more favorable for low-voltage and low-power applications. The reference current chosen was 150nA. All the blocks are using transistors operating in subthreshold or weak inversion region of operation, to work in low-voltage and low current supply. The DNL and INL plots are given in simulation results section. The area of the overall ADC was 0.046 mm2 only.

This report discusses some of the uses of algorithms within number theory. Topics examined include the applications of algorithms in the study of cryptology, the Euclidean Algorithm, prime generating functions, and the connections between algorithmic number theory and high school algebra. / text

An algorithm known as the Musical Imitation and Creativity Algorithm (MICA) that composes stylistic music based on a corpus of works in a given style is presented. The corpus works are digital music scores created from the widely available MIDI format. The algorithm restricts the note placement in compositions using a Markov chain model built from discrete-time representations of the corpus pieces. New compositions are evolved using a genetic algorithm with a fitness function based on Zipf's Law properties of various musical metrics in the corpus pieces. The resulting compositions are evaluated by a panel of both musical and non-musical volunteers in a blind survey.

The field of algorithmic mechanism design is concerned with the design of computationally efficient algorithms for use when inputs are provided by rational agents, who may misreport their private values in order to strategically manipulate the algorithm for their own benefit. We revisit classic problems in this field by considering settings of incomplete information, where the players' private values are drawn from publicly-known distributions. Such Bayesian models of partial information are common in economics, but have been largely unexplored by the computer science community. In the first part of this thesis we show that, for a very broad class of single-parameter problems, any computationally efficient algorithm can be converted without loss into a mechanism that is truthful in the Bayesian sense of partial information. That is, we exhibit a transformation that generates mechanisms for which it is in each agent's best (expected) interest to refrain from strategic manipulation. The problem of constructing mechanisms for use by rational agents therefore reduces to the design of approximation algorithms without consideration of game-theoretic issues. We furthermore prove that no such general transformation is possible if we require mechanisms that are truthful in the stronger non-Bayesian sense of dominant strategies. In the second part of the thesis we study simple greedy methods for resolving complex auctions. We show that while such greedy algorithms are not truthful, they suffer very little loss in worst-case performance bounds when agents apply strategies at equilibrium, even in settings of partial information. Our analysis applies to various different equilibrium concepts, including Bayes-Nash equilibrium, regret-minimizing strategies, and asynchronous best-response dynamics. Thus, even though greedy auctions are not truthful, they may be appropriate for use as mechanisms under the goal of achieving high social efficiency at equilibrium. Moreover, we prove that no algorithm in a broad class of greedy-like methods can be used to create a deterministic truthful mechanism while retaining a non-trivial approximation to the optimal social welfare. Our overall conclusion is that while full-information models of agent rationality currently dominate the algorithmic mechanism design literature, a relaxation to settings of partial information is well-motivated and provides additional power in solving central problems in the field.

The field of algorithmic mechanism design is concerned with the design of computationally efficient algorithms for use when inputs are provided by rational agents, who may misreport their private values in order to strategically manipulate the algorithm for their own benefit. We revisit classic problems in this field by considering settings of incomplete information, where the players' private values are drawn from publicly-known distributions. Such Bayesian models of partial information are common in economics, but have been largely unexplored by the computer science community. In the first part of this thesis we show that, for a very broad class of single-parameter problems, any computationally efficient algorithm can be converted without loss into a mechanism that is truthful in the Bayesian sense of partial information. That is, we exhibit a transformation that generates mechanisms for which it is in each agent's best (expected) interest to refrain from strategic manipulation. The problem of constructing mechanisms for use by rational agents therefore reduces to the design of approximation algorithms without consideration of game-theoretic issues. We furthermore prove that no such general transformation is possible if we require mechanisms that are truthful in the stronger non-Bayesian sense of dominant strategies. In the second part of the thesis we study simple greedy methods for resolving complex auctions. We show that while such greedy algorithms are not truthful, they suffer very little loss in worst-case performance bounds when agents apply strategies at equilibrium, even in settings of partial information. Our analysis applies to various different equilibrium concepts, including Bayes-Nash equilibrium, regret-minimizing strategies, and asynchronous best-response dynamics. Thus, even though greedy auctions are not truthful, they may be appropriate for use as mechanisms under the goal of achieving high social efficiency at equilibrium. Moreover, we prove that no algorithm in a broad class of greedy-like methods can be used to create a deterministic truthful mechanism while retaining a non-trivial approximation to the optimal social welfare. Our overall conclusion is that while full-information models of agent rationality currently dominate the algorithmic mechanism design literature, a relaxation to settings of partial information is well-motivated and provides additional power in solving central problems in the field.

Doctor of Philosophy (PhD) / In this work, we investigate methods for computing explicitly with homomorphisms (and particularly endomorphisms) of Jacobian varieties of algebraic curves. Our principal tool is the theory of correspondences, in which homomorphisms of Jacobians are represented by divisors on products of curves. We give families of hyperelliptic curves of genus three, five, six, seven, ten and fifteen whose Jacobians have explicit isogenies (given in terms of correspondences) to other hyperelliptic Jacobians. We describe several families of hyperelliptic curves whose Jacobians have complex or real multiplication; we use correspondences to make the complex and real multiplication explicit, in the form of efficiently computable maps on ideal class representatives. These explicit endomorphisms may be used for efficient integer multiplication on hyperelliptic Jacobians, extending Gallant--Lambert--Vanstone fast multiplication techniques from elliptic curves to higher dimensional Jacobians. We then describe Richelot isogenies for curves of genus two; in contrast to classical treatments of these isogenies, we consider all the Richelot isogenies from a given Jacobian simultaneously. The inter-relationship of Richelot isogenies may be used to deduce information about the endomorphism ring structure of Jacobian surfaces; we conclude with a brief exploration of these techniques.

Esta dissertação tem por objetivo apresentar uma abordagem baseada em técnicas de inteligência artificial para automatizar a etapa de particionamento de modelos em simulação distribuída. Essa abordagem utiliza os conceitos da computação evolutiva para o desenvolvimento de um algoritmo genético capaz de otimizar o processo de particionamento e auxiliar a tomada de decisões na tarefa de obtenção dos processos lógicos. Objetiva-se com sua aplicação minimizar o tempo de execução da simulação distribuída, evitando que o pior tempo de execução seja utilizado. Para alcançar esse objetivo, o particionamento apresentado como solução é caracterizado pelo balanceamento de carga e pela baixa latência de comunicação entre processos. Isso é possível porque o algoritmo genético utiliza informações contidas no modelo e na arquitetura de onde a simulação será executada. Esses padrões são utilizados para obter informações sobre a comunicação entre processos, a carga de processamento por centro de serviço e a capacidade de processamento das máquinas / This dissertation presents an approach based on intelligence artificial technics to automatize the model partitioning stage in distributed simulation. This approach makes uses evolutive computing concepts to developed a genetic algorithmic that can optimize the partitioning process and help to take decisions in the task to get the logical process. The propose of this algorithm is reduce to execution time the distributed simulation and to avoid the use of the worst execution time. To reach this target, the partitioning obtained has characteristics such as load balance and the low-communication interprocess. This is possible because the genetic algorithmic uses as input information from the model and the architect where the simulation with be executed. These inputs are used to get information about the interprocess communication, processing load per service center and processing capacity in the machines