Quocientes simples dos torneios de Douglas

Orientador: Jose Carlos de Souza KiihlDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação CientificaResumo: Não informado.Abstract: Not informed.MestradoMestre em Matemátic

A NEW METHODOLOGY FOR STOCHASTIC SIMULATION OF DAILY CLIMATIC DATA PRESERVING THE INTERANNUAL VARIABILITY

In this work we propose a new methodology to reproduce, by means of simulations, the interannual variability of climatic variables which included only the minimum air temperature. To evaluate the performance of the proposed method, it was maked a comparison with other two weather generators (i.e., PGECLIMA_R and LARS-WG). Moreover, it was utilized the historical series of thirty years of five meteorological stations of the state of Parana - Brazil to generate ten sets of thirty years for each model, which were confronted with the respective historical series. The performance of the proposed model as well as weather generators was evaluated by applying tests of central tendency, variability and distribution. Furthermore, was utilized the statistical measures RMSE, MBE and Willmott agreement index (d). In the stations investigated, the proposed methodology reduced the total error and eliminated the negative bias of interannual variability. In only four (of 600) generated sequences the interannual variability differs significantly from the observed one. The series generated by PGECLIMA_R and LARS-WG presented rejection rate of 99% in the variability test. In this case, the bias was ten times greater and the RMSE was twice times greater than the proposed methodology. The d index was always greater than 0.98 for the five locations in the proposed methodology and around 0.83 in other models. Based on these results, the new methodology provides a relevant contribution concerning the interannual variability of climatic variables

Entanglement-assisted Quantum Codes from Algebraic Geometry Codes

Quantum error correcting codes play the role of suppressing noise and decoherence in quantum systems by introducing redundancy. Some strategies can be used to improve the parameters of these codes. For example, entanglement can provide a way for quantum error correcting codes to achieve higher rates than the one obtained via the traditional stabilizer formalism. Such codes are called entanglement-assisted quantum (QUENTA) codes. In this paper, we use algebraic geometry codes to construct several families of QUENTA codes via the Euclidean and the Hermitian construction. Two of the families created have maximal entanglement and have quantum Singleton defect equal to zero or one. Comparing the other families with the codes with the respective quantum Gilbert-Varshamov bound, we show that our codes have a rate that surpasses that bound. At the end, asymptotically good towers of linear complementary dual codes are used to obtain asymptotically good families of maximal entanglement QUENTA codes. Furthermore, a simple comparison with the quantum Gilbert-Varshamov bound demonstrates that using our construction it is possible to create an asymptotically family of QUENTA codes that exceeds this bound.Comment: Some results in this paper were presented at the 2019 IEEE International Symposium on Information Theor

Algebraic and Geometric Characterizations Related to the Quantization Problem of the C2,8C_{2,8} Channel

In this paper, we consider the steps to be followed in the analysis and interpretation of the quantization problem related to the $C_{2,8}$ channel, where the Fuchsian differential equations, the generators of the Fuchsian groups, and the tessellations associated with the cases $g=2$ and $g=3$, related to the hyperbolic case, are determined. In order to obtain these results, it is necessary to determine the genus $g$ of each surface on which this channel may be embedded. After that, the procedure is to determine the algebraic structure (Fuchsian group generators) associated with the fundamental region of each surface. To achieve this goal, an associated linear second-order Fuchsian differential equation whose linearly independent solutions provide the generators of this Fuchsian group is devised. In addition, the tessellations associated with each analyzed case are identified. These structures are identified in four situations, divided into two cases $(g=2$ and $g=3)$, obtaining, therefore, both algebraic and geometric characterizations associated with quantizing the $C_{2,8}$ channel.Comment: 31 pages, 9 figure

Quantum error correction: symmetric, asymmetric, synchronizable, and convolutional codes

This text presents an algebraic approach to the construction of several important families of quantum codes derived from classical codes by applying the well-known Calderbank-Shor-Steane (CSS) construction, the Hermitian, and the Steane’s enlargement construction to certain classes of classical codes. These quantum codes have good parameters and have been introduced recently in the literature. In addition, the book presents families of asymmetric quantum codes with good parameters and provides a detailed description of the procedures adopted to construct families of asymmetric quantum convolutional codes. Featuring accessible language and clear explanations, the book is suitable for use in advanced undergraduate and graduate courses as well as for self-guided study and reference. It provides an expert introduction to algebraic techniques of code construction and, because all of the constructions are performed algebraically, it equips the reader to construct families of codes, rather than only codes with specific parameters. The text offers an abundance of worked examples, exercises, and open-ended problems to motivate the reader to further investigate this rich area of inquiry. End-of-chapter summaries and a glossary of key terms allow for easy review and reference

Construction methods of CSS quantum codes and relationships between quantum codes and matroids

Orientadores: Reginaldo Palazzo Junior, Carlile Campos LavorTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de ComputaçãoResumo: Como principais contribuições desta tese, apresentamos novos métodos de construção que geram novas famílias de códigos quânticos CSS. As construções são baseadas em códigos cíclicos (clássicos) BCH, Reed-Solomon, Reed-Muller, Resíduos quadráticos e também nos códigos derivados do produto tensorial de dois códigos Reed-Solomon. Os principais códigos quânticos construídos neste trabalho, em termos de parâmetros, são os derivados dos códigos BCH clássicos. Além disso, estudamos as condições necessárias para analisar as situações nas quais os códigos cíclicos quânticos (clássicos) são códigos MDS (do inglês, Maximum- Distance-Separable codes). Apresentamos, também, novas conexões entre a teoria de matróides e a teoria dos códigos quânticos CSS, que acreditamos serem as primeiras conexões entre tais teorias. Mais especificamente, demonstramos que a função enumeradora de pesos de um código quântico CSS é uma avaliação do polinômio de Tutte da soma direta dos matróides originados a partir dos códigos clássicos utilizados na construção CSS.Abstract: This thesis proposes, as the main contributions, constructions method of new families of quantum CSS codes. These constructions are based on classical cyclic codes of the types BCH, Reed-Solomon, Reed-Muller, Quadratic Residue and also are based on product codes of classical Reed-Solomon codes. The main family of quantum codes constructed in this work, i. e., quantum codes having better parameters, are the ones derived from classical BCH codes. Moreover, we present some new conditions in which quantum CSS cyclic codes are quantumMDS codes. In addition, we provide the elements to connect matroid theory and quantum coding theory. More specifically, we show that the weight enumerator of a CSS quantum code is equivalent to evaluating the Tutte polynomial of the direct sum of the matroid associated to the classical codes used in the CSS construction.DoutoradoTelecomunicações e TelemáticaDoutor em Engenharia Elétric