Sharif Digital Repository

In this thesis, we analyze and compare switching and CPSP cryptography systems. CPSP is a dynamic system which can act as synchronized or self-synchronized stream cipher under specific conditions. To do the comparison, first we have a brief review of cryptography fundamentals like stream cipher systems, synchronized stream ciphers, and self-synchronized ones. Then, we consider chaos systems in general form and then we present their role in cryptography systems, and in continue by introducing switching cryptography systems and also CPSP cryptography systems, and analyzing their relation with self-synchronized stream ciphers, we do our statistical tests on them  

The application of biocatalysts in organic reactions refers to the use of enzymes, purified or crude, to increase the reaction rate. The usage of biocatalysts in organic reactions have many advantages, including biocompatibility, ease of separation, high yield, reusability without losing activity, high selectivity, and the use of water as the solvent. Furthermore, the carbon–carbon bond formation is one of the most important reactions in the synthesis of organic compounds, drugs, and biomolecules. Using enzymes in organic reactions can provide insightful information about the enzymes catalytic activities and paves the way for systematic investigation of their mechanisms. The enzymes... 

The design of deterministic sensing matrices is an important issue in compressive sensing in sparse signal processing. Various designs using finite field structures, combinatorics, and coding theory have been presented. The contribution of this thesis is designing many codes with large minimum distance using algebraic curves. Here, we initially design a algebraic-geometric code over a maximal curve in a Galoi field Fpm Afterwards, we map the code to the field Fp using trace map. This code has a large minimum distance. Using this code, we design a matrix with low coherence. One of the main issues in presented designs is that the number of matrix rows is considered to specific integers near... 

In recent years, the emergence of semi-supervised learning methods has broadened the scope of machine learning, especially for pattern classification. Besides obviating the need for experts to label the data, efficient use of unlabeled data causes a significant improvement in supervised learning methods in many applications. With the advent of statistical learning theory in the late 80's, and the emergence of the concept of regularization, kernel learning has always been in deep concentration. In recent years, semi-supervised kernel learning, which is a combination of the two above-mentioned viewpoints, has been considered greatly.
Large number of dimensions of the input data along with... 

Portfolio generating functions are positive twice continuously differentiable functions of the common or ranked market weights. The return on such portfolios related to the market with a stochastic differential equation that has two components: the logarithmic change in the value of the generating function, and a drift process that is of bounded variation. The goal of this study is to generalized portfolio generating functions theorem for ’ functions, in order to cover some important functions in economic such as Gini coefficients  

Cluster analysis is one of the basic tools for exploring the underlying structure of a given data set. It is being used in a wide variety of engineering and scientific disciplines. It can be broadly defined as the process of dividing a set of objects into clusters, each representing
a meaningful sub-group of data. Clustering techniques require the definition of a similarity measure between patterns. This similarity measure is not easy to specify in the absence of any prior knowledge about cluster shapes. Recently, constrained clustering has been emerged as an efficient approach for data clustering and learning the similarity measure between patterns. It has become popular because it can... 

In this thesis we study one of the applications of algebraic topology to computer science and define some tools to analyze concurrent programs. For this purpose a geometric space is corresponded to every concurrent program and a partial order is considered on this space, so every path on it corresponds to an execution of the program. Some of these paths which are dihomotop (homotop in partial ordered spaces) with each other induce the same execution of the program. By defining “Fundamental Category” in which objects are points of the space and morphisms are dihomotopy classes, the space that should be analyzed shrinks to a smaller one. By defining component category in the next step, without... 

In this thesis we study three versions of K−theory. The most well-known vesrsion is topological K−theory, a generalization of Grothendieck works on algebraic varieties to the topological setting by Atyiah and Hirzebruch. Since its birth it has been an indespensible tool in topology,differential geometry and index theory. In the early 1970s C∗−algebraic version of K−theory introduced through associating two abelian groups,K0(A)and K1(A)to a C∗−algebra like A. These functors proved to be a powerful machine, making it possible to calculate the K−theory of a great many C∗−algebras. At last,algebraic K−theory is dealig with linear algebra over a ring R by associating it, a sequence of abelian... 

In this essay, by putting in the framework of linear-quadratic optimal control (LQ),we study and solve the mean-variance portfolio selection problem. Two models will be studied in our work; in one we assume that the price process satisfies a diffusion stochastic differential equation, while in the second model, we assume it to satisfy a jump-diffusion stochastic differential equation. In both models, a formula for the efficient frontier is obtained. This essay is mainly obtained from the works of the following articles and books:
1)X.Y. Zhou and D. Li, Continuous-Time Mean-Variance Portfolio Selection:A Stochastic LQ Framework. Applied Mathematics and Optimization. 42(2000),...