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Data-driven Control of Complex Systems

,
M.Sc. Thesis
Sharif University of Technology
;
Rahimi Tabar, Mohammad Reza
(Supervisor)
Abstract

In this thesis, we first briefly review the basic concepts of stochastic processes. After reviewing and studying the dynamic equation that can explain a stochastic process, we show how one can find on a data-driven basis, the first-, second- and higher-order interactions between different subunits of a complex system by disentangling the dynamics of multivariate time series into stochastic and deterministic parts. Our data-driven approach is to detect different degrees of interactions obtained using conditional moments of Kramers-Moyal coefficients from unconditioned correlation functions and statistical moments of multivariate N-dimensional multivariate time series. Finally, we study the...

#### A Special Stokes’s Theorem For Some Incomplete Riemannian Manifolds

, M.Sc. Thesis Sharif University of Technology ; Bahraini, Alireza (Supervisor)
Abstract

Let (M; g) be a Riemannian manifold. Using classical Stokes’ theorem one can show that the equality (dω; η)L2 = (ω; δη)L2 holds for smooth forms ! and η with compact supports, where δ is the formal adjoint of d . There are some examples of Riemannian manifolds for which the above equality does not hold for general forms ! and η i:e: smooth square-integrable forms such taht d! and δη are also squareintegrable. In the case that the above equality holds for such general forms on a Riemannian manifold (M; g) , we say that the L2 - Stokes theorem holds for (M; g) . In 1952, Gaffney showed that the L2 - Stokes theorem holds for complete Riemannian manifolds. But at that time, there was no powerful...

#### A High Capacity Image Steganography in Wavelet Transform Domain

, M.Sc. Thesis Sharif University of Technology ; Ghaemmaghami, Shahrokh (Supervisor)
Abstract

Recent developments of internet technology and digital media have led to the rapid growth of the steganography systems. Steganography is the art and science of concealing a secret message in a cover without leaving a perceptible or detectable trace of the message. Therefore, steganography methods, capable of embedding the largest possible amount of data with least distortion to the cover media, are highly demanding. The LSB steganography is a primary and simple method with high embedding capacity, where higher robustness is achieved if it is applied to the cover signal in the transform domain. However, regardless of the embedding domain, an essential robustness issue with the LSB...

#### A New Immunization Algorithm Based on Spectral Properties for Complex Networks

, M.Sc. Thesis Sharif University of Technology ; Khansari, Mohammd (Supervisor)
Abstract

Vaccination is one of the ways of disease control and prevention, which not only protect individuals against the disease, but also reduce the disease spread rate. Mass vaccination of individuals is not always possible due to the high cost and limitation of immunization resources. Therefore, researchers are always seeking solutions to find the persons that their immunization may have a greater impact in reduction of disease spread rate. The advent of network epidemic models and the possibility of removal the secured nodes in those models, showed that this problem is equivalent to finding a limited set of individuals that their removal will eliminate or minimize the number of people at risk of...

#### A Prevention Strategy Against Rumor Spreading in Complex Networks

, M.Sc. Thesis Sharif University of Technology ; Khansari, Mohammad (Supervisor)
Abstract

Complex networks have recently become a very noticeable subject because of their remarkable theory on real networks such as rumor spreading. This thesis contributes to a prevention strategy which uses a maximal clique algorithm to find overlapping communities and also uses inverse targeting immunization strategy to immune these communities. By the using maximal clique algorithm combined with inverse targeting strategy we have achieved that the TIK method (targeted immunization using k-clique percolation) obtains 10% of better immunization than HD (highest degree) method which is one of the best methods in targeted immunization strategies. The TIK also demonstrates that rumor spreading is...

#### Control of Complex Networks Dynamics by a Minimum Energy Approach

, M.Sc. Thesis Sharif University of Technology ; Rahimi Tabar, Mohammad Reza (Supervisor)
Abstract

Control of complex networks is the main topic in this study. In this thesis, we consider the methods to steer the dynamics of a network from an initial state to the desired final state. To achieve this goal, one needs to inject appropriate control signals from some of the network nodes, known as driver nodes. We consider the quadratic sum of control signals as a cost function, to control the dynamics of the network. By minimising the cost function, we obtain the control signals as well as driver nodes for a linear time-invariant system. As an example, we provide the results of an energy minimization strategy to control the second order Kuramoto and Rössler dynamics in Erdos-Renyi and...

#### Immobilized Manganese-porphyrin and Molybdenum-Schiff Base Complexes on Functionalized Magnetic Nanoparticles as Efficient Recyclable Nanocatalysts in Hydrocarbon and Sulfide Oxidation Reactions

, Ph.D. Dissertation Sharif University of Technology ; Bagherzadeh, Mojtaba (Supervisor)
Abstract

In this thesis, functionalized Fe3O4 nanoparticles have been utilized as a support for immobilization of homogeneous catalysts. The catalytic activity of the supported heterogeneous nanocatalysts was investigated in hydrocarbon and sulfide oxidation reactions. In the first part of this research, imidazole functionalized Fe3O4 nanoparticles (Fe3O4@SiO2-Im) were used as a support to anchor manganese porphyrin complex, [MnT(4-OMeP)P]OAc; via axial ligation. Catalytic application of the immobilized manganese porphyrin was studied in oxidation of alkenes and sulfides. To find suitable reaction conditions, the effect of different parameters such as solvent and temperature on immobilization process...

#### Community Detection in Very Large Networks

, M.Sc. Thesis Sharif University of Technology ; Beigy, Hamid (Supervisor)
Abstract

Nowadays Systems in different fields of research like computer science, biology, social networks, information networks, and economics are modeled as graphs. The graphs which model real world systems have very different topological characteristics than those of classic networks. One of the prominent characteristics of these networks, is that its not practical to describe a general model for their structure and behavior. As a consequence of this complexity in modeling and structure, these networks are called complex networks. One of the most important observations in complex networks is the presence of communities, it means that in such networks one can separate vertices in disjoint sets, such...

#### Discovering Communities in Complex Networks by Distributed Edge Label Propagation Algorithm

, M.Sc. Thesis Sharif University of Technology ; Hematyar, Ali Mohammad Afshin (Supervisor) ; Kavousi, Kaveh (Supervisor)
Abstract

Network methods have had profound influence in many domains and fields in the past decade. Community structure is a very important property of complex networks, but the precise definition of a community remains an unresolved problem and Community detection in complex networks has recently attracted wide attention in several research areas such as social networks, communication networks, and biological systems. Complex network studies grow by the scientific community, thanks to the increasing accessibility of real-world network data. The emphasis of use analysis on the network algorithms and community structure is one of the most important problems in the field of complex network. Many...

#### Complexity Reduction in AoA Estimation with root-MUSIC

, M.Sc. Thesis Sharif University of Technology ; Bastani, Mohammad Hassan (Supervisor) ; Karbasi, Mohammad (Co-Supervisor)
Abstract

Localization of radio sources has various applications in civil and military communications. Some of important localization methods consist of Angle of Arrival (AoA) estimation of the illuminated signals from the interested sources. Between various Direction Finding (DF) methods, subspace based methods are of special importance, because of their high resolution and accuracy. And from beginning of invention, because of new challenges, have been focus of numerous researches. In this thesis, first we explain the most important subspace based DF methods called MUSIC and root-MUSIC. Then a novel modification for root-MUSIC is introduced. In our new method the computational complexity of...

#### Canards in Complex Oscillatory Systems

, M.Sc. Thesis Sharif University of Technology ; Razvan, Mohammad Reza (Supervisor)
Abstract

Canard, first observed in Van der Pol oscillations, is a typical phenomenon in oscillatory systems. Canard is also observed in many oscillatory systems such as electrical circuits and neurons. In many fields of science and engineering there are complex oscillations that exhibit canard for certain values of parameters. These three dimensional systems exhibit complex oscillatory behavior never observed in two dimensional dynamics. Some of these systems are chaotic for certain parameter values. It seems than in oscillatory systems canards can make complex behavior. Several methods such as the singular perturbation theory have been used to study this complexity. In this project, we study canard...

#### The Completeness in Statistical Mechanics

, M.Sc. Thesis Sharif University of Technology ; Karimipour, Vahid (Supervisor)
Abstract

Ising model. It means that the partition function of each lattice model is equal to the partition function of 2D Ising model. This completeness is proved by using concepts and techniques from quantum information theory and is based on the universality of cluster states. We have now proved this important result, by using independent and general concepts and methods which are accessible to a wide audience of researchers across many disciplines. Furthermore, our method has the advantage of eing algorithmic in nature so that, by following a set of simple graphical transformations, one is able to transform any discrete lattice model to an Ising model defined on a (polynomially) larger 2D...

#### Axiomatic Design Science: Application in reducing Design Complexities of Special Structures

, Ph.D. Dissertation Sharif University of Technology ; Abedian, Ali (Supervisor) ; Malaek, Mohammad Bagher (Supervisor)
Abstract

This research aims to study fundamentals of design as a science for possible use in special structures. Special structures are referred to those structures that designers’ knowledge for which are insufficient. Designs of such structures are complex in the sense that we lack all necessary elements of design matrix; as well as proper steps to reach the unknowns. Introducing appropriate design strategy for such structures; we show how a design could be developed without specific needs for trial and errors. In this work, various design methodologies and especially “Axiomatic Design” have been examined. In addition, functional requirement and associated design parameters for structural design are...

#### Graph Reductions and its Application in Parallel Gene Assembly

, M.Sc. Thesis Sharif University of Technology ; Mahmoodian, Ebadollah (Supervisor)
Abstract

In the process of gene assembling, the molecular structure of a DNA chain, can be modeled by a signed graph. After that by means of a composition of three reduction rules: gnr, gpr and gdr, that is called reduction strategy, this graph is reduced to a null graph. If the composition of any ordering of rules in a reduction strategy such as S, is applicable on a signed graph G, then we say that S can be applied in parallel to G and the set S is said to be a parallel step for reduction of that graph. Also we define the least number of parallel steps in reduction of a graph, to be the parallel complexity of that graph, and denote it C(G). In this thesis, a collection of particular signed graphs,...

#### Multi-agent based Blockchain Simulation Framework

, M.Sc. Thesis Sharif University of Technology ; Tefagh, Mojtaba (Supervisor)
Abstract

A multi-agent system is a system consisting of several intelligent agents. In fact, a multi-agent system is a system that includes a large number of agents that communicate with each other through message transmission in a network structure. Multi-agent systems can solve problems that are difficult or impossible for a single agent or an integrated system to solve. Blockchain is an example of these multi-agent systems that has many use cases in different fields for example cryptocurrencies . A blockchain is a growing ledger consisting of records called blocks. In this thesis, we want to provide tools for the simulation of this multi-agent system so that we can model the issues surrounding...

#### Theoretical Prediction of Free-Energy for Complex Macromolecules Self-Assembly

, M.Sc. Thesis Sharif University of Technology ; Tafazzoli, Mohsen (Supervisor) ; Ejtehadi, Mohammad Reza (Supervisor)
Abstract

These days, self-assembly is one of the most significant phenomena in chemistry and biology. Although There are some Experiments and Simulations which help us to understand self-assembly much more than before, their mechanism is poorly understood. As a result, Calculating Free-energy landscape could be a great development in this area.We use the Flat-histogram monte Carlo algorithm to calculate the density of states of a complex system. In this way, there is a comparison between the exact density of states of Ising Model and the same quantities that are obtained from Flat histogram Method. After that, there would be a combination of statistical thermodynamics and Graph theory toward drawing...

#### Forecasting Science Hotspots Based on Keywords Network

, M.Sc. Thesis Sharif University of Technology ; Hajsadeghi, Khosrow (Supervisor) ; Khosravi, Kaveh (Supervisor)
Abstract

When the keywords in academic articles are collected and accumulated to achieve a certain amount, they will display a network property. This property can help us to get the hotspot graph of science by using the keywords network, which is directly related to the subject of the paper. Also by analyzing this network, it is possible to forecast the future science hotspots.By analyzing keywords network from complex networks point of view, we are able to predict the future hotspots based on current trends, previous growth patterns that happened or with the power of different centrality measures like eigenvector etc. As an example, when a new keyword appears in a paper for the first time, a complex...

#### Finding Influential Nodes in Complex Networks

, M.Sc. Thesis Sharif University of Technology ; Jalili, Mahdi (Supervisor)
Abstract

The modern science of networks helps us to have a better understanding of complex systems. Networked systems can be found everywhere and many systems can be represented by a complex network. A networked structure consists of a number of nodes and links connecting to them. Networks’ ability in information propagation is one of their amazing features that have attracted lots of scholars to work on. It has potential applications in many fields ranging from marketing to biology, epidemiology and sociology. Information propagation studies how information such as computer viruses, contagion, rumor, or new product’s interest propagates over a network. Percolation theory and various epidemic models...

#### Efficient Implementation of Elliptic Curve Scalar Multiplication without Division and Inversion Operations

, M.Sc. Thesis Sharif University of Technology ; Bayat-Sarmadi, Siavash (Supervisor)
Abstract

Elliptic curve cryptography (ECC) has received attention because it can achieve a security level similar to other asymmetric methods while using a key with smaller length. Although ECC is more efficient compared to other asymmetric methods, fast computation of ECC is always desirable. In this thesis,a fixed-base comb point multiplication method has been modified to perform regular point multiplication. Additionally, two low-complexity and lowlatency architectures for the modified point multiplication algorithm has been proposed. In order to achieve these architectures, a low-latency pipelined digit-level field multiplier for all national institute of standards and technology (NIST)...

#### Efficient Implementation of Elliptic Curve Cryptography on Curve-25519

, M.Sc. Thesis Sharif University of Technology ; Bayat Sarmadi, Siavash (Supervisor)
Abstract

Elliptic curve cryptography (ECC) has received attention because it can achieve a security level similar to other asymmetric methods while using a key with smaller length. Although ECC is more efficient compared to other asymmetric methods, fast computation of ECC is always desirable. In this thesis, a fixed-base comb point multiplication method has been modified to perform regular point multiplication. Additionally, two low-complexity and lowlatency architectures for the modified point multiplication algorithm has been proposed. In order to achieve these architectures, a low-latency pipelined digit-level field multiplier for all national institute of standards and technology (NIST)...