Sharif Digital Repository

This dissertation is organized into three chapters. The first chapter presents the necessary concepts and theorems. The second chapter addresses the primary objectives of the study. The third chapter is devoted to the proof and analysis of the convergence theorem for the attention matrix to low-rank Boolean matrices. The objective of this thesis is to investigate the mathematical model of the selfattention mechanism in deep learning, which is examined through the lens of optimal transport theory. It includes two theorems concerning clustering and the convergence of solutions to the differential equation describing the self-attention mechanism.
 

A major medical revolution that is helping us overcome some of the worst diseases, including cancer, is angiogenesis, which is based on the processes our bodies use to develop blood vessels. Most human cancers have acquired six essential capabilities: self-sufficiency in growth signals, insensitivity to growth-inhibitory signals, programmed cell death escape, unlimited replication potential, persistent angiogenesis, and tissue invasion that can induce metastasis. In other words, the defense mechanism that prevents any of these acquired capabilities must be neutralized before the cells become malignant and invasive tumors. In fact, tumors in the non-vascular growth stage can only grow up to... 

Recently complex networks, have been widely used as a model to study the behavior of human brain. By affecting different parts the brain, Neuronal disorders change the structure of functional brain networks. Investigating these changes using different graph theory metrics can be a useful methodology for human brain analysis in health and disease. Alzheimer's disease (AD) is a neural disease causing impairment in different brain activities including memory and cognition.The aim of this study is to construct the functional brain network of 17 AD patients and 17 healthy control subjects at resting state condition and analyzing them using the theory of complex networks in order to achieve a... 

The concept of entanglement exists in the common area of the quantum optics and quantum information. Quantum optics is the best tools for investigating of this quantum informational phenomenon experimentally. One of the instruments that let us observes experimentally macroscopy entangeled state is Fabry-Perot Cavity. Striking of photons with the mirror of cavity transfer effective mommentom to it, and oscilating of mirror creates new modes: stocks and anti-stocks modes. Studing quantum state of these modes shows the entangling between photon and phonon (oscilating of mirror) modes. We assume that light beam enters the cavity from a semi-transparent mirror. So cavity is the system with... 

Surface phenomena and dynamic interfacial properties plays a significant role in multiphase gas-liquid & liquid-liquid processes applied in different industrial applications. However, current laboratory equipment and represented methods for dynamic and unsteady state condition caused by motivation of interface of two phases (like rising bubble), in purpose of qualitative investigation of interphase properties are not satisfying enough. Also, common modeling methods are represented with lots of modified assumptions which are not validated properly with experimental results. In current thesis, with development of laboratory tools and applying the “rising bubble method” for investigating the... 

Given the growing advantage of exploiting renewable energy resources over fossil fuels and using distributed generation systems, microgrids seem to be the best solution for reaching the energy-efficient world of the future. Hybrid microgrids are the best options among all other types of microgrids because they make it possible to use AC and DC sources and loads together and at the same time. Since connecting AC and DC sections of a hybrid microgrid leads to the interaction between them, proper control of interlinking converter(s) is crucial for the reliable and stable operation of the entire microgrid. In this study, small signal model of a hybrid AC/DC microgrid consisting of static and... 

The present study has been performed for better understanding about the dynamic behavior of fluid interfaces in presence of surfactants, nanoparticles and their interactions in gas-liquid dispersion systems. One of the main purposes of this work is to investigate the influence of surface modified nanoparticles on the dynamic behavior of gas-liquid interfaces. For this purpose, the rising bubble experiment was used as one of the most conventional procedures. Local velocities of bubbles rising in nanoparticle solutions were determined experimentally. Influences of silica nanoparticles which were modified via three approaches were investigated in these experiments. Heat treatment was applied to... 

The Reliability of substation structures with consideration of earthquake uncertainties is one of the most important subjects in structural analysis in recent years. In this project we first introduce IEEE-693-2005, which is the most effective and comprehensive seismic design code for electronic substations. Also in second chapter the rudimentary aspects of Reliability Theory and methods for evaluating the reliability of substation structures is introduced. Then with modeling the most common and most important electronic substation devices in Iran, with consideration of all seismic parameters and their uncertainties, the reliability of these structures evaluated. In this project for... 

This research deals with the problem of scheduling independent preemptive jobs on identical parallel machines, to minimize the total completion time (makespan). The transportation of an interrupted job from a machine to another machine requires considering a constant transportation delay i.e., Pm|prmp(delay)| Cmax. This delay is called transportation delay. We propose a Mixed Integer Linear Programming formulation for the research problem in case of two machines i.e., P2|prmp(delay)| Cmax. Since the research problem is shown to be NP-hard, a particle swarm optimization (PSO) algorithm is applied to solve the problem approximately. Based on the frequency of using local search procedure, three... 

Recently various speaker adaptation methods in HMM-based speech synthesis are proposed. The importance of adaptation techniques is that we can design a system in which speech is generated with high quality and target speaker characteristics through limited adaptation data sets.
In this research, we focus on adaptation based on clustering and develop a new and novel method using eigenvoices in order to adapt a new speaker. We employ this approach for the first time in HSMM-based speech synthesis systems and its goal is to reduce the parameters and adaptation data of the system. In our proposed method, first some speaker dependent models are trained. For each model we combine the... 

Today, computer simulations are employed prevalently by researchers to understand biological processes. The tendency to use computational methods has been increased recently due to the high costs and errors of experimental methods. Integrins are membrane proteins that mechanically attach cells to the extra cellular matrix (ECM) and derive some behaviors such as cell migration. Moreover, integrins have biochemical functions. They transduce environment signals and trigger chemical pathways. As a result, integrins regulate cell shape, motility, etc. The investigation of integrin behavior in a real environment is very difficult due to the presence of many other proteins that interfere with the... 

Surface phenomena is one of the fundamental branches of science that has many applications in industries related to multiphase processes. One of the most important issues of this knowledge is inter-phase transport phenomena in contacting gas - liquid and liquid – liquid systems. Multiphase systems generally include dispersions such that in many cases are associated with the relative motion between the continuous and dispersed phase. One of the most widely used inter-phase flow systems is dispersion of gas bubbles in the bulk of liquid. The overall efficiency of these systems is often determined by the characteristics of the gas phase. In order to understand the dynamic behavior of such... 

Signal transmission of information on noiseless and lossy channels is an important issue in data transmission. Using the amplifier in the transmission channels is a good solution to help send information on longer channels. In classical communication, information can be coded in the amplitude or phase of the field and an amplifier is responsible for amplifying these parameters. If we consider the conditions ideal and ignore electrical noises, Classical mechanics does not impose any restrictions on the amplification of arbitrary classical signals. Instead, in quantum telecommunications the information encoded on the quadrature of the electromagnetic field are mounted on quantum states, such... 

This study investigated the relationships between team identification and attendance intention in Iranian football matches, specifically examining the impact of constraints on this relationship. The research focused on Esteghlal Football Club, one of Iran's most popular teams, which faces a paradox of having a large fan base (35-40 million supporters) but relatively low stadium attendance rates (below 50% capacity). The study employed a mixed online sampling method (convenience and snowball) with 182 Esteghlal fans who had attended at least one stadium match. Data was collected using three validated questionnaires: team identification (18 items, 6 dimensions), attendance intention (4 items,...