Sharif Digital Repository

Representation learning refers to mapping the input data to another space, usually with lower dimensions than the input space. This task can be helpful in improving the performance of methods in downstream tasks, compression, and improving sample generation in generative models. Representation learning is a problem connected to information theory, and information theory's concepts and quantities are used widely in representation learning models. Besides, the representation learning problem is closely related to latent variable generative models. These models usually learn useful representations in their process of training, implicitly or explicitly. So, the usage of latent variable... 

In this research, we focus on r-gather and (r; ϵ)-gather clustering. In the r-gather clustering, the input points are in metric space and must be clustered such that each cluster has at least r points and the objective is to minimize the radius of clustering. (r; ϵ)-gather clustering is a kind of r-gather clustering such that at most nϵ points can be unclustered. MapReduce model is one of the most used parallel models to process huge data and processes the input data in some machine simultaneously in parallel.In this research, we give a lower bound for the approximation factor of r-gather clustering in MapReduce model. This lower bound works in MapReduce model even an optimal algorithm... 

One of the attractive fields of applied quantum mechanics in recent two-three decades is the field of quantum computing. Up to now different substrates have been proposed for a quantum computer. One of them is cavity quantum electrodynamics in which some quantum systems with finite energy states like atoms interact with quantized Bosonic modes like photons inside a cavity. In this dissertation we study a particular structure in this substrate. This structure consists of some quantum dots inside coupled cavities. Since we would like to build these cavities in a photonic crystal slab, we first introduce two new methods for analysis of this type of crystals. These methods are much faster than... 

A perturbed lattice is a point process π={x+Y_x ∶x ∈Z^d} where the lattice points in Z^d are perturbed by i.i.d . random variables {Y_x }_(x∈Z^d ). A random point process π is said to be rigid if π∩B_1 (0) , the number of points in a ball , can be exactly determined given π∩B_1^c (0) , the points outside the ball . The process π is called deletion tolerant if removing one point of π yields a process with distribution indistinguishable from that of π . Suppose that Y_x~N_d (0,σ^2 I) are Gaussian vectors with d independent components of variance σ^2 . Holroyd and Soo showed that in dimensions d = 1 , 2 the resulting Gaussian perturbed lattice π is rigid and deletion... 

In this thesis we focus on the extraction of resonance modes in photonic crystal resonators. This work could be divided in two different parts: in the first part we apply the Galerkin’s method effectively to the two and three dimensional structures, in the second part that constitutes the main part of this thesis we derive transmission line models for these structures. Fist we derive transmission line models for resonators based on the point defect and line defect in two-dimensional photonic crystals. Then we generalize this model to the three-dimensional photonic crystals. Finally we apply the same approach to the coupled resonators and analyze the coupled resonator optical waveguide. In... 

Reducing noise, vibration and damage to the vehicle's passenger compartment was always a problem that has been investigatedin many researches. Here engine mounts as connecting members between engine and chassis play a big role. Because both of engine and road vibration put on it. Many studies have been done to optimize the engine mounts. As a result, many of hydraulic engine mounts with different variety of system control. But a few researches did about optimization of location and orientation of engine mounts. Therefore this project is to provide a process to optimize the location and orientation of engine mounts. The optimization process is First the dynamic equations of dynamic system are... 

Arising from the intersection of two modern ideas in logic and mathematics, namely Type Theory - specifically Martin-Löf’s intuitionistic type theory, and Homotopy Theory, Homotopy Type Theory has introduced a novel formalism that formalizes every mathematical object - including constructions, definitions, and proofs - in a specific and fundamentally different way from other interpretive frameworks (such as set theory), bringing forth new results - both philosophically and mathematically. The first goal of this research is to understand the meaning of Homotopy Type Theory as a foundation for mathematics through exploring this new formalism. The second goal of this research is to understand... 

One of the crucial matters in the area of Supply Chain Management is the ability of a supply chain to act and react under different circumstances. A helpful tool to understand the supply chain is simulation modeling. With the help of simulation modeling, we can provide the opportunity for the agents in a model to perform based on the defined environment.In the current research, a complete literature review is performed on the topics of supply chain planning and various distribution models and algorithms. With the focus on the vaccine as a critical item, we propose a model to distribute vaccines based on the degree of agents, and we realize that vaccine distribution, while facing huge demand... 

The detection and on-site measurement of vanillylmandelic acid (VMA), homovanillic acid (HVA), and dopamine (DA) as key biomarkers for a wide range of neurological disorders, including neuroblastoma, is of significant importance. To date, several colorimetric sensors have been introduced with mechanisms based on nanoparticle aggregation or their coating with silver. However, these mechanisms have drawbacks such as sensitivity to environmental factors and probe toxicity. Therefore, there is a high demand for a robust and non-toxic colorimetric sensor that utilizes a novel approach for the effective monitoring of these biomarkers. In this study, a single-component multicolor probe was designed... 

In this paper, we introduce a novel decision making strategy on how to assign markets to a multi-item newsvendor’s problem. We present a new formulation method based on the integration of news-vendor problem and dynamic programming approach alongside an efficient solution method. Suppose there are n distinct products and corresponding time intervals for selling them in different markets. These products will be worthless (perishable) at the end of each interval. Our proposed framework represents a trade-off between costs associated with staying in a market for further periods and costs of relocating the business in a new market. The objective is to maximize the total profit of our decisions... 

Nowadays, with the increasing number of polyethylene terephthalate wastes, the issue of its recycling has become very important. Among the problems of polyethylene terephthalate recycling are its loss of crystallinity and mechanical properties. Recycled polyethylene terephthalate does not have the properties of new polyethylene terephthalate and using its mixture with other materials is an effective way to remove its waste from nature and return it to the production cycle. The aim of this study is to produce a mixture of recycled polyethylene terephthalate with polycarbonate and glass fibers with mechanical properties such as good impact strength, which ultimately leads to the production of... 

In the current digital era, the large number of mobile developers and android applications has led to intense competition. Users can easily access many android applications to meet their needs. This abundance of available software makes it difficult for developers to attract and retain users, as they can easily switch from one application to another. This switch can happen if the current application does not meet the user’s needs, has issues, or if a better alternative is available. Therefore, developers must focus on keeping their users satisfied. To ensure user satisfaction, developers need to address user needs effectively. This includes fixing reported issues, adding new features, and... 

First, we peruse the intraction between a quantized light and a two level atom which has been described by Janes-Cummings-Paul Hamiltonian. By solving Heisenberg equations in Fourier space and describing electric field by a generalized-transverse Green function, we obtain spectral density for a quantum dot which is in the strong coupling to a slab photonic crystal cavity. Afterward, by solving Shrouding equations precisely we demonstrate when quantum dot is in a very strong coupling to cavity, rotate wave approximation is not reliable anymore. It means that if coupling constant gets comparable to cavity mode frequency then the prevalent approach to solve this Hamiltonian will not be correct.... 

In this project, we were intended to study the ultra-strong coupling in optical waveguides. Hence, we analyze the interaction of an electromagnetic wave with a quantum well embedded in a dielectric slab waveguide. First, we designed a QW with and alloys, which the energy of its electron-heavy holes transition is . By exploiting the envelope function approximation, we derived the wavefunction of electrons and holes, their eigen-energies, and the dipole moment of electon-holes. For finding the wavefunction of holes and their eigen-energies, we used the Luttinger Hamiltonian. Next, we calculated the electrical susceptibility of a three level quantum system (as a model for QW), by using... 

Cavity Quantum Electro-Dynamics (CQED) in Weak, Strong and Ultra-Strong coupling Regimes are studied. A MATLAB m-file is written which is able to solve any arbitrary CQED configuration. This program demands input data such as number of Quantum Dots, number of energy levels of each Quantum Dot, energies of each energy level of Quantum Dots, Number of cavity modes, eign-frequency of each cavity mode, coupling constant, dipole strength of each allowed transition of Quantum Dots and initial state of system from user and begins to solve the Schrodinger equation for annihilation and atomic ladder operators. In addition, coefficients of each possible ket will be calculated. Since, any approximation... 

Thin Walled Beams are widely used in engineering applications with the minimum weight design criteria, ranging from civil to aerospace and many other industrial fields. The weight reduction of the beam leads to importance of the dynamic behavior of the structure. Frequently used thin walled beams have low torsional stiffness and their torsional deformations may be of such magnitudes that it is not adequate to treat the angles of cross section rotation as small. When the vibration amplitudes are moderate or large, the geometric nonlinearity must be included and some new phenomena which do not exist in linear torsional dynamic come into play. Unfortunately, the equations of motion of nonlinear...