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#### The spherical ensemble and uniform distribution of points on the sphere

, Article Electronic Journal of Probability ; Volume 20 , 2015 , 23, 27 pp ; 10836489 (ISSN) ; Zamani, M ; Sharif University of Technology
University of Washington
2015

Abstract

The spherical ensemble is a well-studied determinantal process with a fixed number of points on $2. The points of this process correspond to the generalized eigenvalues of two appropriately chosen random matrices, mapped to the surface of the sphere by stereographic projection. This model can be considered as a spherical analogue for other random matrix models on the unit circle and complex plane such as the circular unitary ensemble or the Ginibre ensemble, and is one of the most natural constructions of a (statistically) rotation invariant point process with repelling property on the sphere. In this paper we study the spherical ensemble and its local repelling property by investigating the...

#### Irregularities of Some Random Point Processes

, M.Sc. Thesis Sharif University of Technology ; Alishahi, Kasra (Supervisor)
Abstract

The spherical ensemble is a well-studied determinantal process with a fixed number of points on the sphere. The points of this process correspond to the generalized eigenvalues of two appropriately chosen random matrices, mapped to the surface of the sphere by stereographic projection. This model can be considered as a spherical analogue for other random matrix models on the unit circle and complex plane such as the circular unitary ensemble or the Ginibre ensemble, and is one of the most natural constructions of a (statistically) rotation invariant point process with repelling property on the sphere. In this dissertation we study the spherical ensemble and its local repelling property by...

#### Transverse Localization in Optical Waveguide Arrays

, Ph.D. Dissertation Sharif University of Technology ; Langari, Abdollah (Supervisor) ; Bahrampour, Alireza (Co-Advisor) ; Mahdavi, Mohammad (Co-Advisor)
Abstract

In recent years, a strong interplay between quantum mechanics and the physics of waveguide arrays was established based on a formal analogy between atomic and photonic lattices. The study of light evolution in photonic lattices has provided deep insights into the physics of wave function dynamics and, hence, peculiar quantum mechanical features. Arrays of evanescently coupled waveguides is a very versatile model system for discrete physics. Anderson localization and Bloch oscillations are two examples of coherent quantum transport phenomena, which have been investigated in this thesis. In the first part of this thesis, we investigate numerically the effect of long-range interaction on the...

#### Distribution of Points on the Sphere

, M.Sc. Thesis Sharif University of Technology ; Alishahi, Kasra (Supervisor) ; Shahshahani, Mehrdad (Co-Advisor) ; Kamalinejad, Ali (Co-Advisor)
Abstract

The focus of this thesis is the computation of the discrepancy for any given distribution of points on S2. The problem of the distribution of points on the sphere has a long history and Thomson’s Problem, inspired by early atomic theory dating back to 1904, was a landmark. While Thomson’s Problem is based on the Coulomb potential, the discrepancy measures the deviation of the number of points in a set from the expected one. The Polar Coordinates method was introduced in the context of Thomson’s problem. In this thesis the order of the growth of the discrepancy for this method is investigated and a modification of it is shown to lead to the best known results. In addition a new algorithm is...

#### Claims Prevention Management & Counter Claim Management in Oil Industry Projects of Iran

, M.Sc. Thesis Sharif University of Technology ; Ebrahimi, Nasrollah (Supervisor) ; Mortaheb, Mohammad Mehdi (Supervisor)
Abstract

In recent years, frequent involvements in claims have been inevitable due to unpredictable economic changes and increasing complexities in construction industry. Therefore, even appropriately made contracts are not exempted from claims. On the other hand, construction contract claims are time-consuming, expense-involving and most likely leading to unsatisfactory results. However, there may be some positive outcomes, such as time extension or compensation of damages. To launch investigationson claim management, a list of important and frequent claims in oil and gas industry projects of Iran was extracted after a succinct documents review. Further, the most important claim causes were...

#### Determinantal Processes

, M.Sc. Thesis Sharif University of Technology ; Alishahi, Kasra (Supervisor)
Abstract

Determinantal processes are a special family of stochastic processes that arise in physics (fermions), random matrices (eigenvalues), and in combinatorics (random spanning trees and non-intersecting paths). These processes have repelling property (points close to each other are chosen with low probability). Because of this repelling property, determinantal processes are approporiat for modeling some physical quantities (e.g. the position of electrons). Their probabilistic structure is described by operators on complex vector spaces and their eigenvalues. Determinantal processes have interesting properties, e.g. number of points in a region is a sum of independent Bernoulli random variables....

#### Causal Discovery and Generative Neural Networks to Identify the Functional Causal Model

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

Causal discovery is of utmost importance for agents who must plan and decide based on observations. Since mistaking correlation with causation might lead to un- wanted consequences. The gold standard to discover causal relation is to perform experiments. However, experiments are in many cases expensive, unethical or impossible to perform. In these situations, there is a need for observational causal discovery. Causal discovery in the observational data setting involves making significant assumptions on the data and on the underlying causal model. This thesis aims to alleviate some of the assumptions and tries to identify the causal relationships and causal mechanisms using generative neural...

#### Generative Adversarial Networks

, M.Sc. Thesis Sharif University of Technology ; Haji Mirsadeghi, Mir Omid (Supervisor)
Abstract

In this thesis we try to understand one of the most important subfield of deep learning, the generative adversarial networks. In this framework the goal is to reach a generator that generates samples from a target distribution. The target distribution is usually su- per high dimensional and we only have sample access to it. primarily , this distribution was used to be for set of Images (e.g. images of celebrity faces) and GANs performed well in this setting. In this framework two models work simultaneously: a generator tries to generate realistic samples from the target distribution and a discriminator or critic tries to distinguish real samples from generated (fake) samples or more...

#### Graph Generation by Deep Generative Models

, M.Sc. Thesis Sharif University of Technology ; Khedmati, Majid (Supervisor)
Abstract

Graphs are a language to describe and analyze connections and relations. Recent developments have increased graphs' applications in real-world problems such as social networks, researchers' collaborations, and chemical compounds. Now that we can extract graphs from real life, how can we model and generate graphs similar to a set of known graphs or that are very likely to exist but haven't been discovered yet? Therefore, this research will focus on the problem of graph generation. In graph generation, a set of graphs is a training dataset, and the goal of the thesis is to present an improved deep generative model to learn the training data's distribution, structure, and features.Identifying...

#### Prediction of waterflood performance using a modified capacitance-resistance model: A proxy with a time-correlated model error

, Article Journal of Petroleum Science and Engineering ; Volume 198 , March , 2020 ; Aminshahidy, B ; Bazargan, H ; Sharif University of Technology
Elsevier B. V
2020

Abstract

Capacitance-Resistive Model (CRM), as a fast yet efficient proxy model, suffers from some limitations in modeling relatively complex reservoirs. Some current improvements on this proxy made it a more powerful simulator with updating parameters over time. However, the model's intrinsic uncertainty arisen from simplifying fluid-flow modeling by some limited number of constant parameters is not addressed yet. In this study, this structural limitation of CRM has been addressed by introducing a time-correlated model error, including stochastic and non-stochastic parameters, embedded into this proxy's formulation. The error term's non-stochastic parameters have been tuned to be used in forecasting...