Sharif Digital Repository

Reservoir simulation models are profound tools in reservoir management. Number of grid blocks in a simulation model is much less than the number of grid blocks in geological model, therefore geological model must become upscaled in order to construct simulation model with convenient dimensions. This causes loosing of some details and introduces errors due to discretization and homogenization. One method of construction of an efficient computational grid is use of adaptive mesh refinement (AMR) methods. These methods refine computational grid in regions needing further resolution. An error indicator is used for determining regions candidate for refinement or coarsening. In present study... 

Non-statistical dynamics are those dynamical systems for which a large subset of points in the phase space (positive measure subset) have non-statistical behavior, meaning that the orbit of these points does not have asymptotic distribution in the phase space. We introduce two new classes of these kinds of dynamics: non-statistical rational maps on the Reimann sphere and non-statistical Anosov-Katok maps of the annulus. We then give a general formalization of the notion of "statistical (in)stability" and show how it is connected to the existence of non-statistical dynamics in a general family of maps  

Face recognition, which is one of the most important biometrics, has always been one of the main challenges in many security issues, such as verifying the identity of customers of financial institutions and passengers at the airport, and such issues have many applications in daily life. Face recognition has always been an important issue in computer vision and pattern recognition. Currently, several methods based on deep networks have shown great results in face recognition, among which the following can be mentioned.1.The deep face was introduced by Facebook in 2014; 2.Face-net was presented by Google in 2015 ;3.VGGFace was presented by Oxford University in 2015; 4.Openface was presented by... 

For neurodegenerative diseases like Multiple Sclerosis, Alzheimer’s, or Parkinson’s disease early detection is required to slow progression and prevent disease onset. To do so, identifying early signs and symptoms of the disease as well as modifying lifestyle can play a crucial role. Nowadays, the increasing use of smart gadgets and sensors has paved the way for collecting behavioral data and therefore analyzing and extracting meaningful patterns. In this study, lifestyle and cognitive performance data have been collected via a platform called OptiMind. Previous studies have shown that the Integrated Cognitive Assessment (ICA) can identify patients with neurodegenerative disorders (such as... 

Detection text in natural images is a challenging task due to the complex backgrounds in an image. complex backgrounds, changes in ambient light, changing viewing angles, and other factors can make systems difficult to detection text. Hence text detection is always an problem. Since detection and recognizing a text in an image has many uses such as translating texts for tourists, helping the blind, etc., recognizing a text in different languages is important. In this thesis, we first examine the three methods of Reading Text in the Wild with Convolutional Neural Networks and FOTS and CRAFT. Then we prepared two Persian data sets. The first data set contains images to which Persian texts have... 

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 numerical solution of differential equations in high dimensions has always been a challenge and has been associated with various computational difficulties. These equations appear naturally in a variety of problems such as financial mathematics, control, and physics, and their optimal solution with high accuracy and speed can open new windows on new applications. Conventional methods such as Finite element and finite difference method in high dimensions lose their efficiency, which is a barrier to fast and accurate calculation of these equations. In this dissertation first, we review some theoretical and practical aspects of deep neural networks and then we try to examine the recent... 

Excitability is one of the most important characteristics of a neuron. In 1948, Hodgkin identified three different types of excitability of neurons. Excitability an all of its types can be observed in Hodgkin-Huxley model of neuronal dynamics (H-H model) as a four-dimensional system of differential equations and in at least two dimensional reductions of H-H type models. By applying the theory of dynamical systems (e.g. bifurcation theory), one can give a mathematical definition of excitability.Excitability of the neuron is equivalent to that the neuronal model is near a bifurcation through which the state of the system approaches to a stable limit cycle. In this thesis, a two-dimensional... 

Non-overlapping Cameras in multi-camera systems have become prevalent in robotics and computer vision research; therefore, it is possible to cover the wide field of view, and researches have been done for computing extrinsic parameters of cameras. These cameras do not have any overlap in their views, so obtaining the corresponding point in their images is somehow impossible. Light and shadow geometry is analogous to Structure from Motion problem. In this thesis,we study Structure from Motion problem and have tried to propose an approach for estimating extrinsic parameters of non-overlapping cameras in Multi-camera systems. We formulate the problem by using light and shadow geometry and... 

Let M be a connected, compact, Riemannian manifold. Geodesic flow is a flow on the unit tangent bundle of M . This flow can be studied in dynamics prespective. for example entropy or complexity of the geodesic flow. in this thesis we will follow methods of entropy estimation or computing for geodesic flow. we will follow the method of anthony manning and Ricardo Mañe for proving such result. Maning present two results linking the topological entropy of the geodesic flow on M. we expalin how he find exponential growth rate volume of balls in universal cover as a lower bound for topologycal entropy. another theorem , Mañe represent the equlity between exponential growth rate of avrage of... 

In this thesis, we review some models for mathematical modeling of neuronal circuits of brain and especially, the main aim of this thesis is chapter two that we review a rigorous model for cortical microcir-cuits which is called liquid state machine. The structure of this thesis is as follows, first in the introduction we give some prerequisites that are essential for understanding contents of this thesis and also, one of the first mathematical model for neural computations, attractor neural networks, has been mentioned. In chapter one, we introduce feedforward neural networks equipped with dynamical synapses. In fact in this chapter we review two experimental models for dynam-ical synapses... 

Invariant manifolds are important objects in the theory of dynamical systems. The stable manifold theorem is a very important theorem about this concept which proves the existence of stable and unstable manifolds in a wide range of dynamical systems. The importance of invariant manifolds encourages us to view their pictures. It helps us to understand their bahavior. For this purpose, at first we need to approximate the invariant manifold we want to visualize. There are several algorithms designed to approximate invariant manifolds. Those algorithms approximate a set of points on an invariant manifold and then provide an approximation of the manifold by the calculated points. Visualizing an... 

The problem of learning using high volume of data as stream, has attracted much attention recently. In this thesis, the problem is modeled and analized using Online Convex Optimization tools [1], [2]. General performance bounds are stated and clarified in this framework [8]. Using the practical experience in Online Decision Making (e.g., predicting price in Stock Market), the need for a more flexible model, which adapts to changes in problem, is presented. In this thesis, after reviewing the literature and online convex optimization framework, we will define ”Concept Drift”, which describes changes in the dynamics of the problem and the statistical tools to detect it [13], [5]. And finally,... 

Application of optimal control in cancer modeling is studied through both linear and nonlinear modeling of the dynamics in ordinary differential equations. At the outset, a fairly straight-forward analysis of a linear model in presented. Through comparably simple machinery, this seminal work published at early 2000s covers some of most important techniques previously developed. The model here is infinite- dimensional, taking different number of gene amplifications into account. Thereafter by surveying recently published papers, the literature is reviewed and different lines of progress is followed, culminating in detailed study of a specific approach which is theoretically of interest.... 

Image retrieval refers to the task of finding images related to a query image within an image set. Due to ever-increasing volumes of data, it has become increasingly necessary to find suitable and efficient methods for searching in massive databases. In this thesis, modern image retrieval techniques developed within the last 15 years have been studied, with an aim to satisfy three primary constraints of efficiency, accuracy, and low memory usage. Our focus has been on content-based retrieval; meaning that instead of using text and other information, we directly utilize image features for analysis and processing. To achieve this, we studied two established techniques, the bag-of-words model,... 

Reservoir simulation, recognition of the past and present reservoir behavior and prediction of its behavior in the future, which forms one of the most important parts of the management of a reservoir. In fact, the reservoir is like a living creature and increasing the accuracy in predicting its behavior requires a precise model. Reservoirs have high physical dimensions that are associated with high physical changes. As a result, a large number of computational cells are needed to simulate the reservoirs, which results in a very large linear equation system. The numerical solution of these systems is very time consuming. Many observed examples indicate that 80 \% of the runtime is included.... 

In this thesis we employ finite elements and conjugate gradient methods to exibit a numerical solution for governing equations of borehole stability  

In this thesis, we study a homological invariant in Knot theory, called Khovanov homology. The main property of this invariants is that it gives us the Jones polynomial, as its graded Euler characteristic. Besides, the functor (1+1) TQFT, from the category of closed one-manifolds to the category of vector spaces is employed in its construction. By making some changes to this functor and defining another functor and some other steps, the so-called Lee spectral sequence is derived which starts from Khovanov homology and converges to another homological invariant of links, called Lee-Khovanov homology. Computation of this homology is very simple. By using this spectral sequence, a numerical... 

This thesis presents an investigation of the dynamics of two coupled non-identical FitzHugh–Nagumo neurons. It is known that signal transmission in coupled neurons is not instantaneous in general, and time delay is inevitable in signal transmission for real neurons. Therefore we consider the system of two coupled neurons with delayed synaptic connection. We consider coupling strength and time delay as bifurcation parameters, and try to classify all possible dynamics which is fairly rich and we will study the excitability of the neurons. By bifurcation study of the system the coupling strength and delay-dependent stability regions are illustrated in the parameter plane, to describe typical... 

Networks of neurons produce diverse patterns of oscillations, arising from the net-work’s global properties, the propensity of individual neurons to oscillate, or a mixture of the two. Here we describe noisy limit cycles and quasi-cycles, two related mech-anisms underlying emergent oscillations in neuronal networks whose individual com- ponents, stochastic spiking neurons, do not themselves oscillate. Both mechanisms are shown to produce gamma band oscillations atthepopulation level while individualneu-rons fire at a rate much lower than the population frequency. Spike trains in a network undergoing noisy limit cycles display a preferred period which is not found in the case...