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Spectral controllability of some singular hyperbolic equations on networks
, Article Journal of Dynamical and Control Systems ; 2016 , Pages 1-22 ; 10792724 (ISSN) ; Salimi, L ; Sharif University of Technology
Springer New York LLC
2016
Abstract
The purpose of this paper is to address the question of well-posedness and spectral controllability of the wave equation perturbed by potential on networks which may contain unbounded potentials in the external edges. It has been shown before that in the absence of any potential, there exists an optimal time T∗ (which turns out to be simply twice the sum of all length of the strings of the network) that describes the spectral controllability of the system. We will show that this holds in our case too, i.e., the potentials have no effect on the value of the optimal time T∗. The proof is based on the famous Beurling-Malliavin’s Theorem on the completeness interval of real exponentials and on a...
Extracting Homography Matrix to Determine 3D Position of Soccer Players
, Ph.D. Dissertation Sharif University of Technology ; Kasaei, Shohreh (Supervisor)
Abstract
Determination of the position of an object in the 3D world is one of the most basic preprocessing steps in the field of computer vision. It is used in many practical applications such as video surveillance, human action analysis, and human-computer interaction. For this determination, calibrated cameras are usually used for which the internal and external camera parameters are already known. But, in some real-life applications, a pre-access to the camera is not possible. This thesis studies the homography matrix extraction for determination of the position of soccer players. The pan-tilt-zoom (PTZ) cameras are used. (For a stationary camera, a Homography matrix is obtained once.) To...
A semilinear PDE with free boundary
, Article Nonlinear Analysis, Theory, Methods and Applications ; Volume 151 , 2017 , Pages 145-163 ; 0362546X (ISSN) ; Shahgholian, H ; Sharif University of Technology
Elsevier Ltd
2017
Abstract
We study the semilinear problem Δu=λ+(x)(u+)q−1−λ−(x)(u−)q−1inB1, from a regularity point of view for solutions and the free boundary ∂{±u>0}. Here B1 is the unit ball, 1
General least gradient problems with obstacle
, Article Calculus of Variations and Partial Differential Equations ; Volume 58, Issue 5 , 2019 ; 09442669 (ISSN) ; Moradifam, A ; Sharif University of Technology
Springer New York LLC
2019
Abstract
We study existence, structure, uniqueness and regularity of solutions of the obstacle problem infu∈BVf(Ω)∫Ωϕ(x,Du),where BVf(Ω)={u∈BV(Rn):u≥ψinΩandu|∂Ω=f|∂Ω}, f∈W01,1(Rn), ψ is the obstacle, and ϕ(x, ξ) is a convex, continuous and homogeneous function of degree one with respect to the ξ variable. We show that every minimizer of this problem is also a minimizer of the least gradient problem infu∈Af(Ω)∫Rnϕ(x,Du),where Af(Ω)={u∈BV(Ω):u≥ψ,andu=finΩc}. Moreover, there exists a vector field T with ∇ · T≤ 0 in Ω which determines the structure of all minimizers of these two problems, and T is divergence free on { x∈ Ω : u(x) > ψ(x) } for any minimizer u. We also present uniqueness and regularity...
Geometrical Structure of Neuron Morphology
, Ph.D. Dissertation Sharif University of Technology ; Fotouhi, Morteza (Supervisor)
Abstract
The tree structure of neuron morphologies has excited neuroscientists since their discovery in the 19-th century. Many theories assign computational meaning to morphologies, but it is still hard to generate realistic looking morphologies. There are a few growth models for generating neuron morphologies that correctly reproduce some features (e.g. branching angles) of morphologies, but they tend to fall short on other features. Here we present an approach that builds a generative model by extracting a set of human-chosen features from a database of neurons by using the naïve Bayes approach. Then by starting from a neuron with a soma we use statistical sampling techniques to generate...
Spectral controllability of some singular hyperbolic equations on networks
, Article Journal of Dynamical and Control Systems ; Volume 23, Issue 3 , 2017 , Pages 459-480 ; 10792724 (ISSN) ; Salimi, L ; Sharif University of Technology
2017
Abstract
The purpose of this paper is to address the question of well-posedness and spectral controllability of the wave equation perturbed by potential on networks which may contain unbounded potentials in the external edges. It has been shown before that in the absence of any potential, there exists an optimal time T∗ (which turns out to be simply twice the sum of all length of the strings of the network) that describes the spectral controllability of the system. We will show that this holds in our case too, i.e., the potentials have no effect on the value of the optimal time T∗. The proof is based on the famous Beurling-Malliavin’s Theorem on the completeness interval of real exponentials and on a...
Deep Learning and Optimal Control
, M.Sc. Thesis Sharif University of Technology ; Fotouhi, Morteza (Supervisor)
Abstract
Our main focus in this thesis is on optimal control methods for the analysis of deep neural networks, such as the supervised learning problem. A neural network with a large number of layers can be modeled with an ordinary differential equation, whose control parameters play the role of intermediary functions in the neural network. This model gives us a more powerful tool to analyze the asymptotic behavior of the neural network. Also, in this thesis, the problems of numerical implementation of these methods will be discussed
Mathematical Modeling and Simulation of Tumor Angiogenesis
, M.Sc. Thesis Sharif University of Technology ; Fotouhi, Morteza (Supervisor)
Abstract
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...
SC-RANSAC: spatial consistency on RANSAC
, Article Multimedia Tools and Applications ; 2018 ; 13807501 (ISSN) ; Hekmatian, H ; Kashani Nezhad, M. A ; Kasaei, S ; Sharif University of Technology
Springer New York LLC
2018
Abstract
The goal of robust parameter estimation is developing a model which can properly fit to data. Parameter estimation of a geometric model, in presence of noise and error, is an important step in many image processing and computer vision applications. As the random sample consensus (RANSAC) algorithm is one of the most well-known algorithms in this field, there have been several attempts to improve its performance. In this paper, after giving a short review on existing methods, a robust and efficient method that detects the gross outliers to increase the inlier to outlier ratio in a reduced set of corresponding image points is proposed. It has a new hypothesis and verification scheme which...
SC-RANSAC: Spatial consistency on RANSAC
, Article Multimedia Tools and Applications ; Volume 78, Issue 7 , 2019 , Pages 9429-9461 ; 13807501 (ISSN) ; Hekmatian, H ; Kashani Nezhad, M. A ; Kasaei, S ; Sharif University of Technology
Springer New York LLC
2019
Abstract
The goal of robust parameter estimation is developing a model which can properly fit to data. Parameter estimation of a geometric model, in presence of noise and error, is an important step in many image processing and computer vision applications. As the random sample consensus (RANSAC) algorithm is one of the most well-known algorithms in this field, there have been several attempts to improve its performance. In this paper, after giving a short review on existing methods, a robust and efficient method that detects the gross outliers to increase the inlier to outlier ratio in a reduced set of corresponding image points is proposed. It has a new hypothesis and verification scheme which...
Travel Time Estimation for Signalized Arterials Using a Probabilistic Approach
, M.Sc. Thesis Sharif University of Technology ; Nassiri, Habibollah (Supervisor)
Abstract
Estimation of travel time in transportation engineering has always been an important issue. So far, most of travel time studies have focused on freeways and highways, and very few research have been done on travel time estimation for arterials. In this study, by using shock wave concept, a probabilistic model is developed for estimating the travel time of a signalized arterials consisting of two pre-timed signalized intersections. This model can be used in both coordinated and non-coordinated signals. In this study, travel time and traffic volume data were collected for Fatemi Ave. in Tehran, Iran. By using these data, some parameters of VISSIM simulation package were calibrated to reflect...
Cancer Models Based on Reaction-Diffusion Equations
, M.Sc. Thesis Sharif University of Technology ; Fotouhi, Morteza (Supervisor)
Abstract
The role of a mathematical model is to explain a set of experiments, and to make predictions. In setting up a mathematical model of a biological process, by a set of differential equations, it is very important to determine the numerical value of the parameters. For biological processes are typically valid only within a limited range of parameters. In the last decades, various cancer models have been developed in which the evolution of the densities of cells (abnormal, normal, or dead) and the concentrations of biochemical species are described in terms of differential equations. Some of these models use only ordinary differential equations (ODEs), ignoring the spatial effects of tumor...
, M.Sc. Thesis Sharif University of Technology ; Fotouhi Firouzabadi, Morteza (Supervisor)
Abstract
A typical problem in applied mathematics and science is to estimate the future state of a dynamical system given its current state. One approach aimed at understanding one or more aspects determining the behavior of the system is mathematical modeling. This method frequently entails formulation of a set of equations, usually a system of partial or ordinary differential equations. Model parameters are then measured from experimental data or estimated from computer simulation or other methods. Solutions to the model are then studied through mathematical analysis and numerical simulation usually for qualitative fit to the dynamical system of interest and any relative time-series data that is...
Acoustic emission-based methodology to evaluate delamination crack growth under quasi-static and fatigue loading conditions
, Article Journal of Nondestructive Evaluation ; Volume 37, Issue 1 , March , 2018 ; 01959298 (ISSN) ; Ahmadi Najafabadi, M ; Mohammadi, K ; Fotouhi, M ; Hosseini Toudeshky, H ; Mohammadi, R ; Sharif University of Technology
Springer New York LLC
2018
Abstract
The aim of this study was to investigate the applicability of acoustic emission (AE) technique to evaluate delamination crack in glass/epoxy composite laminates under quasi-static and fatigue loading. To this aim, double cantilever beam specimens were subjected to mode I quasi-static and fatigue loading conditions and the generated AE signals were recorded during the tests. By analyzing the mechanical and AE results, an analytical correlation between the AE energy with the released strain energy and the crack growth was established. It was found that there is a 3rd degree polynomial correlation between the crack growth and the cumulative AE energy. Using this correlation the delamination...
Cuckoo-PC: An evolutionary synchronization-aware placement of SDN controllers for optimizing the network performance in WSNs
, Article Sensors (Switzerland) ; Volume 20, Issue 11 , 2020 , Pages 1-19 ; Safi, M ; Zolfi, S ; Maghsoudi, M. R ; Faragardi, H. R ; Fotouhi, H ; Sharif University of Technology
MDPI AG
2020
Abstract
Due to reliability and performance considerations, employing multiple software-defined networking (SDN) controllers is known as a promising technique in Wireless Sensor Networks (WSNs). Nevertheless, employing multiple controllers increases the inter-controller synchronization overhead. Therefore, optimal placement of SDN controllers to optimize the performance of a WSN, subject to the maximum number of controllers, determined based on the synchronization overhead, is a challenging research problem. In this paper, we first formulate this research problem as an optimization problem, then to address the optimization problem, we propose the Cuckoo Placement of Controllers (Cuckoo-PC) algorithm....
Assessment of Optimal Power Flow (OPF)Uncertainty in Hybrid Wind- PV Power Systems
, M.Sc. Thesis Sharif University of Technology ; Fotouhi Firouzabad, Mahmoud (Supervisor)
Abstract
As a matter of fact, power systems are always faced with a variety of uncertainties. These uncertainties change system parameters in an unwanted manner which may deteriorate the system security and reliability. For instance, a transmission line which is designed for a certain capacity may be suffered as a result of load increment and consequently may influence the normal operation of other network elements. In recent years, as a result of environmental considerations and especially after the oil shock at 1973 which caused the the energy prices to increase unprecedentedly, the human has taken more attention to renewable energies exploitation. Theses energies have a fluctuating nature and are...
Control of Heat Equations
, Ph.D. Dissertation Sharif University of Technology ; Fotouhi Firouzabad, Morteza (Supervisor)
Abstract
The controllability problem may be formulated roughly as follows. Consider an evolution system (either described in terms of partial or ordinary differential equations) on which we are allowed to act by means of a suitable choice of the control (the right-hand side of the system, the boundary conditions, etc.). Given a time interval 0 < t < T, and initial and final states, the goal is to determine whether there exists a control driving the given initial data to the given final ones in time T. Now, consider the simplest parabolic equation, namely heat equation and suppose that one could act by appropraite controls on this system. The null controllability problem which is one of the very...
The Existence and Stability of Classical Solutions in the Neural Fields Equations
, M.Sc. Thesis Sharif University of Technology ; Fotouhi Firouzabadi, Morteza (Supervisor)
Abstract
In this thesis, first, the modeling method of neural fields is precisely presented. Then, Existence and Stability of different solutions of one dimensional neural fields like Standing Pulses, Traveling Waves and ... are investigated in three different models of neural fields. In order for proving Existence and Stability of the solutions the mathematical tools like Fourier transform and Evans function are applied. All the models which analysed in this thesis have the following Integro-Differential Equation form:
τ
∂u(x, t)
∂t
= −u(x, t) +
∫ +∞
−∞
w(x, y)f[u(y, t)]dy + I(x, t) + s(x, t)
and also in some models the parameters might be changed
τ
∂u(x, t)
∂t
= −u(x, t) +
∫ +∞
−∞
w(x, y)f[u(y, t)]dy + I(x, t) + s(x, t)
and also in some models the parameters might be changed
Projection matrix by orthogonal vanishing points
, Article Multimedia Tools and Applications ; 2016 , Pages 1-35 ; 13807501 (ISSN) ; Fouladi, S ; Kasaei, Sh ; Sharif University of Technology
Springer New York LLC
2016
Abstract
Calculation of camera projection matrix, also called camera calibration, is an essential task in many computer vision and 3D data processing applications. Calculation of projection matrix using vanishing points and vanishing lines is well suited in the literature; where the intersection of parallel lines (in 3D Euclidean space) when projected on the camera image plane (by a perspective transformation) is called vanishing point and the intersection of two vanishing points (in the image plane) is called vanishing line. The aim of this paper is to propose a new formulation for easily computing the projection matrix based on three orthogonal vanishing points. It can also be used to calculate the...
Automatic soccer field line recognition by minimum information
, Article 2015 International Symposium on Artificial Intelligence and Signal Processing, AISP 2015, 3 March 2015 through 5 March 2015 ; March , 2015 , Pages 136-142 ; 9781479988174 (ISBN) ; Bozorgpour, A ; Kasaei, S ; Sharif University of Technology
Institute of Electrical and Electronics Engineers Inc
2015
Abstract
Automatic analysis in soccer scenes is still a difficult task in the absence of soccer field information. The first and most important step in almost all analysis, is soccer field line recognition and homography extraction. The aim of this paper is introducing a novel approach for automatic detection and recognition of soccer field lines and arcs by minimal information. A simple camera model and perspective map is assumed to reduce unknown parameters. An accurate method is utilized for detecting line pixels. The side of playfield area is determined based on the orientation of lines and arcs. Based on the detected playfield area side, an initial perspective map is obtained. An optimization...