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A Feasible Method for Optimization with Orthogonality Constraints
, M.Sc. Thesis Sharif University of Technology ; Mahdavi Amiri, Nezameddin (Supervisor)
Abstract
Minimizing problems with either orthogonal or spherical constraints has a great number of applications in combinatorial optimization, polynomial optimization,eigenvalue problem, estimation to the nearest correlation between matrices of low rank, etc. Solving this kind of problem is hard, because feasible spaces for constraints are non-convex, and solving them is very costly as well. For confronting with this issue, The Cayley transform is used for keeping constraints,and, based on this technique, a smooth curve algorithm with low flop is compared with some algorithms based on is projections and geodesics . Efficiency of the algorithm, recently in introduced the literature, is proved on a...
Sutures, Taut Manifolds and the Topology of 3-Manifolds
, M.Sc. Thesis Sharif University of Technology ; Esfahani Zadeh, Mostafa (Supervisor)
Abstract
In this essay we focus on the question of whether a 3-manifold (possibly with bound- ary) like M supports a codimension-1 transversely oriented foliation like F , such that F is transverse to ∂M and does not have Reeb components. If such foliation exists, then ∂M is necessarily a (possibly
empty) union of tori and (based on the works of Novikov, Reeb and Rosenberg) M is either S2 × S1(with F being the prod- uct foliation) or M is irreducible. In a paper by David Gabai, which we discuss, the sufficiency of these conditions is proved in case of non-trivial second homology group.Furthermore, from the works of Thurston it is concluded that compact leaves of such foliation are norm minimizing...
empty) union of tori and (based on the works of Novikov, Reeb and Rosenberg) M is either S2 × S1(with F being the prod- uct foliation) or M is irreducible. In a paper by David Gabai, which we discuss, the sufficiency of these conditions is proved in case of non-trivial second homology group.Furthermore, from the works of Thurston it is concluded that compact leaves of such foliation are norm minimizing...
Recognition of Human Activities by Using Machine Learning Methods
, M.Sc. Thesis Sharif University of Technology ; Rabiee, Hamid Reza (Supervisor)
Abstract
In this research, we have used machine learning methods to approach the problem of human activity recognition. As the process of labeling the data in this problem is so costly and time consuming, and regarding the copious available unlabeled data, semi supervised methods have a high performance in this problem. In recent years, graph based methods have became very populaer among semi supervised learning methods. However, constructing a graph on the data which presents their structure in a proper manner has remained a main challenge in these methods. One of the causes of this problem is the existance of the shortcut edges. In this report, we will first introduce a method to solve the problem...
Online Semi-supervised Learning and its Application in Image Classification
, M.Sc. Thesis Sharif University of Technology ; Rabiee, Hamid Reza (Supervisor)
Abstract
Image classification, i.e. the task of assigning an image to a class chosen from a predefined set of classes, has addressed in this thesis. At first the classifier is divided into two major sub partitions, feature extraction and classifier. Then we show that by using local feature extraction techniques such as BOW the classification accuracy will improve. In addition, using unlabeled data is argued as the fact to deal with high nonlinear structure of features. Recently, many SSL methods have been developed based on the manifold assumption in a batch mode. However, when data arrive sequentially and in large quantities, both computation and storage limitations become a bottleneck. So in large...
Improving Graph Construction for Semi-supervised Learning in Computer Vision Applications
, M.Sc. Thesis Sharif University of Technology ; Rabiee, Hamid Reza (Supervisor)
Abstract
Semi-supervised Learning (SSL) is an extremely useful approach in many applications where unlabeled data can be easily obtained. Graph based methods are among the most studied branches in SSL. Since neighborhood graph is a key component in these methods, we focus on methods of graph construction in this project. Graph construction methods based on Euclidean distance have the common problem of creating shortcut edges. Shortcut edges refer to the edges which connect two nearby points that are far apart on the manifold. Specifically, we show both in theory and practice that using geodesic distance for selecting and weighting edges results in more appropriate neighborhood graphs. We propose an...
Adaptation for Evolving Domains
, M.Sc. Thesis Sharif University of Technology ; Soleymani Baghshah, Mahdieh (Supervisor)
Abstract
Until now many domain adaptation methods have been proposed. A major limitation of almost all of these methods is their assumption that all test data belong to a single stationary target distribution and a large amount of unlabeled data is available for modeling this target distribution. In fact, in many real world applications, such as classifying scene image with gradually changing lighting and spam email identification, data arrives sequentially and the data distribution is continuously evolving. In this thesis, we tackle the problem of adaptation to a continuously evolving target domain that has been recently introduced and propose the Evolving Domain Adaptation (EDA) method to classify...
Some New Approaches to Rigidity Problems in Riemannian Geometry: Lie Groupoids, Poisson Manifolds and Von Neumann Algebras
, Ph.D. Dissertation Sharif University of Technology ; Fanai, Hamid Reza (Supervisor)
Abstract
In this thesis, we study a rigidity problem for a 2-step nilmanifold such as Γ by some information about its geodesic flows, where is a simply connected 2-step nilpotent Lie group with a left invariant metric, and Γ is a discrete cocompact subgroup of . For the solution to this problem, first, we consider an algebraic aspect of it; since isometry groups of simply connected Riemannian manifolds can be characterized in a purely algebraic way, i.e., normalizers. Also, as we will show, proper and smooth actions of Lie groups and closed subgroups of isometries for smooth Riemannian structures can be regarded as the same topic. Then, in a generalized setting, when passing from the case of...
Seiberg-Witten Invariants and Low Dimensional Topology
, M.Sc. Thesis Sharif University of Technology ; Bahraini, Alireza (Supervisor)A Gluing Construction for Calabi-Yau Metrics of Kummer Surfaces
, M.Sc. Thesis Sharif University of Technology ; Esfahanizadeh, Mostafa (Supervisor) ; Seyyed Ali, Reza (Co-Supervisor)
Abstract
let T4 = C2/ be a complex torus with induced flat Kähler metic. The quotient X = T4/Z2 (where the generator of Z2 acts by multiplication by −1) is an orbifold with 24 singularities, called a singular Kummer Surface. Locally any of the singularities are modelled on the singularity of C2/Z2. We can describe the minimal resolution X of X by resolving all of the singularities as : TCP1 ! C2/Z2.There is a well known Calabi–Yau metric on TCP1 named the Eguchi–Hanson metric, with the important property that far from the exceptional divisor −1(0) the metric is asymptotically locally Euclidean (ALE). We identify a small annulus around any singular point of X/Z2 with a large annulus over TCP1 far...
Developing a Reduced-order Model of Hysteretic Shear Building by a Modal Transformation Method based on Mathematical Expansions
, M.Sc. Thesis Sharif University of Technology ; Rahimzadeh Rofouei, Fayyaz (Supervisor)
Abstract
With the advent of virtual memory machines and parallel processing, there has been a considerable shift toward computer-aided design and nonlinear analysis of structures. But increasing the size of computer memory or increasing the number of processing units are not the only ways to achieve a satisfactory solution to a large, complex problem. Another useful method is to reduce the size of the problem so that the reduced model is small enough to be solved at an appropriate processing level, and yet the important engineering behavior of the model is preserved in the reduced problem.Reduced models as an alternative, have gained considerable attention throughout the years in order to meet the...
On the Topological Entropy of Geodesic Flows
, M.Sc. Thesis Sharif University of Technology ; Razvan, Mohammad Reza (Supervisor) ; Nassiri, Meysam (Supervisor)
Abstract
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...
Some Applications of Seiberg-Witten Theory in Symplectic Geometry
, M.Sc. Thesis Sharif University of Technology ; Esfahanizadeh, Mostafa (Supervisor)
Abstract
Incoporating Gauge theory to study 4-dimensional manifolds,initiated by works of Donaldson,leading to resolve many problems of 4-dimensional topology.after Donaldson ,Seiberg and Witten introduced a novel Gauge theory that we will introduce and study some application of this theory.at beginning, we will establish Seiberg-Witten equation on these manifolds, following that we investigate moduli space of solutions of Seiberg Witten equations and later we define Seiberg - Witten invariants on these manifolds.at f we probe some applications of Seiberg-Witten invariants in Symplectic Geometry and we will show that Seiberg-Witten invariants are non-zero for Symplectic manifolds with canonical SpinC...
Studying the Gait kinematics of Cerebral Palsy Patients Using the Uncontrolled Manifold Method
, M.Sc. Thesis Sharif University of Technology ; Farahmand, Farzam (Supervisor)
Abstract
Cerebral Palsy is the most common motor disability in childhood. It’s caused by an injury or impaired development of brain. As result, CP children have disability in motor system. All people with cerebral palsy have problem with movement. The symptoms of CP vary from person to person. Therefore, gait analysis was used to investigate those child’s problems and help therapist to find better therapy. Given that, we analyze stance phase of gait cycle of CP children. Also, we calculate and compare variability between traditional development (TD) children and CPs to find a better understanding of how central nerves system (CNS) work. Kinematic Data during walking were collected from 100 CP and TD...
K-Stabilty of Kahler Manifolds
, M.Sc. Thesis Sharif University of Technology ; Bahraini, Alireza (Supervisor)
Abstract
The Yau-Tian-Donaldson conjecture is a challenging problem in complex geometry which currently caught the attention of some birational geometers. This conjecture is about a formulation of the problem of finding the best metric over a Kahler manifold in terms of an asymptotic GIT stability condition. The first stability condition was proposed by Mumford in ICM 1962 which surprisingly just needs the vector bundle to be“more ample” among its subbundles. Another important theorem by Narasimhan and seshadri provides a connection between the slope stability and the existence constant curvature connections for the flat holomorphic vector bundles over compact Rieman surfaces. In 1983, Donaldson...
Multiview face recognition based on multilinear decomposition and pose manifold
, Article IET Image Processing ; Volume 8, Issue 5 , 2014 , Pages 300-309 ; ISSN: 17519659 ; Kasaei, S ; Sharif University of Technology
Abstract
One major challenge encountered in face recognition is how to handle the wide pose variation and in-depth rotations of head. A multiview face recognition method is proposed in this study that addresses this challenge based on multilinear decomposition approach and pose subspace. In order to preserve the pose manifold geometry among different individuals in pose subspace, a pose-biased distance measure is proposed. In addition, as one of the impediments in manifold-based methods is the lack of sufficient data, a new half-ellipsoid-based pose generation method is presented. For performance evaluation of the proposed multiview face recognition method, three different experiments are run on...
3D human pose estimation from image using couple sparse coding
, Article Machine Vision and Applications ; Vol. 25, issue. 6 , 2014 , p. 1489-1499 ; Jourabloo, A ; Gozlou, S.G ; Pedrood, B ; Manzuri-Shalmani, M.T ; Sharif University of Technology
Abstract
Recent studies have demonstrated that high-level semantics in data can be captured using sparse representation. In this paper, we propose an approach to human body pose estimation in static images based on sparse representation. Given a visual input, the objective is to estimate 3D human body pose using feature space information and geometrical information of the pose space. On the assumption that each data point and its neighbors are likely to reside on a locally linear patch of the underlying manifold, our method learns the sparse representation of the new input using both feature and pose space information and then estimates the corresponding 3D pose by a linear combination of the bases...
Manifold coarse graining for online semi-supervised learning
, Article Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 5 September 2011 through 9 September 2011 ; Volume 6911 LNAI, Issue PART 1 , September , 2011 , Pages 391-406 ; 03029743 (ISSN) ; 9783642237799 (ISBN) ; Shaban, A ; Rabiee, H. R ; Rohban, M. H ; Sharif University of Technology
2011
Abstract
When the number of labeled data is not sufficient, Semi-Supervised Learning (SSL) methods utilize unlabeled data to enhance classification. Recently, many SSL methods have been developed based on the manifold assumption in a batch mode. However, when data arrive sequentially and in large quantities, both computation and storage limitations become a bottleneck. In this paper, we present a new semi-supervised coarse graining (CG) algorithm to reduce the required number of data points for preserving the manifold structure. First, an equivalent formulation of Label Propagation (LP) is derived. Then a novel spectral view of the Harmonic Solution (HS) is proposed. Finally an algorithm to reduce...
Echocardiography frames quantification by empirical mode decomposition method
, Article 2014 21st Iranian Conference on Biomedical Engineering, ICBME 2014, 26 November 2014 through 28 November 2014 ; November , 2014 , Pages 201-205 ; 9781479974177 (ISBN) ; Behnam, H ; Fatemizadeh, E ; Sani, Z. A ; Sharif University of Technology
Institute of Electrical and Electronics Engineers Inc
2014
Abstract
In this study a new method is proposed for quantification of cardiac muscle motions in echocardiography frames based on empirical mode decomposition (EMD) and manifold learning method. EMD algorithm is able to extract intrinsic mode functions (IMF) from a signal. In the first bi-dimension intrinsic mode functions (BIMF) of echocardiography frames myocardial is shown with more details than the second BIMF and the second BIMF shows more details than the third BIMF. By using manifold learning method, quantification difference between each pair of consecutive frames in the first, second and third BIMF series (similarities between the frames were extracted). Acquired trajectories of three...
Presumed Joint-PDF modelling for turbulent stratified flames
, Article Flow, Turbulence and Combustion ; Volume 107, Issue 2 , 2021 , Pages 405-439 ; 13866184 (ISSN) ; Atayizadeh, H ; Salehi, M. M ; Sharif University of Technology
Springer Science and Business Media B.V
2021
Abstract
Turbulence–chemistry interaction models such as the conditional moment closure and various flamelet models require a presumed Probability Density Function (PDF) model of the conditioning variables. In turbulent stratified flames, a joint-PDF model for a reaction progress variable and the mixture fraction is required. The joint-PDF is often modelled by two beta functions using the first and second moments of the two conditioning variables. In this work, the performance of a joint-PDF model based on the flamelet PDF approach is compared to the double beta-PDF model. The conditional PDF of the reaction progress variable conditioned on mixture fraction is modelled with the flamelet PDF. Unlike...
Multijoint coordination during sit-to-stand task in people with non-specific chronic low back pain
, Article Biomedical Engineering - Applications, Basis and Communications ; Volume 25, Issue 1 , 2013 ; 10162372 (ISSN) ; Negahban, H ; Shaterzadeh, M. J ; Mehravar, M ; Salehi, R ; Narimani, R ; Parnianpour, M ; Sharif University of Technology
2013
Abstract
Sit-to-stand (STS) is an important functional task affected by low back pain (LBP). It requires fundamental coordination among all segments of the body to control important performance variables such as body's center of mass (CM) and head positions. This study was conducted to determine whether LBPs could coordinate their multiple joints to achieve the task stability to the same extent as healthy controls. About 11 non-specific chronic LBP and 12 healthy control subjects performed STS task at three postural difficulty levels: rigid surface - open eyes (RO), rigid surface - closed eyes (RC) and narrow surface - closed eyes (NC). Motion variability of seven body segments, CM and head positions...