Sharif Digital Repository

Disturbance rejection is one of the most important criteria that should be considered when designing control systems. The problem has been widely investigated and studied when the parameters of disturbance signal is known. However, there are still ongoing researches in the field when the parameters of disturbance signals are uncertain and/or varying with time. In some applications the disturbance signal can be modelled by special dynamics, e.g., step type disturbances with unknown magnitude, sinusoidal disturbances with unknown magnitude and frequency, and damped sinusoidal disturbances with unknown magnitude, frequency and damping factor. In such cases, an adaptive scheme for estimating the... 

Traditional methods for data classification only make use of the labeled data. However, in most of the applications, labeling the unlabeled data is expensive, time consuming and requires expert knowledge. To overcome these problems, Semi-supervised Learning (SSL) methods have become an area of recent research that aim to effectively addressing the problem of limited labeled data.One of the recently introduced SSL methods is the classification based on geometric structure of the data, namely the data manifold. In this approach unlabeled data is utilized to recover the underlying structure of the data. The common assumption is that despite of being represented in a high dimensional space, data... 

The human heart is a complex system that contains many clues about its function in its electrocardiogram (ECG) signal. Due to the high mortality rate of heart diseases, detection and recognition of ECG arrhythmias is essential. The most difficult problem faced by ECG analysis is the vast variations among morphologies of ECG signals. In this study, we propose an approach for y detection of abnormal beats and data visualization with respect to ECG morphologies by using manifold learning. In order to do so, a nonlinear dimensionality reduction method based on the Laplacian Eigenmaps is used to reduce the high dimensions of the ECG signals, followed by the application of Bayesian and FLDA method... 

Given a principal bundle a characteristic class is an element of the cohomology al- gebra of the classifying space of structure group of the bundle with coefficients in a commutative ring with unit ,which have a functorial property .When the structure groupe of the bundle is a Lie group and the coefficient ring is the real or complex num- bers , the Chern–Weil approach provides a geometric construction of char-acteristic classes. Classical Chern–Weil formalism relates geometry to topology, assigning to the cur- vature of a connection, de Rham cohomology classes of the underlying manifold.This theory developped in the 40’s by Shiing-ShenChern and Andre Weil which can be seen as a generalisation... 

Brain-Computer Interface (BCI) presents a way for brain’s direct connection with external world. BCI system is composed of three parts: 1) Signal acquisition, 2) Signal processing and 3) External device control. The main part of this system is signal processing which includes three subparts: 1) Feature extraction, 2) Dimension reduction and 3) Signal separation and classification. In this thesis, we focus on the signal processing section in BCI systems. One of the most successful works done in signal processing is the use of covariance matrices in feature extraction from brain signals. Since covariance matrices are positive semi-definite and symmetric, they belong to certain manifolds called... 

A number of questions from a variety of areas of mathematics lead one to the problem of analyzing the topology of a simplicial complex. However, there are few general techniques available to aid us in this study. On the other hand, some very general theories have been developed for the study of smooth manifolds. One of the most powerful, and useful, of these theories is Morse Theory. We present a combinatorial adaptation of Morse Theory, which we call discrete Morse theory that may be applied to any simplicial complex (or more general cell complex). Our goal is to present an overview of the subject of discrete Morse Theory that is sufficient both to understand the major applications of the... 

Let (M; g) be a Riemannian manifold. Using classical Stokes’ theorem one can show that the equality (dω; η)L2 = (ω; δη)L2 holds for smooth forms ! and η with compact supports, where δ is the formal adjoint of d . There are some examples of Riemannian manifolds for which the above equality does not hold for general forms ! and η i:e: smooth square-integrable forms such taht d! and δη are also squareintegrable. In the case that the above equality holds for such general forms on a Riemannian manifold (M; g) , we say that the L2 - Stokes theorem holds for (M; g) . In 1952, Gaffney showed that the L2 - Stokes theorem holds for complete Riemannian manifolds. But at that time, there was no powerful... 

Nowadays, fuel optimum used in engines is an important matter. To achieve this aim, we need to tune engine. The big companies have paid attention to these cases. Because of it, there are strict standard in the world and in other side the internal combustion engine is very common.
In the internal combustion engine after cylinder, the gas inter to an encasement which is called exhaust manifold. In the other hand, exhaust manifold is in upstairs of turbine and waste-gate in turbocharged SI engines. To control fuel used and descries the amount of emissions, exhaust manifold pressure is very important. In the other hand, monitoring of exhaust manifold pressure can use for fault detection of... 

Reducing fossil fuels and increasing urban air pollution, has made the automotive industry to reduce the fuel consumption of their engines by various approaches. Removing the compressor of air conditioning system by replacing the absorption chiller instead of inverse rankin cycle is a shortcut to reduce the fuel consumption which at the same time reduces costs of using air conditioning system for occupants. Design of a 3 kW lithium bromide-water absorbent chiller has verified based on environmental conditions and car space limitations and using the combustion products as the heat source of system. K4M engine of L90 sedan Car as an internal combustion engine sample’s exhaust manifold has been... 

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... 

All known examples of homogeneous Einstein spaces with negative scalar curvature (non compact) are isometric to standard Einstein solvmanifolds . we prove that any nilpotent Lie algebra having a codimension-one abelian ideal is the nilradical of a rank –one Einstein solvmanifold . In other words this nilpotent Lie algebra admits a rank-one solvable extension which can be endowed with an Einstein left invariant Riemannian metric . also a curve of pairwise non-isometric 8-dimensional rank-one Einstein solvmanifold is given .
 

Injuries of neuro-musculoskeletal system impose large costs to the modem societies. Studying the strategies of CNS in planning and control of movements can be helpful in developing diagnoSiS, prognosis and treatment procedures in clinical view and also in designing rehabilitation system and humanoid robots. Tow important features of human movements are redundancy problem and structured variability. Previous studies solved the redundancy problem mainly with optimization methods. Also optimal feedback control theory is the only method that successfully modeled structured variability in voluntary movements. Despite the appropriate outputs this methods are not based on physiological facts... 

In this thesis, we first define the pseudo-distance p on the group of Hamiltonian diffeomorphisms.Using the concept of displacement energy, we show that the pseudo-distance p is degenerate and if the manifold is closed, p will be zero for each p = 1; 2; 3; : : : Then, we introduce Lagrangian submanifolds and prove that if L R2n is a rational Lagrangian submanifold, we have the following inequality e(L) ≥ 1γ(L). : Finally, using the above inequality and the concept of displacement energy, for M = R2n we prove that 1 is non-degenerate. Therefore, the hypothesis for 1 to be a metric, are satisfied. This metric is called Hofer’s metric  

We introduce a refinement of the Ozsváth-Szabó complex associated by Juhász [8] to a balanced sutured manifold (X; ). An algebra A is associated to the boundary of a sutured manifold. For a fixed class s of a Spinc structure over the manifold X, which is obtained from X by filling out the sutures, the Ozsváth-Szabó chain complex CF(X; ; s) is then defined as a chain complex with coefficients in A and filtered by the relative Spinc classes in Spinc(X; ). The filtered chain homotopy type of this chain complex is an invariant of (X; ) and the Spinc class s 2 Spinc(X). The construction generalizes the construction of Juhász. It plays the role of CF (X; s) when X is a closed three-manifold,... 

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... 

In this dissertation we study compact gradient shrinking ricci solitons and the ricci solitons with Jacobi-type potential field for manifolds with positive ricci curvature and consider the cases that they are Einstein manifolds. Also we prove that the Identity map i : (M; g) ! (M;Ric) where M is a complete connected manifold is a harmonic map and we get a criterion for compactness of a complete Ricci soliton using a Jacobi-type vector field  

Human action recognition is one of the most attended topics in computer vision and robotics.One of the flavors of this problem relates to the situation in which the task of action recognition is carried out by data from several cameras. Different approaches have been proposed for combining information. Various reduction methods have been introduced to decrease the processing load. All of the methods in this particular field of study can be divided into two linear and non-linear methods. In the linear methods, we don’t pay attention to the non-linear structure of the data, and these kind of approaches are not reliable. Furthermore, combining different actions data is done before the dimension... 

Blind Source Separation (BSS) is a technique for estimating individual source components from their mixtures at multiple sensors, where the mixing model is unknown. Although it has been mathematically shown that for linear mixtures, under mild conditions, mutually independent sources can be reconstructed up to accepted ambiguities, there is not such theoretical basis for general nonlinear models. This is why there are relatively few resultsin the literature in this regard in the recent decades, which are focused on specific structured nonlinearities.In the present study, the problem is tackled using a novel approach utilizing temporal information of the signals. The original idea followed in... 

Einstein's general theory of relativity is an admirable successful and unifier geometrical modeling among concepts of space, time and gravity. This theory along with special theory of relativity made a massive change in our physical view and this, especially in its historical context, has deep and interesting consequences in man's philosophical viewpoint which can be studied. Some parts of this thesis relates to these consequences. Some of these interesting consequences may be hidden by computional or mathematical viewpoint and often these equations do not contain enough intuition. in one part, we provide a formulizatin of Einstein's equaion that is intuitional which can be translated in... 

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...