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firouzabadi--siavash
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An introductory course on differentiable manifolds
, Book
Dover Publications, Inc
2016
Abstract
Based on author Siavash Shahshahani's extensive teaching experience, this volume presents a thorough, rigorous course on the theory of differentiable manifolds. Geared toward advanced undergraduates and graduate students in mathematics, the treatment's prerequisites include a strong background in undergraduate mathematics, including multivariable calculus, linear algebra, elementary abstract algebra, and point set topology. More than 200 exercises offer students ample opportunity to gauge their skills and gain additional insights.
The four-part treatment begins with a single chapter devoted to the tensor algebra of linear spaces and their mappings. Part II brings in neighboring points to...
The four-part treatment begins with a single chapter devoted to the tensor algebra of linear spaces and their mappings. Part II brings in neighboring points to...
The Evolution of a Geometric Space in in the Nineteenth Century
, M.Sc. Thesis Sharif University of Technology ; Shahshahani, Siavash (Supervisor)
Abstract
The meaning and the nature of space and it’s essential properties seems to be one of the oldest problems which has been continuing to occupy human’s mind during centuries. It can be counted as a common ground between philosophy, mathematics, physics and even art. However this thesis concentrates on the philosophical and mathematical attitudes, neglecting the other aspects of the issue. Prima facie, it appears that the concept of space is essentially mingled with geometry, the science which seems to investigate the essentials of space. Taking it for granted, Kant regarded space, and so Euclidean geometry which dominates it, as an indispensible and necessary structure of the human’s mind....
P - Adic L Functions
, M.Sc. Thesis Sharif University of Technology ; Shahshahani, Siavash (Supervisor)
Abstract
Using interpolation and starting with Bernoulli numbers, posed by Leopold and Kubota, the aspect of adic function was constructed as adic analogues of the Dirichlet functions.Studing Galois module theory of ideal class group and his favorite structure extensions and modules related to them,Iwasawa found a new method for constructing adic functions by using Stickelberger’s elements.These results wich established by Iwasawa are known as Iwasawa Theory and they have many application in Algebriac Number Theory. Iwasawa’s most remarkable disconvry is the facet that at least in some important cases, there is a similar deep algebraic and analytic dichotomy in arithmetic of extensions. A...
Improving the Scalability of the DBSCAN Clustering Algorithm using Intelligent Histogram-Based Partitioning
, M.Sc. Thesis Sharif University of Technology ; Bayat, Siavash (Supervisor)
Abstract
The density-based clustering algorithm, DBSCAN, is widely recognized for its unique ability to identify arbitrarily shaped clusters and handle noise. However, with the exponential growth of data in modern applications, the algorithm's high computational complexity has become a significant bottleneck, limiting its scalability for large datasets. This research addresses this challenge by introducing and evaluating a novel hybrid clustering algorithm, named HB-DBSCAN. The proposed method is based on a "divide and conquer" strategy, with its core innovation lying in a fast and non-iterative partitioning process driven by one-dimensional histogram analysis. In this algorithm, the natural...
A modified model on solute alloying element effect in Al-Mg alloys: Mechanical properties and dislocation density evolutions
, Article Materials and Design ; Volume 36 , 2012 , Pages 804-808 ; 02641275 (ISSN) ; Kazeminezhad, M ; Sharif University of Technology
2012
Abstract
A modified dislocation based model is introduced to explain the flow stress of Al-Mg alloys at different temperatures and strain rates considering solute alloying element concentration. The solute effect on flow stress is studied on the basis of storage and annihilation of dislocation. It is studied that how the increase of solute content can postpone the dislocation annihilation and how this can affect the storage phenomenon. It is found that the increasing of solute concentration can postpone the beginning of dislocation annihilation through deformation and also increase the critical strain that plateau occurs in plot of annihilation of dislocation versus shear strain. Thus, the plateau...
Cell-structure and flow stress investigation of largely strained non-heat-treatable Al-alloys using dislocation based model
, Article Materials Science and Engineering A ; Volume 739 , 2019 , Pages 167-172 ; 09215093 (ISSN) ; Kazeminezhad, M ; Sharif University of Technology
Elsevier Ltd
2019
Abstract
A severe plastic deformation is widely used to improve the mechanical properties of non-heat-treatable alloys. Thus, the investigation and modeling of microstructural evolutions of materials during large straining are of great importance. In this research, substructural evolutions of four different kinds of Al alloys namely Al-1Mn, Al-1Mg, Al-2.77Mg and Al-5Mg, have been studied using a dislocation based model and the mechanical properties of these alloys have been compared considering all microstructural parameters such as dislocation density, subgrain size, cell wall misorientation and the effect of alloying element. As a result, a simplified general equation has been expressed in order to...
Modeling on Mechanical Properties of Aluminum of 5xxx Series in Constrained Grooved Pressing Process
, M.Sc. Thesis Sharif University of Technology ; Kazeminezhad, Mohsen (Supervisor)
Abstract
Al-Mg alloys are used in many industrial fields, thus improvement of their mechanical properties is so important. Expressing mathematical models on the basis of physical and microstructural properties can be useful for this purpose. In this research, in order to study the microstructural evolutions and mechanical properties of the material, a dislocation based model and microstructural parameters such as grains and subgrains during plastic deformation and subsequent annealing are considered. In addition, a modification is used to make the model capable of justify the solute atom and temperature effect simultaneously. This makes the results to be more precise and accurate considering...
, 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...
Integration of the inertial navigation system with consecutive images of a camera by relative position and attitude updating
, Article Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering ; Volume 233, Issue 15 , 2019 , Pages 5592-5605 ; 09544100 (ISSN) ; Dehghani Firouzabadi, A ; Sharif University of Technology
SAGE Publications Ltd
2019
Abstract
This paper introduces a new method for improving the inertial navigation system errors using information provided by the camera. An unscented Kalman filter is used for integrating the inertial measurement unit data with the features’ constraints extracted from the camera’s image. The constraints, in our approach, comprise epipolar geometry of two consecutive images with more than 65% coverage. Tracking down a known feature in two consecutive images results in emergence of stochastic epipolar constraint. It emerges in the form of an implicit measurement equation of the Kalman filter. Correctly matching features of the two images is necessary for reducing the navigation system errors because...
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
Free Vibration Analysis of Thin Truncated Cylindrical Shells using Galerkin Approach
, M.Sc. Thesis Sharif University of Technology ; Dehghani Firouzabadi, Rohollah (Supervisor)
Abstract
The current study is dedicated to free vibration analysis of a thin cylindrical shell with an oblique end. To this end, governing equations of motion and the corresponding boundary conditions are derived using Hamiltonian formulations. The differential form of equations is obtained by applying by part integration to the integral form of equations of motion. Equations of motions have been solved by Galerkin method for two different kinds of boundary conditions. Convergence process for different kinds of conditions has been done and results compared with papers. The effect of different parameters such as, length of cylinder, oblique angle, thickness etc. on the fundamental frequencies has been...
Exploiting structural information of data in active learning
, Article Artificial Intelligence and Soft Computing: Lecture Notes in Computer Science ; Volume 8468 LNAI, Issue PART 2 , 2014 , Pages 796-808 ; Beigy, Hamid ; Haghiri, Siavash ; Sharif University of Technology
2014
Abstract
In recent years, the active learning algorithms have focused on combining correlation criterion and uncertainty criterion for evaluating instances. Although these criteria might be useful, applying these measures on whole input space globally may lead to inefficient selected instances for active learning. The proposed method takes advantage of clustering to partition input space to subspaces. Then it exploits both labeled and unlabeled data locally for selection of instances by using a graph-based active learning. We define a novel utility score for selecting clusters by combining uncertainty criterion, local entropy of clusters and the factor of contribution of each cluster in queries....
A Trusted Design Platform for Trojan Detection in FPGA Bitstreams Using Partial Reconfiguration
, M.Sc. Thesis Sharif University of Technology ; Bayat-Sarmadi, Siavash (Supervisor)
Abstract
Hardware Trojans have emerged as a major concern for integrated circuits in recent years. As a result, detecting Trojans has become an important issue in critical applications, such as finance and health. In this work, a trusted platform for detecting Trojans in FPGA bitstreams is presented. The proposed methodology takes advantage of increased Trojan activation, caused by transition aware partitioning of the circuit, while it benefits partial reconfiguration feature of FPGAs to reduce area overhead. Simulation results, performed for the transition probability thresholds of 〖10〗^(-4) and 〖2×10〗^(-5), show that this method increases the ratio of the number of transitions in the Trojan...
Performance Evaluation of Physical Unclonable Functions and Proposing a Scheme on FPGA
, M.Sc. Thesis Sharif University of Technology ; Bayat-Sarmadi, Siavash (Supervisor)
Abstract
In recent years, in addition to traditional cryptographic blocks, a hardware blocks in this work namely PUF, has been used mostly for chip ID generation, authentication and so on. In this work we study recent proposed PUFs and their implementations on FPGA, and the measurement of quality metrics on them. Some of most important characteristics of PUFs are unpredictability, reliability, number of challenge response pairs and area. According to experiments that have been performed in this study and also according to previous work, one high-quality PUF in term of uniqueness and reliability is Ring Oscillator PUF. However, the disadvantage of this PUF is small number of challenge and response...
Increasing BIOS Trust in Personal Computers Using Reconfigurable Devices
, M.Sc. Thesis Sharif University of Technology ; Bayat Sarmadi, Siavash (Supervisor)
Abstract
Due to the expansion of digital system threats, trusted computation with a new approach for countering such threats has emerged. This approach is based on using a hardware module for implementing a trusted platform (TPM). TPM includes a chipset and the trusted systems core. Nowadays many of mobile computers do include this technology. This hardware creates trust using a trust chain and expanding this trust to other parts of the system. The starting point in this chain is the computer BIOS. BIOS is the first code that the system usually executes. One of the most powerful recent attacks on computer systems is to infect the BIOS and other firmware. One of such complicated attacks is the rootkit...
Efficient Implementation of Post-Quantum Cryptography Based on Learning with Errors
, Ph.D. Dissertation Sharif University of Technology ; Bayat Sarmadi, Siavash (Supervisor)
Abstract
Public key encryption (PKE) cryptography plays a big role in securing communication channels of internet. The security of every PKE scheme is usually based on a hard problem that has no polynomial time solution using any computational structure. However, widely used classic PKE schemes such as RSA or ECC, are based on hard problems that have polynomial solutions using a quantum computer. Therefore, such PKE schemes will not be secure in post-quantum era. Among quantum-resistant schemes, lattice-based cryptography and especially learning with errors (LWE) problem have gained high attention due to their low computational complexity. In this thesis, different LWE-based cryptosystems are...
Hardware Acceleration of Convolutional Neural Networks by Computational Prediction
, M.Sc. Thesis Sharif University of Technology ; Bayatsarmadi, Siavash (Supervisor)
Abstract
Recently, Convolutional neural networks (CNNs) are widely used in many artificial intelligence applications such as image processing, speech processing and robotics. The neural networks superior accuracy comes at the cost of high computational complexity. Recent studies show that these operations can be performed in parallel. Therefore, as graphic processing units (GPUs) offer the best performance in terms of computational power and throughput, they are widely used to implement and accelerate neural networks. Nevertheless, the high price and power consumption of these processors have resulted in drawing more attraction towards Field-Programmable Arrays (FPGAs). In order to improve resource...
Implementation of an IoT Edge Computing Module in Compliance with TPM Standards
, M.Sc. Thesis Sharif University of Technology ; Bayat Sarmadi, Siavash (Supervisor)
Abstract
Cloud computing has a significant role in expanding applications of the Internet of Things (IoT). Currently, applications such as virtual reality and augmented reality require low latency, which is not achievable using traditional cloud computing in some scenarios. Edge computing is a new approach in IoT, which solves some of the limitations of the cloud computing by extending and developing its operations. Reducing response time and network traffic are some of the most important achievements of edge computing. Despite of its numerous advantages over cloud computing, edge computing faces serious challenges such as virtualization, implementation infrastructure, resource allocation and task...
Improving Remote Attestation Techniques for IoT Devices using Physical Model
, M.Sc. Thesis Sharif University of Technology ; Bayat Sarmadi, Siavash (Supervisor)
Abstract
Due to the widespread growth in the use of IoT devices, authors consider these devices as an attractive target platform. Several approaches have been proposed to defend IoT devices against various attacks. However, most of them suffer from some shortcomings such as being computationally expensive, not being general, or not being robust enough.Due to the attacks such as firmware modification and the existence of computational limitations, the use of local approaches is inefficient. Another approach is to use remote attestation techniques, which are divided into two categories, static and dynamic. However, static detection techniques are vulnerable to runtime attacks. Furthermore, existing...
Customizing a Privacy-Preserving Blockchain-Based Distributed Ledger for Second-Price Auction Smart Contract
, M.Sc. Thesis Sharif University of Technology ; Bayat Sarmadi, Siavash (Supervisor)
Abstract
A distributed ledger is a method of digital data storage and sharing in different places, and the blockchain technology is a way of implementing a distributed ledger. This technology has been employed in many of the cryptocurrencies like Ethereum to store transactions. In addition to storing transactions, Ethereum deploys scripts called smart contracts that are automatically executable. These scripts execute transparently and without preserving the privacy of participants. On the other hand, confidentiality and privacy are among the important components in data, network, and system security. Models such as Hawk and Enigma have been presented to obtain privacy-preserving in smart contracts;...