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**Search for:**mathematical-operators

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#### Incremental learning of planning operators in stochastic domains

, Article 33rd Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2007, Harrachov, 20 January 2007 through 26 January 2007 ; Volume 4362 LNCS , 2007 , Pages 644-655 ; 03029743 (ISSN); 9783540695066 (ISBN) ; Ghassem Sani, G ; Sharif University of Technology
Springer Verlag
2007

Abstract

In this work we assume that there is an agent in an unknown environment (domain). This agent has some predefined actions and it can perceive its current state in the environment completely. The mission of this agent is to fulfill the tasks (goals) that are often assigned to it as fast as it can. Acting has lots of cost, and usually planning and simulating the environment can reduce this cost. In this paper we address a new approach for incremental induction of probabilistic planning operators, from this environment while the agent tries to reach to its current goals. It should be noted that there have been some works related to incremental induction of deterministic planning operators and...

#### A recursive approach for analysis of snake robots using Kane's equations

, Article DETC2005: ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Long Beach, CA, 24 September 2005 through 28 September 2005 ; Volume 7 B , 2005 , Pages 855-861 ; 0791847446 (ISBN) ; Pishkenari, H. N ; Meghdari, A ; Sharif University of Technology
2005

Abstract

This paper presents a recursive approach for solving kinematic and dynamic problem in snake-like robots using Kane's equations. An n-link model with n-nonholonomic constraints is used as the snake robot model in our analysis. The proposed algorithm which is used to derive kinematic and dynamic equations recursively enhances the computational efficiency of our analysis. Using this method we can determine the number of additions and multiplications as a function of n. The proposed method is compared with the Lagrange and Newton-Euler's method in three different aspects: Number of operations, CPU time and error in the computational procedures. Copyright © 2005 by ASME

#### Stochastic analysis and regeneration of rough surfaces

, Article Physical Review Letters ; Volume 91, Issue 22 , 2003 ; 00319007 (ISSN) ; Fazeli, S. M ; Ghasemi, F ; Vaez Allaei, S. M ; Rahimi Tabar, M ; Iraji zad, A ; Kavei, G ; Sharif University of Technology
2003

Abstract

We investigate the Markov property of rough surfaces. Using stochastic analysis, we characterize the complexity of the surface roughness by means of a Fokker-Planck or Langevin equation. The obtained Langevin equation enables us to regenerate surfaces with similar statistical properties compared with the observed morphology by atomic force microscopy. © 2003 The American Physical Society

#### A hybrid segmentation framework for computer-assisted dental procedures

, Article IEICE Transactions on Information and Systems ; Volume E92-D, Issue 10 , 2009 , Pages 2137-2151 ; 09168532 (ISSN) ; Aghaeizadeh Zoroofi, R ; Abbaspour Tehrani Fard, A ; Shirani, G ; Asharif, M. R ; Sharif University of Technology
Abstract

Teeth segmentation in computed tomography (CT) images is a major and challenging task for various computer assisted procedures. In this paper, we introduced a hybrid method for quantification of teeth in CT volumetric dataset inspired by our previous experiences and anatomical knowledge of teeth and jaws. In this regard, we propose a novel segmentation technique using an adaptive thresholding, morphological operations, panoramic re-sampling and variational level set algorithm. The proposed method consists of several steps as follows: first, we determine the operation region in CT slices. Second, the bony tissues are separated from other tissues by utilizing an adaptive thresholding technique...

#### On the computational complexity of defining sets

, Article Discrete Applied Mathematics ; Volume 149, Issue 1-3 , 2005 , Pages 101-110 ; 0166218X (ISSN) ; Maserrat, H ; Sharif University of Technology
2005

Abstract

Suppose we have a family F of sets. For every S∈F, a set D⊆S is a defining set for (F,S) if S is the only element of F that contains D as a subset. This concept has been studied in numerous cases, such as vertex colorings, perfect matchings, dominating sets, block designs, geodetics, orientations, and Latin squares. In this paper, first, we propose the concept of a defining set of a logical formula, and we prove that the computational complexity of such a problem is Σ2-complete. We also show that the computational complexity of the following problem about the defining set of vertex colorings of graphs is Σ2-complete: INSTANCE: A graph G with a vertex coloring c and an integer k.QUESTION: If...

#### Characterization of two-qubit perfect entanglers

, Article Physical Review A - Atomic, Molecular, and Optical Physics ; Volume 70, Issue 5 A , 2004 , Pages 052313-1-052313-9 ; 10502947 (ISSN) ; Sharif University of Technology
2004

Abstract

The problem of the characterization of perfect entanglers was investigated. Perfect entanglers have been defined as unitary operators that can generate maximally entangled states from some suitably chosen separable states. Some well defined tools have also been used to measure the entangling properties of quantum operators and two-qubit states. It was found that such tools help to analyze perfect entanglers and also have the unique property of maximally entangling a complete set of orthonormal product vectors. The results show that the qubit gates provided minimum universal gate construction and two of them were necessary and sufficient in implementation of a generic two-qubit gate

#### Thermal entanglement of spins in the Heisenberg model at low temperatures

, Article Physical Review A - Atomic, Molecular, and Optical Physics ; Volume 70, Issue 5 A , 2004 , Pages 052307-1-052307-5 ; 10502947 (ISSN) ; Karimipour, V ; Sharif University of Technology
2004

Abstract

The entanglement between two spins in the ferromagnetic Heisenberg chain at low temperatures was calculated. It was shown that if a magnetic field is applied to a ferromagnetic Heisenberg chain, then pairwise entanglement develops between spins at arbitrary given states. It was also shown that the entanglement profile is a Gaussian with a characteristic length depending on the temperature and the coupling between spins only when the ground state and the one-particle states are populated. The magnetic field was shown to affect only the amplitude of the profile and not its characteristic length

#### Exact solutions for universal holonomic quantum gates

, Article Physical Review A - Atomic, Molecular, and Optical Physics ; Volume 70, Issue 1 , 2004 , Pages 012320-1-012320-5 ; 10502947 (ISSN) ; Majd, N ; Sharif University of Technology
American Physical Society
2004

Abstract

Implementation of local quantum gate on specific qubits in an array of qubits by carrying a Hamiltonian around a closed loop is discussed. A family of isospectral Hamiltonians with the same spectrum of the projection operator on the main array is constructed by choice of a suitable curve. For every single qubit gate acting on the k-th qubit, a local operator Xk acts nontrivially on the ancilla and the qubit. Imbedding appropriate operators for a suitable set of qubit gates comprises of a universal set of quantum gates. In tensor product of the array one can enact holonomically any set of gates on any subset of qubits

#### A unified approach to the mathematical analysis of generalized RKPM, gradient RKPM, and GMLS

, Article Computer Methods in Applied Mechanics and Engineering ; Volume 200, Issue 5-8 , January , 2011 , Pages 540-576 ; 00457825 (ISSN) ; Shodja, H. M ; Khezri, M ; Sharif University of Technology
2011

Abstract

It is well-known that the conventional reproducing kernel particle method (RKPM) is unfavorable when dealing with the derivative type essential boundary conditions [1-3]. To remedy this issue a group of meshless methods in which the derivatives of a function can be incorporated in the formulation of the corresponding interpolation operator will be discussed. Formulation of generalized moving least squares (GMLS) on a domain and GMLS on a finite set of points will be presented. The generalized RKPM will be introduced as the discretized form of GMLS on a domain. Another method that helps to deal with derivative type essential boundary conditions is the gradient RKPM which incorporates the...

#### Analog computing using graphene-based metalines

, Article Optics Letters ; Volume 40, Issue 22 , 2015 , Pages 5239-5242 ; 01469592 (ISSN) ; Arik, K ; Khavasi, A ; Kavehvash, Z ; Sharif University of Technology
OSA - The Optical Society
2015

Abstract

We introduce the new concept of "metalines" for manipulating the amplitude and phase profile of an incident wave locally and independently. Thanks to the highly confined graphene plasmons, a transmit-array of graphene-based metalines is used to realize analog computing on an ultracompact, integrable, and planar platform. By employing the general concepts of spatial Fourier transformation, a well-designed structure of such meta-transmit-array, combined with graded index (GRIN) lenses, can perform two mathematical operations, i.e., differentiation and integration, with high efficiency. The presented configuration is about 60 times shorter than the recent structure proposed by Silva et al....

#### A non-linear model for the classification of stored items in supply chain management

, Article Proceedings 2010 International Symposium on Information Technology - System Development and Application and Knowledge Society, ITSim'10, 15 June 2010 through 17 June 2010 ; Volume 3 , June , 2010 , Pages 1636-1641 ; 9781424467181 (ISBN) ; Bozorgi Rad, M. A ; Ishak Desa, M ; Behnam, S ; Lessanibahri, S ; IEEE ; Sharif University of Technology
2010

Abstract

With the significant role that warehouse plays in connection to suppliers, distributors, and clients, and considering the costliness of storage systems, efforts have focused on the reduction of procedural expenses. Among the most significant expenses, one involves the distance traveled by operators or S/R machinery for the selection of ordered items; the common solution to which has been through the classification of stored items. Previous articles have focused on linear solutions to the abovementioned problem, such as P-Median. This article shall focus on the problems arising from the said solution, and instead a non-linear method proposed. Further, a heuristic algorithm is produced for the...

#### Analog computing by Brewster effect

, Article Optics Letters ; Volume 41, Issue 15 , 2016 , Pages 3467-3470 ; 01469592 (ISSN) ; Zangeneh Nejad, F ; Abdollahramezani, S ; Khavasi, A ; Sharif University of Technology
OSA - The Optical Society

Abstract

Optical computing has emerged as a promising candidate for real-time and parallel continuous data processing. Motivated by recent progresses in metamaterial-based analog computing [Science 343, 160 (2014)], we theoretically investigate the realization of two-dimensional complex mathematical operations using rotated configurations, recently reported in [Opt. Lett. 39, 1278 (2014)]. Breaking the reflection symmetry, such configurations could realize both even and odd Green's functions associated with spatial operators. Based on such an appealing theory and by using the Brewster effect, we demonstrate realization of a firstorder differentiator. Such an efficient wave-based computation method...

#### Boundary stabilization of a cosserat elastic body

, Article Asian Journal of Control ; Volume 19, Issue 6 , 2017 , Pages 2219-2225 ; 15618625 (ISSN) ; Alasty, A ; Vatankhah, R ; Eghtesad, M ; Daneshmand, F ; Sharif University of Technology
Abstract

Boundary stabilization of vibrating three-dimensional Cosserat elastic solids are studied using mathematical tools, such as operator theory and semigroup techniques. The advantages of the boundary control laws for both boundary stabilization problems are investigated. The boundary stabilization problems are studied using a Lyapunov stability method and LaSalle's invariant set theorem. Numerical simulations are provided to illustrate the effectiveness and performance of the designed control scheme. © 2017 Chinese Automatic Control Society and John Wiley & Sons Australia, Ltd

#### On the limitations of linear power reactor noise analysis: A point kinetics approach

, Article Annals of Nuclear Energy ; Volume 102 , 2017 , Pages 124-133 ; 03064549 (ISSN) ; Vosoughi, N ; Sharif University of Technology
Elsevier Ltd
2017

Abstract

A novel method is introduced which allows the higher order perturbative solution of a linear operator with a time variant coefficient. This method employs a form of raising and lowering operators which generate higher and lower order harmonics from a given harmonic. The analysis has been applied to the point kinetics equations with a monotone oscillatory reactivity to place bounds on the relative error of the linearization method frequently employed in the power reactor noise techniques. As a result, the maximum permissible reactivity amplitude for a given reactor as a function of frequency has been obtained such that regular power reactor noise methods remain accurate enough. Three...

#### Dielectric metasurfaces solve differential and integro-differential equations

, Article Optics Letters ; Volume 42, Issue 7 , 2017 , Pages 1197-1200 ; 01469592 (ISSN) ; Chizari, A ; Eshaghian Dorche, A ; Jamali, M. V ; Salehi, J. A ; Sharif University of Technology
OSA - The Optical Society
2017

Abstract

Leveraging subwavelength resonant nanostructures, plasmonic metasurfaces have recently attracted much attention as a breakthrough concept for engineering optical waves both spatially and spectrally. However, inherent ohmic losses concomitant with low coupling efficiencies pose fundamental impediments over their practical applications. Not only can all-dielectric metasurfaces tackle such substantial drawbacks, but also their CMOS-compatible configurations support both Mie resonances that are invariant to the incident angle. Here, we report on a transmittive metasurface comprising arrayed silicon nanodisks embedded in a homogeneous dielectric medium to manipulate phase and amplitude of...

#### An extended arbitrary Lagrangian-Eulerian finite element method for large deformation of solid mechanics

, Article Finite Elements in Analysis and Design ; Volume 44, Issue 6-7 , 2008 , Pages 401-416 ; 0168874X (ISSN) ; Anahid, M ; Shahim, K ; Sharif University of Technology
2008

Abstract

In this paper, a new computational technique is presented based on the eXtended arbitrary Lagrangian-Eulerian finite element method (X-ALE-FEM) for large deformation of solid mechanic problems. An arbitrary Lagrangian-Eulerian (ALE) technique is employed to capture the advantages of both Lagrangian and Eulerian methods and alleviate the drawbacks of the mesh distortion in Lagrangian formulation. The X-FEM procedure is implemented to capture the discontinuities independently of element boundaries. The process is accomplished by performing a splitting operator to separate the material (Lagrangian) phase from convective (Eulerian) phase, and partitioning the Lagrangian and relocated meshes with...

#### 2D parallel and stable group explicit finite difference method for solution of diffusion equation

, Article Applied Mathematics and Computation ; Volume 188, Issue 2 , 2007 , Pages 1184-1192 ; 00963003 (ISSN) ; Davami, P ; Sharif University of Technology
2007

Abstract

Recently various versions of alternating group explicit or alternating group explicit-implicit methods were proposed for solution of diffusion equation. The main benefits of these methods are: good stability, accuracy and parallelizing. But these methods were developed for 1D case and stability and accuracy were investigated for 1D case too. In the present study we extend the new group explicit method [R. Tavakoli, P. Davami, New stable group explicit finite difference method for solution of diffusion equation, Appl. Math. Comput. 181 (2006) 1379-1386] to 2D with operator splitting method. The implementation of method is discussed in details. Our numerical experiment shows that such 2D...

#### A non-linear mapping representing human action recognition under missing modality problem in video data

, Article Measurement: Journal of the International Measurement Confederation ; Volume 186 , 2021 ; 02632241 (ISSN) ; Razzazi, F ; Amini, A ; Sharif University of Technology
Elsevier B.V
2021

Abstract

Human action recognition by using standard video files is a well-studied problem in the literature. In this study, we assume to have access to single modality standard data of some actions (training data). Based on this data, we aim at identifying the actions that are present in a target modality video data without any explicit source–target relationship information. In this case, the training and test phases of the recognition task are based on different imaging modalities. Our goal in this paper is to introduce a mapping (a nonlinear operator) on both modalities such that the outcome shares some common features. These common features were then used to recognize the actions in each domain....

#### Recent advances in spatial analog optical computing

, Article 5th International Conference on Millimeter-Wave and Terahertz Technologies, MMWaTT 2018, 18 December 2018 through 20 December 2018 ; Volume 2018-December , 2019 , Pages 6-11 ; 21570965 (ISSN); 9781538677179 (ISBN) ; Karimi, P ; Khavasi, A ; Sharif University of Technology
Institute of Electrical and Electronics Engineers Inc
2019

Abstract

Traditional analog computers that perform mathematical operations electronically or mechanically suffer from their relatively large size and slow response. Recently, the idea of spatial analog optical computing has overcome these restrictions. The different techniques to implement spatial analog optical computation can be categorized into two fundamental approaches: (I) metasurface (MS) approach and (II) Green's function (GF) approach. In the first approach, a metasurface is designed to implement the Green's function of the desired operator in the spatial domain. This means that this approach needs two sub-blocks to perform Fourier and inverse Fourier transform. On the other hand, in the...

#### A stochastic security approach to energy and spinning reserve scheduling considering demand response program

, Article Energy ; Volume 36, Issue 5 , 2011 , Pages 3130-3137 ; 03605442 (ISSN) ; Nikzad, M ; Mozafari, B ; Ranjbar, A. M ; Sharif University of Technology
Abstract

In this paper a new algorithm for allocating energy and determining the optimum amount of network active power reserve capacity and the share of generating units and demand side contribution in providing reserve capacity requirements for day-ahead market is presented. In the proposed method, the optimum amount of reserve requirement is determined based on network security set by operator. In this regard, Expected Load Not Supplied (ELNS) is used to evaluate system security in each hour. The proposed method has been implemented over the IEEE 24-bus test system and the results are compared with a deterministic security approach, which considers certain and fixed amount of reserve capacity in...