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hilbert-spaces
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The Stability of Stochastic Partial Differential Equations in Hilbert Spaces
, M.Sc. Thesis Sharif University of Technology ; Zohori Zangeneh, Bijan (Supervisor) ; Jahanipur, Rouhollah (Supervisor)
Abstract
Stochastic Partial Differential Equations have many applications in other area of science. In this thesis we investigate two pproaches in SPDE.The first approach is semigroup and the second is variational method.Our main purpose is stability of these equations
Stationarity of the Solution for the Semilinear Stochastic Integral Equation on the Whole Real Line
, Article Springer Proceedings in Mathematics and Statistics ; Volume 34 , 2013 , Pages 315-331 ; 21941009 (ISSN) ; 9781461459057 (ISBN) ; Sharif University of Technology
Springer New York LLC
2013
Abstract
In this article we prove the stationarity of the solution of the H-valued integral equation, where H is a real separable Hilbert space. In this equation, U(t) is a semigroup generated by a strictly negative definite, self-adjoint unbounded operator A, such that A-1 is compact and f is of monotone type and is bounded by a polynomial and V (t) is a cadlag adapted stationary process
Symplectic Symmetries and Their Associated Hilbert Spaces
, M.Sc. Thesis Sharif University of Technology ; Sheikh-Jabbari, Mohammad Mehdi (Supervisor) ; Rahvar, Sohrab (Supervisor)
Abstract
In every theory with local symmetries, observales are mainly the gauge invariant quantities and fields are defined up to a local transformation.By choosing boundary conditions on field configurations and on the generating functions of gauge transformations, we can associate conserved charges to a particular subset of the generating functions. Thus field combinations which are related by these particular gauge transformations are physically distinct. These set of conserved charges usually form infinite-dimensional algebras such as Virasoro or BMS algebra. In addition, sets of all combinations of the associated fields form a phase space with a symplectic structure induced form the action of...
Investigation of continuous-time quantum walk by using Krylov subspace-Lanczos algorithm
, Article European Physical Journal B ; Volume 59, Issue 2 , 2007 , Pages 199-216 ; 14346028 (ISSN) ; Sufiani, R ; Salimi, S ; Jafarizadeh, S ; Sharif University of Technology
2007
Abstract
In papers [Jafarizadehn and Salimi, Ann. Phys. 322, 1005 (2007) and J. Phys. A: Math. Gen. 39, 13295 (2006)], the amplitudes of continuous-time quantum walk (CTQW) on graphs possessing quantum decomposition (QD graphs) have been calculated by a new method based on spectral distribution associated with their adjacency matrix. Here in this paper, it is shown that the CTQW on any arbitrary graph can be investigated by spectral analysis method, simply by using Krylov subspace-Lanczos algorithm to generate orthonormal bases of Hilbert space of quantum walk isomorphic to orthogonal polynomials. Also new type of graphs possessing generalized quantum decomposition (GQD) have been introduced, where...
Transition of d -level quantum systems through quantum channels with correlated noise
, Article Physical Review A - Atomic, Molecular, and Optical Physics ; Volume 75, Issue 4 , 2007 ; 10502947 (ISSN) ; Golshani, M ; Sharif University of Technology
2007
Abstract
Entanglement and entanglement assisted are useful resources to enhance the mutual information of the Pauli channels, when the noise on consecutive uses of the channel has some partial correlations. In this paper, we study quantum-communication channels in d -dimensional systems and derive the mutual information of the quantum channels for maximally entangled states and product states coding with correlated noise. Then, we compare fidelity between these states. Our results show that there exists a certain fidelity memory threshold, which depends on the dimension of the Hilbert space (d) and the properties of noisy channels. We calculate the classical capacity of a particular correlated noisy...
An accurate FIR approximation of ideal fractional delay filter with complex coefficients in Hilbert space
, Article Journal of Circuits, Systems and Computers ; Volume 14, Issue 3 , 2005 , Pages 497-505 ; 02181266 (ISSN) ; Nabavi, A ; Hessabi, Sh ; Sharif University of Technology
2005
Abstract
This paper presents a low-order and accurate method for the design of FIR fractional delay (FD) filters with complex coefficients. This method employs least square technique in Hilbert space to approximate the ideal FD transfer function with a FIR filter and to calculate its coefficients. The main advantages of the resulting filter are: very good response at all frequencies compared to other FD filter design methods and a good method to create very small delay. Design examples are presented to illustrate the effectiveness of this new design approach. © World Scientific Publishing Company
Estimating the Interaction Between Sites of a System by Convolutional Neural Networks and Applying Renormalization Group Methods on the Network’s Density Matrix
, M.Sc. Thesis Sharif University of Technology ; Rouhani, Shahin (Supervisor)
Abstract
In the last two decades, Convolutional Neural Networks (CNN) have shown significant capabilities in artificial intelligence. These networks are able to provide comprehensive conclusions about the overall behavior a system by analyzing the relationship between the components of that system; Clearly, these networks have been successful in performing categorization tasks. However, there are no coherent theories as to why they work, and how to optimize them. On the other hand, according to recent research on the relationship between deep networks (in computer science) and Renormalization Group (in physics), convolutional networks seem to use a method similar to the Density Matrix Renormalization...
Generative Adversarial Networks
, M.Sc. Thesis Sharif University of Technology ; Haji Mirsadeghi, Mir Omid (Supervisor)
Abstract
In this thesis we try to understand one of the most important subfield of deep learning, the generative adversarial networks. In this framework the goal is to reach a generator that generates samples from a target distribution. The target distribution is usually su- per high dimensional and we only have sample access to it. primarily , this distribution was used to be for set of Images (e.g. images of celebrity faces) and GANs performed well in this setting. In this framework two models work simultaneously: a generator tries to generate realistic samples from the target distribution and a discriminator or critic tries to distinguish real samples from generated (fake) samples or more...
Ping-pong protocol based on the orbital angular momentum of light
, Article Journal of the Optical Society of America B: Optical Physics ; Volume 35, Issue 10 , 2018 , Pages 2348-2355 ; 07403224 (ISSN) ; Tofighi, S ; Bahrampour, A ; Sharif University of Technology
Abstract
Orbital angular momentum (OAM) is one of the photon's degrees of freedom in infinite-dimensional Hilbert space. In this paper, we use this photon property to propose a modified version of the deterministic two-way quantum key distribution protocol, known as ping-pong protocol, based on the OAM of light. The advantage of the protocol is that it does not require Bell measurement for decoding the information being transmitted, which makes the protocol more flexible and feasible for practical applications. We propose an implementation setup and show how the channel capacity of the protocol can be easily increased. The security of the protocol is analyzed and the probability of detecting Eve in a...
Stein’s Method, Malliavin Calculus,Relations and Applications
, M.Sc. Thesis Sharif University of Technology ; Zohuri Zangeneh, Bijan (Supervisor) ; Tahmasebi, Mahdieh (Co-Supervisor)
Abstract
In this thesis, after introducing some preliminary concepts, Stein’s method and Malliavin calculus is discussed. Our approach for introducing Malliavin calculus is based on isonormal Gaussian processes, which is more general and natural than Gaussian noises. After dealing with isonormal Gaussian processes, Wiener chaos and important operators of Malliavin calculus, namely differential, divergence and Ornstein-Uhlenbeck operators are discussed and some relation between them is studied. At last, some connections between Stein’s method and Malliavin calculus is developed. As a result, some exact asymptotics for central limit theorems on Gaussian functionals are obtained. These results are used,...