We explore a hybrid technique to quantify the variability in the numerical solutions to a free boundary problem associated with magnetic equilibrium in axisymmetric fusion reactors amidst parameter uncertainties. The ...
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Suppose we have two chemical reactions occurring simultaneously. Then theamount y of a reactant changes due to both processes and behaves as a function of time t as y(t) =x_1e~(α_1t) + x_2e~(α_2t), where x_1, x_2, ...
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Suppose we have two chemical reactions occurring simultaneously. Then theamount y of a reactant changes due to both processes and behaves as a function of time t as y(t) =x_1e~(α_1t) + x_2e~(α_2t), where x_1, x_2, α_1, and α_2 are fixed parameters. Typically, weobserve the function y(t) for m fixed t values, perhaps t = 0, Δt, 2Δt, ..., t_(final).
In the last issue''s installment of your homework assignment, we investigatedmultigrid methods for solving linear systems. (please see p. 10 of this issue of CiSE for moreinformation about multigrid methods, o...
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In the last issue''s installment of your homework assignment, we investigatedmultigrid methods for solving linear systems. (please see p. 10 of this issue of CiSE for moreinformation about multigrid methods, or visit our Web site at ***/ cise/homework/.).
If you breadk your leg on a mountain but have a cell phone or othertransmitter with you, you would hope a rescuer could determine the direction in which to travel toreach you. Similarly, if a navy detects a transmissi...
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If you breadk your leg on a mountain but have a cell phone or othertransmitter with you, you would hope a rescuer could determine the direction in which to travel toreach you. Similarly, if a navy detects a transmission from a submarine, it would want to determinethe signal's direction of arrival (DOAto locate that sub. The problem is complicated if more thanone signal appears―especially if the number of signals is unknown―and even more complicated if youor the submarine is moving. Surprisingly, we will see that your rescuer can solve an eigenvalueproblem (involving the product of some unknown matricesand use that information to find you. TheDOA-finding algorithm we'll use is called Esprit. To understand the process, we also will useseveral matrix decompositions and illustrate the necessity of using update techniques for real-timecomputations.
Existing schemes for demonstrating quantum computational advantage are subject to various practical restrictions, including the hardness of verification and challenges in experimental implementation. Meanwhile, analog...
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Existing schemes for demonstrating quantum computational advantage are subject to various practical restrictions, including the hardness of verification and challenges in experimental implementation. Meanwhile, analog quantum simulators have been realized in many experiments to study novel physics. In this work, we propose a quantum advantage protocol based on single-step Feynman-Kitaev verification of an analog quantum simulation, in which the verifier need only run an O(λ2)-time classical computation, and the prover need only prepare O(1) samples of a history state and perform O(λ2) single-qubit measurements, for a security parameter λ. We also propose a near-term feasible strategy for honest provers and discuss potential experimental realizations.
The development of artificial intelligence(AI) and the mining of biomedical data complement each other. From the direct use of computer vision results to analyze medical images for disease screening, to now integratin...
The development of artificial intelligence(AI) and the mining of biomedical data complement each other. From the direct use of computer vision results to analyze medical images for disease screening, to now integrating biological knowledge into models and even accelerating the development of new AI based on biological discoveries, the boundaries of both are constantly expanding, and their connections are becoming closer.
The article discusses the partial solution to image deblurring. In this problem, the best way to choose the regularization parameter is by eye. Some nonlinear reconstruction algorithms that reduce the problem are also...
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The article discusses the partial solution to image deblurring. In this problem, the best way to choose the regularization parameter is by eye. Some nonlinear reconstruction algorithms that reduce the problem are also discussed. In many applications, one must choose the regularization parameter by automatic methods rather than by eye.
In this paper we study problems with critical and sandwich-type growth represented by − div (|∇u|p−2∇u + a(x)|∇u|q−2∇u) = λw(x)|u|s−2u + θB (x, u) in Ω, u = 0 on ∂Ω, where Ω ⊂ RN is a bounded domain with Lipschitz b...
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The distance between two vertices u and v in a connected graph G is the number of edges lying in a shortest path(geodesic)between them.A vertex x of G performs the metric identification for a pair(u,v)of vertices in G...
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The distance between two vertices u and v in a connected graph G is the number of edges lying in a shortest path(geodesic)between them.A vertex x of G performs the metric identification for a pair(u,v)of vertices in G if and only if the equality between the distances of u and v with x implies that u=v(That is,the distance between u and x is different from the distance between v and x).The minimum number of vertices performing the metric identification for every pair of vertices in G defines themetric dimension of *** this paper,we performthemetric identification of vertices in two types of polygonal cacti:chain polygonal cactus and star polygonal cactus.
The reduced basis methodology is an efficient approach to solve parameterized discrete partial differential equations when the solution is needed at many parameter values. An offline step approximates the solution spa...
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