Given a graph with k greater than or equal to 2 different nonnegative weights associated with each edge e and a cost function c: R-k --> R+, consider the problem of finding a minimum-cost edge subset possessing a c...
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Given a graph with k greater than or equal to 2 different nonnegative weights associated with each edge e and a cost function c: R-k --> R+, consider the problem of finding a minimum-cost edge subset possessing a certain property P. We prove that this problem is weakly NP-hard for a wide class of properties P and costs c, including paths, spanning trees, cuts, joins, etc. We suggest a simple approximation algorithm for this problem and find its performance guarantee. (C) 2002 Elsevier Science B.V. All rights reserved.
Discusses the design of machine-building production, certain steps of which are formalized problems of the forecast of the number of parts and calculate their estimated time. Simulation of application tasks is perform...
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ISBN:
(纸本)9781509036806
Discusses the design of machine-building production, certain steps of which are formalized problems of the forecast of the number of parts and calculate their estimated time. Simulation of application tasks is performed by the approximation of the fractional - power series. The possibility is shown for the numerical solution of models using combined genetic algorithms.
Background: Ever since endoscopes were invented, surgeons try to widen their field of usage by developing novel surgical approaches. An obvious advantage of the endoscope is the minimal invasiveness, but this comes at...
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ISBN:
(纸本)9781450367707
Background: Ever since endoscopes were invented, surgeons try to widen their field of usage by developing novel surgical approaches. An obvious advantage of the endoscope is the minimal invasiveness, but this comes at a price of reduced dexterity, loss of tactile feedback and difficulty in orientation. One of the challenges is to acquire the data of the neighborhood to find the relative position of the endoscope to the surrounding tissues. Methods & Results: In this paper, we present a mathematical approach to reconstruct unknown source(s) position(s) (e.g. endoscope, which produces a signal in different frequencies) and a medium (e.g. tissue surrounding the endoscope). We solve the joint Inverse Medium and Optimal Control on the Helmholtz equation, where both source(s) and medium velocity are unknown. The use of the Adaptive Eigenspace Inversion (AEI) in combination with frequency stepping, proofs itself to be a good solution. We underline our claim, with two-dimensional numerical experiments. Conclusion: The application of this method together with its promising results can potentially aid to navigate an endoscope through the body while collecting information on the surrounding tissue. These results may also find their application in geophysics.
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