The Experts below are selected from a list of 153 Experts worldwide ranked by ideXlab platform
Paoli G - One of the best experts on this subject based on the ideXlab platform.
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Numerical method for the interpolation of digitized lines (unrolling method).
Journal of nuclear biology and medicine (Turin Italy : 1991), 1994Co-Authors: Paoli GAbstract:The proposed method can be used for reconstructing, from n not necessarily equidistant Points of a digitized polydrome line, a set of n1 equidistant Points (wIth n1 > n) interpolating the original Points. This method is based on a transformation of the original line into a digitized monodrome function D(1i) (unrolling function), where 1i is the line length between the origin and the Ith Point (i = 1,..., n1). Advantage of this method consists in reducing the two-dimensional interpolation problem to the one-dimensional field. In scintigraphic imaging, it is possible to achieve interpolation and coding of ROI's (Regions Of Interest) edges. For n samples of a monodrome line this method can also be applied, representing a possible alternative to splines. The numerical procedure is developed to reduce the noise on the Points.
Mikkel Thorup - One of the best experts on this subject based on the ideXlab platform.
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SODA - The entropy of backwards analysis
2018Co-Authors: Mathias Bæk Tejs Knudsen, Mikkel ThorupAbstract:Backwards analysis, first popularized by Seidel, is often the simplest most elegant way of analyzing a randomized algorIthm. It applies to incremental algorIthms where elements are added incrementally, following some random permutation, e.g., incremental Delauney triangulation of a Pointset, where Points are added one by one, and where we always maintain the Delauney triangulation of the Points added thus far. For backwards analysis, we think of the permutation as generated backwards, implying that the Ith Point in the permutation is picked uniformly at random from the i Points not picked yet in the backwards direction. Backwards analysis has also been applied elegantly by Chan to the randomized linear time minimum spanning tree algorIthm of Karger, Klein, and Tarjan. The question considered in this paper is how much randomness we need in order to trust the expected bounds obtained using backwards analysis, exactly and approximately. For the exact case, it turns out that a random permutation works if and only if it is minwise, that is, for any given subset, each element has the same chance of being first. Minwise permutations are known to have Θ(n) entropy, and this is then also what we need for exact backwards analysis. However, when it comes to approximation, the two concepts diverge dramatically. To get backwards analysis to hold wIthin a factor α, the random permutation needs entropy Ω(n/α). This contrasts wIth minwise permutations, where it is known that a 1 + e approximation only needs Θ(log(n/e)) entropy. Our negative result for backwards analysis essentially shows that it is as abstract as any analysis based on full randomness.
Gonglin Yuan - One of the best experts on this subject based on the ideXlab platform.
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A Numerical AlgorIthm for the Coupled PDEs Control Problem
Computational Economics, 2017Co-Authors: Gonglin YuanAbstract:For the coupled PDE control problem, at time \(t_i\) wIth the Ith Point, the standard algorIthm will first obtain the two space variables \((z_i,v_i)\) and then obtain the control variables \((\varsigma _i^{opt},\mu _i^{opt})\) from the given initial Points \((\varsigma _i^0,\mu _i^0)\). How many Points i are determined by the facts of the case? We usually believe that the largest i defined by n is big because the small step size \(\tau =\frac{T-t_0}{n}\) will generate a good approximation, where T denotes the terminal time. Thus, the solution process is very tedious, and much CPU time is required. In this paper, we present a new method to overcome this drawback. This presented method, which fully utilizes the first-order conditions, simultaneously considers the two space variables \((z_i,v_i)\) and the control variables \((\varsigma _i^{opt},\mu _i^{opt})\) wIth \(t_i\) at i. The computational complexity of the new algorIthm is \(O(N^3)\), whereas that of the normal algorIthm is \(O(N^3+N^3K)\). The performance of the proposed algorIthm is tested using an example.
L.a. Sklyarov - One of the best experts on this subject based on the ideXlab platform.
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Technology of diagnostics and monitoring of state of building structures based on the microseismic vibration analysis
2007 International Forum on Strategic Technology, 2007Co-Authors: A.f. Emanov, V.n. Maksimenko, L.a. SklyarovAbstract:Subjected to microseismic actions, any structure performs vibrations. To thoroughly inspect a building using microseismics, it is desirable to implement a dense system of simultaneous recording of vibrations , but this is rarely possible. We consider another observation system and its potentialities. The vibrations of a building subjected to microseismics are recorded simultaneously at the reference Point and the i'th Point (groups of Points), then location of the Ith Point (groups of Points) is changed and the seismic vibrations are recorded again. These observations allow one to inspect an object using a thin-route system. The problem is to transform records made at different Points at different times into the record of standing waves of the entire observation system. We propose an algorIthm for obtaining the data of simultaneous recording of a vibration process at different Points of a structure for the data recorded at different times using one reference Point.
Mathias Bæk Tejs Knudsen - One of the best experts on this subject based on the ideXlab platform.
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SODA - The entropy of backwards analysis
2018Co-Authors: Mathias Bæk Tejs Knudsen, Mikkel ThorupAbstract:Backwards analysis, first popularized by Seidel, is often the simplest most elegant way of analyzing a randomized algorIthm. It applies to incremental algorIthms where elements are added incrementally, following some random permutation, e.g., incremental Delauney triangulation of a Pointset, where Points are added one by one, and where we always maintain the Delauney triangulation of the Points added thus far. For backwards analysis, we think of the permutation as generated backwards, implying that the Ith Point in the permutation is picked uniformly at random from the i Points not picked yet in the backwards direction. Backwards analysis has also been applied elegantly by Chan to the randomized linear time minimum spanning tree algorIthm of Karger, Klein, and Tarjan. The question considered in this paper is how much randomness we need in order to trust the expected bounds obtained using backwards analysis, exactly and approximately. For the exact case, it turns out that a random permutation works if and only if it is minwise, that is, for any given subset, each element has the same chance of being first. Minwise permutations are known to have Θ(n) entropy, and this is then also what we need for exact backwards analysis. However, when it comes to approximation, the two concepts diverge dramatically. To get backwards analysis to hold wIthin a factor α, the random permutation needs entropy Ω(n/α). This contrasts wIth minwise permutations, where it is known that a 1 + e approximation only needs Θ(log(n/e)) entropy. Our negative result for backwards analysis essentially shows that it is as abstract as any analysis based on full randomness.
