8,098 research outputs found
Melham's Conjecture on Odd Power Sums of Fibonacci Numbers
Ozeki and Prodinger showed that the odd power sum of the first several
consecutive Fibonacci numbers of even order is equal to a polynomial evaluated
at certain Fibonacci number of odd order. We prove that this polynomial and its
derivative both vanish at , and will be an integer polynomial after
multiplying it by a product of the first consecutive Lucas numbers of odd
order. This presents an affirmative answer to a conjecture of Melham.Comment: 15page
Division and the Giambelli Identity
Given two polynomials f(x) and g(x), we extend the formula expressing the
remainder in terms of the roots of these two polynomials to the case where f(x)
is a Laurent polynomial. This allows us to give new expressions of a Schur
function, which generalize the Giambelli identity.Comment: 9 pages, 1 figur
A Compressed Sensing Algorithm for Sparse-View Pinhole Single Photon Emission Computed Tomography
Single Photon Emission Computed Tomography (SPECT) systems are being developed with multiple cameras and without gantry rotation to provide rapid dynamic acquisitions. However, the resulting data is angularly undersampled, due to the limited number of views. We propose a novel reconstruction algorithm for sparse-view SPECT based on Compressed Sensing (CS) theory. The algorithm models Poisson noise by modifying the Iterative Hard Thresholding algorithm to minimize the Kullback-Leibler (KL) distance by gradient descent. Because the underlying objects of SPECT images are expected to be smooth, a discrete wavelet transform (DWT) using an orthogonal spline wavelet kernel is used as the sparsifying transform. Preliminary feasibility of the algorithm was tested on simulated data of a phantom consisting of two Gaussian distributions. Single-pinhole projection data with Poisson noise were simulated at 128, 60, 15, 10, and 5 views over 360 degrees. Image quality was assessed using the coefficient of variation and the relative contrast between the two objects in the phantom. Overall, the results demonstrate preliminary feasibility of the proposed CS algorithm for sparse-view SPECT imaging
Emergence of Cooperation and Organization in an Evolutionary Game
A binary game is introduced and analysed. N players have to choose one of the
two sides independently and those on the minority side win. Players uses a
finite set of ad hoc strategies to make their decision, based on the past
record. The analysing power is limited and can adapt when necessary.
Interesting cooperation and competition pattern of the society seem to arise
and to be responsive to the payoff function.Comment: 8 pages, 13 figure
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