33,066 research outputs found
Computing the multifractal spectrum from time series: An algorithmic approach
We show that the existing methods for computing the f(\alpha) spectrum from a
time series can be improved by using a new algorithmic scheme. The scheme
relies on the basic idea that the smooth convex profile of a typical f(\alpha)
spectrum can be fitted with an analytic function involving a set of four
independent parameters. While the standard existing schemes [16, 18] generally
compute only an incomplete f(\alpha) spectrum (usually the top portion), we
show that this can be overcome by an algorithmic approach which is automated to
compute the Dq and f(\alpha) spectrum from a time series for any embedding
dimension. The scheme is first tested with the logistic attractor with known
f(\alpha) curve and subsequently applied to higher dimensional cases. We also
show that the scheme can be effectively adapted for analysing practcal time
series involving noise, with examples from two widely different real world
systems. Moreover, some preliminary results indicating that the set of four
independant parameters may be used as diagnostic measures is also included.Comment: 10 pages, 16 figures, submitted to CHAO
An Algorithmic Argument for Nonadaptive Query Complexity Lower Bounds on Advised Quantum Computation
This paper employs a powerful argument, called an algorithmic argument, to
prove lower bounds of the quantum query complexity of a multiple-block ordered
search problem in which, given a block number i, we are to find a location of a
target keyword in an ordered list of the i-th block. Apart from much studied
polynomial and adversary methods for quantum query complexity lower bounds, our
argument shows that the multiple-block ordered search needs a large number of
nonadaptive oracle queries on a black-box model of quantum computation that is
also supplemented with advice. Our argument is also applied to the notions of
computational complexity theory: quantum truth-table reducibility and quantum
truth-table autoreducibility.Comment: 16 pages. An extended abstract will appear in the Proceedings of the
29th International Symposium on Mathematical Foundations of Computer Science,
Lecture Notes in Computer Science, Springer-Verlag, Prague, August 22-27,
200
Shapley Meets Shapley
This paper concerns the analysis of the Shapley value in matching games.
Matching games constitute a fundamental class of cooperative games which help
understand and model auctions and assignments. In a matching game, the value of
a coalition of vertices is the weight of the maximum size matching in the
subgraph induced by the coalition. The Shapley value is one of the most
important solution concepts in cooperative game theory.
After establishing some general insights, we show that the Shapley value of
matching games can be computed in polynomial time for some special cases:
graphs with maximum degree two, and graphs that have a small modular
decomposition into cliques or cocliques (complete k-partite graphs are a
notable special case of this). The latter result extends to various other
well-known classes of graph-based cooperative games.
We continue by showing that computing the Shapley value of unweighted
matching games is #P-complete in general. Finally, a fully polynomial-time
randomized approximation scheme (FPRAS) is presented. This FPRAS can be
considered the best positive result conceivable, in view of the #P-completeness
result.Comment: 17 page
Streaming Algorithm for Euler Characteristic Curves of Multidimensional Images
We present an efficient algorithm to compute Euler characteristic curves of
gray scale images of arbitrary dimension. In various applications the Euler
characteristic curve is used as a descriptor of an image.
Our algorithm is the first streaming algorithm for Euler characteristic
curves. The usage of streaming removes the necessity to store the entire image
in RAM. Experiments show that our implementation handles terabyte scale images
on commodity hardware. Due to lock-free parallelism, it scales well with the
number of processor cores. Our software---CHUNKYEuler---is available as open
source on Bitbucket.
Additionally, we put the concept of the Euler characteristic curve in the
wider context of computational topology. In particular, we explain the
connection with persistence diagrams
Computing functions on Jacobians and their quotients
We show how to efficiently compute functions on jacobian varieties and their
quotients. We deduce a quasi-optimal algorithm to compute isogenies
between jacobians of genus two curves
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