398 research outputs found
Enumeration of symmetry classes of convex polyominoes on the honeycomb lattice
Hexagonal polyominoes are polyominoes on the honeycomb lattice. We enumerate
the symmetry classes of convex hexagonal polyominoes. Here convexity is to be
understood as convexity along the three main column directions. We deduce the
generating series of free (i.e. up to reflection and rotation) and of
asymmetric convex hexagonal polyominoes, according to area and half-perimeter.
We give explicit formulas or implicit functional equations for the generating
series, which are convenient for computer algebra.Comment: 21 pages, 16 figures, 2 tables. This is the full version of a paper
presented at the FPSAC Conference in Vancouver, Canada, June 28 -- July 2,
200
Forecasting chaotic systems : the role of local Lyapunov exponents
We propose a novel methodology for forecasting chaotic systems which is based on the nearest-neighbor predictor and improves upon it by incorporating local Lyapunov exponents to correct for its inevitable bias. Using simulated data, we show that gains in prediction accuracy can be substantial. The general intuition behind the proposed method can readily be applied to other non-parametric predictors.Chaos theory, Lyapunov exponent, logistic map, Monte Carlo simulations.
Local Lyapunov exponents: Zero plays no role in Forecasting chaotic systems
We propose a novel methodology for forecasting chaotic systems which uses information on local Lyapunov exponents (LLEs) to improve upon existing predictors by correcting for their inevitable bias. Using simulated data on the nearest-neighbor predictor, we show that accuracy gains can be substantial and that the candidate selection problem identified in Guégan and Leroux (2009) can be solved irrespective of the value of LLEs. An important corollary follows: the focal value of zero, which traditionally distinguishes order from chaos, plays no role whatsoever when forecasting deterministic systems.Chaos theory, Lyapunov exponent, Lorenz attractor Rössler attractor, Monte Carlo Simulations.
Predicting chaos with Lyapunov exponents : Zero plays no role in forecasting chaotic systems
We propose a nouvel methodology for forecasting chaotic systems which uses information on local Lyapunov exponents (LLEs) to improve upon existing predictors by correcting for their inevitable bias. Using simulations of the Rössler, Lorenz and Chua attractors, we find that accuracy gains can be substantial. Also, we show that the candidate selection problem identified in Guégan and Leroux (2009a,b) can be solved irrespective of the value of LLEs. An important corrolary follows : the focal value of zero, which traditionally distinguishes order from chaos, plays no role whatsoever when forecasting deterministic systems.Chaos theory, forecasting, Lyapunov exponent, Lorenz attractor, Rössler attractor, Chua attractor, Monte Carlo simulations.
Forecasting chaotic systems: The role of local Lyapunov exponents.
We propose a novel methodology for forecasting chaotic systems which is based on the nearest-neighbor predictor and improves upon it by incorporating local Lyapunov exponents to correct for its inevitable bias. Using simulated data, we show that gains in prediction accuracy can be substantial. The general intuition behind the proposed method can readily be applied to other non-parametric predictors.
Partial Sums Generation Architecture for Successive Cancellation Decoding of Polar Codes
Polar codes are a new family of error correction codes for which efficient
hardware architectures have to be defined for the encoder and the decoder.
Polar codes are decoded using the successive cancellation decoding algorithm
that includes partial sums computations. We take advantage of the recursive
structure of polar codes to introduce an efficient partial sums computation
unit that can also implements the encoder. The proposed architecture is
synthesized for several codelengths in 65nm ASIC technology. The area of the
resulting design is reduced up to 26% and the maximum working frequency is
improved by ~25%.Comment: Submitted to IEEE Workshop on Signal Processing Systems (SiPS)(26
April 2012). Accepted (28 June 2013
Partial Sums Computation In Polar Codes Decoding
Polar codes are the first error-correcting codes to provably achieve the
channel capacity but with infinite codelengths. For finite codelengths the
existing decoder architectures are limited in working frequency by the partial
sums computation unit. We explain in this paper how the partial sums
computation can be seen as a matrix multiplication. Then, an efficient hardware
implementation of this product is investigated. It has reduced logic resources
and interconnections. Formalized architectures, to compute partial sums and to
generate the bits of the generator matrix k^n, are presented. The proposed
architecture allows removing the multiplexing resources used to assigned to
each processing elements the required partial sums.Comment: Accepted to ISCAS 201
Forecasting chaotic systems: The role of local Lyapunov exponents
International audienceWe propose a novel methodology for forecasting chaotic systems which is based on exploiting the information conveyed by the local Lyapunov exponents of a system. This information is used to correct for the inevitable bias of most non-parametric predictors. Using simulated data, we show that gains in prediction accuracy can be substantial
Predicting Chaos with Lyapunov Exponents: Zero Plays no Role in Forecasting Chaotic Systems
We propose a nouvel methodology for forecasting chaotic systems which uses information on local Lyapunov exponents (LLEs) to improve upon existing predictors by correcting for their inevitable bias. Using simulations of the Rössler, Lorenz and Chua attractors, we find that accuracy gains can be substantial. Also, we show that the candidate selection problem identified in Guégan and Leroux (2009a,b) can be solved irrespective of the value of LLEs. An important corrolary follows : the focal value of zero, which traditionally distinguishes order from chaos, plays no role whatsoever when forecasting deterministic systems
Local Lyapunov Exponents: A new way to predict chaotic systems
We propose a novel methodology for forecasting chaotic systems which is based on exploiting the information conveyed by the local Lyapunov ex- ponent of a system. We show how our methodology can improve forecast- ing within the attractor and illustrate our results on the Lorenz system.Lyapunov exponent - Chaos - Forecasting
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