Global attractivity in a recursive sequence

In this paper, we Study the invariant intervals, the globally attractivity of the two equilibrium points, and the oscillatory behavior of tile solutions of the difference equation x(n =) ax(n-1) - bx(n-2)/c + x(n-2), n = 1,2,......, where a, b. c > 0. (C) 2003 Elsevier Inc. All rights reserved.

Maximum induced subgraph of a recursive circulant

The recursive circulant RC(2(n), 4) enjoys several attractive topological properties. Let max_epsilon(G) (m) denote the maximum number of edges in a subgraph of graph G induced by m nodes. In this paper, we show that max_epsilon(RC(2n,4))(m) = Sigma(i)(r)=(0)(p(i)/2 + i)2(Pi), where p(0) > p(1) > ... > p(r) are nonnegative integers defined by m = Sigma(i)(r)=(0)2(Pi). We then apply this formula to find the bisection width of RC(2(n), 4). The conclusion shows that, as n-dimensional cube, RC(2(n), 4) enjoys a linear bisection width. (c) 2005 Elsevier B.V. All rights reserved.

Global asymptotic stability in a rational recursive sequence

In this paper, we study the global stability of the difference equation x(n) = a + bx(n-1) + cx(n-1)(2)/d - x(n-2), n = 1,2,....., where a, b greater than or equal to 0 and c, d > 0. We show that one nonnegative equilibrium point of the equation is a global attractor with a basin that is determined by the parameters, and every positive Solution of the equation in the basin exponentially converges to the attractor. (C) 2003 Elsevier Inc. All rights reserved.

On the recursive sequence Xn = axn-1+bxn-2/c+dxn-1xn-2

In this Paper, we study the invariant intervals, the global attractivity of the equilibrium points, and the asymptotic behavior of the solutions of the difference equation x(n) = ax(n-1) + bx(n-2) / c + dx(n-1)x(n-2), n =1, 2, ..., where a greater than or equal to 0, b, c, d > 0. (C) 2004 Elsevier Inc. All rights reserved.

Simplified recursive identifier for ARMA processes

Symmetrical behaviour of the covariance matrix and the positive-definite criterion are used to simplify identification of single-input/single-output systems using recursive least squares. Simulation results are obtained and these are compared with ordinary recursive least squares. The adaptive nature of the identifier is verified by varying the system parameters on convergence.

Adaptive recursive control of a soil testing load frame

Recursive Learning Control (RLC) has the potential to significantly reduce the tracking error in many repetitive trajectory applications. This paper presents an application of RLC to a soil testing load frame where non-adaptive techniques struggle with the highly nonlinear nature of soil. The main purpose of the controller is to apply a sinusoidal force reference trajectory on a soil sample with a high degree of accuracy and repeatability. The controller uses a feedforward control structure, recursive least squares adaptation algorithm and RLC to compensate for periodic errors. Tracking error is reduced and stability is maintained across various soil sample responses.

Finite sample weighting of recursive forecast errors

This paper proposes and tests a new framework for weighting recursive out-of-sample prediction errors according to their corresponding levels of in-sample estimation uncertainty. In essence, we show how to use the maximum possible amount of information from the sample in the evaluation of the prediction accuracy, by commencing the forecasts at the earliest opportunity and weighting the prediction errors. Via a Monte Carlo study, we demonstrate that the proposed framework selects the correct model from a set of candidate models considerably more often than the existing standard approach when only a small sample is available. We also show that the proposed weighting approaches result in tests of equal predictive accuracy that have much better sizes than the standard approach. An application to an exchange rate dataset highlights relevant differences in the results of tests of predictive accuracy based on the standard approach versus the framework proposed in this paper.

Zero attracting recursive least squares algorithms

The l1-norm sparsity constraint is a widely used technique for constructing sparse models. In this contribution, two zero-attracting recursive least squares algorithms, referred to as ZA-RLS-I and ZA-RLS-II, are derived by employing the l1-norm of parameter vector constraint to facilitate the model sparsity. In order to achieve a closed-form solution, the l1-norm of the parameter vector is approximated by an adaptively weighted l2-norm, in which the weighting factors are set as the inversion of the associated l1-norm of parameter estimates that are readily available in the adaptive learning environment. ZA-RLS-II is computationally more efficient than ZA-RLS-I by exploiting the known results from linear algebra as well as the sparsity of the system. The proposed algorithms are proven to converge, and adaptive sparse channel estimation is used to demonstrate the effectiveness of the proposed approach.

A constrained recursive least squares algorithm for adaptive combination of multiple models

In this paper, we develop a novel constrained recursive least squares algorithm for adaptively combining a set of given multiple models. With data available in an online fashion, the linear combination coefficients of submodels are adapted via the proposed algorithm.We propose to minimize the mean square error with a forgetting factor, and apply the sum to one constraint to the combination parameters. Moreover an l1-norm constraint to the combination parameters is also applied with the aim to achieve sparsity of multiple models so that only a subset of models may be selected into the final model. Then a weighted l2-norm is applied as an approximation to the l1-norm term. As such at each time step, a closed solution of the model combination parameters is available. The contribution of this paper is to derive the proposed constrained recursive least squares algorithm that is computational efficient by exploiting matrix theory. The effectiveness of the approach has been demonstrated using both simulated and real time series examples.

Language processing with dynamic fields

We construct a mapping from complex recursive linguistic data structures to spherical wave functions using Smolensky's filler/role bindings and tensor product representations. Syntactic language processing is then described by the transient evolution of these spherical patterns whose amplitudes are governed by nonlinear order parameter equations. Implications of the model in terms of brain wave dynamics are indicated.

Is the Indian Ocean SST variability a homogeneous diffusion process.

Whereas the predominance of El Niño Southern Oscillation (ENSO) mode in the tropical Pacific sea surface temperature (SST) variability is well established, no such consensus seems to have been reached by climate scientists regarding the Indian Ocean. While a number of researchers think that the Indian Ocean SST variability is dominated by an active dipolar-type mode of variability, similar to ENSO, others suggest that the variability is mostly passive and behaves like an autocorrelated noise. For example, it is suggested recently that the Indian Ocean SST variability is consistent with the null hypothesis of a homogeneous diffusion process. However, the existence of the basin-wide warming trend represents a deviation from a homogeneous diffusion process, which needs to be considered. An efficient way of detrending, based on differencing, is introduced and applied to the Hadley Centre ice and SST. The filtered SST anomalies over the basin (23.5N-29.5S, 30.5E-119.5E) are then analysed and found to be inconsistent with the null hypothesis on intraseasonal and interannual timescales. The same differencing method is then applied to the smaller tropical Indian Ocean domain. This smaller domain is also inconsistent with the null hypothesis on intraseasonal and interannual timescales. In particular, it is found that the leading mode of variability yields the Indian Ocean dipole, and departs significantly from the null hypothesis only in the autumn season.

Are cold winters in Europe associated with low solar activity?

Solar activity during the current sunspot minimum has fallen to levels unknown since the start of the 20th century. The Maunder minimum (about 1650–1700) was a prolonged episode of low solar activity which coincided with more severe winters in the United Kingdom and continental Europe. Motivated by recent relatively cold winters in the UK, we investigate the possible connection with solar activity. We identify regionally anomalous cold winters by detrending the Central England temperature (CET) record using reconstructions of the northern hemisphere mean temperature. We show that cold winter excursions from the hemispheric trend occur more commonly in the UK during low solar activity, consistent with the solar influence on the occurrence of persistent blocking events in the eastern Atlantic. We stress that this is a regional and seasonal effect relating to European winters and not a global effect. Average solar activity has declined rapidly since 1985 and cosmogenic isotopes suggest an 8% chance of a return to Maunder minimum conditions within the next 50 years (Lockwood 2010 Proc. R. Soc. A 466 303–29): the results presented here indicate that, despite hemispheric warming, the UK and Europe could experience more cold winters than during recent decades.

An on-line algorithm of uncertain time delay estimation in a continuous system

In this paper, we present an on-line estimation algorithm for an uncertain time delay in a continuous system based on the observational input-output data, subject to observational noise. The first order Pade approximation is used to approximate the time delay. At each time step, the algorithm combines the well known Kalman filter algorithm and the recursive instrumental variable least squares (RIVLS) algorithm in cascade form. The instrumental variable least squares algorithm is used in order to achieve the consistency of the delay parameter estimate, since an error-in-the-variable model is involved. An illustrative example is utilized to demonstrate the efficacy of the proposed approach.