Regularization of time-varying descriptor systems by the asvd

We study linear variable coefficient control problems in descriptor form. Based on a behaviour approach and the general theory for linear differential algebraic systems we give the theoretical analysis and describe numerically stable methods to determine the structural properties of the system.

Structure adaptation of linear MMSE adaptive filters

The tap-length, or the number of the taps, is an important structural parameter of the linear MMSE adaptive filter. Although the optimum tap-length that balances performance and complexity varies with scenarios, most current adaptive filters fix the tap-length at some compromise value, making them inefficient to implement especially in time-varying scenarios. A novel gradient search based variable tap-length algorithm is proposed, using the concept of the pseudo-fractional tap-length, and it is shown that the new algorithm can converge to the optimum tap-length in the mean. Results of computer simulations are also provided to verify the analysis.

Declining survival rates in a reintroduced population of the Mauritius kestrel: evidence for non-linear density dependence and environmental stochasticity

1. We studied a reintroduced population of the formerly critically endangered Mauritius kestrel Falco punctatus Temmink from its inception in 1987 until 2002, by which time the population had attained carrying capacity for the study area. Post-1994 the population received minimal management other than the provision of nestboxes. 2. We analysed data collected on survival (1987-2002) using program MARK to explore the influence of density-dependent and independent processes on survival over the course of the population's development. 3.We found evidence for non-linear, threshold density dependence in juvenile survival rates. Juvenile survival was also strongly influenced by climate, with the temporal distribution of rainfall during the cyclone season being the most influential climatic variable. Adult survival remained constant throughout. 4. Our most parsimonious capture-mark-recapture statistical model, which was constrained by density and climate, explained 75.4% of the temporal variation exhibited in juvenile survival rates over the course of the population's development. 5. This study is an example of how data collected as part of a threatened species recovery programme can be used to explore the role and functional form of natural population regulatory processes. With the improvements in conservation management techniques and the resulting success stories, formerly threatened species offer unique opportunities to further our understanding of the fundamental principles of population ecology.

Facile strategies for the synthesis and crystallization of linear trinuclear nickel(II)-Schiff base, complexes with carboxylate bridges: Tuning of coordination geometry and magnetic properties

Three new linear trinuclear nickel(II) complexes, [Ni-3(salpen)(2)(OAc)(2)(H2O)(2)]center dot 4H(2)O (1) (OAc = acetate, CH3COO-), [Ni-3(salpen)(2)(OBz)(2)] (2) (OBz=benzoate, PhCOO-) and [Ni-3(salpen)(2)(OCn)(2)(CH3CN)(2)] (4) (OCn = cinnamate, PhCH=CHCOO-), H(2)salpen = tetradentate ligand, N,N'-bis(salicylidene)-1,3-pentanediamine have been synthesized and characterized structurally and magnetically. The choice of solvent for growing single crystal was made by inspecting the morphology of the initially obtained solids with the help of SEM study. The magnetic properties of a closely related complex, [Ni-3(salpen)(2)(OPh)(2)(EtOH)] (3) (OPh = phenyl acetate, PhCH2COO-) whose structure and solution properties have been reported recently, has also been studied here. The structural analyses reveal that both phenoxo and carboxylate bridging are present in all the complexes and the three Ni(II) atoms remain in linear disposition. Although the Schiff base ligand and the syn-syn bridging bidentate mode of the carboxylate group remain the same in complexes 1-4, the change of alkyl/aryl group of the carboxylates brings about systematic variations between six- and five-coordination in the geometry of the terminal Ni(II) centres of the trinuclear units. The steric demand as well as hydrophobic nature of the alkyl/aryl group of the carboxylate is found to play a crucial role in the tuning of the geometry. Variable-temperature (2-300 K) magnetic susceptibility measurements show that complexes 1-4 are antiferromagnetically coupled (J = -3.2(1), -4.6(1). -3.2(1) and -2.8(1) cm(-1) in 1-4, respectively). Calculations of the zero-field splitting parameter indicate that the values of D for complexes 1-4 are in the high range (D = +9.1(2), +14.2(2), +9.8(2) and +8.6(1) cm(-1) for 1-4, respectively). The highest D value of +14.2(2) and +9.8(2) cm(-1) for complexes 2 and 3, respectively, are consistent with the pentacoordinated geometry of the two terminal nickel(II) ions in 2 and one terminal nickel(II) ion in 3. (C) 2009 Elsevier Ltd. All rights reserved.

Power properties if invariant tests for spatial autocorrelation in linear regression

This paper derives some exact power properties of tests for spatial autocorrelation in the context of a linear regression model. In particular, we characterize the circumstances in which the power vanishes as the autocorrelation increases, thus extending the work of Krämer (2005). More generally, the analysis in the paper sheds new light on how the power of tests for spatial autocorrelation is affected by the matrix of regressors and by the spatial structure. We mainly focus on the problem of residual spatial autocorrelation, in which case it is appropriate to restrict attention to the class of invariant tests, but we also consider the case when the autocorrelation is due to the presence of a spatially lagged dependent variable among the regressors. A numerical study aimed at assessing the practical relevance of the theoretical results is included

Variable selection algorithm for the construction of MIMO operating point dependent neurofuzzy networks

An input variable selection procedure is introduced for the identification and construction of multi-input multi-output (MIMO) neurofuzzy operating point dependent models. The algorithm is an extension of a forward modified Gram-Schmidt orthogonal least squares procedure for a linear model structure which is modified to accommodate nonlinear system modeling by incorporating piecewise locally linear model fitting. The proposed input nodes selection procedure effectively tackles the problem of the curse of dimensionality associated with lattice-based modeling algorithms such as radial basis function neurofuzzy networks, enabling the resulting neurofuzzy operating point dependent model to be widely applied in control and estimation. Some numerical examples are given to demonstrate the effectiveness of the proposed construction algorithm.

Optimal control of a class of discrete–continuous non-linear systems — decomposition and hierarchical structure

A technique is derived for solving a non-linear optimal control problem by iterating on a sequence of simplified problems in linear quadratic form. The technique is designed to achieve the correct solution of the original non-linear optimal control problem in spite of these simplifications. A mixed approach with a discrete performance index and continuous state variable system description is used as the basis of the design, and it is shown how the global problem can be decomposed into local sub-system problems and a co-ordinator within a hierarchical framework. An analysis of the optimality and convergence properties of the algorithm is presented and the effectiveness of the technique is demonstrated using a simulation example with a non-separable performance index.

Variable step-size LMS blind CDMA multiuser detectors

Adaptive least mean square (LMS) filters with or without training sequences, which are known as training-based and blind detectors respectively, have been formulated to counter interference in CDMA systems. The convergence characteristics of these two LMS detectors are analyzed and compared in this paper. We show that the blind detector is superior to the training-based detector with respect to convergence rate. On the other hand, the training-based detector performs better in the steady state, giving a lower excess mean-square error (MSE) for a given adaptation step size. A novel decision-directed LMS detector which achieves the low excess MSE of the training-based detector and the superior convergence performance of the blind detector is proposed.

Ensemble clustering in deterministic ensemble Kalman filters

Ensemble clustering (EC) can arise in data assimilation with ensemble square root filters (EnSRFs) using non-linear models: an M-member ensemble splits into a single outlier and a cluster of M−1 members. The stochastic Ensemble Kalman Filter does not present this problem. Modifications to the EnSRFs by a periodic resampling of the ensemble through random rotations have been proposed to address it. We introduce a metric to quantify the presence of EC and present evidence to dispel the notion that EC leads to filter failure. Starting from a univariate model, we show that EC is not a permanent but transient phenomenon; it occurs intermittently in non-linear models. We perform a series of data assimilation experiments using a standard EnSRF and a modified EnSRF by a resampling though random rotations. The modified EnSRF thus alleviates issues associated with EC at the cost of traceability of individual ensemble trajectories and cannot use some of algorithms that enhance performance of standard EnSRF. In the non-linear regimes of low-dimensional models, the analysis root mean square error of the standard EnSRF slowly grows with ensemble size if the size is larger than the dimension of the model state. However, we do not observe this problem in a more complex model that uses an ensemble size much smaller than the dimension of the model state, along with inflation and localisation. Overall, we find that transient EC does not handicap the performance of the standard EnSRF.

Superfast non-linear diffusion: capillary transport in particulate porous media

The migration of liquids in porous media, such as sand, has been commonly considered at high saturation levels with liquid pathways at pore dimensions. In this letter we reveal a low saturation regime observed in our experiments with droplets of extremely low volatility liquids deposited on sand. In this regime the liquid is mostly found within the grain surface roughness and in the capillary bridges formed at the contacts between the grains. The bridges act as variable-volume reservoirs and the flow is driven by the capillary pressure arising at the wetting front according to the roughness length scales. We propose that this migration (spreading) is the result of interplay between the bridge volume adjustment to this pressure distribution and viscous losses of a creeping flow within the roughness. The net macroscopic result is a special case of non-linear diffusion described by a superfast diffusion equation (SFDE) for saturation with distinctive mathematical character. We obtain solutions to a moving boundary problem defined by SFDE that robustly convey a time power law of spreading as seen in our experiments.

Radar bright band correction using the linear depolarisation ratio

The enhanced radar return associated with melting snow, ‘the bright band’, can lead to large overestimates of rain rates. Most correction schemes rely on fitting the radar observations to a vertical profile of reflectivity (VPR) which includes the bright band enhancement. Observations show that the VPR is very variable in space and time; large enhancements occur for melting snow, but none for the melting graupel in embedded convection. Applying a bright band VPR correction to a region of embedded convection will lead to a severe underestimate of rainfall. We revive an earlier suggestion that high values of the linear depolarisation ratio (LDR) are an excellent means of detecting when bright band contamination is occurring and that the value of LDR may be used to correct the value of Z in the bright band.

Ensemble transform Kalman-Bucy filters

Two recent works have adapted the Kalman–Bucy filter into an ensemble setting. In the first formulation, the ensemble of perturbations is updated by the solution of an ordinary differential equation (ODE) in pseudo-time, while the mean is updated as in the standard Kalman filter. In the second formulation, the full ensemble is updated in the analysis step as the solution of single set of ODEs in pseudo-time. Neither requires matrix inversions except for the frequently diagonal observation error covariance. We analyse the behaviour of the ODEs involved in these formulations. We demonstrate that they stiffen for large magnitudes of the ratio of background error to observational error variance, and that using the integration scheme proposed in both formulations can lead to failure. A numerical integration scheme that is both stable and is not computationally expensive is proposed. We develop transform-based alternatives for these Bucy-type approaches so that the integrations are computed in ensemble space where the variables are weights (of dimension equal to the ensemble size) rather than model variables. Finally, the performance of our ensemble transform Kalman–Bucy implementations is evaluated using three models: the 3-variable Lorenz 1963 model, the 40-variable Lorenz 1996 model, and a medium complexity atmospheric general circulation model known as SPEEDY. The results from all three models are encouraging and warrant further exploration of these assimilation techniques.