Practical stability of approximating discrete-time filters with respect to model mismatch using relative entropy concepts

This paper establishes practical stability results for an important range of approximate discrete-time filtering problems involving mismatch between the true system and the approximating filter model. Using local consistency assumption, the practical stability established is in the sense of an asymptotic bound on the amount of bias introduced by the model approximation. Significantly, these practical stability results do not require the approximating model to be of the same model type as the true system. Our analysis applies to a wide range of estimation problems and justifies the common practice of approximating intractable infinite dimensional nonlinear filters by simpler computationally tractable filters.

Practical stability with respect to model mismatch of approximate discrete-time output feedback control

This paper establishes a practical stability result for discrete-time output feedback control involving mismatch between the exact system to be stabilised and the approximating system used to design the controller. The practical stability is in the sense of an asymptotic bound on the amount of error bias introduced by the model approximation, and is established using local consistency properties of the systems. Importantly, the practical stability established here does not require the approximating system to be of the same model type as the exact system. Examples are presented to illustrate the nature of our practical stability result.

Oscillatory regulation of Hes1: Discrete stochastic delay modelling and simulation

Discrete stochastic simulations are a powerful tool for understanding the dynamics of chemical kinetics when there are small-to-moderate numbers of certain molecular species. In this paper we introduce delays into the stochastic simulation algorithm, thus mimicking delays associated with transcription and translation. We then show that this process may well explain more faithfully than continuous deterministic models the observed sustained oscillations in expression levels of hes1 mRNA and Hes1 protein.

Numerical analysis of the time variable fractional order mobile-immobile advection-dispersion model

Many physical processes exhibit fractional order behavior that varies with time or space. The continuum of order in the fractional calculus allows the order of the fractional operator to be considered as a variable. In this paper, we consider the time variable fractional order mobile-immobile advection-dispersion model. Numerical methods and analyses of stability and convergence for the fractional partial differential equations are quite limited and difficult to derive. This motivates us to develop efficient numerical methods as well as stability and convergence of the implicit numerical methods for the fractional order mobile immobile advection-dispersion model. In the paper, we use the Coimbra variable time fractional derivative which is more efficient from the numerical standpoint and is preferable for modeling dynamical systems. An implicit Euler approximation for the equation is proposed and then the stability of the approximation are investigated. As for the convergence of the numerical scheme we only consider a special case, i.e. the time fractional derivative is independent of time variable t. The case where the time fractional derivative depends both the time variable t and the space variable x will be considered in the future work. Finally, numerical examples are provided to show that the implicit Euler approximation is computationally efficient.

Practical stability of approximating discrete-time filters with respect to model mismatch

This paper establishes practical stability results for an important range of approximate discrete-time filtering problems involving mismatch between the true system and the approximating filter model. Practical stability is established in the sense of an asymptotic bound on the amount of bias introduced by the model approximation. Our analysis applies to a wide range of estimation problems and justifies the common practice of approximating intractable infinite dimensional nonlinear filters by simpler computationally tractable filters.

Permutation polynomials of the form (xp −x +δ)s +L(x)

Recently, several classes of permutation polynomials of the form (x2 + x + δ)s + x over F2m have been discovered. They are related to Kloosterman sums. In this paper, the permutation behavior of polynomials of the form (xp − x + δ)s + L(x) over Fpm is investigated, where L(x) is a linearized polynomial with coefficients in Fp. Six classes of permutation polynomials on F2m are derived. Three classes of permutation polynomials over F3m are also presented.

Modeling and analysis of a novel variable-speed cage induction generator

This paper introduces a novel cage induction generator and presents a mathematical model, through which its behavior can be accurately predicted. The proposed generator system employs a three-phase cage induction machine and generates single-phase and constant-frequency electricity at varying rotor speeds without an intermediate inverter stage. The technique uses any one of the three stator phases of the machine as the excitation winding and the remaining two phases, which are connected in series, as the power winding. The two-series-connected-and-one-isolated (TSCAOI) phase winding configuration magnetically decouples the two sets of windings, enabling independent control. Electricity is generated through the power winding at both sub- and super-synchronous speeds with appropriate excitation to the isolated single winding at any frequency of generation. A dynamic mathematical model, which accurately predicts the behavior of the proposed generator, is also presented and implemented in MATLAB/Simulink. Experimental results of a 2-kW prototype generator under various operating conditions are presented, together with theoretical results, to demonstrate the viability of the TSCAOI power generation. The proposed generator is simple and capable of both storage and retrieval of energy through its excitation winding and is expected to be suitable for applications, such as small wind turbines and microhydro systems.

Low-frequency dispersion properties of plasmas with variable-charge impurities

A theory of low-frequency dust-acoustic waves in low-temperature collisional plasmas containing variable-charge impurities is presented. Physical processes such as dust-charge relaxation, ionization-recombination of the electrons and ions, electron and ion elastic collisions with neutrals and dusts, as well as charging collisions with the dusts, are taken into account. Inclusion of these processes allows a balance of the plasma particles and thus a self-consistent determination of the stationary state of the unperturbed plasma. The generalized dispersion relation describing the propagation and damping of the dust acoustic waves is derived and analyzed. © 2000 American Institute of Physics.

Serum levels of soluble receptor for advanced glycation end products and of S100 proteins are associated with inflammatory, autoantibody, and classical risk markers of joint and vascular damage in rheumatoid arthritis

Introduction: The receptor for advanced glycation end products (RAGE) is a member of the immunoglobulin superfamily of cell surface receptor molecules. High concentrations of three of its putative proinflammatory ligands, S100A8/A9 complex (calprotectin), S100A8, and S100A12, are found in rheumatoid arthritis (RA) serum and synovial fluid. In contrast, soluble RAGE (sRAGE) may prevent proinflammatory effects by acting as a decoy. This study evaluated the serum levels of S100A9, S100A8, S100A12 and sRAGE in RA patients, to determine their relationship to inflammation and joint and vascular damage. Methods: Serum sRAGE, S100A9, S100A8 and S100A12 levels from 138 patients with established RA and 44 healthy controls were measured by ELISA and compared by unpaired t test. In RA patients, associations with disease activity and severity variables were analyzed by simple and multiple linear regressions. Results: Serum S100A9, S100A8 and S100A12 levels were correlated in RA patients. S100A9 levels were associated with body mass index (BMI), and with serum levels of S100A8 and S100A12. S100A8 levels were associated with serum levels of S100A9, presence of anti-citrullinated peptide antibodies (ACPA), and rheumatoid factor (RF). S100A12 levels were associated with presence of ACPA, history of diabetes, and serum S100A9 levels. sRAGE levels were negatively associated with serum levels of C-reactive protein (CRP) and high-density lipoprotein (HDL), history of vasculitis, and the presence of the RAGE 82Ser polymorphism. Conclusions: sRAGE and S100 proteins were associated not just with RA inflammation and autoantibody production, but also with classical vascular risk factors for end-organ damage. Consistent with its role as a RAGE decoy molecule, sRAGE had the opposite effects to S100 proteins in that S100 proteins were associated with autoantibodies and vascular risk, whereas sRAGE was associated with protection against joint and vascular damage. These data suggest that RAGE activity influences co-development of joint and vascular disease in rheumatoid arthritis patients.

The assessment of ecological condition in south-east Queensland, Australia: An evaluation of reliability across variable environments and surrogate efficacy for biodiversity values

Multimetric ecological condition assessment has become an important biodiversity management tool. This study was the first to examine the reliability of these ecological surrogates across variable environments, and the implications for surrogate efficacy. It was demonstrated that through strategic application and design of the multimetric ecological condition index, the effects of environmental gradients and disturbance regimes can be mitigated, and that ecological condition assessment may serve as a scientifically rigorous approach for conservation planning.

Novel application of a discrete choice experiment to identify preferences for a national healthcare-associated infection surveillance programme: A cross-sectional study

Objective: To identify key stakeholder preferences and priorities when considering a national healthcare-associated infection (HAI) surveillance programme through the use of a discrete choice experiment (DCE). Setting: Australia does not have a national HAI surveillance programme. An online web-based DCE was developed and made available to participants in Australia. Participants: A sample of 184 purposively selected healthcare workers based on their senior leadership role in infection prevention in Australia. Primary and secondary outcomes: A DCE requiring respondents to select 1 HAI surveillance programme over another based on 5 different characteristics (or attributes) in repeated hypothetical scenarios. Data were analysed using a mixed logit model to evaluate preferences and identify the relative importance of each attribute. Results: A total of 122 participants completed the survey (response rate 66%) over a 5-week period. Excluding 22 who mismatched a duplicate choice scenario, analysis was conducted on 100 responses. The key findings included: 72% of stakeholders exhibited a preference for a surveillance programme with continuous mandatory core components (mean coefficient 0.640 (p<0.01)), 65% for a standard surveillance protocol where patient-level data are collected on infected and non-infected patients (mean coefficient 0.641 (p<0.01)), and 92% for hospital-level data that are publicly reported on a website and not associated with financial penalties (mean coefficient 1.663 (p<0.01)). Conclusions: The use of the DCE has provided a unique insight to key stakeholder priorities when considering a national HAI surveillance programme. The application of a DCE offers a meaningful method to explore and quantify preferences in this setting.

The statistics of refractive error maps : managing wavefront aberration analysis without Zernike polynomials

The refractive error of a human eye varies across the pupil and therefore may be treated as a random variable. The probability distribution of this random variable provides a means for assessing the main refractive properties of the eye without the necessity of traditional functional representation of wavefront aberrations. To demonstrate this approach, the statistical properties of refractive error maps are investigated. Closed-form expressions are derived for the probability density function (PDF) and its statistical moments for the general case of rotationally-symmetric aberrations. A closed-form expression for a PDF for a general non-rotationally symmetric wavefront aberration is difficult to derive. However, for specific cases, such as astigmatism, a closed-form expression of the PDF can be obtained. Further, interpretation of the distribution of the refractive error map as well as its moments is provided for a range of wavefront aberrations measured in real eyes. These are evaluated using a kernel density and sample moments estimators. It is concluded that the refractive error domain allows non-functional analysis of wavefront aberrations based on simple statistics in the form of its sample moments. Clinicians may find this approach to wavefront analysis easier to interpret due to the clinical familiarity and intuitive appeal of refractive error maps.

Order tracking for discrete-random separation in variable speed conditions

The transmission path from the excitation to the measured vibration on the surface of a mechanical system introduces a distortion both in amplitude and in phase. Moreover, in variable speed conditions, the amplification/attenuation and the phase shift, due to the transfer function of the mechanical system, varies in time. This phenomenon reduces the effectiveness of the traditionally tachometer based order tracking, compromising the results of a discrete-random separation performed by a synchronous averaging. In this paper, for the first time, the extent of the distortion is identified both in the time domain and in the order spectrum of the signal, highlighting the consequences for the diagnostics of rotating machinery. A particular focus is given to gears, providing some indications on how to take advantage of the quantification of the disturbance to better tune the techniques developed for the compensation of the distortion. The full theoretical analysis is presented and the results are applied to an experimental case.