A uniform white-noise model for fixed-point roundoff errors in digital systems

Fixed-point roundoff noise in digital implementation of linear systems arises due to overflow, quantization of coefficients and input signals, and arithmetical errors. In uniform white-noise models, the last two types of roundoff errors are regarded as uniformly distributed independent random vectors on cubes of suitable size. For input signal quantization errors, the heuristic model is justified by a quantization theorem, which cannot be directly applied to arithmetical errors due to the complicated input-dependence of errors. The complete uniform white-noise model is shown to be valid in the sense of weak convergence of probabilistic measures as the lattice step tends to zero if the matrices of realization of the system in the state space satisfy certain nonresonance conditions and the finite-dimensional distributions of the input signal are absolutely continuous.

Robust model-order reduction of complex biological processes

This paper addresses robust model-order reduction of a high dimensional nonlinear partial differential equation (PDE) model of a complex biological process. Based on a nonlinear, distributed parameter model of the same process which was validated against experimental data of an existing, pilot-scale BNR activated sludge plant, we developed a state-space model with 154 state variables in this work. A general algorithm for robustly reducing the nonlinear PDE model is presented and based on an investigation of five state-of-the-art model-order reduction techniques, we are able to reduce the original model to a model with only 30 states without incurring pronounced modelling errors. The Singular perturbation approximation balanced truncating technique is found to give the lowest modelling errors in low frequency ranges and hence is deemed most suitable for controller design and other real-time applications. (C) 2002 Elsevier Science Ltd. All rights reserved.

Evaluating plant breeding strategies by simulating gene action and dryland environment effects

Functional genomics is the systematic study of genome-wide effects of gene expression on organism growth and development with the ultimate aim of understanding how networks of genes influence traits. Here, we use a dynamic biophysical cropping systems model (APSIM-Sorg) to generate a state space of genotype performance based on 15 genes controlling four adaptive traits and then search this spice using a quantitative genetics model of a plant breeding program (QU-GENE) to simulate recurrent selection. Complex epistatic and gene X environment effects were generated for yield even though gene action at the trait level had been defined as simple additive effects. Given alternative breeding strategies that restricted either the cultivar maturity type or the drought environment type, the positive (+) alleles for 15 genes associated with the four adaptive traits were accumulated at different rates over cycles of selection. While early maturing genotypes were favored in the Severe-Terminal drought environment type, late genotypes were favored in the Mild-Terminal and Midseason drought environment types. In the Severe-Terminal environment, there was an interaction of the stay-green (SG) trait with other traits: Selection for + alleles of the SG genes was delayed until + alleles for genes associated with the transpiration efficiency and osmotic adjustment traits had been fixed. Given limitations in our current understanding of trait interaction and genetic control, the results are not conclusive. However, they demonstrate how the per se complexity of gene X gene X environment interactions will challenge the application of genomics and marker-assisted selection in crop improvement for dryland adaptation.

Existence and uniqueness of Q-processes with a given finite μ-invariant measure

Let Q be a stable and conservative Q-matrix over a countable state space S consisting of an irreducible class C and a single absorbing state 0 that is accessible from C. Suppose that Q admits a finite mu-subinvariant measure in on C. We derive necessary and sufficient conditions for there to exist a Q-process for which m is mu-invariant on C, as well as a necessary condition for the uniqueness of such a process.

Estimating trends and seasonality in coronary heart disease

We present two methods of estimating the trend, seasonality and noise in time series of coronary heart disease events. In contrast to previous work we use a non-linear trend, allow multiple seasonal components, and carefully examine the residuals from the fitted model. We show the importance of estimating these three aspects of the observed data to aid insight of the underlying process, although our major focus is on the seasonal components. For one method we allow the seasonal effects to vary over time and show how this helps the understanding of the association between coronary heart disease and varying temperature patterns. Copyright (C) 2004 John Wiley Sons, Ltd.

Subgeometric rates of convergence for a class of continuous-time Markov process

Let (Phi(t))(t is an element of R+) be a Harris ergodic continuous-time Markov process on a general state space, with invariant probability measure pi. We investigate the rates of convergence of the transition function P-t(x, (.)) to pi; specifically, we find conditions under which r(t) vertical bar vertical bar P-t (x, (.)) - pi vertical bar vertical bar -> 0 as t -> infinity, for suitable subgeometric rate functions r(t), where vertical bar vertical bar - vertical bar vertical bar denotes the usual total variation norm for a signed measure. We derive sufficient conditions for the convergence to hold, in terms of the existence of suitable points on which the first hitting time moments are bounded. In particular, for stochastically ordered Markov processes, explicit bounds on subgeometric rates of convergence are obtained. These results are illustrated in several examples.

A diffusion approach to approximating preservation probabilities for gene duplicates

Consider a haploid population and, within its genome, a gene whose presence is vital for the survival of any individual. Each copy of this gene is subject to mutations which destroy its function. Suppose one member of the population somehow acquires a duplicate copy of the gene, where the duplicate is fully linked to the original gene's locus. Preservation is said to occur if eventually the entire population consists of individuals descended from this one which initially carried the duplicate. The system is modelled by a finite state-space Markov process which in turn is approximated by a diffusion process, whence an explicit expression for the probability of preservation is derived. The event of preservation can be compared to the fixation of a selectively neutral gene variant initially present in a single individual, the probability of which is the reciprocal of the population size. For very weak mutation, this and the probability of preservation are equal, while as mutation becomes stronger, the preservation probability tends to double this reciprocal. This is in excellent agreement with simulation studies.

Distillability of Werner states using entanglement witnesses and robust semidefinite programs

We use robust semidefinite programs and entanglement witnesses to study the distillability of Werner states. We perform exact numerical calculations that show two-undistillability in a region of the state space, which was previously conjectured to be undistillable. We also introduce bases that yield interesting expressions for the distillability witnesses and for a tensor product of Werner states with an arbitrary number of copies.

Anisotropy-based robust performance analysis of finite horizon linear discrete time varying systems

We consider a problem of robust performance analysis of linear discrete time varying systems on a bounded time interval. The system is represented in the state-space form. It is driven by a random input disturbance with imprecisely known probability distribution; this distributional uncertainty is described in terms of entropy. The worst-case performance of the system is quantified by its a-anisotropic norm. Computing the anisotropic norm is reduced to solving a set of difference Riccati and Lyapunov equations and a special form equation.

A helicopter named Dolly: Behavioural cloning for autonomous helicopter control

This paper considers the pros and cons of using behavioural cloning for the development of low-level helicopter automation modules. Over the course of this project several Behavioural cloning approaches have been investigated. The results of the most effective Behavioural cloning approach are then compared to PID modules designed for the same aircraft. The comparison takes into consideration development time, reliability, and control performance. It has been found that Behavioural cloning techniques employing local approximators and a wide state-space coverage during training can produce stabilising control modules in less time than tuning PID controllers. However, performance and reliabity deficits have been found to exist with the Behavioural Cloning, attributable largely to the time variant nature of the dynamics due to the operating environment, and the pilot actions being poor for teaching. The final conclusion drawn here is that tuning PID modules remains superior to behavioural cloning for low-level helicopter automation.

Modeling of phase equilibrium and vapor adsorption on carbon black based on a combination of a lattice theory and equation of state

A thermodynamic approach is developed in this paper to describe the behavior of a subcritical fluid in the neighborhood of vapor-liquid interface and close to a graphite surface. The fluid is modeled as a system of parallel molecular layers. The Helmholtz free energy of the fluid is expressed as the sum of the intrinsic Helmholtz free energies of separate layers and the potential energy of their mutual interactions calculated by the 10-4 potential. This Helmholtz free energy is described by an equation of state (such as the Bender or Peng-Robinson equation), which allows us a convenient means to obtain the intrinsic Helmholtz free energy of each molecular layer as a function of its two-dimensional density. All molecular layers of the bulk fluid are in mechanical equilibrium corresponding to the minimum of the total potential energy. In the case of adsorption the external potential exerted by the graphite layers is added to the free energy. The state of the interface zone between the liquid and the vapor phases or the state of the adsorbed phase is determined by the minimum of the grand potential. In the case of phase equilibrium the approach leads to the distribution of density and pressure over the transition zone. The interrelation between the collision diameter and the potential well depth was determined by the surface tension. It was shown that the distance between neighboring molecular layers substantially changes in the vapor-liquid transition zone and in the adsorbed phase with loading. The approach is considered in this paper for the case of adsorption of argon and nitrogen on carbon black. In both cases an excellent agreement with the experimental data was achieved without additional assumptions and fitting parameters, except for the fluid-solid potential well depth. The approach has far-reaching consequences and can be readily extended to the model of adsorption in slit pores of carbonaceous materials and to the analysis of multicomponent adsorption systems. (C) 2002 Elsevier Science (USA).

Modeling of gas adsorption equilibrium over a wide range of pressure: A thermodynamic approach based on equation of state

A thermodynamic approach based on the Bender equation of state is suggested for the analysis of supercritical gas adsorption on activated carbons at high pressure. The approach accounts for the equality of the chemical potential in the adsorbed phase and that in the corresponding bulk phase and the distribution of elements of the adsorption volume (EAV) over the potential energy for gas-solid interaction. This scheme is extended to subcritical fluid adsorption and takes into account the phase transition in EAV The method is adapted to gravimetric measurements of mass excess adsorption and has been applied to the adsorption of argon, nitrogen, methane, ethane, carbon dioxide, and helium on activated carbon Norit R I in the temperature range from 25 to 70 C. The distribution function of adsorption volume elements over potentials exhibits overlapping peaks and is consistently reproduced for different gases. It was found that the distribution function changes weakly with temperature, which was confirmed by its comparison with the distribution function obtained by the same method using nitrogen adsorption isotherm at 77 K. It was shown that parameters such as pore volume and skeleton density can be determined directly from adsorption measurements, while the conventional approach of helium expansion at room temperature can lead to erroneous results due to the adsorption of helium in small pores of activated carbon. The approach is a convenient tool for analysis and correlation of excess adsorption isotherms over a wide range of pressure and temperature. This approach can be readily extended to the analysis of multicomponent adsorption systems. (C) 2002 Elsevier Science (USA).

Modeling diffraction in free-space optical interconnects by the mode expansion method

Free-space optical interconnects (FSOIs), made up of dense arrays of vertical-cavity surface-emitting lasers, photodetectors and microlenses can be used for implementing high-speed and high-density communication links, and hence replace the inferior electrical interconnects. A major concern in the design of FSOIs is minimization of the optical channel cross talk arising from laser beam diffraction. In this article we introduce modifications to the mode expansion method of Tanaka et al. [IEEE Trans. Microwave Theory Tech. MTT-20, 749 (1972)] to make it an efficient tool for modelling and design of FSOIs in the presence of diffraction. We demonstrate that our modified mode expansion method has accuracy similar to the exact solution of the Huygens-Kirchhoff diffraction integral in cases of both weak and strong beam clipping, and that it is much more accurate than the existing approximations. The strength of the method is twofold: first, it is applicable in the region of pronounced diffraction (strong beam clipping) where all other approximations fail and, second, unlike the exact-solution method, it can be efficiently used for modelling diffraction on multiple apertures. These features make the mode expansion method useful for design and optimization of free-space architectures containing multiple optical elements inclusive of optical interconnects and optical clock distribution systems. (C) 2003 Optical Society of America.