Effect of storage temperature and media composition on the survivability of Bifidobacterium breve NCIMB 702257 in a malt hydrolisate

The aim of this study was to evaluate the survivability of Bifidobacterium breve NCIMB 702257 in a three malt-based media supplemented with cysteine and yeast extract, and to determine the protective effect of these growth factors. A number of parameterised mathematical models were used to predict of kinetics of viability and total acidity during storage at different temperatures. Results demonstrated a good fit to the experimental mathematical model. The Arrhenius equations showed only reasonable fits and the polynomial plots contained a large area without data between 4 and 25 degrees C. In addition, it was shown that cysteine promotes growth and acid production by bifidobacteria, but does not extend survivability. On the other hand, increasing the yeast extract content of the fermentation media enhances the survivability of B. breve. To our knowledge, this is the first study to address the modelling of the survivability of probiotic bacteria in a cereal based fermentation media at different temperatures, introducing a more quantitative approach to the study of the shelf-life of a probiotic product. (C) 2009 Elsevier B.V. All rights reserved.

State-space model identification of a wireless THz network

We model the large scale fading of wireless THz communications links deployed in a metropolitan area taking into account reception through direct line of sight, ground or wall reflection and diffraction. The movement of the receiver in the three dimensions is modelled by an autonomous dynamic linear system in state-space whereas the geometric relations involved in the attenuation and multi-path propagation of the electric field are described by a static non-linear mapping. A subspace algorithm in conjunction with polynomial regression is used to identify a Wiener model from time-domain measurements of the field intensity.

Wiener-System subspace identification for mobile wireless mm-wave networks

We discuss the feasibility of wireless terahertz communications links deployed in a metropolitan area and model the large-scale fading of such channels. The model takes into account reception through direct line of sight, ground and wall reflection, as well as diffraction around a corner. The movement of the receiver is modeled by an autonomous dynamic linear system in state space, whereas the geometric relations involved in the attenuation and multipath propagation of the electric field are described by a static nonlinear mapping. A subspace algorithm in conjunction with polynomial regression is used to identify a single-output Wiener model from time-domain measurements of the field intensity when the receiver motion is simulated using a constant angular speed and an exponentially decaying radius. The identification procedure is validated by using the model to perform q-step ahead predictions. The sensitivity of the algorithm to small-scale fading, detector noise, and atmospheric changes are discussed. The performance of the algorithm is tested in the diffraction zone assuming a range of emitter frequencies (2, 38, 60, 100, 140, and 400 GHz). Extensions of the simulation results to situations where a more complicated trajectory describes the motion of the receiver are also implemented, providing information on the performance of the algorithm under a worst case scenario. Finally, a sensitivity analysis to model parameters for the identified Wiener system is proposed.

MIMO Wiener model identification for large scale fading of wireless mobile communications links

The large scale fading of wireless mobile communications links is modelled assuming the mobile receiver motion is described by a dynamic linear system in state-space. The geometric relations involved in the attenuation and multi-path propagation of the electric field are described by a static non-linear mapping. A Wiener system subspace identification algorithm in conjunction with polynomial regression is used to identify a model from time-domain estimates of the field intensity assuming a multitude of emitters and an antenna array at the receiver end.

Search space pruning and global optimisation of Multiple Gravity Assist spacecraft trajectories

We introduce and describe the Multiple Gravity Assist problem, a global optimisation problem that is of great interest in the design of spacecraft and their trajectories. We discuss its formalization and we show, in one particular problem instance, the performance of selected state of the art heuristic global optimisation algorithms. A deterministic search space pruning algorithm is then developed and its polynomial time and space complexity derived. The algorithm is shown to achieve search space reductions of greater than six orders of magnitude, thus reducing significantly the complexity of the subsequent optimisation.

Evaluating the ability of a numerical weather prediction model to forecast tracer concentrations during ETEX 2

In this paper the meteorological processes responsible for transporting tracer during the second ETEX (European Tracer EXperiment) release are determined using the UK Met Office Unified Model (UM). The UM predicted distribution of tracer is also compared with observations from the ETEX campaign. The dominant meteorological process is a warm conveyor belt which transports large amounts of tracer away from the surface up to a height of 4 km over a 36 h period. Convection is also an important process, transporting tracer to heights of up to 8 km. Potential sources of error when using an operational numerical weather prediction model to forecast air quality are also investigated. These potential sources of error include model dynamics, model resolution and model physics. In the UM a semi-Lagrangian monotonic advection scheme is used with cubic polynomial interpolation. This can predict unrealistic negative values of tracer which are subsequently set to zero, and hence results in an overprediction of tracer concentrations. In order to conserve mass in the UM tracer simulations it was necessary to include a flux corrected transport method. Model resolution can also affect the accuracy of predicted tracer distributions. Low resolution simulations (50 km grid length) were unable to resolve a change in wind direction observed during ETEX 2, this led to an error in the transport direction and hence an error in tracer distribution. High resolution simulations (12 km grid length) captured the change in wind direction and hence produced a tracer distribution that compared better with the observations. The representation of convective mixing was found to have a large effect on the vertical transport of tracer. Turning off the convective mixing parameterisation in the UM significantly reduced the vertical transport of tracer. Finally, air quality forecasts were found to be sensitive to the timing of synoptic scale features. Errors in the position of the cold front relative to the tracer release location of only 1 h resulted in changes in the predicted tracer concentrations that were of the same order of magnitude as the absolute tracer concentrations.

Vertex splitting and connectivity augmentation in hypergraphs

We consider problems of splitting and connectivity augmentation in hypergraphs. In a hypergraph G = (V +s, E), to split two edges su, sv, is to replace them with a single edge uv. We are interested in doing this in such a way as to preserve a defined level of connectivity in V . The splitting technique is often used as a way of adding new edges into a graph or hypergraph, so as to augment the connectivity to some prescribed level. We begin by providing a short history of work done in this area. Then several preliminary results are given in a general form so that they may be used to tackle several problems. We then analyse the hypergraphs G = (V + s, E) for which there is no split preserving the local-edge-connectivity present in V. We provide two structural theorems, one of which implies a slight extension to Mader’s classical splitting theorem. We also provide a characterisation of the hypergraphs for which there is no such “good” split and a splitting result concerned with a specialisation of the local-connectivity function. We then use our splitting results to provide an upper bound on the smallest number of size-two edges we must add to any given hypergraph to ensure that in the resulting hypergraph we have λ(x, y) ≥ r(x, y) for all x, y in V, where r is an integer valued, symmetric requirement function on V*V. This is the so called “local-edge-connectivity augmentation problem” for hypergraphs. We also provide an extension to a Theorem of Szigeti, about augmenting to satisfy a requirement r, but using hyperedges. Next, in a result born of collaborative work with Zoltán Király from Budapest, we show that the local-connectivity augmentation problem is NP-complete for hypergraphs. Lastly we concern ourselves with an augmentation problem that includes a locational constraint. The premise is that we are given a hypergraph H = (V,E) with a bipartition P = {P1, P2} of V and asked to augment it with size-two edges, so that the result is k-edge-connected, and has no new edge contained in some P(i). We consider the splitting technique and describe the obstacles that prevent us forming “good” splits. From this we deduce results about which hypergraphs have a complete Pk-split. This leads to a minimax result on the optimal number of edges required and a polynomial algorithm to provide an optimal augmentation.

Perturbation, extraction and refinement of invariant pairs for matrix polynomials

Generalizing the notion of an eigenvector, invariant subspaces are frequently used in the context of linear eigenvalue problems, leading to conceptually elegant and numerically stable formulations in applications that require the computation of several eigenvalues and/or eigenvectors. Similar benefits can be expected for polynomial eigenvalue problems, for which the concept of an invariant subspace needs to be replaced by the concept of an invariant pair. Little has been known so far about numerical aspects of such invariant pairs. The aim of this paper is to fill this gap. The behavior of invariant pairs under perturbations of the matrix polynomial is studied and a first-order perturbation expansion is given. From a computational point of view, we investigate how to best extract invariant pairs from a linearization of the matrix polynomial. Moreover, we describe efficient refinement procedures directly based on the polynomial formulation. Numerical experiments with matrix polynomials from a number of applications demonstrate the effectiveness of our extraction and refinement procedures.

High frequency scattering by convex curvilinear polygons

We consider the scattering of a time-harmonic acoustic incident plane wave by a sound soft convex curvilinear polygon with Lipschitz boundary. For standard boundary or finite element methods, with a piecewise polynomial approximation space, the number of degrees of freedom required to achieve a prescribed level of accuracy grows at least linearly with respect to the frequency of the incident wave. Here we propose a novel Galerkin boundary element method with a hybrid approximation space, consisting of the products of plane wave basis functions with piecewise polynomials supported on several overlapping meshes; a uniform mesh on illuminated sides, and graded meshes refined towards the corners of the polygon on illuminated and shadow sides. Numerical experiments suggest that the number of degrees of freedom required to achieve a prescribed level of accuracy need only grow logarithmically as the frequency of the incident wave increases.

Filtering techniques in self-tuning

In the last few years a state-space formulation has been introduced into self-tuning control. This has not only allowed for a wider choice of possible control actions, but has also provided an insight into the theory underlying—and hidden by—that used in the polynomial description. This paper considers many of the self-tuning algorithms, both state-space and polynomial, presently in use, and by starting from first principles develops the observers which are, effectively, used in each case. At any specific time instant the state estimator can be regarded as taking one of two forms. In the first case the most recently available output measurement is excluded, and here an optimal and conditionally stable observer is obtained. In the second case the present output signal is included, and here it is shown that although the observer is once again conditionally stable, it is no longer optimal. This result is of significance, as many of the popular self-tuning controllers lie in the second, rather than first, category.

Self-tuning regulators—a state space approach

This paper employs a state space system description to provide a pole placement scheme via state feedback. It is shown that when a recursive least squares estimation scheme is used, the feedback employed can be expressed simply in terms of the estimated system parameters. To complement the state feedback approach, a method employing both state feedback and linear output feedback is discussed. Both methods arc then compared with the previous output polynomial type feedback schemes.

Optimal observers for ARMA models

A polynomial-based ARMA model, when posed in a state-space framework can be regarded in many different ways. In this paper two particular state-space forms of the ARMA model are considered, and although both are canonical in structure they differ in respect of the mode in which disturbances are fed into the state and output equations. For both forms a solution is found to the optimal discrete-time observer problem and algebraic connections between the two optimal observers are shown. The purpose of the paper is to highlight the fact that the optimal observer obtained from the first state-space form, commonly known as the innovations form, is not that employed in an optimal controller, in the minimum-output variance sense, whereas the optimal observer obtained from the second form is. Hence the second form is a much more appropriate state-space description to use for controller design, particularly when employed in self-tuning control schemes.

Data based constructive identification - overcoming the curse of dimensionality

The modelling of a nonlinear stochastic dynamical processes from data involves solving the problems of data gathering, preprocessing, model architecture selection, learning or adaptation, parametric evaluation and model validation. For a given model architecture such as associative memory networks, a common problem in non-linear modelling is the problem of "the curse of dimensionality". A series of complementary data based constructive identification schemes, mainly based on but not limited to an operating point dependent fuzzy models, are introduced in this paper with the aim to overcome the curse of dimensionality. These include (i) a mixture of experts algorithm based on a forward constrained regression algorithm; (ii) an inherent parsimonious delaunay input space partition based piecewise local lineal modelling concept; (iii) a neurofuzzy model constructive approach based on forward orthogonal least squares and optimal experimental design and finally (iv) the neurofuzzy model construction algorithm based on basis functions that are Bézier Bernstein polynomial functions and the additive decomposition. Illustrative examples demonstrate their applicability, showing that the final major hurdle in data based modelling has almost been removed.

A new approach to reduced-order modelling

An error polynomial is defined, the coefficients of which indicate the difference at any instant between a system and a model of lower order approximating the system. It is shown how Markov parameters and time series proportionals of the model can be matched with those of the system by setting error polynomial coefficients to zero. Also discussed is the way in which the error between system and model can be considered as being a filtered form of an error input function specified by means of model parameter selection.

Survival of Lactobacillus plantarum in model solutions and fruit juices

The aim of the work was to study the survival of Lactobacillus plantarum NCIMB 8826 in model solutions and develop a mathematical model describing its dependence on pH, citric acid and ascorbic acid. A Central Composite Design (CCD) was developed studying each of the three factors at five levels within the following ranges, i.e., pH (3.0-4.2), citric acid (6-40 g/L), and ascorbic acid (100-1000 mg/L). In total, 17 experimental runs were carried out. The initial cell concentration in the model solutions was approximately 1 × 10(8)CFU/mL; the solutions were stored at 4°C for 6 weeks. Analysis of variance (ANOVA) of the stepwise regression demonstrated that a second order polynomial model fits well the data. The results demonstrated that high pH and citric acid concentration enhanced cell survival; one the other hand, ascorbic acid did not have an effect. Cell survival during storage was also investigated in various types of juices, including orange, grapefruit, blackcurrant, pineapple, pomegranate, cranberry and lemon juice. The model predicted well the cell survival in orange, blackcurrant and pineapple, however it failed to predict cell survival in grapefruit and pomegranate, indicating the influence of additional factors, besides pH and citric acid, on cell survival. Very good cell survival (less than 0.4 log decrease) was observed after 6 weeks of storage in orange, blackcurrant and pineapple juice, all of which had a pH of about 3.8. Cell survival in cranberry and pomegranate decreased very quickly, whereas in the case of lemon juice, the cell concentration decreased approximately 1.1 logs after 6 weeks of storage, albeit the fact that lemon juice had the lowest pH (pH~2.5) among all the juices tested. Taking into account the results from the compositional analysis of the juices and the model, it was deduced that in certain juices, other compounds seemed to protect the cells during storage; these were likely to be proteins and dietary fibre In contrast, in certain juices, such as pomegranate, cell survival was much lower than expected; this could be due to the presence of antimicrobial compounds, such as phenolic compounds.