Interpolation with function space representation of membership functions

This paper generalizes a previous Cartesian approach for interpolating fuzzy rules comprised of membership functions with finite number of characteristic points. Instead of representing membership functions as points in Cartesian spaces, they now become elements in the space of square, integrable function. Interpolation is thus conducted between the antecedent and consequent function spaces. The generalized representation allows an extended class of membership functions satisfying two monotonicity conditions to be accommodated in the interpolation process. They include the popular bell-shaped membership functions, which were not possible before with the Cartesian representation. The work also extends the similarity triangle-based interpolation technique from the previous Cartesian representation to the new representation. Ensuing issues on computational complexity and nonunique conclusion are discussed. Other concepts such as spanning set and extensibility functions are also presented under the generalized framework. Examples to illustrate the extended approach and to compare with the Cartesian approach are given.     

TRADE‐OFF BETWEEN APPROXIMATION ACCURACY AND COMPLEXITY FOR TS FUZZY MODELS

This paper proposes a transformation method that serves the trade‐off between the modelling complexity and accuracy of multi‐variable Takagi‐Sugeno fuzzy inference operator‐based modelling (TS fuzzy modelling). The relation between the number of fuzzy rules and the modelling accuracy is defined in the paper. The proposed transformation method is capable of finding the minimal number of fuzzy rules for a given accuracy of a given TS fuzzy model. A case study, focusing on a benchmark problem of fault diagnosis, developed in the framework of EC‐founded Research Training Network DAMADICS, of an actuator in a sugar factory, is presented to provide feasibility of the proposed method.     

Environmentally friendly phthalocyanine catalysts for water decontamination—Non-photocatalytic systems

Macrocyclic porphyrin-like compounds known as phthalocyanines (Pcs) have been shown to produce singlet oxygen species upon illumination with light of an appropriate wavelength. Singlet oxygen is an effective agent for complete oxidation of common water-soluble pollutants including chlorinated phenols. The most active are, in this respect, phthalocyanines bearing Al, Zn and Si central atoms. Although these compounds were proofed to be virtually non-toxic, the presence of the Al³⁺ and Zn²⁺ ions may contradict this. On the other hand e.g. iron phthalocyanine (FePc) does not represent any danger from this point of view. However, due to the specific coordination of its central metal ion and also because of the number of electrons occupying its valence orbitals, the FePc cannot be effectively activated by the photon flux. Here we report on an alternative system in the dark. It is based on the initial catalytic decomposition of various peroxo substances by metal Pc, producing oxidising species which can decompose chlorinated phenols. A series of Pcs and peroxo substances were compared and the reaction system optimised. It was shown that the highest activity was revealed for the system comprising of FePc and tert-butylhydroperoxide. Iron phthalocyanine was also successfully immobilised on an Al₂O₃ solid matrix, and this heterogeneous system was tested analogously to the homogeneous one. Virtually zero leaching of the anchored complex was detected and the activity was found to be comfortably high.     

COMPLEXITY RELAXATION OF THE TENSOR PRODUCT MODEL TRANSFORMATION FOR HIGHER DIMENSIONAL PROBLEMS

The Tensor Product (TP) model transformation method was proposed recently as an automated gateway between a class of non‐linear models and linear matrix inequality based control design. The core of the TP model transformation is the higher order singular value decomposition of a large sized tensor, which requires high computational power that is usually outside of a regular computer capacity in cases of higher dimensionality. This disadvantage restricts the utilization of the TP model transformation to models having smaller dimensionality. The aim of this paper is to propose a computationally relaxed version of the TP model transformation. The paper also presents a 6 dimensional example to show the effectiveness of the modified transformation.     

Adaptation of TS fuzzy models without complexity expansion: HOSVD-based approach

One direction of measured data-set based modeling applies fuzzy logic identification tools and results in a fuzzy rule-base model. A typical problem of fuzzy identification methods is that the complexity of the resulting fuzzy rule-base, namely the number of rules in the rule-base, explodes with the modeling accuracy. As a result, the topic of fuzzy rule-base complexity reduction techniques emerged in the last decade. A common disadvantage of fuzzy rule-base complexity reduction methods is that the resulting complexity minimized fuzzy-rule bases cannot be simply adapted to new information. If we have new information that cannot be described by the fuzzy rules of the complexity minimized fuzzy rule-base, then we have two choices. The first choice is to add new fuzzy rules to the fuzzy rule-base until the new information can be described. The second choice is to modify the new information until it can be described by the fuzzy rule-base without using additional fuzzy rules. This second case has the prominent role if the number of fuzzy rules in the fuzzy rule-base is limited. This paper proposes a method for the second choice. The proposed method minimizes the necessary modification of the new information. This paper focuses attention on a recent complexity reduction method, termed Higher Order Singular Value Decomposition (HOSVD)-based complexity reduction, and Takagi-Sugeno (TS) inference operator-based fuzzy rule-bases. An example is used to provide the validation of the proposed method. In order to demonstrate the effectiveness of the proposed method, a control system of a differential-steered automatic guided vehicle is modeled in the paper.     

Stochastic modelling of individual cell growth using flow chamber microscopy images

In this paper, we analysed individual cell growth images obtained by flow chamber microscopy system. We used replicate flow chamber experiment data as reported by [Elfwing, A., Le Marc, Y., Baranyi, J., Ballagi, A., 2004. Observing the growth and division of large number of individual bacteria using image analysis. Applied and Environmental Microbiology 70, 675-678] involving both unstressed and heat shocked Listeria innocua cells. After observing the kinetics of a large number of cells, we propose a new stochastic model for their individual growth. By comparing our model with other existing models in the literature, we demonstrate that ours can accurately describe the growth of both stressed and unstressed cells. Our results indicate that the lag period, in terms of cell division, coincides dominantly with a lag period in terms of cell size. We also reveal various connections between cell length, lag time and cell division models. Finally, we present the results of our investigation on the effect of the duration of sublethal heat shock on the found growth properties.     

Does proximity to neighbours affect germination of spores of non-proteolytic Clostridium botulinum?

It is recognised that inoculum size affects the rate and extent of bacterial spore germination. It has been proposed that this is due to spores interacting: molecules released from germinated spores trigger germination of dormant neighbours. This study investigated whether changes to the total number of spores in a system or proximity to other spores (local spore density) had a more significant effect on interaction between spores of non-proteolytic Clostridium botulinum strain Eklund 17B attached to defined areas of microscope slides. Both the number of spores attached to the slides and local spore density (number of spores per mm²) were varied by a factor of nine. Germination was observed microscopically at 15 °C for 8 h and the probability of, and time to, germination calculated from image analysis measurements. Statistical analysis revealed that the effect of total spore number on the probability of germination within 8 h was more significant than that of proximity to neighbours (local spore density); its influence on germination probability was approximately four-times greater. Total spore number had an even more significant affect on time to germination; it had a nine-fold greater influence than proximity to neighbours. The applied models provide a means to characterise, quantitatively, the effect of the total spore number on spore germination relative to the effect of proximity to neighbouring spores.     

Methods to determine the growth domain in a multidimensional environmental space

Data from a database on microbial responses to the food environment (ComBase, see www.combase.cc) were used to study the boundary of growth several pathogens (Aeromonas hydrophila, Escherichia coli, Listeria monocytogenes, Yersinia enterocolitica). Two methods were used to evaluate the growth/no growth interface. The first one is an application of the Minimum Convex Polyhedron (MCP) introduced by Baranyi et al. [Baranyi, J., Ross, T., McMeekin, T., Roberts, T.A., 1996. The effect of parameterisation on the performance of empirical models used in Predictive Microbiology. Food Microbiol. 13, 83–91.]. The second method applies logistic regression to define the boundary of growth. The combination of these two different techniques can be a useful tool to handle the problem of extrapolation of predictive models at the growth limits.     

Effect of rabbit kappa-casein expression on the properties of milk from transgenic mice

Transgenic mice were produced carrying the coding region of the rabbit kappa-casein gene linked to the upstream region of the rabbit whey acidic protein gene. Mice from the highest-expressing line produced 2.5 mg rabbit kappa-casein/ml in their milk. The foreign protein was associated with the casein micelles and altered micelle size, though in the high-expressing line rabbit kappa-casein also segregated into the whey fraction obtained after centrifuging the milk samples. Milk from transgenic mice had the same overall protein content as that from non-transgenic mice, except for the transgene product. However, litters fed with this transgenic mouse milk grew less well than litters given milk from non-transgenic mice. This reduction in growth was not related to changes in mammary gland structure or mammary cell morphology. Preliminary results indicated that milk from the transgenic mice had a higher viscosity.     

The effect of reuterin on the lag time of single cells of Listeria innocua grown on a solid agar surface at different pH and NaCl concentrations

The lag time of single cells of Listeria innocua grown on the surface of Brain Heart Infusion Agar was studied by microscopy and image analysis. An experimental set-up that enabled relocation of the cells on the agar surface was developed and used to collect data from 50 to 100 individual cells at a time. Reuterin was added at different concentrations (0-10 AU/ml) and it was observed that it increased both the lag time of the cells and its variance. Furthermore, for a large proportion of cells, reuterin completely prevented the cell division within the time of observation. Reuterin in combination with low pH inhibited the cell division even more efficiently. A similar effect was observed for the combination of reuterin and sodium chloride. Our experimental set-up provides a good model system for generating data on the lag time of single cells on solid surfaces, which can improve the predictions of microbial growth on solid food matrices.