A fuzzy max-flow min-cut theorem

Interval-valued versions of the max-flow min-cut theorem and Karp-Edmonds algorithm are developed and provide robustness estimates for flows in networks in an imprecise or uncertain environment. These results are extended to networks with fuzzy capacities and flows. (C) 2001 Elsevier Science B.V. All rights reserved.

Star factorizations of graph products

A k-star is the graph K-1,K-k. We prove a general theorem about k-star factorizations of Cayley graphs. This is used to give necessary and sufficient conditions for the existence of k-star factorizations of any power (K-q)(S) of a complete graph with prime power order q, products C-r1 x C-r2 x ... x C-rk of k cycles of arbitrary lengths, and any power (C-r)(S) of a cycle of arbitrary length. (C) 2001 John Wiley & Sons, Inc.

The expression of fibroblast growth factors and their receptors in the embryonic and neonatal mouse inner ear

Four different fibroblast growth factor receptors (FGFR) are known, three of which have splice variants (known as the b and c variants) in the FGF-binding domain, to give different patterns of sensitivity to the different FGFs. The expression of the b and c variants of the FGF receptors. together with the expression of the ligands FGF1. FGF2, FGF3, FGF7, FGF8b and FGF8c, was determined by quantitative reverse transcription-polymerase chain reaction in developing whole mouse inner ears, and in dissected components of the postnatal mouse inner ear. At embryonic age (E)10.5 days, when the otocyst is a simple closed sac, the receptor most heavily expressed was FGFR2b, relative to the postnatal day 0 level. Over the period E10.5-E12.5. during which the structures of the inner ear start to form, the expression of the different FGF receptors increased 10(2)-10(4) fold per unit of tissue, and there was a gradual switch towards expression of the 'c' splice variants of FGFR2 and FGFR3 rather than the 'b' variants. At E10.5, the ligands most heavily expressed, relative to the postnatal day 0 level, were FGF3, FGF8b and FGF8c. In the postnatal inner eat. the patterns of expression of receptors and ligands tended to be correlated, such that receptor variants were expressed in the same regions as the ligands that are known to activate them effectively. The neural/sensory region expressed high levels of FGFR3c, and high levels of the ligand FGF8b. The same area also expressed high levels of FGFR1b and FGFR2b, and high levels of FGF3. The lateral wall of the cochlea (including the stria vascularis and the spiral ligament) expressed high levels of FGFR1c and FGF1. 11 is suggested that the different FGF receptors and ligands are expressed in a spatially coordinated pattern to selectively program cochlear development. (C) 2001 Elsevier Science B.V. All rights reserved.

Supervisory control of wastewater treatment plants by combining principal component analysis and fuzzy c-means clustering

In this paper a methodology for integrated multivariate monitoring and control of biological wastewater treatment plants during extreme events is presented. To monitor the process, on-line dynamic principal component analysis (PCA) is performed on the process data to extract the principal components that represent the underlying mechanisms of the process. Fuzzy c-means (FCM) clustering is used to classify the operational state. Performing clustering on scores from PCA solves computational problems as well as increases robustness due to noise attenuation. The class-membership information from FCM is used to derive adequate control set points for the local control loops. The methodology is illustrated by a simulation study of a biological wastewater treatment plant, on which disturbances of various types are imposed. The results show that the methodology can be used to determine and co-ordinate control actions in order to shift the control objective and improve the effluent quality.

A semi-analytical solution for vibration of rectangular plates with abrupt thickness variation

A semi-analytical analysis of free vibration of plates with cross-sectional discontinuities due to abrupt changes in thickness is presented. A basic square element divided into suitable subdomains dependent upon the positions of these abrupt changes is used as the basic building element, Admissible functions that satisfy the essential or geometric boundary conditions are used to define the transverse deflection of each subdomain. Continuities in the displacement, slope, moment and higher derivatives between adjacent subdomains are enforced at the interconnecting edges. The resulting global energy functional from the proper assembly of the coupled strain and kinetic energy contributions of each subdomain is then minimized via the Ritz procedure to extract the frequencies and mode shapes. Contour plots of a range of new mode shapes are presented for the enhancement of understanding the dynamic behavior of this class of plates, (C) 2001 Elsevier Science Ltd, All rights reserved.

Evaluation of liquid Bacillus thuringiensis var. israelensis products for control of Australian Aedes arbovirus vectors

Laboratory bioassay studies were conducted in southeast Queensland, Australia,: on the efficacy of Teknar (R), VectoBac (R) 12AS, and Cybate (R) (active ingredient: 1,200 international toxic units Bacillus thuringiensis var, israelensis [Bti]) against 3rd instars of the arbovirus vectors Aedes aegypti. Ae. notoscriptus, Ae. vigilax, and Ae. camptorhynchus. Probit analyses were then used to determine LD,, (median lethal dose), LD95, and lethal dose ratios (LDR). Aedes aegypti and Ae. notoscriptus, both container-habitat species, tolerated the highest Bti concentrations compared with saltmarsh Ae. vigilax and Ae. camptorhynchus. For example, the LDR for Ae. vigilax versus Ae. notoscriptus exposed to Cybate was 0.14 (95% confidence limit [CL] 0.03-0.61). Similarly, the Cybate LDR for Ae. camptorhynchus versus Ae. notoscriptus was 0.22 (95% CL 0.07-0.70). Teknar produced similar results with an LDR of 0.21 (95% CL 0.04-1.10) for Aedes vigilax versus Aedes notoscriptus. Differences in product efficacy were found when tested against the 2 container-breeding species. Cybate was less effective than Teknar with LDRs of 1.55 (95% CL 0.65-3.67) and 1.87 (95% CL 0.68-5.15) for Aedes aegypti and Ae. notoscriptus, respectively. The significant differences in susceptibility between mosquito species and varying efficacy between products highlight the importance of evaluating concentration-response data prior to contracting with distributors of mosquito control products. This information is crucial to resistance management strategies.

Brief note on the variation of constants formula for fuzzy differential equations

This note gives a theory of state transition matrices for linear systems of fuzzy differential equations. This is used to give a fuzzy version of the classical variation of constants formula. A simple example of a time-independent control system is used to illustrate the methods. While similar problems to the crisp case arise for time-dependent systems, in time-independent cases the calculations are elementary solutions of eigenvalue-eigenvector problems. In particular, for nonnegative or nonpositive matrices, the problems at each level set, can easily be solved in MATLAB to give the level sets of the fuzzy solution. (C) 2002 Elsevier Science B.V. All rights reserved.

Theory and applications of fuzzy Volterra integral equations

Formulations of fuzzy integral equations in terms of the Aumann integral do not reflect the behavior of corresponding crisp models. Consequently, they are ill-adapted to describe physical phenomena, even when vagueness and uncertainty are present. A similar situation for fuzzy ODEs has been obviated by interpretation in terms of families of differential inclusions. The paper extends this formalism to fuzzy integral equations and shows that the resulting solution sets and attainability sets are fuzzy and far better descriptions of uncertain models involving integral equations. The investigation is restricted to Volterra type equations with mildly restrictive conditions, but the methods are capable of extensive generalization to other types and more general assumptions. The results are illustrated by integral equations relating to control models with fuzzy uncertainties.