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The aim of this paper is the predictive control of Timed Event Graphs with specifications defined by P-time Event Graphs. We propose a fixed-point approach which leads to a pseudopolynomial algorithm. As the performance of the algorithm is crucial in on-line control, we highlight an important case where the resolution of this first algorithm is efficient. The second technique is a space controller on a horizon leading to a strongly polynomial algorithm.keywords: Timed Event Graphs, P-time Petri nets, (min, max, +) functions, fixed point, predictive control. II. INTRODUCTIONIn this paper, we focus on model predictive control of Timed Event Graphs with specifications defined by P-time Event Graphs. A classical problem is the control of a Timed Event Graph where some events are stated as controllable, meaning that the corresponding transitions (input) may be delayed from firing until some arbitrary time provided by a supervisor. The specifications are defined by a P-time Event Graph [11] [6] which describes the desired behavior of the interconnections of all the internal transitions. We wish to determine an input in order to obtain the desired behavior defined by the specifications.Model predictive control is an on-line approach which needs efficient algorithms: a crucial point is that a calculation of the control that is too slow can postpone the application of the control at the calculated dates. With the aim of a strongly polynomial algorithm, one objective is the analysis of the state space.Naturally, variations of the classical problem have been considered in the literature. A first class of approaches [7] considers extremal points of the state space and develops optimal control in order to keep trajectories close to a reference trajectory following additional constraints. Contrary to these approaches where the resolution uses conventional algebra, our approach describes every trajectory in the formalism of the (max, +) algebra. Moreover, we only use classical operations such as the Kleene star which can be determined by known efficient algorithms: They are polynomial in the strong sense, that is, the complexity depends only on the dimensions but not on the values of the parameters. We can recall that the classical algorithms of linear programming are not polynomial in the strong sense (the complexities of the ellipsoid algorithm of Khashiyan and the interior point algorithm of Karmarkar are respectively O(n 4 .L) and O(n 3.5 .L) where n is the number of variables and L is the number of bits necessary in the storage of the data [14]).P. Declerck is with LISA EA4014,

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The purpose of this technical note is the optimal control synthesis of a Timed Event Graph when the state and control trajectories should follow the specifications defined by an interval model. The problem is reformulated in the fixed point form and the spectral theory gives the conditions of existence of a solution.

OBJECTIVE: To assess the value of the new differential culture medium CHROMagar Candida for routine investigation of clinical specimens. METHODS: During a whole year, 6150 clinical samples were plated on CHROMagar Candida medium. After incubation, the green colonies were considered to be Candida albicans. The colonies of other colors were identified using Bichrolatex-krusei, or by their assimilation pattern on ID 32C test strips and their morphology on rice cream-agar-Tween. RESULTS: Among the 6150 clinical samples, 1643 were positive for fungi. Aspergillus fumigatus and Geotrichum sp. were the predominant filamentous fungi isolated. Candida albicans was the most common species isolated (1274 of the positive samples; 77.5%), and Candida glabrata was the second most common yeast isolated (174 positive samples; 10.6%). Other yeast species were detected at lower frequencies, mainly Candida tropicalis (3.8%), Candida krusei (2.7%), Saccharomyces cerevisiae (2.7%) and Candida kefyr (2.3%), and 16 samples revealed a lipophilic species, Malassezia furfur. Mixed fungal populations accounted for 14.7% of the positive samples. Two or more yeast species were detected in 206 of the 242 specimens containing mixed fungal populations, and five yeast species were detected in one sample. Additionally, we did not observe significant differences in the isolation of yeasts or filamentous fungi from the 366 samples simultaneously plated on CHROMagar Candida and Sabouraud dextrose agar. Close agreement between the two culture media was observed for 89.9% of these samples. CONCLUSIONS: CHROMagar Candida medium was shown to be extremely helpful in a routine clinical mycology service, facilitating the detection of mixed cultures of yeasts and allowing direct identification of C. albicans, as well as rapid presumptive identification of the other yeasts: C. glabrata, C. tropicalis, C. krusei and S. cerevisiae. This chromogenic medium thus appears to be suitable as a primary culture medium, particularly for the mycologic surveillance of immunocompromised patients.