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We present an extremum seeking control algorithm for discrete-time systems applied to a class of plants that are represented as a series combination of a linear input dynamics, a static nonlinearity with an extremum, and a linear output dynamics. By using the two-time scale averaging theory, we derive a mild sufficient condition under which the plant output exponentially converges to an [OMICRON] ([[alpha].sup.2]) neighborhood of the extremum value, where [alpha] is the magnitude of modulation signal. The sufficient condition is related to positive realness of linear parts of the plant but only at the modulation frequency. The algorithm is illustrated with a brief simulation study. Index Terms--Averaging, discrete-time systems, extremum seeking.

The expression of the retinoic acid receptor-beta appears to be lost in precancerous oral lesions but can be restored by isotretinoin. Researchers used RNA hybridization techniques to detect messenger RNA (mRNA) for the six types of retinoic acid receptors in oral biopsy samples of seven healthy people and 52 people with precancerous oral lesions. Messenger RNA for the retinoic acid receptor-beta was detected in all samples from the healthy volunteers, but in only 40% of samples from those with precancerous oral lesions. The group with precancerous oral lesions started taking 1.5 milligrams per kilogram of isotretinoin every day. Three months later, oral biopsies from 39 were tested for retinoic acid receptor-beta mRNA. It was found in 90% of the samples. Twenty-two patients responded to the treatment, and 82% had increased levels of retinoic acid receptor-beta mRNA, compared to 47% of those who did not respond to isotretinoin.

Some cancer patients respond better to treatment than other patients with apparently identical stages and grades of tumors. Until the advent of some modern laboratory technologies, however, it has not been practical to attempt to identify the differences which might distinguish one patient from another. Today the search for prognostic factors is an important part of cancer research. Reliable prognostic indicators may have direct clinical relevance, since patients with especially poor prognosis might be given more aggressive treatment from the outset, while patients with especially good prognosis might be spared some of the side effects of the more aggressive approaches. Researchers examining prognostic factors in cases of non-small-cell lung cancer have found that the presence or absence of a particular blood group antigen on tumor cells is an important predictor of survival. While the A antigen is usually thought of in the context blood transfusions, the antigen is present in other tissues besides the red blood cells of people with type A or type AB blood. In a study of 164 patients with non-small-cell lung cancer, 61 patients were found to have type A blood and 10 had type AB. Of these, 43 were found to have the A antigen on their tumor cells as well; the remainder had tumors which were missing the A antigen. The patients with tumors lacking the A antigen had a median survival of 15 months, in contrast to a 71-month survival for patients with the A antigen on their tumor cells. The absence of the A antigen itself is not sufficient to account for this short survival, since patients with blood types B and O, who cannot make the A antigen anywhere in their bodies, had a median survival which, at 39 months, was significantly longer than the median survival for the type A patients who lacked the A antigen on their cancer cells. The researchers performed a Cox proportional hazards analysis and confirmed that the predictive value of the presence of the A antigen is independent of the other known prognostic variables for lung cancer. The authors conclude that the presence of the A antigen on non-small-cell lung cancer cells is a favorable prognostic indicator, and that this factor should be taken into account in the design of future clinical trials. (Consumer Summary produced by Reliance Medical Information, Inc.)

Although surgery and radiotherapy are effective against primary squamous-cell carcinoma (a type of cancer) of the head and neck, tumors recur in between 30 and 50 percent of treated patients. An additional 20 to 30 percent of treated patients develop distant metastasis (spread), and yet another large group develop a second primary tumor. Second primary tumors account for most deaths among patients treated for early disease. Retinoids, a class of compounds derived from vitamin A, appear to be active against cancers of the epithelia (the lining of the mouth, respiratory tract, and lung). To test the effectiveness of a synthetic retinoid, isotretinoin, 100 patients, who had undergone surgery or radiotherapy, or both, were evaluated for primary squamous-cell carcinoma of the oral cavity, pharyngeal area, or larynx. All of the patients were free of disease when the study began. They were randomly assigned to receive either isotretinoin or placebo (an inactive drug) for 12 months, and monitored for several months longer by regular physical examinations, laboratory tests, and chest X-rays. Failure of the primary treatment (a cancer at the same or nearby site) or the appearance of second primary tumors (which could be at different sites) were noted. The results showed that the proportion of placebo and isotretinoin patients did not differ in regard to disease progression; however, the isotretinoin group had significantly fewer second primary tumors (4 percent as compared with 24 percent). Toxic effects due to the drug included skin dryness, lip inflammation, increased blood levels of triglycerides, and conjunctivitis (inflammation of the membrane covering the eyeball). One third of the patients in the isotretinoin group dropped out of treatment because of side effects or noncompliance; these patients were included in the statistical analysis, so the true effect of isotretinoin may be considerably better than it appeared. The findings suggest that isotretinoin could be a valuable chemopreventive agent against carcinoma of the head and neck. (Consumer Summary produced by Reliance Medical Information, Inc.)