so that this process is a martingale. More often that not, martingales are used in combinatorics to show that a particular random variable is concentrated around its mean. We can show (via the second moment method, for example) that for the above sequence X0, . . . , Xt describing a t-step random walk, the outcome of Xt is concentrated in an interval of length c √ t. This concentration property...

BACKGROUND An exaggerated inflammatory response occurs in the first few days of life in infants who subsequently develop bronchopulmonary dysplasia (BPD). The increase of inflammatory cytokines in many disease processes is generally balanced by a rise in anti-inflammatory cytokines. Interleukin-4 (IL-4) and interleukin-13 (IL-13) have been shown to inhibit production of several inflammatory cyt...

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