In this lecture we discuss how to derandomize algorithms. We will see a brute force algorithm (enumeration) for derandomization. We will also see that some random algorithms do not need true randomness. Specifically, we will see an example where only pairwise random bits are needed. Next, we will see how we can generate pairwise random values and how this conservation on the amount of randomnes...

1 Last two lectures ¯ probability spaces ¯ probability measure ¯ random variables and stochastic processes ¯ distribution functions ¯ independence ¯ conditional probability ¯ memoriless property of geometric and exponential distributions ¯ expectation ¯ conditional expectation (double expectation) ¯ mean-square estimation 1

In this paper we investigate the notion of conditional independence and prove several information inequalities for conditionally independent random variables. Keywords— Conditionally independent random variables, common information, rate region.

In this paper, we introduce a new fragment of the rst-order temporal language, called the monodic fragment, in which all formulas beginning with a temporal operator (Since or Until) have at most one free variable. We show that the satissability problem for monodic formulas in various linear time structures can be reduced to the satissability problem for a certain fragment of classical rst-order...

the purpose of this research was to formulate and systemically evaluate in-vitro and in-vivo performances of mucoadhesive propranolol hydrochloride microspheres for its potential use in the treatment of hypertension, myocardial infraction and cardiac arrhythmias. propranolol hydrochloride mucoadhesive microspheres, containing carbopol-934p as mucoadhesive polymer and ethyl cellulose as carrier ...