Counting Backwards: A Doctor’s Notes on Anesthesia.

Notes on Counting

It is important to be able to count exactly the number of elements in any finite set. We will see many applications of counting as we proceed (number of Enigma plugboard arrangements, computer passwords of a certain form, telephone area codes, automobile license plates, binary strings of a certain length needed to encode uniquely each possible English message of a certain length, etc.). In this...

Notes on walk-counting

th th 0 1 1 2 2 1 0 1 ij ij m m m m 1 Walks and graphs v e v i e v v m v j Let 0 be a nite, undirected, simple graph with vertices. We will use the notation to indicate that two v ertices and in 0 are joined by a n edge. Let be an adjacency matrix for 0. That is, is an matrix with rows and columns indexed by t h e v ertices o f 0 , a n d [ ] = 1 if 0 if We use the notation [ ] to denote the ent...

Notes on counting finite sets

Notes on Counting Process in Survival Analysis

Distribution of some statistics, especially rank based, with censored data are hard to get. Even if they can be worked out for small samples, they are likely to be prohibitively expensive for larger sample sizes. Therefore we need to work on the asymptotic distribution which often works well for moderate and large sample sizes. This notes is intended to be read along with Fleming and Harrington...

Notes on Counting with Finite Machines

We determine the descriptional complexity (smallest number of states, up to constant factors) of recognizing languages {1} and {1 : t = 0, 1, 2, . . .} with state-based finite machines of various kinds. This task is understood as counting to n and modulo n, respectively, and was previously studied for classes of finite-state automata by Kupferman, Ta-Shma, and Vardi (2001). We show that for Tur...