Notes on Counting

Expressive Completeness for LTL With Modulo Counting and Group Quantifiers

Kamp showed that linear temporal logic is expressively complete for first order logic over words. We give a Gabbay style proof to show that linear temporal logic extended with modulo counting and group quantifiers (introduced by Baziramwabo,McKenzie,Thérien) is expressively complete for first order logic with modulo counting (introduced by Straubing, Thérien, Thomas) and group quantifiers (intr...

Notes on counting finite sets

Dyadic Decision Trees

These notes introduce a new kind of classifier called a dyadic decision tree (DDT). We also introduce a discrimination rule for learning a DDT that achieves the optimal rate of convergence, ER(ĥn) − R∗ = O(n−1/d), for the box-counting class, which was defined in the previous set of notes. This improves on the rate of ER(ĥn)−R = O(n−1/(d+2)) for the histogram sieve estimator from the previous no...

Counting in hypergraphs via regularity inheritance

We develop a theory of regularity inheritance in 3-uniform hypergraphs. As a simple consequence we deduce a strengthening of a counting lemma of Frankl and Rödl. We believe that the approach is sufficiently flexible and general to permit extensions of our results in the direction of a hypergraph blow-up lemma.

Counting Spanning Trees in Cographs

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...