Here we provide a unifying treatment of the convergence general form sampling type operators, given by so-called Durrmeyer series. In particular pointwise and uniform theorem on $\mathbb{R}$, in this context also furnish quantitative estimate for order approximation, using modulus continuity function to be approximated. Then obtain modular setting Orlicz spaces $L^\varphi(\mathbb{R})$. From lat...

We give some new estimates for the Truncation Error of sampling series of functions on regular sampling subspaces of L2(R). These estimates lower the well known Jagerman’s bound on Shannon’s sampling expansions. Mathematics Subject Classification: 41A17, 41A80, 65G99.

This paper applies type-based Markov Chain Monte Carlo (MCMC) algorithms to the problem of learning Synchronous Context-Free Grammar (SCFG) rules from a forest that represents all possible rules consistent with a fixed word alignment. While type-based MCMC has been shown to be effective in a number of NLP applications, our setting, where the tree structure of the sentence is itself a hidden var...

The harmonizable Piranashvili – type stochastic processes are approximated by a finite time shifted average sampling sum. Truncation error upper bound is established; various consequences and special cases are discussed. MSC(2000): 42C15, 60G12, 94A20.

This course focuses on Markov chain based algorithms for randomly sampling from probability distributions defined on a large state space. Typically we are interested in generating a sample in time polynomial of the logarithm of the size of the state space. In other words, we want to sample from the distribution after exploring only an exponentially small portion of it. We’ll begin with two clas...