We consider quantitative versions of Helly-type questions, that is, instead finding a point in the intersection, we bound volume intersection. Our first main result is version Fractional Helly Theorem Katchalski and Liu, second one ( p , q ) -Theorem Alon Kleitman.

We prove the converse part of the theorem for quantum Hoeffding bound on the asymptotics of quantum hypothesis testing, essentially based on an argument developed by Nussbaum and Szkola in proving the converse part of the quantum Chernoff bound. Our result complements Hayashi’s proof of the direct (achievability) part of the theorem, so that the quantum Hoeffding bound has now been established.

This paper gives an explicit bound for the prime number theorem in short intervals under assumption of Riemann hypothesis.

Recently an error bound theorem was reported to conclude analytic error bounds for approximate Markov chains. The theorem required a uniform bound for marginal expectations of the approximate model. This note will relax this bound to steady state rather than marginal expectations as of practical interest: (i) to simplify verification and/or (ii) to obtain a more accurate error bound. An ALOHA-t...

Knowing an upper bound on the number of optimal design points greatly simplifies the search for an optimal design. Carathéodory’s Theorem is commonly used to identify an upper bound. However, the upper bound from Carathéodory’s Theorem is relative loose when there are three or more parameters in the model. In this paper, an alternative approach of finding a sharper upper bound for classical opt...