When Janson meets McDiarmid: Bounded difference inequalities under graph-dependence

When graph theory meets knot theory

Since the early 1980s, graph theory has been a favorite topic for undergraduate research due to its accessibility and breadth of applications. By the early 1990s, knot theory was recognized as another such area of mathematics, in large part due to C. Adams’ text, The Knot Book. In this paper, we discuss the intersection of these two fields and provide a survey of current work in this area, much...

Probability and Moment Inequalities under Dependence

We establish Nagaev and Rosenthal-type inequalities for dependent random variables. The imposed dependence conditions, which are expressed in terms of functional dependence measures, are directly related to the physical mechanisms of the underlying processes and are easy to work with. Our results are applied to nonlinear time series and kernel density estimates of linear processes.

Search in BigData 2 - When Big Text meets Big Graph

Search in BigData - When Big Text meets Big Graph

Factoring Cryptosystem Moduli When the Co-factors Difference Is Bounded

LET P, Q BE TWO LARGE PRIMES AND N= . WE SHOW, IN THIS PAPER, THAT IF | − | ≤ 2 WHERE IS THE BIT-SIZE OF AND ∈ N, THEN WE CAN COMPUTE EFFICIENTLY THE INTEGERS AND IN AT MOST COMPARISONS. OUR APPROACH CAN BE USED TO BUILD ATTACKS AGAINST RSA OR RABIN CRYPTOSYSTEMS.