We present a new family of subgradient methods that dynamically incorporate knowledge of
the geometry of the data observed in earlier iterations to perform more informative gradient …

Minkowski summation is a basic and ubiquitous operation on sets. Indeed, the Minkowski
sum ACBD fa C b W a 2 A; b 2 Bg of sets A and B makes sense as long as A and B are …

We show that the number of independent sets in an N-vertex, d-regular graph is at most (2d+
1− 1) N/2d, where the bound is sharp for a disjoint union of complete d-regular bipartite …

A marginal problem asks whether a given family of marginal distributions for some set of
random variables arises from some joint distribution of these variables. Here, we point out …

Measuring the dependence of data plays a central role in statistics and machine learning. In
this work, we summarize and generalize the main idea of existing information-theoretic …

Sumset estimates, which provide bounds on the cardinality of sumsets of finite sets in a
group, form an essential part of the toolkit of additive combinatorics. In recent years …

The capacity for multiterminal secret-key agreement inspires a natural generalization of
Shannon's mutual information from two random variables to multiple random variables …

It is shown that the entropy of a sum of independent random vectors is a submodular set
function, and upper bounds on the entropy of sums are obtained as a result in both discrete …

Three tutorial lectures on entropy and counting arXiv:1406.7872v1 [math.CO] 30 Jun 2014
Page 1 Three tutorial lectures on entropy and counting 1 David Galvin2 1st Lake Michigan …

We explore some inequalities in convex geometry restricted to the class of zonoids. We
show the equivalence, in the class of zonoids, between a local Alexandrov-Fenchel …