Lev Meerovich Bregman

Lev Manovich

The appearance of New Media Reader is a milestone in the history a new field that, just a few years ago, was somewhat of a cultural underground. Before taking up the theoretical challenge of defining what new media actually is, as well as discussing the particular contributions this reader makes to answering this question, I would like very briefly to sketch the history of the field for the ben...

Welding Fume Local Exhaust Ventilation (LEV)Evaluation: the Lincoln Electric X-Tractor Portable LEV System

Restricted Sumsets and a Conjecture of Lev

Let A, B, S be finite subsets of an abelian group G. Suppose that the restricted sumset C = {a + b: a ∈ A, b ∈ B, and a − b 6∈ S} is nonempty and some c ∈ C can be written as a + b with a ∈ A and b ∈ B in at most m ways. We show that if G is torsion-free or elementary abelian then |C| > |A| + |B| − |S| − m. We also prove that |C| > |A| + |B| − 2|S| − m if the torsion subgroup of G is cyclic. In...

Submodular-Bregman and the Lovász-Bregman Divergences with Applications

We introduce a class of discrete divergences on sets (equivalently binary vectors) that we call the submodular-Bregman divergences. We consider two kinds, defined either from tight modular upper or tight modular lower bounds of a submodular function. We show that the properties of these divergences are analogous to the (standard continuous) Bregman divergence. We demonstrate how they generalize...

Multitask Bregman Clustering

Traditional clustering methods deal with a single clustering task on a single data set. However, in some newly emerging applications, multiple similar clustering tasks are involved simultaneously. In this case, we not only desire a partition for each task, but also want to discover the relationship among clusters of different tasks. It’s also expected that the learnt relationship among tasks ca...