The main mathematical result of this paper may be stated as follows: Given a matrix M∈{− 1,
1} n× n and any matrix M ̃∈ R n× n such that sign (M ̃ i, j)= M i, j for all i, j, then rank (M ̃)⩾ n …

This paper has two main focal points. We first consider an important class of machine
learning algorithms: large margin classifiers, such as Support Vector Machines. The notion …

We prove an essentially tight lower bound on the unbounded-error communication
complexity of every symmetric function, ie, f (x, y)= D (| x∧ y|), where D:{0, 1,…, n}→{0, 1} is …

We prove three different types of complexity lower bounds for the one-way unbounded-error
and bounded-error error probabilistic communication protocols for boolean functions. The …

We solve a 17 year old problem of ACC Yao (1979). In the two-player communication model
introduced by Yao in 1979, Alice and Bob wish to collaboratively evaluate a function f (x, y) …

Communication is a bottleneck in many distributed computations. In VLSI, communication
constraints dictate lower bounds on the performance of chips. The two-processor information …

Let d= d (n) be the minimum d such that for every sequence of n subsets F1, F2,..., Fn of {1,
2,..., n} there exist n points P1, P2,..., Pn and n hyperplanes H1, H2...., Hn in Rd such that Pj …

Publisher Summary This chapter focuses on Kolmogorov complexity and its applications.
The mathematical theory of Kolmogorov complexity contains deep and sophisticated …

We use Fourier analysis to get general lower bounds for the probabilistic communication
complexity of large classes of functions. We give some examples showing how to use our …

Abstract} Fe present several results regarding randomized oneround communication
complexity. These include a connection to the VC-dimension, a study-of the problem of …