We study the complexity of learning and approximation of self-bounding functions over the uniform distribution on the Boolean hypercube {0, 1}n. Informally, a function f : {0, 1}n → R is self-bounding if for every x ∈ {0, 1}n, f(x) upper bounds the sum of all the n marginal decreases in the value of the function at x. Self-bounding functions include such well-known classes of functions as submo...

We study the complexity of learning and approximation of self-bounding functions over the uniform distribution on the Boolean hypercube {0, 1}. Informally, a function f : {0, 1} → R is self-bounding if for every x ∈ {0, 1}, f(x) upper bounds the sum of all the n marginal decreases in the value of the function at x. Self-bounding functions include such well-known classes of functions as submodul...

Let M(x) = ∑ 1≤n≤x μ(n) where μ is the Möbius function. It is well-known that the Riemann Hypothesis is equivalent to the assertion that M(x) = O(x1/2+ ) for all > 0. There has been much interest and progress in further bounding M(x) under the assumption of the Riemann Hypothesis. In 2009, Soundararajan established the current best bound of M(x) √ x exp ( (log x)(log log x) ) (setting c to 14, ...

The greatst drawback of Monte Carlo Markov chain methods is lack of knowledge of the mixing time of the chain. The use of bounding chains solves this difficulty for some chains by giving theoretical and experimental upper bounds on the mixing time. Moreover, when used with methodologies such as coupling from the past, bounding chains allow the user to take samples drawn exactly from the station...

the present paper is devoted to a new critical state based plasticity model able to predict drained and undrained behaviour of granular material. it incorporates a bounding surface plasticity model describing in multilaminate framework to capitalize on advantages of this mathematical framework. most of the models developed using stress/strain invariants are not capable of identifying the parame...

In this paper we present a compact structure to index semistatic collections of MBRs that solves range queries while keeping a good trade-off between the space needed to store the index and its search efficiency. This is very relevant considering the current sizes and gaps in the memory hierarchy. Our index is based on the wavelet tree, a structure used to represent sequences, permutations, and...

Let K be a totally real Galois number field. C. J. Hillar proved that if f ∈ Q[x1, . . . , xn] is a sum of m squares in K[x1, . . . , xn], then f is a sum of N(m) squares in Q[x1, . . . , xn], where N(m) ≤ 2[K:Q]+1 · `[K:Q]+1 2 ́ ·4m, the proof being constructive. We show in fact that N(m) ≤ (4[K : Q]−3)·m, the proof being constructive as well.

We study the stability of cooperative games played over an interaction network, in a model that was introduced by Myerson (1977). We show that the cost of stability of such games (i.e., the subsidy required to stabilize the game) can be bounded in terms of natural parameters of their underlying interaction networks. Specifically, we prove that if the treewidth of the interaction network H is k,...

A simple method is presented by which tight bounds on the range of a multivariate rational function over a box can be computed. The approach relies on the expansion of the numerator and denominator polynomials into Bernstein polynomials.