Let P be a set of n points in Euclidean space and let 0< ε< 1. A wellknown result of Johnson and Lindenstrauss states that there is a projection of P onto a subspace of dimension O(ε−2 logn) such that distances change by at most a factor of 1+ ε. We consider an extension of this result. Our goal is to find an analogous dimension reduction where not only pairs but all subsets of at most k points...

Let P be a set of n points in Euclidean space and let 0 < ε < 1. A well-known result of Johnson and Lindenstrauss states that there is a projection of P onto a subspace of dimension O(ε−2 logn) such that distances change by a factor of 1 + ε at most. We consider an extension of this result. Our goal is to find an analogous dimension reduction where not only pairs, but all subsets of at most k p...

where σ is the Lipschitz constant of the extension of f and P is the natural probability on {0, 1}. Here we extend this inequality to more general product probability spaces; in particular, we prove the same inequality for {0, 1} with the product measure ((1− η)δ0 + ηδ1) . We believe this should be useful in proofs involving random selections. As an illustration of possible applications we give...

The maximin share guarantee is, in the context of allocating indivisible goods to a set of agents, a recent fairness criterion. A solution achieving a constant approximation of this guarantee always exists and can be computed in polynomial time. We extend the problem to the case where the goods collectively received by the agents satisfy a matroidal constraint. Polynomial approximation algorith...

Hash then encrypt” is a popular approach to message authentication: first the message is hashed down using an ε-universal hash function, and then the resulting k-bit value is encrypted, say with a block-cipher. The security of this scheme is proportional to εq, where q is the number of MACs the adversary can request. As ε is at least 2, the best one can hope for is O(q/2) security. Unfortunatel...

In this paper we propose a complete axiomatization of the bisimilarity distance of Desharnais et al. for the class of finite labelled Markov chains. Our axiomatization is given in the style of a quantitative extension of equational logic recently proposed by Mardare, Panangaden, and Plotkin (LICS 2016) that uses equality relations t ≡ε s indexed by rationals, expressing that “t is approximately...

Given an n-bit to n-bit MAC (e.g., a fixed key blockcipher) with MAC security ε against q queries, we design a variable-length MAC achieving MAC security O(εq poly(n)) against queries of total length qn. In particular, our construction is the first to break the “birthday barrier” for MAC domain extension from noncompressing primitives, since our security bound is meaningful even for q = 2/poly(...

We are interested in the efficient and reliable numerical solution of parametric multi-scale problems, the multi-scale (parametric) character of which is indicated by ε (μ) if expressed in the general notation of (1). It is well known that solving parametric multi-scale problems accurately can be challenging and computationally costly for small scales ε and for a strong dependency of the soluti...

Replication of hepatitis B virus (HBV) via protein-primed reverse transcription is initiated by binding of the viral P protein to the conserved ε stem-loop on the pregenomic (pg) RNA. This triggers encapsidation of the complex and the ε-templated synthesis of a short P protein-linked DNA oligonucleotide (priming) for subsequent minus-strand DNA extension. ε consists of a lower and upper stem, a...