It can be conjectured that the colored Jones function of a knot can be computed in terms of counting paths on the graph of a planar projection of a knot. On the combinatorial level, the colored Jones function can be replaced by its weight system. We give two curious formulas for the weight system of a colored Jones function: one in terms of the permanent of a matrix associated to a chord diagra...

Poly-random function collections (a.k.a. pseudorandom function collections) are an important cryptographic primitive, rst introduced by Goldreich, Goldwasser and Micali in 1986. Pseudorandom functions provide simple solutions to problems in private key cryptography, including encryption and message au-thentication. In this paper we are interested in the resources required by a test to distingui...

The asymptotic (small distortion) behavior of the rate-distortion function of an n-dimensional source vector with mixed distribution is derived. The source distribution is a nite mixture of components such that under each component distribution a certain subset of the coordinates have a discrete distribution while the remaining coordinates have a joint density. The expected number of coordinate...

In this paper we design several double length hash functions and study their security properties in the random oracle model. We design a class of double length hash functions (and compression functions) which includes some recent constructions [4, 6, 10]. We also propose a secure double length hash function which is as efficient as the insecure concatenated classical hash functions [7].

For the case of smooth concave exchange economies, we provide a characterization of the inner core as the set of feasible allocations such that no coalition can improve on it, even if coalitions are allowed to use some random plans. For the case of compactly generated games, we discuss Myerson’s definition of the inner core, and we characterize it using lexicographic utility weight systems.  2...

Poly-random function collections (a.k.a. pseudorandom function collections) are an important cryptographic primitive, rst introduced by Goldreich, Goldwasser and Micali in 1986. Pseudorandom functions provide simple solutions to problems in private key cryptography, including encryption and message authentication. In this paper we are interested in the resources required by a test to distinguis...

For any class of binary functions on [n] = {1, . . . , n} a classical result by Sauer states a sufficient condition for its VC-dimension to be at least d: its cardinality should be at least O(n). A necessary condition is that its cardinality be at least 2 (which is O(1) with respect to n). How does the size of a ‘typical’ class of VC-dimension d compare to these two extreme thresholds ? To answ...