Interchanging iterated integration

Interchanging heads

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Approximation and Complexity II: Iterated Integration

Iterated Coleman Integration for Hyperelliptic Curves

The Coleman integral is a p-adic line integral. Double Coleman integrals on elliptic curves appear in Kim’s nonabelian Chabauty method, the first numerical examples of which were given by the author, Kedlaya, and Kim [3]. This paper describes the algorithms used to produce those examples, as well as techniques to compute higher iterated integrals on hyperelliptic curves, building on previous jo...

Interchanging distance and capacity in probabilistic mappings

Harald Räcke [STOC 2008] described a new method to obtain hierarchical decompositions of networks in a way that minimizes the congestion. Räcke’s approach is based on an equivalence that he discovered between minimizing congestion and minimizing stretch (in a certain setting). Here we present Räcke’s equivalence in an abstract setting that is more general than the one described in Räcke’s work,...

Integration Identities for Some Iterated Exponentials of Order Three

Inspired by the well-known elegant result for the integral of the power tower of length two x x , namely 1 0 1/x x dx = ∞ n=1 1/n n (first attributed to Johann Bernoulli, and commonly referred to as the " sophomore's dream " in present day literature [1]), we present a number of identities for power towers of length three. In the present communication, we shall be primarily concerned with inte-...