We introduce the phenomenon of rapid self-organized criticality (RSOC) and show that, like some models of self-organized criticality (SOC), RSOC generates scale-invariant event distributions and 1/f noise. Unlike SOC, however, RSOC persists despite more than an order of magnitude variation in driving rate and displays extremely thick and dynamic branching geometry. Starting with an initial set ...

Using the Berele/Remmel/Kerov/Vershik variation of the Robinson-Schensted-Knuth correspondence, we study the cycle and increasing subsequence structure after various methods of shuffling. One consequence is a cycle index for shuffles like: cut a deck into two roughly equal piles, thoroughly mix the first pile and then riffle it with the second pile. Conclusions are drawn concerning the distribu...

We show that if E is a real Banach space such that E′ has the approximation property and such that `1 6↪→ ⊗̂ n,s, E then the set of extreme points of the unit ball of PI(E) is equal to {±φn : φ ∈ E′, ‖φ‖ = 1}. Under the additional assumption that E′ has a countable norming set we see that the set of exposed points of the unit ball of PI(E) is also equal to {±φn : φ ∈ E′, ‖φ‖ = 1}.

We compute the entropy of entanglement between the first N spins and the rest of the system in the ground states of a general class of quantum spin chains. We show that under certain conditions the entropy can be expressed in terms of averages over ensembles of random matrices. These averages can be evaluated, allowing us to prove that at critical points the entropy grows like kappalog(2N+kappa...

Using the Berele/Remmel/Kerov/Vershik variation of the Robinson-Schensted-Knuth correspondence, we study the cycle and increasing subsequence structure after various methods of shuffling. One consequence is a cycle index for shuffles like: cut a deck into roughly two equal piles, thoroughly mix the first pile and then riffle it with the second pile. Conclusions are drawn concerning the distribu...

We characterize the global flow of the restricted threebody problem in which we have two mass points of equal masses m1 = m2 > 0 and equal charge q1 = q2 moving on a straight line under Newtonian and Coulombian forces with their centre of mass being fixed at the origin of coordinates and the third mass point with infinitesimal mass, is moving on the straight line perpendicular to the line of mo...

A set of points in IR n is said to be in acute position, if the angle determined by any triple of points is at most equal to =2. This paper considers the problem of computing the maximum circumradius of any set of n + 1 points in IR n that is in acute and general position and that has diameter one. It is shown that for n = 3, this maximum circumradius is at most equal to one. For arbitrary n, a...

In several research domains concerned with classification tasks, curves like ROC are often used to assess the quality of a particular model or to compare two or more models with respect to various operating points. Researchers also often publish some statistics coming from the ROC, such as the socalled break-even point or equal error rate. The purpose of this paper is to first argue that these ...