We determine the character of the action of the symmetric group on the homology of the induced subposet of the lattice of partitions of the set {1, 2, . . . , n} obtained by restricting block sizes to the set {1, k, k + 1, . . . }. A plethystic formula for the generating function of the Frobenius characteristic of the representation is given. We combine techniques from the theory of nonpure she...

We propose an exact method for generating random deviates from continuous order statistics. This versatile method that generates Beta deviates as a middle step can be applied to any density function without resorting to numerical inversion. We also conduct an exhaustive investigation to document the merits of our method in generating deviates from any Beta distribution.

The labeled stochastic block model is a random graph model representing networks with community structure and interactions of multiple types. In its simplest form, it consists of two communities of approximately equal size, and the edges are drawn and labeled at random with probability depending on whether their two endpoints belong to the same community or not. It has been conjectured in [1] t...

We prove that the least-perimeter partition of the sphere into four regions of equal area is a tetrahedral partition.

A classification tree represents the probability spaceP of posterior probabilities p(y|x) of label given feature by a recursive partition of the feature space X , where each partition is performed by a test on the feature x called a split rule. To each set of the partition is assigned a posterior probability distribution, and p(y|x) for a feature x ∈ X is then defined as the probability distrib...

A linear-time algorithm is presented for the construction of the Gibbs distribution of configurations in the Ising model, on a quantum computer. The algorithm is designed so that each run provides one configuration with a quantum probability equal to the corresponding thermodynamic weight. The partition function is thus approximated efficiently. The algorithm neither suffers from critical slowi...

where F = {yh(x) : ∀ h ∈ H} and φ(h(x), y) is the loss function of interest. The labeled training sample S = {(xi, yi) | i ∈ {1, ..., n}, xi ∈ R, yi ∈ {±1}} is assumed to be generated from an independent, identically distributed (IID) random process. Given each Rademacher random variable σi ∈ {±1} with uniform odds, a realization of the Rademacher random variables σ amounts to a partition of th...

To each partition λ = (λ1, λ2, . . .) with distinct parts we assign the probability Qλ(x)Pλ(y)/Z where Qλ and Pλ are the SchurQ-functions and Z is a normalization constant. This measure, which we call the shifted Schur measure, is analogous to the much-studied Schur measure. For the specialization of the first m coordinates of x and the first n coordinates of y equal to α (0 < α < 1) and the re...

ÐEarly studies of random versus partition testing used the probability of detecting at least one failure as a measure of test effectiveness and indicated that partition testing is not significantly more effective than random testing. More recent studies have focused on proportional partition testing because a proportional allocation of the test cases (according to the probabilities of the subdo...