For any posotive integer m, let [m] := {1, . . . ,m}. Let n, k, t be positive integers. Aharoni and Howard conjectured that if, for i ∈ [t], Fi ⊂ [n] := {(a1, . . . , ak) : aj ∈ [n] for j ∈ [k]} and |Fi| > (t−1)n, then there exist M ⊆ [n] such that |M | = t and |M ∩ Fi| = 1 for i ∈ [t] We show that this conjecture holds when n ≥ 3(k − 1)(t− 1). Let n, t, k1 ≥ k2 ≥ . . . ≥ kt be positive integer...

Genomic data are often characterized by a moderate to large number of categorical variables observed for relatively few subjects. Some of the variables may be missing or noninformative. An example of such data is loss of heterozygosity (LOH), a dichotomous variable, observed on a moderate number of genetic markers. We first consider a latent class model where, conditional on unobserved membersh...

non-sampled cells unobserved incidence of a parallel mutation unobserved back mutation of observed mutation unobserved mutations due to subsampling unobserved mutations, extinct at sampling time end of extinct lineage sampled cells observed back mutation, samples with and without loss sampled observed unique mutation observed parallel mutation, both incidences sampled observed incidence of a pa...

Runs of homozygosity (ROH) represents extended length of homozygotes on a long genomic distance. In oncology, it is known as loss of heterozygosity (LOH) if identified exclusively in cancer cell rather than in matched control cell. Studies have identified several genomic regions which show consistent ROH in different kinds of carcinoma. To query whether this consistency can be observed on broad...

The apparatus which forms the subject of this paper was designed to eliminate some of the variable factors during the preparation of blood films by the slide method, and thus to reduce the errors of differential leucocyte counts. These errors can be grouped, according to their sources, into those arising during the preparation of the films due to a variety of technical factors, and into others ...