The combined investigation of environmental and genetic risk-factors in complex traits will refocus attention on the case-control study. Endometriosis is an example of a complex trait for which most case-control studies have not followed the basic criteria of epidemiological study design. Appropriate control selection has been a particular problem. This article reviews the principles underlying...

Pairing, synapsis, and crossover recombination of homologous chromosomes (homologs) are prerequisite for the proper segregation of homologs during meiosis I. The meiosis-specific cohesin subunit, RAD21L, is essential for such meiotic chromosomal events, but it is unknown to what extent RAD21L by itself contributes to the process since various meiotic genes are also involved. To reveal the exclu...

▶ Following [2]... 1. Split the original network into sub-networks 2. Calculate the frequency-weighted adjacency matrix F of each sub-network; 3. Fij = Fij + Fij ∗ , −0.5 < < 0.5; 4. Run MCL [3], with = 1.6, over F for 30 times; 5. Use the (hard) clustering from each run to create P, a matrix with the probabilities of each pair of words in F belonging to the same cluster; 6. Remove: (a) big clu...

The formal expression of pro positional attitudes, especially when nested (iterated), is an important problem for A I . An interesting first-order extensional logical system for such expression has been proposed by Creary. In this system concepts (and concepts of concepts, etc.) are made explicit. The system includes "concept functions", which are special functions which act on and deliver conc...

It is shown that if a d-regular graph contains s vertices so that the distance between any pair is at least 4k, then its adjacency matrix has at least s eigenvalues which are at least 2 √ d − 1 cos( π 2k ). A similar result has been proved by Friedman using more sophisticated tools.

The Moore bound constitutes both an upper bound on the order of a graph of maximum degree d and diameter D = k and a lower bound on the order of a graph of minimum degree d and odd girth g = 2k + 1. Graphs missing or exceeding the Moore bound by ǫ are called graphs with defect or excess ǫ, respectively. While Moore graphs (graphs with ǫ = 0) and graphs with defect or excess 1 have been characte...

A pseudo (v, k, λ)-design is a pair (X,B), where X is a v-set, and B = {B1, . . . ,Bv−1} is a collection of k-subsets (blocks) of X such that any two distinct Bi,Bj intersect in λ elements, and 0 ≤ λ < k ≤ v−1. We use the notion of pseudo designs to characterize graphs of order n whose (adjacency) spectrum contains zero and ±θ with multiplicity (n− 3)/2 where 0 < θ ≤√2. Meanwhile, partial resul...

Learning takes place over long periods of time that are hard to study directly. Even the learning experience involved in solving a challenging math problem in a collaborative online setting can be spread across hundreds of brief postings during an hour or more. Such long-term interactions are constructed out of posting-level interactions, such as the strategic proposing of a next step. This pap...