arXiv subjects
Publications and source records attributed to David Wang.
Let $p$ be a prime. In this short note we study some families of super congruences involving the following alternating sums \begin{equation*} \sum_{\substack{j_1+j_2+\cdots+j_n=2 p^r p\nmid j_1 j_2 \cdots j_n}} \frac{(-1)^{j_1+\cdots+j_b}}{j_1\cdots j_n} \pmod{p^r}, \end{equation*} which extend similar statements proved by Shen and Cai who treated the cases when $n=4,5$.
Methods to effectively detect multi-locus genetic association are becoming increasingly relevant in the genetic dissection of complex trait in humans. Current approaches typically consider a limited number of hypotheses, most of which are related to the effect of a single locus or of a relatively small number of neighboring loci on a chromosomal region. We have developed a novel method that is specifically designed to detect genetic association involving multiple disease-susceptibility loci, possibly on different chromosomes. Our approach relies on the efficient discovery of patterns comprising spatially unrestricted polymorphic markers and on the use of appropriate test statistics to evaluate pattern-trait association. Power calculations using multi-locus disease models demonstrate significant gain of power by using this method in detecting multi-locus genetic association when compared to a standard single marker analysis method. When analyzing a Schizophrenia dataset, we confirmed a previously identified gene-gene interaction. In addition, a less conspicuous association involving different markers on the same two genes was also identified, implicating genetic heterogeneity.