A multivariate to multivariate approach for voxel-wise genome-wide association analysis

The joint analysis of imaging-genetics data facilitates the systematic investigation of genetic effects on brain structures and functions with spatial specificity. We focus on voxel-wise genome-wide association analysis, which may involve trillions of single nucleotide polymorphism (SNP)-voxel pairs. We attempt to identify underlying organized association patterns of SNP-voxel pairs and understand the polygenic and pleiotropic networks on brain imaging traits. We propose a bi-clique graph structure (i.e., a set of SNPs highly correlated with a cluster of voxels) for the systematic association pattern. Next, we develop computational strategies to detect latent SNP-voxel bi-cliques and inference model for statistical testing. We further provide theoretical results to guarantee the accuracy of our computational algorithms and statistical inference. We validate our method by extensive simulation studies and then apply it to the whole genome genetic and voxel-level white matter integrity data collected from 1052 participants of the human connectome project (HCP). The results demonstrate multiple genetic loci influencing white matter integrity measures on splenium and genu of the corpus callosum.

Finding the shortest path for a Hypergraph

A hypergraph is given by [Formula: see text], where [Formula: see text] is a set of vertices and [Formula: see text] is a set of nonempty subsets of [Formula: see text], the member of [Formula: see text] is named hyperedge. So, a hypergraph is a nature generalization of a graph. A hypergraph has a complex structure, thus some researchers try to transform a hypergraph to a graph. In this paper, we define two graphs, Clique graph and Persian graph. These relations are one to one. We can find the shortest path between two vertices in a hypergraph [Formula: see text], by using the Dijkstra algorithm in graph theory on the graphs corresponding to [Formula: see text].

Nested-Clique Network Model of Neural Associative Memory

Clique-based neural associative memories introduced by Gripon and Berrou (GB), have been shown to have good performance, and in our previous work we improved the learning capacity and retrieval rate by local coding and precoding in the presence of partial erasures. We now take a step forward and consider nested-clique graph structures for the network. The GB model stores patterns as small cliques, and we here replace these by nested cliques. Simulation results show that the nested-clique structure enhances the clique-based model.