The structure and function of the human brain are highly stereotyped, implying a conserved molecular program responsible for its development, cellular structure, and function. We applied a correlation-based metric of “differential stability” (DS) to assess reproducibility of gene expression patterning across 132 structures in six individual brains, revealing meso-scale genetic organization. The highest DS genes are highly biologically relevant, with enrichment for brain-related biological annotations, disease associations, drug targets, and literature citations. Using high DS genes we identified 32 anatomically diverse and reproducible gene expression signatures, which represent distinct cell types, intracellular components, and/or associations with neurodevelopmental and neurodegenerative disorders. Genes in neuron-associated compared to non-neuronal networks showed higher preservation between human and mouse; however, many diversely-patterned genes displayed dramatic shifts in regulation between species. Finally, highly consistent transcriptional architecture in neocortex is correlated with resting state functional connectivity, suggesting a link between conserved gene expression and functionally relevant circuitry.

An edge‐scheduled network N is a multigraph G = (V, E), where each edge e ϵ E has been assigned two real weights: a start time α(e) and a finish time β(e). Such a multigraph models a communication or transportation network. A multiedge joining vertices u and v represents a direct communication (transportation) link between u and v, and the edges of the multiedge represent potential communications (transportations) between u and v over a fixed period of time. For a, b ϵ V, and k a nonnegative integer, we say that N is k‐failure ab‐invulnerable for the time period [0, t] if information can be relayed from a to b within that time period, even if up to k edges are deleted, i.e., “fail.” The k‐failure ab‐vulnerability threshold νab(k) is the earliest time t such that N is k‐failure ab‐invulnerable for the time period [0, t] [where νab(k) = ∞ if no such t exists]. Let κ denote the smallest k such that νab(k) = ∞. In this paper, we present an O(κ|E|) algorithm for computing νab(i), i = 0, …, κ −1. The latter algorithm constructs a set of κ pairwise edge‐disjoint schedule‐conforming paths P0, …, Pκ −1 such that the finish time of Pi is νab(i), i = 0, 1, …, κ −1. (A path P = ae1u1e2 ··· Upp−1epb is schedule‐conforming if the finish time of edge ei is no greater than the start time of the next edge ei + 1.) The existence of such paths when α(e) = β(e) = 0, for all e ϵ E, implies Menger's Theorem. In this paper, we also show that the obvious analogs of these results for either multiedge deletions or vertex deletions do not hold. In fact, we show that the problem of finding k schedule‐conforming paths such that no two paths pass through the same vertex (multiedge) is NP‐complete, even for k = 2. © 1996 John Wiley & Sons, Inc.

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BackgroundA rare or orphan disease (OD) is any disease that affects a small percentage of the population. While opportunities now exist to accelerate progress toward understanding the basis for many more ODs, the prioritization of candidate genes is still a critical step for disease-gene identification. Several network-based frameworks have been developed to address this problem with varied results.ResultWe have developed a novel vertex similarity (VS) based parameter-free prioritizing framework to identify and rank orphan disease candidate genes. We validate our approach by using 1598 known orphan disease-causing genes (ODGs) representing 172 orphan diseases (ODs). We compare our approach with a state-of-art parameter-based approach (PageRank with Priors or PRP) and with another parameter-free method (Interconnectedness or ICN). Our results show that VS-based approach outperforms ICN and is comparable to PRP. We further apply VS-based ranking to identify and rank potential novel candidate genes for several ODs.ConclusionWe demonstrate that VS-based parameter-free ranking approach can be successfully used for disease candidate gene prioritization and can complement other network-based methods for candidate disease gene ranking. Importantly, our VS-ranked top candidate genes for the ODs match the known literature, suggesting several novel causal relationships for further investigation.

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