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—Suppose there is a need to swiftly navigate through a spatial arrangement of possibly forbidden regions, with each region marked with the probability that it is, indeed, forbidden. In close proximity to any of these regions, you have the dynamic capability of disambiguating the region and learning for certain whether or not the region is forbidden—only in… (More)

- D E Fishkind, V Lyzinski, H Pao, L Chen, C E Priebe
- 2015

Suppose that a graph is realized from a stochastic block model where one of the blocks is of interest, but many or all of the vertices' block labels are unobserved. The task is to order the vertices with unobserved block labels into a " nomination list " such that, with high probability, vertices from the interesting block are concentrated near the list's… (More)

We wish to navigate from source s to destination d through a spatial configuration of detections x i and associated potential risk regions B i , i = 1, · · · , n. Associated with each detection x i is a mark ρ i indicating the probability that entering B i incurs non-zero risk. In accordance with application we may, upon approaching x i , disambiguate the… (More)

In this paper we exhibit, under suitable conditions, a neat relationship between the Moore–Penrose generalized inverse of a sum of two matrices and the Moore–Penrose generalized inverses of the individual terms. We include an application to the parallel sum of matrices.

We consider the problem of safely and swiftly navigating through a spatial arrangement of potential hazard detections in which each detection has associated with it a probability that the detection is indeed a true hazard. When in close proximity to a detection, we assume the ability—for a cost—to determine whether or not the hazard is real. Our approach to… (More)

Graph matching-aligning a pair of graphs to minimize their edge disagreements-has received wide-spread attention from both theoretical and applied communities over the past several decades, including combinatorics, computer vision, and connectomics. Its attention can be partially attributed to its computational difficulty. Although many heuristics have… (More)

We present a parallelized bijective graph matching algorithm that leverages seeds and is designed to match very large graphs. Our algorithm combines spectral graph embedding with existing state-of-the-art seeded graph matching procedures. We justify our approach by proving that modestly correlated, large stochastic block model random graphs are correctly… (More)

The human cerebral cortex is topologically equivalent to a sphere when it is viewed as closed at the brain stem. Due to noise and/or resolution issues, magnetic resonance imaging may see "handles" that need to be eliminated to reflect the true spherical topology. Shattuck and Leahy present an algorithm to correct such an image. The basis for their… (More)

- Joshua T. Vogelstein, John M. Conroy, Vince Lyzinski, Louis J. Podrazik, Steven G. Kratzer, Eric T. Harley +3 others
- 2011

Graph matching (GM)—the process of finding an optimal permutation of the vertices of one graph to minimize adjacency disagreements with the vertices of another—is rapidly becoming an increasingly important computational problem, arising in fields ranging from machine vision to neuroscience. Because GM is N P-hard, exact algorithms are unsuitable for today's… (More)