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By definition, transverse intersections are stable under in-finitesimal perturbations. Using persistent homology, we extend this notion to sizeable perturbations. Specifically, we assign to each homology class of the intersection its robust-ness, the magnitude of a perturbation necessary to kill it, and prove that robustness is stable. Among the(More)
Given a function f : X → R on a topological space, we consider the preimages of intervals and their homology groups and show how to read the ranks of these groups from the extended persistence diagram of f. In addition, we quantify the robustness of the homology classes under perturbations of f using well groups. After characterizing these groups, we show(More)
We define the robustness of a level set homology class of a function f : X → R as the magnitude of a perturbation necessary to kill the class. Casting this notion into a group theoretic framework, we compute the robustness for each class, using a connection to extended persistent homology. The special case X = R 3 has ramifications in medical imaging and(More)
  • Miryam A. Fragoso, Amit K. Patel, Rei E. I. Nakamura, Hyun Yi, Krishna Surapaneni, Abigail S. Hackam
  • 2012
Wnt/β-catenin signaling is an essential pathway that regulates numerous cellular processes, including cell survival. The molecular mechanisms contributing to pro-survival Wnt signaling are mostly unknown. Signal transducer and activator of transcription proteins (STATs) are a well-described family of transcription factors. STAT3 induces expression of(More)
Using ideas from persistent homology, the robustness of a level set of a real-valued function is defined in terms of the magnitude of the perturbation necessary to kill the classes. Prior work has shown that the homology and robustness information can be read off the extended persistence diagram of the function. This paper extends these results to a(More)
The canonical Wnt/β-catenin ("Wnt") pathway is an essential signaling cascade in the embryonic central nervous system (CNS) that regulates neuronal differentiation and survival. Loss of Wnt signaling in developing and adult tissue has been implicated in numerous CNS diseases, but the precise role of Wnt in regulating neuronal survival, and how its absence(More)
  • James O. Burton, Hassan A. Hamali, Ruchir Singh, Nima Abbasian, Ruth Parsons, Amit K. Patel +2 others
  • 2013
Cardiovascular (CV) death remains the largest cause of mortality in dialysis patients, unexplained by traditional risk factors. Endothelial microvesicles (EMVs) are elevated in patients with traditional CV risk factors and acute coronary syndromes while platelet MVs (PMVs) are associated with atherosclerotic disease states. This study compared relative(More)
PURPOSE The purpose of this study was to identify how changes in retinal structure and function correlate with visual deficits during increasing amounts of retinal degeneration. MATERIALS AND METHODS Retinal degeneration was induced in adult mice by subretinal injections of paraquat (PQ) (0.2-1 mM). Retinal anatomy and photoreceptor layer thickness were(More)
PURPOSE To present a case with posterior segment findings in a patient with cloudy corneas secondary to immunotactoid glomerulonephritis (ITG). METHODS A 57-year-old female was known to have bilateral cloudy corneas diagnosed 12 years ago secondary to immunotactoid glomerulonephritis. Clinically, fundus examination was difficult to visualise due to the(More)