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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)
Recent evidence has implicated innate immunity in regulating neuronal survival in the brain during stroke and other neurodegenerations. Photoreceptors are specialized light-detecting neurons in the retina that are essential for vision. In this study, we investigated the role of the innate immunity receptor TLR4 in photoreceptors. TLR4 activation by(More)
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)
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)
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)
PURPOSE To compare three microkeratome-assisted techniques for the preparation of ultrathin (UT) grafts for Descemet stripping automated endothelial keratoplasty. METHODS After dissection with a 300-μm microkeratome head in 40 donor tissues, a second cut was performed with a 130-μm head either after manual stromal hydration (group A, n = 10) or osmotic(More)
The innate immune system and inflammatory pathways play key roles in numerous diseases of the central nervous system (CNS). Recent evidence indicates that innate immunity induces both pathogenesis and protection during neuronal injury. To test the possibility that the conflicting roles of innate immunity in the CNS depends on the cellular environment in(More)
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)