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Persistent homology is a method for computing topological features of a space at different spatial resolutions. More persistent features are detected over a wide range of spatial scales and are deemed more likely to represent true features of the underlying space rather than artifacts of sampling, noise, or particular choice of parameters.
Topological data analysis and persistent homology have had impacts on Morse theory. [121] Morse theory has played a very important role in the theory of TDA, including on computation. Some work in persistent homology has extended results about Morse functions to tame functions or, even to continuous functions [citation needed]. A forgotten ...
P-persistent This approach lies between the 1-persistent and non-persistent CSMA access modes. [1] When the transmitting node is ready to transmit data, it senses the transmission medium for idle or busy. If idle, then it transmits immediately. If busy, then it senses the transmission medium continuously until it becomes idle, then transmits ...
Persistent homology groups were first introduced by Herbert Edelsbrunner, David Letscher, and Afra Zomorodian in a 2002 paper Topological Persistence and Simplification, one of the foundational papers in the fields of persistent homology and topological data analysis, [1] based largely on the persistence barcodes and the persistence algorithm ...
A persistence module is a mathematical structure in persistent homology and topological data analysis that formally captures the persistence of topological features of an object across a range of scale parameters.
Trap emission is a multistep process wherein a carrier falls into defect-related wave states in the middle of the bandgap. A trap is a defect capable of holding a carrier. The trap emission process recombines electrons with holes and emits photons to conserve energy. Due to the multistep nature of trap emission, a phonon is also often emitted.
Diagram of the Meissner effect. Magnetic field lines, represented as arrows, are excluded from a superconductor when it is below its critical temperature. In condensed-matter physics , the Meissner effect (or Meißner–Ochsenfeld effect ) is the expulsion of a magnetic field from a superconductor during its transition to the superconducting ...
Persistent luminescence involves energy traps (such as electron or hole traps) in a material, [4] which are filled during the excitation. Afterward, the stored energy is gradually released to light emitter centers, usually by a fluorescence-like mechanism.