In this paper we study the relationship between a very classical algebraic object associated to a filtration of topological spaces, namely a spectral sequence introduced by Leray in the 1940’s, and a more recently invented object that has found many applications – namely, its persistent homology groups. We show the existence of a long exact sequence of groups linking these two objects and using...

We report a local probe investigation of the frustrated antiferromagnet ${\mathrm{Pr}}_{3}{\mathrm{BWO}}_{9}$ with distorted kagome lattice. The absence magnetic order or spin-freezing is indicated by spectral analysis down to 0.3 K and specific heat measurements 0.09 K. Knight shifts show an upturn behavior sample cooling down, which further suppressed external field. For spin dynamics, gapped...

Persistent memory is a new tier of memory that functions as a hybrid of traditional storage systems and main memory. It combines the benefits of both: the data persistence property of storage with the fast load/store interface of memory. Yet, efficiently supporting data persistence in memory requires non-trivial effort. In particular, logging is a widely used data persistence scheme due to its ...

Principal neurons in layer III of the rat lateral entorhinal cortex (LEC) generate a self-sustained plateau potential and persistent spiking following the application of a brief suprathreshold excitatory stimulus delivered in the presence of the muscarinic receptor agonist carbachol. This persistent activity can be terminated by application of a second excitatory stimulus, and these cells can b...

Wideband SAR systems such as TerraSAR-X allow estimation of the absolute interferometric phase without resorting to error prone phase unwrapping. This is achieved through the delta-k technique that exploits frequency diversity within the range bandwidth to simulate a SAR system with a much longer carrier wavelength. This benefits all interferometric applications including DEM generation and lan...

We consider random subgroups of Thompson’s group F with respect to two natural stratifications of the set of all k generator subgroups. We find that the isomorphism classes of subgroups which occur with positive density are not the same for the two stratifications. We give the first known examples of persistent subgroups, whose isomorphism classes occur with positive density within the set of k...

We consider the problem of deciding whether the persistent homology group of a simplicial pair (K, L) can be realized as the homology H∗(X) of some complex X with L ⊂ X ⊂ K. We show that this problem is NP-complete even if K is embedded in R3. As a consequence, we show that it is NP-hard to simplify level and sublevel sets of scalar functions on S3 within a given tolerance constraint. This prob...