Given a Newtonian coalgebra we associate to it a chain complex. The homology groups of this Newtonian chain complex are computed for two important Newtonian coalgebras arising in the study of flag vectors of polytopes: R〈a,b〉 and R〈c,d〉. The homology of R〈a,b〉 corresponds to the homology of the boundary of the n-crosspolytope. In contrast, the homology of R〈c,d〉 depends on the characteristic of...

Human factor D purified to homogeneity by a modified procedure was subjected to NH2-terminal amino acid sequence analysis by using a modified automated Beckman sequencer. We identified 48 of the first 57 NH2-terminal amino acids in a single sequencer run, using microgram quantities of factor D. The deduced amino acid sequence represents approximately 25% of the primary structure of factor D. Th...

A graph's spectral wavelet signature determines a filtration, and consequently an associated set of extended persistence diagrams. We propose framework that optimises the choice for dataset graphs, such their diagrams capture features graphs are best suited to given data science problem. Since graph is derived from its Laplacian, our encodes geometric properties in can be applied without priori...

An extended synthetic oligonucleotide (58-mer) has been used to identify and characterize a human liver gap junction cDNA. The cDNA is 1,574 bases long and contains the entire coding region for a gap junction protein. In vitro translation of the RNA products of this cDNA is consistent with it coding for a 32,022-D protein. Southern blot analysis indicates that the gap junction gene is present a...

A recent result on size functions is extended to higher homology modules: the persistent homology based on a multidimensional measuring function is reduced to a 1-dimensional one. This leads to a stable distance for multidimensional persistent homology. Some reflections on i-essentiality of homological critical values conclude the paper.

In this lecture we will discuss one of the most interesting recent developments in mathematical physics, the classification of D-brane charges in string theory using Ktheoretic methods [1]–[6]. Our presentation will be in the context of explaining how certain mathematical structures find very natural physical explanations in string theory. In particular, we will focus on two very important feat...