quantitative relationships between molecular structure and azolo-adamantanes derivatives were discovered by different chemometric tools including factor analysis based multiple linear regressions (fa-mlr), principle component regression analysis (pcra), and genetic algorithm-partial least squares ga-pls. the fa-mlr describes the effect of geometrical and quantum indices on enzyme inhibition act...

Features such as photon rings, jets, or hot. spots can leave particular topological signatures in a black hole image. As such, data analysis be used to characterize images resulting from high resolution observations (synthetic real) of holes the electromagnetic sector. We demonstrate that persistent homology allows for this characterization made automatically by counting number connected compon...

Even after decades of quantum computing development, examples generally useful algorithms with exponential speedups over classical counterparts are scarce. Recent progress in for linear-algebra positioned machine learning (QML) as a potential source such improvements. Yet, an unexpected recent series "dequantization" results has equally rapidly removed the promise several QML algorithms. This r...

In this work, we introduce persistent homology for the analysis of cryo-electron microscopy (cryo-EM) density maps. We identify the topological fingerprint or topological signature of noise, which is widespread in cryo-EM data. For low signal-to-noise ratio (SNR) volumetric data, intrinsic topological features of biomolecular structures are indistinguishable from noise. To remove noise, we empl...

The half filled Hubbard model is studied in the pair approximation of the Cluster Variation Method. The use of the SO(4) symmetry of the model makes possible to give a complete analytical characterization of the ground state, by means of explicit expressions for the double occupancy and the nearest neighbor correlation functions. The finite temperature analysis is reduced to the numerical solut...

motivated by the recent study on categorical properties of latticevalued topology, the paper considers a generalization of the notion of topological system introduced by s. vickers, providing an algebraic and a coalgebraic category of the new structures. as a result, the nature of the category   topsys   of s. vickers gets clari ed, and a metatheorem is stated, claiming that (latticevalu...