A Mayer–Vietoris Formula for Persistent Homology with an Application to Shape Recognition in the Presence of Occlusions

In algebraic topology it is well known that, using the Mayer–Vietoris sequence, the homology of a space X can be studied by splitting X into subspaces A and B and computing the homology of A, B, and A∩B. A natural question is: To what extent does persistent homology benefit from a similar property? In this paper we show that persistent homology has a Mayer–Vietoris sequence that is generally not exact but only of order 2. However, we obtain a Mayer–Vietoris formula involving the ranks of the persistent homology groups of X, A, B, and A∩B plus three extra terms. This implies that persistent homological features of A and B can be found either as persistent homological features of X or of A∩B. As an application of this result, we show that persistence diagrams are able to recognize an occluded shape by showing a common subset of points.     

Topological insulators in ternary compounds with a honeycomb lattice

We investigate a new class of ternary materials such as LiAuSe and KHgSb with a honeycomb structure in Au-Se and Hg-Sb layers. We demonstrate the band inversion in these materials similar to HgTe, which is a strong precondition for existence of the topological surface states. In contrast with graphene, these materials exhibit strong spin-orbit coupling and a small direct band gap at the Γ point. Since these materials are centrosymmetric, it is straightforward to determine the parity of their wave functions, and hence their topological character. Surprisingly, the compound with strong spin-orbit coupling (KHgSb) is trivial, whereas LiAuSe is found to be a topological insulator.     

Efficient spin injector scheme based on Heusler materials

We present a rational design scheme intended to provide stable high spin polarization at the interfaces of the magnetoresistive junctions by fulfilling the criteria of structural and chemical compatibilities at the interface. This can be realized by joining the semiconducting and half-metallic Heusler materials with similar structures. The present first-principles calculations verify that the interface remains half-metallic if the nearest interface layers effectively form a stable Heusler material with the properties intermediately between the surrounding bulk parts. This leads to a simple rule for selecting the proper combinations.     

Symmetry of valence states of Heusler compounds explored by linear dichroism in hard-x-ray photoelectron spectroscopy

This study reports on the linear dichroism in angular-resolved photoemission from the valence band of the Heusler compounds NiTi0.9Sc0.1Sn and NiMnSb. High-resolution photoelectron spectroscopy was performed with an excitation energy of hν = 7.938 keV. The linear polarization of the photons was changed using an in-vacuum diamond phase retarder. The valence band spectra exhibit the typical structure expected from first-principles calculations of the electronic structure of these compounds. Noticeable linear dichroism is found in the valence band of both materials, and this allows for a symmetry analysis of the contributing states. The differences in the spectra are found to be caused by symmetry-dependent angular asymmetry parameters, and these occur even in polycrystalline samples without preferential crystallographic orientation.     

Epitaxial interfaces between crystallographically mismatched materials

We report an unexpected mechanism by which an epitaxial interface can form between materials having strongly mismatched lattice constants. A simple model is proposed in which one material tilts out of the interface plane to create a coincidence-site lattice that balances two competing geometrical criteria--low residual strain and short coincidence-lattice period. We apply this model, along with complementary first-principles total-energy calculations, to the interface formed by molecular-beam epitaxy of cubic Fe on hexagonal GaN and find excellent agreement between theory and experiment.     

Optical absorption in degenerately doped semiconductors: Mott transition or Mahan excitons?

Electron doping turns semiconductors conductive even when they have wide fundamental band gaps. The degenerate electron gas in the lowest conduction-band states, e.g., of a transparent conducting oxide, drastically modifies the Coulomb interaction between the electrons and, hence, the optical properties close to the absorption edge. We describe these effects by developing an ab initio technique which captures also the Pauli blocking and the Fermi-edge singularity at the optical-absorption onset, that occur in addition to quasiparticle and excitonic effects. We answer the question whether free carriers induce an excitonic Mott transition or trigger the evolution of Wannier-Mott excitons into Mahan excitons. The prototypical n-type zinc oxide is studied as an example.     

Steric control of the donor/acceptor interface: implications in organic photovoltaic charge generation

The performance of organic photovoltaic (OPV) devices is currently limited by modest short-circuit current densities. Approaches toward improving this output parameter may provide new avenues to advance OPV technologies and the basic science of charge transfer in organic semiconductors. This work highlights how steric control of the charge separation interface can be effectively tuned in OPV devices. By introducing an octylphenyl substituent onto the investigated polymer backbones, the thermally relaxed charge-transfer state, and potentially excited charge-transfer states, can be raised in energy. This decreases the barrier to charge separation and results in increased photocurrent generation. This finding is of particular significance for nonfullerene OPVs, which have many potential advantages such as tunable energy levels and spectral breadth, but are prone to poor exciton separation efficiencies. Computational, spectroscopic, and synthetic methods were combined to develop a structure-property relationship that correlates polymer substituents with charge-transfer state energies and, ultimately, device efficiencies.     

Discovery and synthesis of new UV-induced intrastrand C(4-8)G and G(8-4)C photolesions

UV irradiation of cellular DNA leads to the formation of a number of defined mutagenic DNA lesions. Here we report the discovery of new intrastrand C(4-8)G and G(8-4)C cross-link lesions in which the C(4) amino group of the cytosine base is covalently linked to the C(8) position of an adjacent dG base. The structure of the novel lesions was clarified by HPLC-MS/MS data for UV-irradiated DNA in combination with chemical synthesis and direct comparison of the synthetic material with irradiated DNA. We also report the ability to generate the lesions directly in DNA with the help of a photoactive precursor that was site-specifically incorporated into DNA. This should enable detailed chemical and biochemical investigations of these lesions.     

High temperature stability of nanocrystalline anatase powders prepared by chemical vapour synthesis under varying process parameters

Systematic variation in the high temperature stability of nanocrystalline anatase powders prepared by chemical vapour synthesis (CVS) using titanium (IV) isopropoxide under varying flow rates of oxygen and helium was obtained by progressively shifting the decomposition product from C₃H₆ to CO₂. The as-synthesised powders were characterised by high temperature X-ray diffraction (HTXRD), simultaneous thermo-gravimetric analyses (STA), X-ray photoelectron spectroscopy (XPS), Fourier transform infrared spectroscopy (FTIR) and transmission electron microscopy (TEM). It was observed that the anatase to rutile transformation temperature progressively increased for samples synthesised at higher O₂/He flow rate ratios. The improved anatase stability was attributed to the presence of incorporated carbon within the titania structure and confirmed by a high temperature carbon desorption peak.     

Measurement of Angstrom to Nanometer Molecular Distances with 19F Nuclear Spins by EPR/ENDOR Spectroscopy

Spectroscopic and biophysical methods for structural determination at atomic resolution are fundamental in studies of biological function. Here we introduce an approach to measure molecular distances in bio‐macromolecules using ¹⁹F nuclear spins and nitroxide radicals in combination with high‐frequency (94 GHz/3.4 T) electron–nuclear double resonance (ENDOR). The small size and large gyromagnetic ratio of the ¹⁹F label enables to access distances up to about 1.5 nm with an accuracy of 0.1–1 Å. The experiment is not limited by the size of the bio‐macromolecule. Performance is illustrated on synthesized fluorinated model compounds as well as spin‐labelled RNA duplexes. The results demonstrate that our simple but strategic spin‐labelling procedure combined with state‐of‐the‐art spectroscopy accesses a distance range crucial to elucidate active sites of nucleic acids or proteins in the solution state.