Eigenvalue confinement and spectral gap for random simplicial complexes

We consider the adjacency operator of the Linial‐Meshulam model for random simplicial complexes on n vertices, where each d‐cell is added independently with probability p to the complete ‐skeleton. Under the assumption , we prove that the spectral gap between the smallest eigenvalues and the remaining eigenvalues is with high probability. This estimate follows from a more general result on eigenvalue confinement. In addition, we prove that the global distribution of the eigenvalues is asymptotically given by the semicircle law. The main ingredient of the proof is a Füredi‐Komlós‐type argument for random simplicial complexes, which may be regarded as sparse random matrix models with dependent entries. © 2017 Wiley Periodicals, Inc. Random Struct. Alg., 51, 506–537, 2017     

The formation of dimetallocycles from reactions of alkynes with (η-C5Me5)2Rh2(CO)2; X-ray structure of [(η-C5Me5)2Rh2(η-CO) {μ-η2,η2-C(O)C2-(CF3)2}]

The complexes (η-C₅Me₅)₂Rh₂(μ-CO) {μ-η²,η²-C(O)CRCR} are obtained from reactions between (η-C₅Me₅)₂Rh₂(CO)₂ and the alkynes RCCR (R  CF₃, CO₂Me, or Ph) at 25°C. The molecular geometry of the complex with R  CF₃ has been established by X-ray diffraction; the bridging 'ene-one' unit adopts a μ-η²,η² conformation. Other complexes isolated from these reactions include (η-C₅Me₅)Rh(C₆R₆) (R  CF₃, CO₂Me), (η-C₅Me)₂Rh₂(C₄R₄) (R  CO₂Me) and (η-C₅Me₅)₂Rh₂(CO₂C₂R₂) (R  Ph). The reaction between (η-C₅Me₅)₂Rh₂(CO)₂ and C₆F₅CCC₆F₅ gives (η-C₅Me₅)₂Rh₂(CO)₂(C₆F₅C₂C₆F₅). Mononuclear complexes such as (η-C₅Me₅)Co(C₄R₄CO) are the major products isolated from reactions between (η-C₅Me₅)₂CO₂(CO)₂ and alkynes at 25°C.     

Fine Tuning of Chlorophyll Spectra by Protein‐Induced Ring Deformation

The ability to tune the light‐absorption properties of chlorophylls by their protein environment is the key to the robustness and high efficiency of photosynthetic light‐harvesting proteins. Unfortunately, the intricacy of the natural complexes makes it very difficult to identify and isolate specific protein–pigment interactions that underlie the spectral‐tuning mechanisms. Herein we identify and demonstrate the tuning mechanism of chlorophyll spectra in type II water‐soluble chlorophyll binding proteins from Brassicaceae (WSCPs). By comparing the molecular structures of two natural WSCPs we correlate a shift in the chlorophyll red absorption band with deformation of its tetrapyrrole macrocycle that is induced by changing the position of a nearby tryptophan residue. We show by a set of reciprocal point mutations that this change accounts for up to 2/3 of the observed spectral shift between the two natural variants.     

Stochastic integrators indexed by a multi-dimensional parameter

Summary Multi-parameter stochastic integrators are described and classified according to directions of integrability. Sets of directions are distinguished precisely by the combinatorial dimension of corresponding fractional Cartesian products. The main theorem establishes existence of stochastic processes which are integrators in prescribed directions but not others.     

Constructing near spanning trees with few local inspections

Constructing a spanning tree of a graph is one of the most basic tasks in graph theory. Motivated by several recent studies of local graph algorithms, we consider the following variant of this problem. Let G be a connected bounded‐degree graph. Given an edge e in G we would like to decide whether e belongs to a connected subgraph consisting of edges (for a prespecified constant ), where the decision for different edges should be consistent with the same subgraph . Can this task be performed by inspecting only a constant number of edges in G ? Our main results are:

• We show that if every t‐vertex subgraph of G has expansion then one can (deterministically) construct a sparse spanning subgraph of G using few inspections. To this end we analyze a “local” version of a famous minimum‐weight spanning tree algorithm.
• We show that the above expansion requirement is sharp even when allowing randomization. To this end we construct a family of 3‐regular graphs of high girth, in which every t‐vertex subgraph has expansion . We prove that for this family of graphs, any local algorithm for the sparse spanning graph problem requires inspecting a number of edges which is proportional to the girth.

© 2016 Wiley Periodicals, Inc. Random Struct. Alg., 50, 183–200, 2017     

Spin Selectivity in Electron Transfer in Photosystem I

Photosystem I (PSI) is one of the most studied electron transfer (ET) systems in nature; it is found in plants, algae, and bacteria. The effect of the system structure and its electronic properties on the electron transfer rate and yield was investigated for years in details. In this work we show that not only those system properties affect the ET efficiency, but also the electrons’ spin. Using a newly developed spintronic device and a technique which enables control over the orientation of the PSI monolayer relative to the device (silver) surface, it was possible to evaluate the degree and direction of the spin polarization in ET in PSI. We find high‐spin selectivity throughout the entire ET path and establish that the spins of the electrons being transferred are aligned parallel to their momenta. The spin selectivity peaks at 300 K and vanishes at temperatures below about 150 K. A mechanism is suggested in which the chiral structure of the protein complex plays an important role in determining the high‐spin selectivity and its temperature dependence. Our observation of high light induced spin dependent ET in PSI introduces the possibility that spin may play an important role in ET in biology.     

PHOTO-CIDNP DETECTION OF PYRIMIDINE DIMER RADICAL CATIONS IN ANTHRAQUINONESULFONATE- SENSITIZED SPLITTING

Anthraquinone-2-sulfonate (AQS) photosensitizes pyrimidine dimer splitting. Electron abstraction from the dimer is thought to induce dimer splitting, but direct evidence for the existence and intermediacy of dimer radical cations has been lacking. By employing photochemically induced dynamic nuclear polarization, we have found emission signals in the NMR spectra of dimers upon photolysis of dimers in the presence of anthraquinone-2-sulfonate. The two dimers employed were cis, syn-thymine dimer in which the N(1)-positions were linked by a three-carbon bridge and the N(3), N(3')-dimethyl derivative of that compound. The anthraquinone-2-sulfonate sensitized photochemically induced dynamic nuclear polarization spectrum of the methylated derivative exhibited an emission signal from the dimer-C(6) hydrogens. This result implied the existence of a dimer radical cation (mD+.) formed by electron abstraction by excited anthraquinone-2-sulfonate and nuclear spin sorting within a solvent caged radical ion pair [mD+. AQS-.]. Product pyrimidine photochemically induced dynamic nuclear polarization signals were also seen [enhanced absorption by C(6)-hydrogens and emission by C(5)-methyl groups]. Nuclear spin polarization in the product resulted from spin sorting in one or more of its precursors, including mD+. The results support the conclusion that dimer radical cations not only exist but are intermediates in the photosensitized splitting of pyrimidine dimers by anthraquinonesulfonate.     

Upgrading of paper grade pulps to dissolving pulps by nitren extraction: yields,molecular and supramolecular structures of nitren extracted pulps

Different paper grade pulps were extracted with nitren in order to produce dissolving pulps and polymeric xylan. The yield and molecular structure of the extracted pulps were investigated by carbohydrate analysis and HPSEC combined with fluorescence labelling in order to additionally monitor the carbonyl and carboxyl group profiles of the pulps. The supramolecular structure of selected pulps were further studied by solid state ¹³C-CP/MAS-NMR and wide-angle X-ray scattering (WAXS). These supramolecular data of nitren extracted pulps were compared to samples extracted with NaOH and a conventional dissolving pulp in order to classify the properties of nitren extracted pulps. Nitren extraction results in selective xylan removal without noticeable degradation or oxidation of the cellulose fraction. The resulting dissolving pulps have high molar masses, a narrow molar mass distribution and the typical contents of carbonyl and carboxyl groups. The supramolecular structure of cellulose is less affected by nitren compared to strong NaOH, and the resultant dissolving pulps still have the cellulose I structure. All laboratories are members of the European polysaccharide network of excellence EPNOE.