Metric sparsification and operator norm localization

We study an operator norm localization property and its applications to the coarse Novikov conjecture in operator K-theory. A metric space X is said to have operator norm localization property if there exists a positive number c such that for every r>0, there is R>0 for which, if m is a positive locally finite Borel measure on X, H is a separable infinite dimensional Hilbert space and T is a bounded linear operator acting on L^2(X,m) with propagation r, then there exists an unit vector v satisfying with support of diameter at most R and such that |Tv| is larger or equal than c|T|. If X has finite asymptotic dimension, then X has operator norm localization property. In this paper, we introduce a sufficient geometric condition for the operator norm localization property. This is used to give many examples of finitely generated groups with infinite asymptotic dimension and the operator norm localization property. We also show that any sequence of expanding graphs does not possess the operator norm localization property

Counterexample-Preserving Reduction for Symbolic Model Checking

The cost of LTL model checking is highly sensitive to the length of the formula under verification. We observe that, under some specific conditions, the input LTL formula can be reduced to an easier-to-handle one before model checking. In our reduction, these two formulae need not to be logically equivalent, but they share the same counterexample set w.r.t the model. In the case that the model is symbolically represented, the condition enabling such reduction can be detected with a lightweight effort (e.g., with SAT-solving). In this paper, we tentatively name such technique "Counterexample-Preserving Reduction" (CePRe for short), and finally the proposed technquie is experimentally evaluated by adapting NuSMV

Characterization of spatio-temporal epidural event-related potentials for mouse models of psychiatric disorders.

Distinctive features in sensory event-related potentials (ERPs) are endophenotypic biomarkers of psychiatric disorders, widely studied using electroencephalographic (EEG) methods in humans and model animals. Despite the popularity and unique significance of the mouse as a model species in basic research, existing EEG methods applicable to mice are far less powerful than those available for humans and large animals. We developed a new method for multi-channel epidural ERP characterization in behaving mice with high precision, reliability and convenience and report an application to time-domain ERP feature characterization of the Sp4 hypomorphic mouse model for schizophrenia. Compared to previous methods, our spatio-temporal ERP measurement robustly improved the resolving power of key signatures characteristic of the disease model. The high performance and low cost of this technique makes it suitable for high-throughput behavioral and pharmacological studies

Terephthalic acid–4,4′-bipyridine (2/1)

In the title compound, 2C8H6O4·C10H8N2, the 4,4′-bipyridine mol­ecule is located on an inversion centre. In the crystal structure, strong inter­molecular O—H⋯N hydrogen bonds between the terephthalic acid and 4,4′-bipyridine mol­ecules lead to the formation of chains with graph-set motif C 2 2(8) along the diagonal of the bc plane

catena-Poly[[bis­(p-toluene­sulfonato-κO)palladium(II)]bis­(μ-1,3-di-4-pyridylpropane-κ2 N:N′)]

In the title compound, [Pd(C7H7O3S)2(C13H14N2)2]n, the metal ion, located on a twofold rotation axis, exhibits a slightly distorted octa­hedral coordination environment, with bond angles that deviate by at most 2.2° from an ideal geometry, completed by two O atoms from two deprotonated p-toluene­sulfonic acid ligands and four N atoms from four 1,3-di-4-pyridylpropane ligands. One of the sulfonate O atoms is disordered over two positions [ratio 0.70 (5):0.30 (5)]

Zirconium-Catalyzed Atom-Economical Synthesis of 1,1-Diborylalkanes from Terminal and Internal Alkenes

A general and atom-economical synthesis of 1,1-diborylalkanes from alkenes and a borane without the need for an additional H2 acceptor is reported for the first time. The key to our success is the use of an earth-abundant zirconium-based catalyst, which allows a balance of self-contradictory reactivities (dehydrogenative boration and hydroboration) to be achieved. Our method avoids using an excess amount of another alkene as an H2 acceptor, which was required in other reported systems. Furthermore, substrates such as simple long-chain aliphatic alkenes that did not react before also underwent 1,1-diboration in our system. Significantly, the unprecedented 1,1-diboration of internal alkenes enabled the preparation of 1,1-diborylalkanes. © 2020 The Authors. Published by Wiley-VCH Verlag GmbH & Co. KGaA

Bis(ethano­lato-κO)(5,10,15,20-tetra­phenyl­calix[4]pyrrole)manganese(III) hexa­fluoro­phosphate

The title compound, [Mn(C2H5O)2(C44H28N4)]PF6, was synthesized from manganese(III) 2,4-penta­nedionate and 5,10,15,20-tetra­phenyl­calix[4]pyrrole by a hydro­thermal reaction. The MnIII atom is located on an inversion centre and the asymmetric unit comprises one half-formula unit. The MnIII ion is hexa­coordinated by four N atoms from one 5,10,15,20-tetra­phenyl­calix[4]pyrrole ligand and two O atoms from two deprotonated ethanol mol­ecules. The equatorially located atoms (the Mn and four N atoms) are planar. The dihedral angles between the planes of the phenyl rings and the equatorial plane are 53.3 (2) and 81.8 (2)°. One hexa­fluoro­phosphate anion balances the charge