Direct optical detection of singlet oxygen from a single cell

Singlet oxygen has been detected in single nerve cells by its weak 1270 nm phosphorescence (a1deltag --> X3sigmag-) upon irradiation of a photosensitizer incorporated in the cell. Thus, one can now consider the application of direct optical imaging techniques to mechanistic studies of singlet oxygen at the single-cell level.     

Unbounded derivations and invariant states

Let be a von Neumann algebra with a cyclic and separating vector . Let =i[H, ·] be the spatial derivation implemented by a selfadjoint operatorH, such thatH=0. Let be the modular operator associated with the pair (, ). We prove the equivalence of the following three conditions:1)H is essential selfadjoint onD(), andH commutes strongly with .2) The restriction ofH toD() is essential selfadjoint onD(^1/2) equipped with the inner product(|)_#=(|)+(^1/2|^1/2), , D(^1/2).3) exp (itH) exp (–itH)= for anyt.We show by an example, that the first part of 1),H is essential selfadjoint onD(), does not imply 3). This disproves a conjecture due to Bratteli and Robinson [3].Part of this work was done while O.B. was a member of Zentrum für interdisziplinäre Forschung der Universität Bielefeld     

Modeling chemoadaptive behavior: X-ray structure of the trimethylamine oxide-urea (1∶4) complex

The structure of a trimethylamine oxide (TMAO)-urea 14 complex was investigated by x-ray crystallographic methods. C₃H₉NO, 4CH₄N₂O, M_r=315.33, monoclinic P2₁/n, a=11.004(2), b=9.8259, c=15.419(2),=106.88(4), V=1595.4(2) å₃, Z=4, D_x=1.313(1) g cm^–3, monochromatized Cu (=1.5418 å),=8.94 cm^–1, F(OOO)=680, temperature = 110K, final R=0.067, for 1786 unique observed reflections. Based on these studies and comparison with related compounds a model of the interaction of urea and TMAO with proteins, especially enzymes, is proposed. This is important in the physiology of many organisms, especially elasmobranchs. The counteracting effect of TMAO on urea perturbation of protein structure and function is interpreted in terms of water structure as a balance between the structure breaking effect of urea and the structure-stabilizing effect of TMAO.     

Hierarchical Tubular Structures Grown from the Gel/Liquid Interface

Three dimensional hierarchical materials are widespread in nature but are difficult to synthesize by using self‐assembly/organization. Here, we employ a gel–liquid interface to obtain centimeter‐long ～100 μm diameter tubes with complex mineral wall structures that grow from the interface into solution. The gel, made from gelatin, is loaded with metal chloride salt, whereas the solution is a high pH anion source. Tubes were obtained with a range of cations (Ca²⁺, Sr²⁺, Ba²⁺, Cu²⁺, and Zn²⁺) and anions (CO₃^2? and PO₄^3?). The crystalline phases found in the tube walls corresponded to expectations from solution chemistries and phase solubilities. The growth mechanism is found to be akin to that of chemical gardens. The divalent cations modify the strength of the gelatin gel in a manner that involves not only simple electrostatic screening, but also ion‐specific effects. Thus, tubes were not obtained for those ions and/or concentrations that significantly changed the gel’s mechanical structure. At high Cu²⁺ loading, for example, vertical convection bands, not Liesegang bands, were observed in the gels.     

Operator valued weights in von Neumann algebras,II

Let M be a von Neumann algebra, and N a sub von Neumann algebra of M. We prove that if φ and ψ are n.f.s. weights on N and M respectively, such that σ_t^ψ extends σ_t^φ, then there is a unique n.f.s. operator valued weight T from M to N, such that ψ = φ ° T. Moreover we generalize the notion of modular automorphism groups associated with conditional expectations to operator valued weights.     

Factorization and Dilation Problems for Completely Positive Maps on von Neumann Algebras

We study factorization and dilation properties of Markov maps between von Neumann algebras equipped with normal faithful states, i.e., completely positive unital maps which preserve the given states and also intertwine their automorphism groups. The starting point for our investigation has been the question of existence of non-factorizable Markov maps, as formulated by C. Anantharaman-Delaroche. We provide simple examples of non-factorizable Markov maps on M_n(\mathbbC){M_n(\mathbb{C})} for all n ≥ 3, as well as an example of a one-parameter semigroup (T(t)) _t≥0 of Markov maps on M₄(\mathbbC){M_4(\mathbb{C})} such that T(t) fails to be factorizable for all small values of t > 0. As applications, we solve in the negative an open problem in quantum information theory concerning an asymptotic version of the quantum Birkhoff conjecture, as well as we sharpen the existing lower bound estimate for the best constant in the noncommutative little Grothendieck inequality.     

Random matrices with complex Gaussian entries

In this paper we give new and purely analytical proofs of a number of classical results on the asymptotic behavior of large random matrices of complex Wigner type (the GUE-case) or of complex Wishart type: Wigner's semi-circle law, the Harer-Zagier recursion formula, the Marchenko-Pastur law, the Geman-Silverstein results on the largest and smallest eigenvalues and other related results. Our approach is based on the derivation of explicit formulae for the moment generating functions for random matrices of the two considered types.     

A new proof of the equivalence of injectivity and hyperfiniteness for factors on a separable Hilbert space

In 1975 A. Connes proved the fundamental result that injective factors on a separable Hilbert space are hyperfinite. In this paper a new proof of this result is presented in which the most technical parts of Connes proof are avoided. Particularly the proof does not rely on automorphism group theory. The starting point in this approach is Wassermann's simple proof of injective ? semidiscrete together with Choi and Effros' characterization of semidiscrete von Neumann algebras as those von Neumann algebras N for which the identity map on N has an approximate completely positive factorization through n × n-matrices.