Connes' embedding problem and Tsirelson's problem

We show that Tsirelson's problem concerning the set of quantum correlations and Connes' embedding problem on finite approximations in von Neumann algebras (known to be equivalent to Kirchberg's QWEP conjecture) are essentially equivalent. Specifically, Tsirelson's problem asks whether the set of bipartite quantum correlations generated between tensor product separated systems is the same as the set of correlations between commuting C*-algebras. Connes' embedding problem asks whether any separable II$_1$ factor is a subfactor of the ultrapower of the hyperfinite II$_1$ factor. We show that an affirmative answer to Connes' question implies a positive answer to Tsirelson's. Conversely, a positve answer to a matrix valued version of Tsirelson's problem implies a positive one to Connes' problem

Activation of protease activated receptor 1 increases the excitability of the dentate granule neurons of hippocampus

Protease activated receptor-1 (PAR1) is expressed in multiple cell types in the CNS, with the most prominent expression in glial cells. PAR1 activation enhances excitatory synaptic transmission secondary to the release of glutamate from astrocytes following activation of astrocytically-expressed PAR1. In addition, PAR1 activation exacerbates neuronal damage in multiple in vivo models of brain injury in a manner that is dependent on NMDA receptors. In the hippocampal formation, PAR1 mRNA appears to be expressed by a subset of neurons, including granule cells in the dentate gyrus. In this study we investigate the role of PAR activation in controlling neuronal excitability of dentate granule cells. We confirm that PAR1 protein is expressed in neurons of the dentate cell body layer as well as in astrocytes throughout the dentate. Activation of PAR1 receptors by the selective peptide agonist TFLLR increased the intracellular Ca2+ concentration in a subset of acutely dissociated dentate neurons as well as non-neuronal cells. Bath application of TFLLR in acute hippocampal slices depolarized the dentate gyrus, including the hilar region in wild type but not in the PAR1-/- mice. PAR1 activation increased the frequency of action potential generation in a subset of dentate granule neurons; cells in which PAR1 activation triggered action potentials showed a significant depolarization. The activation of PAR1 by thrombin increased the amplitude of NMDA receptor-mediated component of EPSPs. These data suggest that activation of PAR1 during normal function or pathological conditions, such as during ischemia or hemorrhage, can increase the excitability of dentate granule cells

Особенности и закономерности изменения восстановлености углей башкирского яруса Западного Донбасса

В статье приведена детальная петрографическая характеристика углей башкирского яруса Западного Донбасса. Проведена классификация по восстановлености в соответствии с петрографическими типами. Установлены стратиграфические и площадные закономерности изменения степени восстановлености.У статті наведена детальна петрографічна характеристика вугілля башкирського ярусу Західного Донбасу. Проведена класифікація відновленості, згідно з петрографічними типами. Встановлені стратиграфічні та просторові закономірності зміни ступеню відновленості.The article gives detailed petrographic characteristics of coal of Bashkirian formation of Western Donbas. The classifications for recovery in accordance with petrographic types are given. The stratigraphic and areal patterns of change in the degree of recovery are established

Multiplicativity of completely bounded p-norms implies a new additivity result

We prove additivity of the minimal conditional entropy associated with a quantum channel Phi, represented by a completely positive (CP), trace-preserving map, when the infimum of S(gamma_{12}) - S(gamma_1) is restricted to states of the form gamma_{12} = (I \ot Phi)(| psi >< psi |). We show that this follows from multiplicativity of the completely bounded norm of Phi considered as a map from L_1 -> L_p for L_p spaces defined by the Schatten p-norm on matrices; we also give an independent proof based on entropy inequalities. Several related multiplicativity results are discussed and proved. In particular, we show that both the usual L_1 -> L_p norm of a CP map and the corresponding completely bounded norm are achieved for positive semi-definite matrices. Physical interpretations are considered, and a new proof of strong subadditivity is presented.Comment: Final version for Commun. Math. Physics. Section 5.2 of previous version deleted in view of the results in quant-ph/0601071 Other changes mino

Experimental estimation of the dimension of classical and quantum systems

An overwhelming majority of experiments in classical and quantum physics make a priori assumptions about the dimension of the system under consideration. However, would it be possible to assess the dimension of a completely unknown system only from the results of measurements performed on it, without any extra assumption? The concept of a dimension witness answers this question, as it allows one to bound the dimension of an unknown classical or quantum system in a device-independent manner, that is, only from the statistics of measurements performed on it. Here, we report on the experimental demonstration of dimension witnesses in a prepare and measure scenario. We use pairs of photons entangled in both polarization and orbital angular momentum to generate ensembles of classical and quantum states of dimensions up to 4. We then use a dimension witness to certify their dimensionality as well as their quantum nature. Our results open new avenues for the device-independent estimation of unknown quantum systems and for applications in quantum information science.Comment: See also similar, independent and jointly submitted work of J. Ahrens et al., quant-ph/1111.127

The Hilbertian Tensor Norm and Entangled Two-Prover Games

We study tensor norms over Banach spaces and their relations to quantum information theory, in particular their connection with two-prover games. We consider a version of the Hilbertian tensor norm $\gamma_2$ and its dual $\gamma_2^*$ that allow us to consider games with arbitrary output alphabet sizes. We establish direct-product theorems and prove a generalized Grothendieck inequality for these tensor norms. Furthermore, we investigate the connection between the Hilbertian tensor norm and the set of quantum probability distributions, and show two applications to quantum information theory: firstly, we give an alternative proof of the perfect parallel repetition theorem for entangled XOR games; and secondly, we prove a new upper bound on the ratio between the entangled and the classical value of two-prover games.Comment: 33 pages, some of the results have been obtained independently in arXiv:1007.3043v2, v2: an error in Theorem 4 has been corrected; Section 6 rewritten, v3: completely rewritten in order to improve readability; title changed; references added; published versio

Molecular and biogeochemical evidence for methane cycling beneath the western margin of the Greenland Ice Sheet

Microbial processes that mineralize organic carbon and enhance solute production at the bed of polar ice sheets could be of a magnitude sufficient to affect global elemental cycles. To investigate the biogeochemistry of a polar subglacial microbial ecosystem, we analyzed water discharged during the summer of 2012 and 2013 from Russell Glacier, a land-terminating outlet glacier at the western margin of the Greenland Ice Sheet. The molecular data implied that the most abundant and active component of the subglacial microbial community at these marginal locations were bacteria within the order Methylococcales (59–100% of reverse transcribed (RT)-rRNA sequences). mRNA transcripts of the particulate methane monooxygenase (pmoA) from these taxa were also detected, confirming that methanotrophic bacteria were functional members of this subglacial ecosystem. Dissolved methane ranged between 2.7 and 83 μM in the subglacial waters analyzed, and the concentration was inversely correlated with dissolved oxygen while positively correlated with electrical conductivity. Subglacial microbial methane production was supported by δ(13)C-CH(4) values between −64‰ and −62‰ together with the recovery of RT-rRNA sequences that classified within the Methanosarcinales and Methanomicrobiales. Under aerobic conditions, >98% of the methane in the subglacial water was consumed over ∼30 days incubation at ∼4 °C and rates of methane oxidation were estimated at 0.32 μM per day. Our results support the occurrence of active methane cycling beneath this region of the Greenland Ice Sheet, where microbial communities poised in oxygenated subglacial drainage channels could serve as significant methane sinks

Selective Earth-Abundant System for CO2 Reduction: Comparing Photo- and Electrocatalytic Processes

The valorization of CO2 via photo- or electrocatalytic reduction constitutes a promising approach toward the sustainable production of fuels or value-added chemicals using intermittent renewable energy sources. For this purpose, molecular catalysts are generally studied independently with respect to the photo- or the electrochemical application, although a unifying approach would be much more effective with respect to the mechanistic understanding and the catalyst optimization. In this context, we present a combined photo- and electrocatalytic study of three Mn diimine catalysts, which demonstrates the synergistic interplay between the two methods. The photochemical part of our study involves the development of a catalytic system containing a heteroleptic Cu photosensitizer and the sacrificial BIH reagent. The system shows exclusive selectivity for CO generation and renders turnover numbers which are among the highest reported thus far within the group of fully earth-abundant photocatalytic systems. The electrochemical part of our investigations complements the mechanistic understanding of the photochemical process and demonstrates that in the present case the sacrificial reagent, the photosensitizer, and the irradiation source can be replaced by the electrode and a weak Brønsted acid. © 2019 American Chemical Society

Analytical model of brittle destruction based on hypothesis of scale similarity

The size distribution of dust particles in nuclear fusion devices is close to the power function. A function of this kind can be the result of brittle destruction. From the similarity assumption it follows that the size distribution obeys the power law with the exponent between -4 and -1. The model of destruction has much in common with the fractal theory. The power exponent can be expressed in terms of the fractal dimension. Reasonable assumptions on the shape of fragments concretize the power exponent, and vice versa possible destruction laws can be inferred on the basis of measured size distributions.Comment: 10 pages, 3 figure