Both AdS/CFT duality and more general reasoning from quantum gravity point to a rich collection of boundary observables that always evolve unitarily. The physical quantum gravity states described by these observables must be solutions of the spatial diffeomorphism and Wheeler-deWitt constraints, which implies that the state space does not factorize into a tensor product of localized degrees of freedom. The "firewall" argument that unitarity of black hole S-matrix implies the presence of a highly excited quantum state near the horizon is based on such a factorization, hence is not applicable in quantum gravity. In fact, there appears to be no conflict between boundary unitarity and regularity of the event horizon.

It is known that the dynamics of planar billiards satisfies strong mixing properties (e.g. exponential decay of correlations) provided that some expansion condition on unstable curves is satisfied. This condition has been shown to always hold for smooth dispersing planar billiards, but it needed to be assumed separately in the case of dispersing planar billiards with corner points. We prove that this expansion condition holds for any dispersing planar billiard with corner points, no cusps and bounded horizon.

Background: Autoantibodies against the second extracellular loop of the β1-adrenergic receptor (β1-AA) not only contribute to increased susceptibility to heart failure, but also play a causative role in myocardial remodeling through their sympathomimetic-like effects that are induced upon binding to the β1-adrenergic receptor. However, their role in the function of T lymphocytes has never been previously investigated. Our present study was designed to determine whether β1-AA isolated from the sera of dilated cardiomyopathy (DCM) patients caused the proliferation of T cells and the secretion of cytokines. Methods: Blood samples were collected from 95 DCM patients as well as 95 healthy subjects, and β1-AA was detected using ELISA. The CD3+T lymphocytes were selected separately through flow cytometry and the effect of β1-AA on T lymphocyte proliferation was examined by CCK-8 kits and CFSE assay. Western blotting was used to analyze the expressions of phospho-VASP and phospho-p38 MAPK. Results: β1-AA enhanced the proliferation of T lymphocytes. This effect could be blocked by the selective β1-adrenergic receptor antagonist metoprolol, PKA inhibitor H89, and p38 MAPK inhibitor SB203580. Furthermore, the expression of the phosphorylated forms of phospho-VASP and phospho-p38 MAPK were markedly increased in the presence of β1-AA. β1-AA also inhibited the secretion of interferon-γ (IFN-γ) while promoting an increase in interleukin-4 (IL-4) levels. Conclusions: These results demonstrate that β1-AA isolated from DCM patients binds to β1-AR on the surface of T cells, causing changes in T-cell proliferation and secretion through the β1-AR/cAMP/PKA and p38 MAPK pathways.

In this paper, we consider situations in which a given logical function is realized by a multithreshold threshold function. In such situations, constant functions can be easily obtained from multithreshold threshold functions, and therefore, we can show that it becomes possible to optimize a class of high-order neural networks. We begin by proposing a generating method for threshold functions in which we use a vector that determines the boundary between the linearly separable function and the high-order threshold function. By applying this method to high-order threshold functions, we show that functions with the same weight as, but a different threshold than, a threshold function generated by the generation process can be easily obtained. We also show that the order of the entire network can be extended while maintaining the structure of given functions.

The many intricate connections between scattering amplitudes, on-shell diagrams, and the positroid stratification of the Grassmannian has recently been described in great detail. In order to facilitate the exploration of this rich correspondence, we have prepared a public Mathematica package called "positroids" which includes an array of useful tools including those for the construction of canonical coordinates for positroid configurations, the drawing of representative on-shell (plabic) graphs, and the evaluation of on-shell differential forms. This note documents the functions made available by the positroids package; the package's source code together with a Mathematica notebook containing many detailed examples of its functionality are included with this note's submission files on the arXiv.

The extraction of a desired speech signal from a noisy environment has become a challenging issue. In the recent years, the scientific community has particularly focused on multichannel techniques which are dealt with in this review. In fact, this study tries to classify these multichannel techniques into three main ones: Beamforming, Independent Com-ponent Analysis (ICA) and Time Frequency (T-F) masking. This paper also highlights their advantages and drawbacks. However these previously mentioned techniques could not afford satisfactory results. This fact leads to the idea that a combination of those techniques, which is depicted along this study, may probably provide more efficient results. In-deed, giving the fact that those approaches are still be considered as being not totally efficient, has led us to review these mentioned above in the hope that further researches will provide this domain with suitable innovations.

Given an ideal $a \subseteq R$ in a (log) $Q$-Gorenstein $F$-finite ring of characteristic $p > 0$, we study and provide a new perspective on the test ideal $\tau(R, a^t)$ for a real number $t > 0$. Generalizing a number of known results from the principal case, we show how to effectively compute the test ideal and also describe $\tau(R, a^t)$ using (regular) alterations with a formula analogous to that of multiplier ideals in characteristic zero. We further prove that the $F$-jumping numbers of $\tau(R, a^t)$ as $t$ varies are rational and have no limit points, including the important case where $R$ is a formal power series ring. Additionally, we obtain a global division theorem for test ideals related to results of Ein and Lazarsfeld from characteristic zero, and also recover a new proof of Skoda's theorem for test ideals which directly mimics the proof for multiplier ideals.

Cub domain containing protein 1 (CDCP1) is strongly expressed in tumors derived from lung, colon, ovary, or kidney. It is a membrane protein that is phosphorylated and then bound by Src family kinases. Although expression and phosphorylation of CDCP1 have been investigated in many tumor cell lines, the CDCP1 features responsible for transformation have not been fully evaluated. This is in part due to the lack of an experimental system in which cellular transformation depends on expression of exogenous CDCP1 and Src. Here we use retrovirus mediated co-overexpression of c-Src and CDCP1 to induce focus formation of NIH3T3 cells. Employing different mutants of CDCP1 we show that for a full transformation capacity, the intact amino- and carboxy-termini of CDCP1 are essential. Mutation of any of the core intracellular tyrosine residues (Y734, Y743, or Y762) abolished transformation, and mutation of a palmitoylation motif (C689,690G) strongly reduced it. Src kinase binding to CDCP1 was not required since Src with a defective SH2 domain generated even more CDCP1 dependent foci whereas Src myristoylation was necessary. Taken together, the focus formation assay allowed us to define structural requirements of CDCP1/Src dependent transformation and to characterize the interaction of CDCP1 and Src.

A novel assay procedure has been developed to allow simultaneous activity discrimination in crude tissue extracts of the three known mammalian nicotinamide mononucleotide adenylyltransferase (NMNAT, EC 2.7.7.1) isozymes. These enzymes catalyse the same key reaction for NAD biosynthesis in different cellular compartments. The present method has been optimized for NMNAT isozymes derived from Mus musculus, a species often used as a model for NAD-biosynthesis-related physiology and disorders, such as peripheral neuropathies. Suitable assay conditions were initially assessed by exploiting the metal-ion dependence of each isozyme recombinantly expressed in bacteria, and further tested after mixing them in vitro. The variable contributions of the three individual isozymes to total NAD synthesis in the complex mixture was calculated by measuring reaction rates under three selected assay conditions, generating three linear simultaneous equations that can be solved by a substitution matrix calculation. Final assay validation was achieved in a tissue extract by comparing the activity and expression levels of individual isozymes, considering their distinctive catalytic efficiencies. Furthermore, considering the key role played by NMNAT activity in preserving axon integrity and physiological function, this assay procedure was applied to both liver and brain extracts from wild-type and Wallerian degeneration slow (WldS) mouse. WldS is a spontaneous mutation causing overexpression of NMNAT1 as a fusion protein, which protects injured axons through a gain-of-function. The results validate our method as a reliable determination of the contributions of the three isozymes to cellular NAD synthesis in different organelles and tissues, and in mutant animals such as WldS.

Magnetic field observations of low-mass stars reveal an increase of magnetic activity with increasing rotation rate. The so-called activity-rotation relation is usually attributed to changes in the underlying dynamo processes generating the magnetic field. We examine the dependence of the field strength on rotation in global numerical dynamo models and interpret our results on the basis of energy considerations. In agreement with the scaling law proposed by Christensen & Aubert (2006), the field strength in our simulations is set by the fraction of the available power used for the magnetic field generation. This is controlled by the dynamo efficiency calculated as the ratio of Ohmic to total dissipation in our models. The dynamo efficiency grows strongly with increasing rotation rate at a Rossby number of 0.1 until it reaches its upper bound of one and becomes independent of rotation. This gain in efficiency is related to the strong rotational dependence of the mean electromotive force in this parameter regime. For multipolar models at Rossby numbers clearly larger than 0.1, on the other hand, we do not find a systematic dependence of the field strength on rotation. Whether the enhancement of the dynamo efficiency found in our dipolar models explains the observed activity-rotation relation needs to be further assessed.