Conformal loop ensembles and the stress-energy tensor

We give a construction of the stress-energy tensor of conformal field theory (CFT) as a local "object" in conformal loop ensembles CLE_\kappa, for all values of \kappa in the dilute regime 8/3 < \kappa <= 4 (corresponding to the central charges 0 < c <= 1, and including all CFT minimal models). We provide a quick introduction to CLE, a mathematical theory for random loops in simply connected domains with properties of conformal invariance, developed by Sheffield and Werner (2006). We consider its extension to more general regions of definition, and make various hypotheses that are needed for our construction and expected to hold for CLE in the dilute regime. Using this, we identify the stress-energy tensor in the context of CLE. This is done by deriving its associated conformal Ward identities for single insertions in CLE probability functions, along with the appropriate boundary conditions on simply connected domains; its properties under conformal maps, involving the Schwarzian derivative; and its one-point average in terms of the "relative partition function." Part of the construction is in the same spirit as, but widely generalizes, that found in the context of SLE_{8/3} by the author, Riva and Cardy (2006), which only dealt with the case of zero central charge in simply connected hyperbolic regions. We do not use the explicit construction of the CLE probability measure, but only its defining and expected general properties.Comment: 49 pages, 3 figures. This is a concatenated, reduced and simplified version of arXiv:0903.0372 and (especially) arXiv:0908.151

Initial data for a head on collision of two Kerr-like black holes with close limit

We prove the existence of a family of initial data for the Einstein vacuum equation which can be interpreted as the data for two Kerr-like black holes in arbitrary location and with spin in arbitrary direction. This family of initial data has the following properties: (i) When the mass parameter of one of them is zero or when the distance between them goes to infinity, it reduces exactly to the Kerr initial data. (ii) When the distance between them is zero, we obtain exactly a Kerr initial data with mass and angular momentum equal to the sum of the mass and angular momentum parameters of each of them. The initial data depends smoothly on the distance, the mass and the angular momentum parameters.Comment: 15 pages, no figures, Latex2

670 nm laser light and EGCG complementarily reduce amyloid-β aggregates in human neuroblastoma cells: basis for treatment of Alzheimer's disease?

Objective: The aim of the present study is to present the results of in vitro experiments with possible relevance in the treatment of Alzheimer's disease (AD). Background Data: Despite intensive research efforts, there is no treatment for AD. One root cause of AD is the extra- and intracellular deposition of amyloid-beta (A{beta}) fibrils in the brain. Recently, it was shown that extracellular A{beta} can enter brain cells, resulting in neurotoxicity. Methods: After internalization of A{beta}(42) into human neuroblastoma (SH-EP) cells, they were irradiated with moderately intense 670-nm laser light (1000 Wm(-2)) and/or treated with epigallocatechin gallate (EGCG). Results: In irradiated cells, A{beta}(42) aggregate amounts were significantly lower than in nonirradiated cells. Likewise, in EGCG-treated cells, A{beta}(42) aggregate amounts were significantly lower than in non-EGCG-treated cells. Except for the cells simultaneously laden with A{beta}(42) and EGCG, there was a significant increase in cell numbers in response to laser irradiation. EGCG alone had no effect on cell proliferation. Laser irradiation significantly increased ATP levels in A{beta}(42)-free cells, when compared to nonirradiated cells. Laser-induced clearance of Aβ(42) aggregates occurred at the expense of cellular ATP. Conclusions: Irradiation with moderate levels of 670-nm light and EGCG supplementation complementarily reduces A{beta} aggregates in SH-EP cells. Transcranial penetration of moderate levels of red to near-infrared (NIR) light has already been amply exploited in the treatment of patients with acute stroke; the blood-brain barrier (BBB) penetration of EGCG has been demonstrated in animals. We hope that our approach will inspire a practical therapy for AD

Hadamard states from null infinity

Free field theories on a four dimensional, globally hyperbolic spacetime, whose dynamics is ruled by a Green hyperbolic partial differential operator, can be quantized following the algebraic approach. It consists of a two-step procedure: In the first part one identifies the observables of the underlying physical system collecting them in a *-algebra which encodes their relational and structural properties. In the second step one must identify a quantum state, that is a positive, normalized linear functional on the *-algebra out of which one recovers the interpretation proper of quantum mechanical theories via the so-called Gelfand-Naimark-Segal theorem. In between the plethora of possible states, only few of them are considered physically acceptable and they are all characterized by the so-called Hadamard condition, a constraint on the singular structure of the associated two-point function. Goal of this paper is to outline a construction scheme for these states which can be applied whenever the underlying background possesses a null (conformal) boundary. We discuss in particular the examples of a real, massless conformally coupled scalar field and of linearized gravity on a globally hyperbolic and asymptotically flat spacetime.Comment: 23 pages, submitted to the Proceedings of the conference "Quantum Mathematical Physics", held in Regensburg from the 29th of September to the 02nd of October 201

Identification of human proteins that modify misfolding and proteotoxicity of pathogenic ataxin-1

Proteins with long, pathogenic polyglutamine (polyQ) sequences have an enhanced propensity to spontaneously misfold and self-assemble into insoluble protein aggregates. Here, we have identified 21 human proteins that influence polyQ-induced ataxin-1 misfolding and proteotoxicity in cell model systems. By analyzing the protein sequences of these modifiers, we discovered a recurrent presence of coiled-coil (CC) domains in ataxin-1 toxicity enhancers, while such domains were not present in suppressors. This suggests that CC domains contribute to the aggregation- and toxicity-promoting effects of modifiers in mammalian cells. We found that the ataxin-1–interacting protein MED15, computationally predicted to possess an N-terminal CC domain, enhances spontaneous ataxin-1 aggregation in cell-based assays, while no such effect was observed with the truncated protein MED15ΔCC, lacking such a domain. Studies with recombinant proteins confirmed these results and demonstrated that the N-terminal CC domain of MED15 (MED15CC) per se is sufficient to promote spontaneous ataxin-1 aggregation in vitro. Moreover, we observed that a hybrid Pum1 protein harboring the MED15CC domain promotes ataxin-1 aggregation in cell model systems. In strong contrast, wild-type Pum1 lacking a CC domain did not stimulate ataxin-1 polymerization. These results suggest that proteins with CC domains are potent enhancers of polyQ-mediated protein misfolding and aggregation in vitro and in vivo

On the construction of a geometric invariant measuring the deviation from Kerr data

This article contains a detailed and rigorous proof of the construction of a geometric invariant for initial data sets for the Einstein vacuum field equations. This geometric invariant vanishes if and only if the initial data set corresponds to data for the Kerr spacetime, and thus, it characterises this type of data. The construction presented is valid for boosted and non-boosted initial data sets which are, in a sense, asymptotically Schwarzschildean. As a preliminary step to the construction of the geometric invariant, an analysis of a characterisation of the Kerr spacetime in terms of Killing spinors is carried out. A space spinor split of the (spacetime) Killing spinor equation is performed, to obtain a set of three conditions ensuring the existence of a Killing spinor of the development of the initial data set. In order to construct the geometric invariant, we introduce the notion of approximate Killing spinors. These spinors are symmetric valence 2 spinors intrinsic to the initial hypersurface and satisfy a certain second order elliptic equation ---the approximate Killing spinor equation. This equation arises as the Euler-Lagrange equation of a non-negative integral functional. This functional constitutes part of our geometric invariant ---however, the whole functional does not come from a variational principle. The asymptotic behaviour of solutions to the approximate Killing spinor equation is studied and an existence theorem is presented.Comment: 36 pages. Updated references. Technical details correcte

k-Essence, superluminal propagation, causality and emergent geometry

The k-essence theories admit in general the superluminal propagation of the perturbations on classical backgrounds. We show that in spite of the superluminal propagation the causal paradoxes do not arise in these theories and in this respect they are not less safe than General Relativity.Comment: 34 pages, 5 figure

Real and Virtual Compton Scattering: the nucleon polarisabilities

We give an overview of low-energy Compton scattering (gamma^(*) p --> gamma p) with a real or virtual incoming photon. These processes allow the investigation of one of the fundamental properties of the nucleon, i.e. how its internal structure deforms under an applied static electromagnetic field. Our knowledge of nucleon polarisabilities and their generalization to non-zero four-momentum transfer will be reviewed, including the presently ongoing experiments and future perspectives.Comment: 20 pages, 12 figures. Minireview/Proceedings of "Many-Body Structure of Strongly Interacting Systems", Mainz, Germany, Feb. 23-25 2011 . V2: typos corrected. version to appear in EPJ Special Topic

Small-molecule conversion of toxic oligomers to nontoxic β-sheet-rich amyloid fibrils

Several lines of evidence indicate that prefibrillar assemblies of amyloid-{beta} (A{beta}) polypeptides, such as soluble oligomers or protofibrils, rather than mature, end-stage amyloid fibrils cause neuronal dysfunction and memory impairment in Alzheimer's disease. These findings suggest that reducing the prevalence of transient intermediates by small molecule-mediated stimulation of amyloid polymerization might decrease toxicity. Here we demonstrate the acceleration of A{beta} fibrillogenesis through the action of the orcein-related small molecule O4, which directly binds to hydrophobic amino acid residues in A{beta} peptides and stabilizes the self-assembly of seeding-competent, {beta}-sheet-rich protofibrils and fibrils. Notably, the O4-mediated acceleration of amyloid fibril formation efficiently decreases the concentration of small, toxic A{beta} oligomers in complex, heterogeneous aggregation reactions. In addition, O4 treatment suppresses inhibition of long-term potentiation by A{beta} oligomers in hippocampal brain slices. These results support the hypothesis that small, diffusible prefibrillar amyloid species rather than mature fibrillar aggregates are toxic for mammalian cells

Sex-Specific Associations of Brain-Derived Neurotrophic Factor and Cardiorespiratory Fitness in the General Population

The brain-derived neurotrophic factor (BDNF) was initially considered to be neuron-specific. Meanwhile, this neurotrophin is peripherally also secreted by skeletal muscle cells and increases due to exercise. Whether BDNF is related to cardiorespiratory fitness (CRF) is currently unclear. We analyzed the association of serum BDNF levels with CRF in the general population (Study of Health in Pomerania (SHIP-TREND) from Northeast Germany; n = 1607, 51% female; median age 48 years). Sex-stratified linear regression models adjusted for age, height, smoking, body fat, lean mass, physical activity, and depression analyzed the association between BDNF and maximal oxygen consumption (VO2peak), maximal oxygen consumption normalized for body weight (VO2peak/kg), and oxygen consumption at the anaerobic threshold (VO2@AT). In women, 1mL/min higher VO2peak, VO2peak/kg, and VO2@AT were associated with a 2.43 pg/mL (95% confidence interval [CI]: 1.16 to 3.69 pg/mL; p = 0.0002), 150.66 pg/mL (95% CI: 63.42 to 237.90 pg/mL; p = 0.0007), and 2.68 pg/mL (95% CI: 0.5 to 4.8 pg/mL; p = 0.01) higher BDNF serum concentration, respectively. No significant associations were found in men. Further research is needed to understand the sex-specific association between CRF and BDNF. © 2019 by the authors. Licensee MDPI, Basel, Switzerland