Schramm-Loewner Equations Driven by Symmetric Stable Processes

We consider shape, size and regularity of the hulls of the chordal Schramm-Loewner evolution driven by a symmetric alpha-stable process. We obtain derivative estimates, show that the complements of the hulls are Hoelder domains, prove that the hulls have Hausdorff dimension 1, and show that the trace is right-continuous with left limits almost surely.Comment: 22 pages, 4 figure

The trans-activation domain of the sporulation response regulator Spo0A revealed by X-ray crystallography

Sporulation in Bacillus involves the induction of scores of genes in a temporally and spatially co-ordinated programme of cell development. Its initiation is under the control of an expanded two-component signal transduction system termed a phosphorelay. The master control element in the decision to sporulate is the response regulator, Spo0A, which comprises a receiver or phosphoacceptor domain and an effector or transcription activation domain. The receiver domain of Spo0A shares sequence similarity with numerous response regulators, and its structure has been determined in phosphorylated and unphosphorylated forms. However, the effector domain (C-Spo0A) has no detectable sequence similarity to any other protein, and this lack of structural information is an obstacle to understanding how DNA binding and transcription activation are controlled by phosphorylation in Spo0A. Here, we report the crystal structure of C-Spo0A from Bacillus stearothermophilus revealing a single alpha -helical domain comprising six alpha -helices in an unprecedented fold. The structure contains a helix-turn-helix as part of a three alpha -helical bundle reminiscent of the catabolite gene activator protein (CAP), suggesting a mechanism for DNA binding. The residues implicated in forming the sigma (A)-activating region clearly cluster in a flexible segment of the polypeptide on the opposite side of the structure from that predicted to interact with DNA. The structural results are discussed in the context of the rich array of existing mutational data

The road to deterministic matrices with the restricted isometry property

The restricted isometry property (RIP) is a well-known matrix condition that provides state-of-the-art reconstruction guarantees for compressed sensing. While random matrices are known to satisfy this property with high probability, deterministic constructions have found less success. In this paper, we consider various techniques for demonstrating RIP deterministically, some popular and some novel, and we evaluate their performance. In evaluating some techniques, we apply random matrix theory and inadvertently find a simple alternative proof that certain random matrices are RIP. Later, we propose a particular class of matrices as candidates for being RIP, namely, equiangular tight frames (ETFs). Using the known correspondence between real ETFs and strongly regular graphs, we investigate certain combinatorial implications of a real ETF being RIP. Specifically, we give probabilistic intuition for a new bound on the clique number of Paley graphs of prime order, and we conjecture that the corresponding ETFs are RIP in a manner similar to random matrices.Comment: 24 page

Black Holes and Instabilities of Negative Tension Branes

We consider the collision in 2+1 dimensions of a black hole and a negative tension brane on an orbifold. Because there is no gravitational radiation in 2+1 dimensions, the horizon area shrinks when part of the brane falls through. This provides a potential violation of the generalized second law of thermodynamics. However, tracing the details of the dynamical evolution one finds that it does not proceed from equilibrium configuration to equilibrium configuration. Instead, a catastrophic space-time singularity develops similar to the `big crunch' of $\Omega >1$ FRW space-times. In the context of classical general relativity, our result demonstrates a new instability of constructions with negative tension branes.Comment: 18 pages, 3 figures, uses RevTeX. Minor typos fixed. References and one footnote adde

(Non)-singular brane-world cosmology induced by quantum effects in d5 dilatonic gravity

5d dilatonic gravity (bosonic sector of gauged supergravity) with non-trivial bulk potential and with surface terms (boundary cosmological constant and trace anomaly induced effective action for brane quantum matter) is considered. For constant bulk potential and maximally SUSY Yang-Mills theory (CFT living on the brane) the inflationary brane-world is constructed. The bulk is singular asymptotically AdS space with non-constant dilaton and dilatonic de Sitter or hyperbolic brane is induced by quantum matter effects. At the same time, dilaton on the brane is determined dynamically. This all is natural realization of warped compactification in AdS/CFT correspondence. For fine-tuned toy example of non-constant bulk potential we found the non-singular dilatonic brane-world where bulk again represents asymptotically AdS space and de Sitter brane (inflationary phase of observable Universe) is induced exclusively by quantum effects. The radius of the brane and dilaton are determined dynamically. The analytically solvable example of exponential bulk potential leading to singular asymptotically AdS dilatonic bulk space with de Sitter (or hyperbolic) brane is also presented.In all cases under discussion the gravity on the brane is trapped via Randall-Sundrum scenario. It is shown that qualitatively the same types of brane-worlds occur when quantum brane matter is described by $N$ dilaton coupled spinors.Comment: LaTeX file 28 pages and two eps files, few misprints are correcte

Dual stem cell therapy synergistically improves cardiac function and vascular regeneration following myocardial infarction

Since both myocardium and vasculature in the heart are excessively damaged following myocardial infarction (MI), therapeutic strategies for treating MI hearts should concurrently target both so as to achieve true cardiac repair. Here we demonstrate a concomitant method that exploits the advantages of cardiomyocytes derived from human induced pluripotent stem cells (hiPSC-CMs) and human mesenchymal stem cell-loaded patch (hMSC-PA) to amplify cardiac repair in a rat MI model. Epicardially implanted hMSC-PA provide a complimentary microenvironment which enhances vascular regeneration through prolonged secretion of paracrine factors, but more importantly it significantly improves the retention and engraftment of intramyocardially injected hiPSC-CMs which ultimately restore the cardiac function. Notably, the majority of injected hiPSC-CMs display adult CMs like morphology suggesting that the secretomic milieu of hMSC-PA constitutes pleiotropic effects in vivo. We provide compelling evidence that this dual approach can be a promising means to enhance cardiac repair on MI hearts.11Ysciescopu

UHECR as Decay Products of Heavy Relics? The Lifetime Problem

The essential features underlying the top-down scenarii for UHECR are discussed, namely, the stability (or lifetime) imposed to the heavy objects (particles) whatever they be: topological and non-topological solitons, X-particles, cosmic defects, microscopic black-holes, fundamental strings. We provide an unified formula for the quantum decay rate of all these objects as well as the particle decays in the standard model. The key point in the top-down scenarii is the necessity to adjust the lifetime of the heavy object to the age of the universe. This ad-hoc requirement needs a very high dimensional operator to govern its decay and/or an extremely small coupling constant. The natural lifetimes of such heavy objects are, however, microscopic times associated to the GUT energy scale (sim 10^{-28} sec. or shorter). It is at this energy scale (by the end of inflation) where they could have been abundantly formed in the early universe and it seems natural that they decayed shortly after being formed.Comment: 11 pages, LaTex, no figures, updated versio

Dilatonic quantum multi-brane-worlds

d5 dilatonic gravity action with surface counterterms motivated by AdS/CFT correspondence and with contributions of brane quantum CFTs is considered around AdS-like bulk. The effective equations of motion are constructed. They admit two (outer and inner) or multi-brane solutions where brane CFTs may be different. The role of quantum brane CFT is in inducing of complicated brane dilatonic gravity. For exponential bulk potentials the number of AdS-like bulk spaces is found in analytical form.The correspondent flat or curved (de Sitter or hyperbolic) dilatonic two branes are created, as a rule, thanks to quantum effects. The observable early Universe may correspond to inflationary brane. The found dilatonic quantum two brane-worlds usually contain the naked singularity but in couple explicit examples the curvature is finite and horizon (corresponding to wormhole-like space) appears.Comment: LaTeX file, 25 pages, discussion is enlarge

Primeval Corrections to the CMB Anisotropies

We show that deviations of the quantum state of the inflaton from the thermal vacuum of inflation may leave an imprint in the CMB anisotropies. The quantum dynamics of the inflaton in such a state produces corrections to the inflationary fluctuations, which may be observable. Because these effects originate from IR physics below the Planck scale, they will dominate over any trans-Planckian imprints in any theory which obeys decoupling. Inflation sweeps away these initial deviations and forces its quantum state closer to the thermal vacuum. We view this as the quantum version of the cosmic no-hair theorem. Such imprints in the CMB may be a useful, independent test of the duration of inflation, or of significant features in the inflaton potential about 60 e-folds before inflation ended, instead of an unlikely discovery of the signatures of quantum gravity. The absence of any such substructure would suggest that inflation lasted uninterrupted much longer than ${\cal O}(100)$ e-folds.Comment: 17 pages, latex, no figures; v3: added references and comments, final version to appear in Phys. Rev.