From constructive field theory to fractional stochastic calculus. (II) Constructive proof of convergence for the L\'evy area of fractional Brownian motion with Hurst index α∈(1/8,1/4)\alpha\in(1/8,1/4)

{Let $B=(B_1(t),...,B_d(t))$ be a $d$-dimensional fractional Brownian motion with Hurst index $\alpha<1/4$, or more generally a Gaussian process whose paths have the same local regularity. Defining properly iterated integrals of $B$ is a difficult task because of the low H\"older regularity index of its paths. Yet rough path theory shows it is the key to the construction of a stochastic calculus with respect to $B$, or to solving differential equations driven by $B$. We intend to show in a series of papers how to desingularize iterated integrals by a weak, singular non-Gaussian perturbation of the Gaussian measure defined by a limit in law procedure. Convergence is proved by using "standard" tools of constructive field theory, in particular cluster expansions and renormalization. These powerful tools allow optimal estimates, and call for an extension of Gaussian tools such as for instance the Malliavin calculus. After a first introductory paper \cite{MagUnt1}, this one concentrates on the details of the constructive proof of convergence for second-order iterated integrals, also known as L\'evy area

Overview of Actual Methods for Characterization of Ash Depostion

Utility operation with frequent fuel switching is a common practice, forced by cheaper coal availability in the international market. Additionally, a substitution of coal by cheaper local secondary fuels, ranging from forest wood to sewage sludge and industrial or domestic residues, is gaining importance. Switching between different fuels, even if these do not differ much from the design coal, enhances operational problems arising from ash deposition. In order to prevent operational problems, through comprehension of the phenomena taking place within the furnace, appropriate sampling and characterization of the deposits are necessary. Methods commonly used for analysis of ash deposits and their characterization are summarized in this paper. The goals of the experimental work at the Institute of Process Engineering and Power Plant Technology (IVD) are then summarized. Finally, work on modeling the slagging and fouling phenomena or their characterization is presented

Characterization of SU(1,1) coherent states in terms of affine group wavelets

The Perelomov coherent states of SU(1,1) are labeled by elements of the quotient of SU(1,1) by the compact subgroup. Taking advantage of the fact that this quotient is isomorphic to the affine group of the real line, we are able to parameterize the coherent states by elements of that group or equivalently by points in the half-plane. Such a formulation permits to find new properties of the SU(1,1) coherent states and to relate them to affine wavelets.Comment: 11 pages, latex, to be published in J. Phys. A : Math. Ge

An explicit formula for the Berezin star product

We prove an explicit formula of the Berezin star product on Kaehler manifolds. The formula is expressed as a summation over certain strongly connected digraphs. The proof relies on a combinatorial interpretation of Englis' work on the asymptotic expansion of the Laplace integral.Comment: 19 pages, to appear in Lett. Math. Phy

Notes on Stein-Sahi representations and some problems of non L2L^2 harmonic analysis

We discuss one natural class of kernels on pseudo-Riemannian symmetric spaces.Comment: 40p

Ageing in the critical contact process: a Monte Carlo study

The long-time dynamics of the critical contact process which is brought suddenly out of an uncorrelated initial state undergoes ageing in close analogy with quenched magnetic systems. In particular, we show through Monte Carlo simulations in one and two dimensions and through mean-field theory that time-translation invariance is broken and that dynamical scaling holds. We find that the autocorrelation and autoresponse exponents lambda_{Gamma} and lambda_R are equal but, in contrast to systems relaxing to equilibrium, the ageing exponents a and b are distinct. A recent proposal to define a non-equilibrium temperature through the short-time limit of the fluctuation-dissipation ratio is therefore not applicable.Comment: 18 pages, 7 figures, Latex2e with IOP macros; final for

Loss of Tet1 associated 5-hydroxymethylcytosine is concomitant with aberrant promoter hypermethylation in liver cancer

Aberrant hypermethylation of CpG islands (CGI) in human tumors occurs predominantly at repressed genes in the host tissue, but the preceding events driving this phenomenon are poorly understood. In this study, we temporally tracked epigenetic and transcriptomic perturbations which occur in a mouse model of liver carcinogenesis. Hypermethylated CGI events in the model were predicted by enrichment of the DNA modification 5-hydroxymethylcytosine (5hmC) and the histone H3 modification H3K27me3 at silenced promoters in the host tissue. During cancer progression, CGI underwent hypo-hydroxymethylation prior to hypermethylation, whilst retaining H3K27me3. In livers from mice deficient in Tet1, a tumor suppressor involved in cytosine demethylation, we observed a similar loss of promoter core 5hmC, suggesting that reduced Tet1 activity at CGI may contribute to epigenetic dysregulation observed during hepatocarcinogenesis. Consistent with this possibility, mouse liver tumors exhibited reduced Tet1 protein levels. Similar to humans, DNA methylation changes at CGI in mice did not appear to be direct drivers of hepatocellular carcinoma progression, rather, dynamic changes in H3K27me3 promoter deposition correlated strongly with tumor-specific activation and repression of transcription. Overall, our results suggest that loss of promoter-associated 5hmC in liver tumors licenses reprogramming of DNA methylation at silent CGI during progression

A method for purification, identification and validation of DNMT1 mRNA binding proteins

DNA methyltransferase 1 (DNMT1) is the enzyme responsible for the maintenance of DNA methylation patterns during cell division. DNMT1 expression is tightly regulated within the cell cycle. Our previous study showed that the binding of a protein with an apparent size of ~40 kDa on DNMT1 3’-UTR triggered the destabilization of DNMT1 mRNA transcript during Go/G1 phase. Using RNA affinity capture with the 3’-UTR of DNMT1 mRNA and matrix-assisted laser desorption-time of flight tandem mass spectrometry (MALDI-TOF-MS-MS) analysis, we isolated and identified AUF 1 (AU-rich element ARE:poly-(U)-binding/degradation factor) as the binding protein. We then validated the role of this protein in the destabilization of DNMT1 mRNA. In this report, we detail the different approaches used for the isolation, the identification of a RNA binding protein and the validation of its role

The deformation quantizations of the hyperbolic plane

We describe the space of (all) invariant deformation quantizations on the hyperbolic plane as solutions of the evolution of a second order hyperbolic differential operator. The construction is entirely explicit and relies on non-commutative harmonic analytical techniques on symplectic symmetric spaces. The present work presents a unified method producing every quantization of the hyperbolic plane, and provides, in the 2-dimensional context, an exact solution to Weinstein's WKB quantization program within geometric terms. The construction reveals the existence of a metric of Lorentz signature canonically attached (or `dual') to the geometry of the hyperbolic plane through the quantization process.Comment: 26 pages, 5 figure

Anthropogenic Space Weather

Anthropogenic effects on the space environment started in the late 19th century and reached their peak in the 1960s when high-altitude nuclear explosions were carried out by the USA and the Soviet Union. These explosions created artificial radiation belts near Earth that resulted in major damages to several satellites. Another, unexpected impact of the high-altitude nuclear tests was the electromagnetic pulse (EMP) that can have devastating effects over a large geographic area (as large as the continental United States). Other anthropogenic impacts on the space environment include chemical release ex- periments, high-frequency wave heating of the ionosphere and the interaction of VLF waves with the radiation belts. This paper reviews the fundamental physical process behind these phenomena and discusses the observations of their impacts.Comment: 71 pages, 35 figure