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

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

Photoelectron diffraction investigation of the structure of the clean TiO2(110)(1×1) surface

The surface relaxations of the rutile TiO2(110)(1×1) clean surface have been determined by O 1 s and Ti 2p3∕2 scanned-energy mode photoelectron diffraction. The results are in excellent agreement with recent low-energy electron diffraction (LEED) and medium energy ion scattering (MEIS) results, but in conflict with the results of some earlier investigations including one by surface x-ray diffraction. In particular, the bridging O atoms at the surface are found to relax outward, rather than inward, relative to the underlying bulk. Combined with the recent LEED and MEIS results, a consistent picture of the structure of this surface is provided. While the results of the most recent theoretical total-energy calculations are qualitatively consistent with this experimental consensus, significant quantitative differences remain

Making SENSE--Sustained Effort Network for treatment of Status Epilepticus as a multicenter prospective registry.

BACKGROUND: Evidence regarding the different treatment options of status epilepticus (SE) in adults is scarce. Large randomized trials cover only one treatment at early stage and suggest the superiority of benzodiazepines over placebo, of intravenous lorazepam over intravenous diazepam or over intravenous phenytoin alone, and of intramuscular midazolam over intravenous lorazepam. However, many patients will not be treated successfully with the first treatment step. A large randomized trial covering the treatment of established status (ESETT) has just been funded recently by the NIH and will not start before 2015, with expected results in 2018; a trial on the treatment of refractory status with general anesthetics was terminated early due to insufficient recruitment. Therefore, a prospective multicenter observational registry was set up; this may help in clinical decision-making until results from randomized trials are available. METHODS/DESIGN: SENSE is a prospective, multicenter registry for patients treated for SE. The primary objective is to document patient characteristics, treatment modalities and in-house outcome of consecutive adults admitted for SE treatment in each of the participating centres and to identify predictors of outcome. Pre-treatment, treatment-related and outcome variables are documented systematically. To allow for meaningful multivariate analysis in the patient subgroups with refractory SE, a cohort size of 1000 patients is targeted. DISCUSSION: The results of the study will provide information about risks and benefits of specific treatment steps in different patient groups with SE at different points of time. Thus, it will support clinical decision-making and, furthermore, it will be helpful in the planning of treatment trials. TRIAL REGISTRATION: DRKS00000725

Computational modeling identifies key gene regulatory interactions underlying phenobarbital-mediated tumor promotion

Gene regulatory interactions underlying the early stages of non-genotoxic carcinogenesis are poorly understood. Here, we have identified key candidate regulators of phenobarbital (PB)-mediated mouse liver tumorigenesis, a well-characterized model of non-genotoxic carcinogenesis, by applying a new computational modeling approach to a comprehensive collection of in vivo gene expression studies. We have combined our previously developed motif activity response analysis (MARA), which models gene expression patterns in terms of computationally predicted transcription factor binding sites with singular value decomposition (SVD) of the inferred motif activities, to disentangle the roles that different transcriptional regulators play in specific biological pathways of tumor promotion. Furthermore, transgenic mouse models enabled us to identify which of these regulatory activities was downstream of constitutive androstane receptor and β-catenin signaling, both crucial components of PB-mediated liver tumorigenesis. We propose novel roles for E2F and ZFP161 in PB-mediated hepatocyte proliferation and suggest that PB-mediated suppression of ESR1 activity contributes to the development of a tumor-prone environment. Our study shows that combining MARA with SVD allows for automated identification of independent transcription regulatory programs within a complex in vivo tissue environment and provides novel mechanistic insights into PB-mediated hepatocarcinogenesi

Staged treatment response in status epilepticus: Lessons from the SENSE registry.

Although in epilepsy patients the likelihood of becoming seizure-free decreases substantially with each unsuccessful treatment, to our knowledge this has been poorly investigated in status epilepticus (SE). We aimed to evaluate the proportion of SE cessation and functional outcome after successive treatment steps. We conducted a post hoc analysis of a prospective, observational, multicenter cohort (Sustained Effort Network for treatment of Status Epilepticus [SENSE]), in which 1049 incident adult SE episodes were prospectively recorded at nine European centers. We analyzed 996 SE episodes without coma induction before the third treatment step. Rates of SE cessation, mortality (in ongoing SE or after SE control), and favorable functional outcome (assessed with modified Rankin scale) were evaluated after each step. SE was treated successfully in 838 patients (84.1%), 147 (14.8%) had a fatal outcome (36% of them died while still in SE), and 11 patients were transferred to palliative care while still in SE. Patients were treated with a median of three treatment steps (range 1-13), with 540 (54.2%) receiving more than two steps (refractory SE [RSE]) and 95 (9.5%) more than five steps. SE was controlled after the first two steps in 45%, with an additional 21% treated after the third, and 14% after the fourth step. Likelihood of SE cessation (p &lt; 0.001), survival (p = 0.003), and reaching good functional outcome (p &lt; 0.001) decreased significantly between the first two treatment lines and the third, especially in patients not experiencing generalized convulsive SE, but remained relatively stable afterwards. The significant worsening of SE prognosis after the second step clinically supports the concept of RSE. However, and differing from findings in human epilepsy, RSE remains treatable in about one third of patients, even after several failed treatment steps. Clinical judgment remains essential to determine the aggressiveness and duration of SE treatment, and to avoid premature treatment cessation in patients with SE

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