Symbolic calculus on the time-frequency half-plane

The study concerns a special symbolic calculus of interest for signal analysis. This calculus associates functions on the time-frequency half-plane f>0 with linear operators defined on the positive-frequency signals. Full attention is given to its construction which is entirely based on the study of the affine group in a simple and direct way. The correspondence rule is detailed and the associated Wigner function is given. Formulas expressing the basic operation (star-bracket) of the Lie algebra of symbols, which is isomorphic to that of the operators, are obtained. In addition, it is shown that the resulting calculus is covariant under a three-parameter group which contains the affine group as subgroup. This observation is the starting point of an investigation leading to a whole class of symbolic calculi which can be considered as modifications of the original one.Comment: 25 pages, Latex, minor changes and more references; to be published in the "Journal of Mathematical Physics" (special issue on "Wavelet and Time-Frequency Analysis"

Phase transitions in optimal strategies for betting

Kelly's criterion is a betting strategy that maximizes the long term growth rate, but which is known to be risky. Here, we find optimal betting strategies that gives the highest capital growth rate while keeping a certain low value of risky fluctuations. We then analyze the trade-off between the average and the fluctuations of the growth rate, in models of horse races, first for two horses then for an arbitrary number of horses, and for uncorrelated or correlated races. We find an analog of a phase transition with a coexistence between two optimal strategies, where one has risk and the other one does not. The above trade-off is also embodied in a general bound on the average growth rate, similar to thermodynamic uncertainty relations. We also prove mathematically the absence of other phase transitions between Kelly's point and the risk free strategy.Comment: 23 pages, 5 figure

Mode d'emploi de la th\'eorie constructive des champs bosoniques (A user's guide to bosonic constructive field theory)

We develop in this article the principal constructive arguments used in quantum field theory, limiting us to bosonic theories, for which there does not exist any recent general presentation. The article is primarily written for mathematicians or mathematical physicists knowing the basic arguments of quantum field theory, and desiring to discover a general framework in which they can be made rigorous. It also provides a glimpse of a recent series of articles \cite{MagUnt1,MagUnt2} whose aim is to give a constructive definition of rough paths and fractionary stochastic calculus.Comment: 44 pages, 4 figures. Paper in French, but with an essential French-English glossar

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

An affine continuum mechanical model for cross-linked F-actin networks with compliant linker proteins

Cross-linked actin networks are important building blocks of the cytoskeleton. In order to gain deeper insight into the interpretation of experimental data on actin networks, adequate models are required. In this paper we introduce an affine constitutive network model for cross-linked F-actin networks based on nonlinear continuum mechanics, and specialize it in order to reproduce the experimental behavior of in vitro reconstituted model networks. The model is based on the elastic properties of single filaments embedded in an isotropic matrix such that the overall properties of the composite are described by a free-energy function. In particular, we are able to obtain the experimentally determined shear and normal stress responses of cross-linked actin networks typically observed in rheometer tests. In the present study an extensive analysis is performed by applying the proposed model network to a simple shear deformation. The single filament model is then extended by incorporating the compliance of cross-linker proteins and further extended by including viscoelasticity. All that is needed for the finite element implementation is the constitutive model for the filaments, the linkers and the matrix, and the associated elasticity tensor in either the Lagrangian or Eulerian formulation. The model facilitates parameter studies of experimental setups such as micropipette aspiration experiments and we present such studies to illustrate the efficacy of this modeling approach

A photoelectron diffraction investigation of vanadyl phthalocyanine on Au(1 1 1)

Scanned-energy mode photoelectron diffraction using the O 1s and V 2p emission perpendicular to the surface has been used to investigate the orientation and internal conformation of vanadyl phthalocyanine (VOPc) adsorbed on Au(1 1 1). The results confirm earlier indications from scanning tunnelling microscopy that the Vdouble bond; length as m-dashO vanadyl bond points out of, and not into, the surface. The Vdouble bond; length as m-dashO bondlength is 1.60 ± 0.04 Å, not significantly different from its value in bulk crystalline VOPc. However, the V atom in the adsorbed molecule is almost coplanar with the surrounding N atoms and is thus pulled down into the approximately planar region defined by the N and C atoms by 0.52 (+0.14/−0.10) Å, relative to its location in crystalline VOPc. This change must be attributed to the bonding interaction between the molecule and the underlying metal surface

Adsorption structure of glycine on TiO2(1 1 0): a photoelectron diffraction determination

High-resolution core-level photoemission and scanned-energy mode photoelectron diffraction (PhD) of the O 1s and N 1s states have been used to investigate the interaction of glycine with the rutile TiO2(1 1 0) surface. Whilst there is clear evidence for the presence of the zwitterion View the MathML sourceCH2COO− with multilayer deposition, at low coverage only the deprotonated glycinate species, NH2CH2COO is present. Multiple-scattering simulations of the O 1s PhD data show the glycinate is bonded to the surface through the two carboxylate O atoms which occupy near-atop sites above the five-fold-coordinated surface Ti atoms, with a Ti–O bondlength of 2.12 ± 0.06 Å. Atomic hydrogen arising from the deprotonation is coadsorbed to form hydroxyl species at the bridging oxygen sites with an associated Ti–O bondlength of 2.01 ± 0.03 Å. Absence of any significant PhD modulations of the N 1s emission is consistent with the amino N atom not being involved in the surface bonding, unlike the case of glycinate on Cu(1 1 0) and Cu(1 0 0)

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

Quantitative adsorbate structure determination under catalytic reaction conditions

Current methods allow quantitative local structure determination of adsorbate geometries on surfaces in ultrahigh vacuum (UHV) but are incompatible with the higher pressures required for a steady-state catalytic reactions. Here we show that photoelectron diffraction can be used to determine the structure of the methoxy and formate reaction intermediates during the steady-state oxidation of methanol over Cu(110) by taking advantage of recent instrumental developments to allow near-ambient pressure x-ray photoelectron spectroscopy. The local methoxy site differs from that under static UHV conditions, attributed to the increased surface mobility and dynamic nature of the surface under reaction conditions