Parameter estimation of ODE's via nonparametric estimators

Ordinary differential equations (ODE's) are widespread models in physics, chemistry and biology. In particular, this mathematical formalism is used for describing the evolution of complex systems and it might consist of high-dimensional sets of coupled nonlinear differential equations. In this setting, we propose a general method for estimating the parameters indexing ODE's from times series. Our method is able to alleviate the computational difficulties encountered by the classical parametric methods. These difficulties are due to the implicit definition of the model. We propose the use of a nonparametric estimator of regression functions as a first-step in the construction of an M-estimator, and we show the consistency of the derived estimator under general conditions. In the case of spline estimators, we prove asymptotic normality, and that the rate of convergence is the usual $\sqrt{n}$-rate for parametric estimators. Some perspectives of refinements of this new family of parametric estimators are given.Comment: Published in at http://dx.doi.org/10.1214/07-EJS132 the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org

Chemistry on the inside: green chemistry in mesoporous materials

An overview of the rapidly expanding area of tailored mesoporous solids is presented. The synthesis of a wide range of the materials is covered, both inorganically and organically modified. Their applications, in particular those relating to green chemistry, are also highlighted. Finally, potential future directions for these materials are discussed

What’s on the Table? The Doha Round as of August 2009

The Doha Round is the longest-running trade liberalization negotiation in the postwar era. Despite its longevity, the end is not yet in sight as parties disagree on the depth of liberalization necessary in agriculture and nonagricultural market access (NAMA). This rift is prolonging the Round's completion and hindering the discussion of other important issues on the negotiating agenda, particularly services. To shed light on the debate concerning the benefits from Doha, this paper first estimates, using three metrics, the potential gains from liberalization in agriculture and NAMA resulting from the specific "modalities" set forth in papers drafted by the chairs of the Doha negotiating groups. Next, the study estimates the benefits that could result from sector initiatives in chemicals, electronic/electrical goods, and environmental goods that go beyond the tariff cuts outlined in the negotiating modalities. Finally, prospective gains from liberalization of services barriers and improvements in trade facilitation are also analyzed. Overall, we estimate that the boost to global exports from concluding the Doha Round could range between $180 billion and$520 billion annually. Likewise, the potential GDP gains are significant, between $300 billion and$700 billion annually, and well balanced between developed and developing countries.International Trade, World Trade Organization, Doha Round, Tariff Liberalization, Nontariff Barrier Liberalization.International Trade, World Trade Organization, Doha Round, Tariff Liberalization, Nontariff Barrier Liberalization.

Signatures of current loop coalescence in solar flares

The nonlinear coalescence instability of current carrying solar loops can explain many of the characteristics of the solar flares such as their impulsive nature, heating and high energy particle acceleration, amplitude oscillations of electromagnetic emission as well as the characteristics of 2-D microwave images obtained during a solar flare. The physical characteristics of the explosive coalescence of currents are presented in detail through computer simulation and theory. Canonical characteristics of the explosive coalescence are: (1) a large amount of impulsive increase of kinetic energies of electrons and ions; (2) simultaneous heating and acceleration of electrons and ions in high and low energy spectra; (3) ensuing quasi-periodic amplitude oscillations in fields and particle quantities; and (4) the double peak (or triple peak) structure in these profiles, participate in the coalescence process, yielding varieties of phenomena

Electron paramagnetic resonance characterization of tetrahydrobiopterin radical formation in bacterial nitric oxide synthase compared to mammalian nitric oxide synthase.

International audienceH(4)B is an essential catalytic cofactor of the mNOSs. It acts as an electron donor and activates the ferrous heme-oxygen complex intermediate during Arg oxidation (first step) and NOHA oxidation (second step) leading to nitric oxide and citrulline as final products. However, its role as a proton donor is still debated. Furthermore, its exact involvement has never been explored for other NOSs such as NOS-like proteins from bacteria. This article proposes a comparative study of the role of H(4)B between iNOS and bsNOS. In this work, we have used freeze-quench to stop the arginine and NOHA oxidation reactions and trap reaction intermediates. We have characterized these intermediates using multifrequency electron paramagnetic resonance. For the first time, to our knowledge, we report a radical formation for a nonmammalian NOS. The results indicate that bsNOS, like iNOS, has the capacity to generate a pterin radical during Arg oxidation. Our current electron paramagnetic resonance data suggest that this radical is protonated indicating that H(4)B may not transfer any proton. In the 2nd step, the radical trapped for iNOS is also suggested to be protonated as in the 1st step, whereas it was not possible to trap a radical for the bsNOS 2nd step. Our data highlight potential differences for the catalytic mechanism of NOHA oxidation between mammalian and bacterial NOSs

Fermionic field theory for directed percolation in (1+1) dimensions

We formulate directed percolation in (1+1) dimensions in the language of a reaction-diffusion process with exclusion taking place in one space dimension. We map the master equation that describes the dynamics of the system onto a quantum spin chain problem. From there we build an interacting fermionic field theory of a new type. We study the resulting theory using renormalization group techniques. This yields numerical estimates for the critical exponents and provides a new alternative analytic systematic procedure to study low-dimensional directed percolation.Comment: 20 pages, 2 figure