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

Multidrug resistant (or antimicrobial-resistant) pathogens - alternatives to new antibiotics?

For the last few decades, multidrug resistance has become an increasing concern for both Gram-positive and Gram-negative bacteria. The number of new molecules has dramatically decreased and antibiotic resistance is now a priority in the international community. Facing this new threat, a large number of new as well as "old" solutions are now being discussed in the medical community to propose an alternative to antibiotic treatments. A first option is to potentiate the effect of existing molecules through combinations to circumvent the individual molecule resistance. The second option is to neutralise either the infectious agent itself or its by-products using specific antibodies. A third option is to use the pathogen signaling mechanism and inhibit the production of virulence factor through quorum sensing inhibition. A fourth pathway would be to interact with the patient's microbiota using either probiotics or faecal transplantation to modulate the innate immune response and improve response to the infectious challenge, but also to act directly against colonisation by resistant bacteria by replacing the flora with susceptible strains. The last option is to target the bacteria using phage therapy. Phages are natural viruses that specifically infect target bacteria independently of any antibiotic-susceptibility profile. In this review, we will discuss each of these options and provide the scientific rationale and the available clinical data. In the majority of cases, these treatments represent an interesting approach but not the ultimate solution to multiresistance. Well-performed clinical trials are still missing and the major priority remains to promote good use and appropriate stewardship of antibiotics to decrease resistance

Modelling the relative contribution of seed nitrogen reserves and external nitrogen uptake during heterotrophic growth in Medicago truncatula

Background and aims Heterotrophic growth relies on remobilisation of seed reserves and mineral absorption. We used a compartmental model to investigate the fluxes of N absorption and remobilisation of N reserves in a legume seed with high protein content. Methods Seedling growth was studied during the heterotrophic stage in two genotypes of Medicago truncatula as a function of N supply. N absorption and seed remobilisation fluxes were distinguished in a 15 N labelling experiment. Results Remobilisation of seed N reserves was high during germination, but N uptake started as soon as the radicle protruded. Both sources contributed to high elongation rates of the radicle and hypocotyl. When organ lengths stabilised, there was an efflux of N from the cotyledons and roots indicating that seedling growth was limited by carbohydrate production. No significant differences between genotypes were observed except for early N uptake, which was lower in the genotype with the highest initial seed N content. Conclusions N fluxes were similar to those of other non-legume dicotyledonous species but differed from monocotyledonous species. These results improve our understanding of the effects of mineral fertilisation on crop establishment. The compartmental model is a useful tool to analyse N fluxes patterns within and between diverse species, in relation to seed characteristics and soil N availability

Parametric Estimation of Ordinary Differential Equations with Orthogonality Conditions

Differential equations are commonly used to model dynamical deterministic systems in applications. When statistical parameter estimation is required to calibrate theoretical models to data, classical statistical estimators are often confronted to complex and potentially ill-posed optimization problem. As a consequence, alternative estimators to classical parametric estimators are needed for obtaining reliable estimates. We propose a gradient matching approach for the estimation of parametric Ordinary Differential Equations observed with noise. Starting from a nonparametric proxy of a true solution of the ODE, we build a parametric estimator based on a variational characterization of the solution. As a Generalized Moment Estimator, our estimator must satisfy a set of orthogonal conditions that are solved in the least squares sense. Despite the use of a nonparametric estimator, we prove the root-$n$ consistency and asymptotic normality of the Orthogonal Conditions estimator. We can derive confidence sets thanks to a closed-form expression for the asymptotic variance. Finally, the OC estimator is compared to classical estimators in several (simulated and real) experiments and ODE models in order to show its versatility and relevance with respect to classical Gradient Matching and Nonlinear Least Squares estimators. In particular, we show on a real dataset of influenza infection that the approach gives reliable estimates. Moreover, we show that our approach can deal directly with more elaborated models such as Delay Differential Equation (DDE).Comment: 35 pages, 5 figure

ESR Study of (C_5H_{12}N)_2CuBr_4

ESR studies at 9.27, 95.4, and 289.7 GHz have been performed on (C$_5$H$_{12}$N)$_2$CuBr$_4$ down to 3.7 K. The 9.27 GHz data were acquired with a single crystal and do not indicate the presence of any structural transitions. The high frequency data were collected with a polycrystalline sample and resolved two absorbances, consistent with two crystallographic orientations of the magnetic sites and with earlier ESR studies performed at 300 K. Below $B_{C1}=6.6$ T, our data confirm the presence of a spin singlet ground state.Comment: 2 pages, 4 figs., submitted 23rd International Conference on Low Temperature Physics (LT-23), Aug. 200

Hot electron cooling by acoustic phonons in graphene

We have investigated the energy loss of hot electrons in metallic graphene by means of GHz noise thermometry at liquid helium temperature. We observe the electronic temperature T / V at low bias in agreement with the heat diffusion to the leads described by the Wiedemann-Franz law. We report on $T\propto\sqrt{V}$ behavior at high bias, which corresponds to a T4 dependence of the cooling power. This is the signature of a 2D acoustic phonon cooling mechanism. From a heat equation analysis of the two regimes we extract accurate values of the electron-acoustic phonon coupling constant $\Sigma$ in monolayer graphene. Our measurements point to an important effect of lattice disorder in the reduction of $\Sigma$, not yet considered by theory. Moreover, our study provides a strong and firm support to the rising field of graphene bolometric detectors.Comment: 5 figure

Optimal static and dynamic recycling of defective binary devices

The binary Defect Combination Problem consists in finding a fully working subset from a given ensemble of imperfect binary components. We determine the typical properties of the model using methods of statistical mechanics, in particular, the region in the parameter space where there is almost surely at least one fully-working subset. Dynamic recycling of a flux of imperfect binary components leads to zero wastage.Comment: 14 pages, 15 figure

Extracting non-linear integrate-and-fire models from experimental data using dynamic I–V curves

The dynamic I–V curve method was recently introduced for the efficient experimental generation of reduced neuron models. The method extracts the response properties of a neuron while it is subject to a naturalistic stimulus that mimics in vivo-like fluctuating synaptic drive. The resulting history-dependent, transmembrane current is then projected onto a one-dimensional current–voltage relation that provides the basis for a tractable non-linear integrate-and-fire model. An attractive feature of the method is that it can be used in spike-triggered mode to quantify the distinct patterns of post-spike refractoriness seen in different classes of cortical neuron. The method is first illustrated using a conductance-based model and is then applied experimentally to generate reduced models of cortical layer-5 pyramidal cells and interneurons, in injected-current and injected- conductance protocols. The resulting low-dimensional neuron models—of the refractory exponential integrate-and-fire type—provide highly accurate predictions for spike-times. The method therefore provides a useful tool for the construction of tractable models and rapid experimental classification of cortical neurons