Extension of explicit formulas in Poissonian white noise analysis using harmonic analysis on configuration spaces

Harmonic analysis on configuration spaces is used in order to extend explicit expressions for the images of creation, annihilation, and second quantization operators in L2-spaces with respect to Poisson point processes to a set of functions larger than the space obtained by directly using chaos expansion. This permits, in particular, to derive an explicit expression for the generator of the second quantization of a sub-Markovian contraction semigroup on a set of functions which forms a core of the generator.

Symmetry breaking, mixing, instability, and low frequency variability in a minimal Lorenz-like system

Starting from the classical Saltzman two-dimensional convection equations, we derive via a severe spectral truncation a minimal 10 ODE system which includes the thermal effect of viscous dissipation. Neglecting this process leads to a dynamical system which includes a decoupled generalized Lorenz system. The consideration of this process breaks an important symmetry and couples the dynamics of fast and slow variables, with the ensuing modifications to the structural properties of the attractor and of the spectral features. When the relevant nondimensional number (Eckert number Ec) is different from zero, an additional time scale of O(Ec−1) is introduced in the system, as shown with standard multiscale analysis and made clear by several numerical evidences. Moreover, the system is ergodic and hyperbolic, the slow variables feature long-term memory with 1/f3/2 power spectra, and the fast variables feature amplitude modulation. Increasing the strength of the thermal-viscous feedback has a stabilizing effect, as both the metric entropy and the Kaplan-Yorke attractor dimension decrease monotonically with Ec. The analyzed system features very rich dynamics: it overcomes some of the limitations of the Lorenz system and might have prototypical value in relevant processes in complex systems dynamics, such as the interaction between slow and fast variables, the presence of long-term memory, and the associated extreme value statistics. This analysis shows how neglecting the coupling of slow and fast variables only on the basis of scale analysis can be catastrophic. In fact, this leads to spurious invariances that affect essential dynamical properties (ergodicity, hyperbolicity) and that cause the model losing ability in describing intrinsically multiscale processes.

Thermodynamic efficiency and entropy production in the climate system

We present an outlook on the climate system thermodynamics. First, we construct an equivalent Carnot engine with efficiency and frame the Lorenz energy cycle in a macroscale thermodynamic context. Then, by exploiting the second law, we prove that the lower bound to the entropy production is times the integrated absolute value of the internal entropy fluctuations. An exergetic interpretation is also proposed. Finally, the controversial maximum entropy production principle is reinterpreted as requiring the joint optimization of heat transport and mechanical work production. These results provide tools for climate change analysis and for climate models’ validation.

Relevance of sampling schemes in light of Ruelle's linear response theory

We reconsider the theory of the linear response of non-equilibrium steady states to perturbations. We �rst show that by using a general functional decomposition for space-time dependent forcings, we can de�ne elementary susceptibilities that allow to construct the response of the system to general perturbations. Starting from the de�nition of SRB measure, we then study the consequence of taking di�erent sampling schemes for analysing the response of the system. We show that only a speci�c choice of the time horizon for evaluating the response of the system to a general time-dependent perturbation allows to obtain the formula �rst presented by Ruelle. We also discuss the special case of periodic perturbations, showing that when they are taken into consideration the sampling can be �ne-tuned to make the de�nition of the correct time horizon immaterial. Finally, we discuss the implications of our results in terms of strategies for analyzing the outputs of numerical experiments by providing a critical review of a formula proposed by Reick.

Root phenomics of crops: opportunities and challenges

Reliable techniques for screening large numbers of plants for root traits are still being developed, but include aeroponic, hydroponic and agar plate systems. Coupled with digital cameras and image analysis software, these systems permit the rapid measurement of root numbers, length and diameter in moderate ( typically <1000) numbers of plants. Usually such systems are employed with relatively small seedlings, and information is recorded in 2D. Recent developments in X-ray microtomography have facilitated 3D non-invasive measurement of small root systems grown in solid media, allowing angular distributions to be obtained in addition to numbers and length. However, because of the time taken to scan samples, only a small number can be screened (typically<10 per day, not including analysis time of the large spatial datasets generated) and, depending on sample size, limited resolution may mean that fine roots remain unresolved. Although agar plates allow differences between lines and genotypes to be discerned in young seedlings, the rank order may not be the same when the same materials are grown in solid media. For example, root length of dwarfing wheat ( Triticum aestivum L.) lines grown on agar plates was increased by similar to 40% relative to wild-type and semi-dwarfing lines, but in a sandy loam soil under well watered conditions it was decreased by 24-33%. Such differences in ranking suggest that significant soil environment-genotype interactions are occurring. Developments in instruments and software mean that a combination of high-throughput simple screens and more in-depth examination of root-soil interactions is becoming viable.

A practical comparison of blinded methods for sample size reviews in survival data clinical trials.

This paper presents practical approaches to the problem of sample size re-estimation in the case of clinical trials with survival data when proportional hazards can be assumed. When data are readily available at the time of the review, on a full range of survival experiences across the recruited patients, it is shown that, as expected, performing a blinded re-estimation procedure is straightforward and can help to maintain the trial's pre-specified error rates. Two alternative methods for dealing with the situation where limited survival experiences are available at the time of the sample size review are then presented and compared. In this instance, extrapolation is required in order to undertake the sample size re-estimation. Worked examples, together with results from a simulation study are described. It is concluded that, as in the standard case, use of either extrapolation approach successfully protects the trial error rates. Copyright © 2012 John Wiley & Sons, Ltd.

A note on an integration by parts formula for the generators of uniform translations on configuration space

An integration by parts formula is derived for the first order differential operator corresponding to the action of translations on the space of locally finite simple configurations of infinitely many points on Rd. As reference measures, tempered grand canonical Gibbs measures are considered corresponding to a non-constant non-smooth intensity (one-body potential) and translation invariant potentials fulfilling the usual conditions. It is proven that such Gibbs measures fulfill the intuitive integration by parts formula if and only if the action of the translation is not broken for this particular measure. The latter is automatically fulfilled in the high temperature and low intensity regime.

Glu298Asp polymorphism influences the beneficial effects of fish oil fatty acids on postprandial vascular function

Our objective was to determine whether the endothelial nitric oxide synthase (eNOS) Glu298Asp polymorphism influences vascular response to raised NEFA enriched with saturated fatty acids (SFA) or long-chain (LC) n-3 polyunsaturated fatty acids (PUFA). Subjects were prospectively recruited for genotype (Glu298, n = 30 and Asp298, n = 29; balanced for age and gender) consumed SFA on two occasions, with and without the substitution of 0.07 g fat/kg body weight with LC n-3 PUFA, and with heparin infusion to elevate NEFA. Endothelial function was measured before and after NEFA elevation (240 min), with blood samples taken every 30 min. Flow-mediated dilation (FMD) decreased following SFA alone and increased following SFA+LC n-3 PUFA. There were 2-fold differences in the change in FMD response to the different fat loads between the Asp298 and Glu298 genotypes (P = 0.002) and between genders (P < 0.02). Sodium nitroprusside-induced reactivity, measured by laser Doppler imaging with iontophoresis, was significantly greater with SFA+LC n-3 PUFA in all female subjects (P < 0.001) but not in males. Elevated NEFA influences both endothelial-dependent and endothelial-independent vasodilation during the postprandial phase. Effects of fat composition appear to be genotype and gender dependent, with the greatest difference in vasodilatory response to the two fat loads seen in the Asp298 females.

Digital predistorter design using B-Spline neural network and inverse of De Boor algorithm

This contribution introduces a new digital predistorter to compensate serious distortions caused by memory high power amplifiers (HPAs) which exhibit output saturation characteristics. The proposed design is based on direct learning using a data-driven B-spline Wiener system modeling approach. The nonlinear HPA with memory is first identified based on the B-spline neural network model using the Gauss-Newton algorithm, which incorporates the efficient De Boor algorithm with both B-spline curve and first derivative recursions. The estimated Wiener HPA model is then used to design the Hammerstein predistorter. In particular, the inverse of the amplitude distortion of the HPA's static nonlinearity can be calculated effectively using the Newton-Raphson formula based on the inverse of De Boor algorithm. A major advantage of this approach is that both the Wiener HPA identification and the Hammerstein predistorter inverse can be achieved very efficiently and accurately. Simulation results obtained are presented to demonstrate the effectiveness of this novel digital predistorter design.

Decay to equilibrium for jump processes with heavy tails

The case is made for a more careful analysis of the large time asymptotic of infinite particle systems in the thermodynamic limit beyond zero density. The insufficiency of current analysis even in the model case of free particles is demonstrated. Recent advances based on more sophisticated analytical tools like functions of mean variation and Hardy spaces are sketched.

Dynamical and cloud-radiation feedbacks in El Niño and greenhouse warming

An El Niño-like steady response is found in a greenhouse warming simulation resulting from coupled ocean-atmosphere dynamical feedbacks similar to those producing the present-day El Niños. There is a strong negative cloud-radiation feedback on the sea surface temperature (SST) anomaly associated with this enhanced eastern equatorial Pacific warm pattern. However, this negative feedback is overwhelmed by the positive dynamical feedbacks and cannot diminish the sensitivity of the tropical SST to enhanced greenhouse gas concentrations. The enhanced eastern-Pacific warming in the coupled ocean-atmosphere system suggests that coupled dynamics can strengthen this sensitivity.

Transition from an anti-phase error-correction-mode to a synchronization mode in the mutual hand tracking

Proactive motion in hand tracking and in finger bending, in which the body motion occurs prior to the reference signal, was reported by the preceding researchers when the target signals were shown to the subjects at relatively high speed or high frequencies. These phenomena indicate that the human sensory-motor system tends to choose an anticipatory mode rather than a reactive mode, when the target motion is relatively fast. The present research was undertaken to study what kind of mode appears in the sensory-motor system when two persons were asked to track the hand position of the partner with each other at various mean tracking frequency. The experimental results showed a transition from a mutual error-correction mode to a synchronization mode occurred in the same region of the tracking frequency with that of the transition from a reactive error-correction mode to a proactive anticipatory mode in the mechanical target tracking experiments. Present research indicated that synchronization of body motion occurred only when both of the pair subjects operated in a proactive anticipatory mode. We also presented mathematical models to explain the behavior of the error-correction mode and the synchronization mode.

Spectral gap for Glauber type dynamics for a special class of potentials

We consider an equilibrium birth and death type process for a particle system in infinite volume, the latter is described by the space of all locally finite point configurations on Rd. These Glauber type dynamics are Markov processes constructed for pre-given reversible measures. A representation for the ``carré du champ'' and ``second carré du champ'' for the associate infinitesimal generators L are calculated in infinite volume and for a large class of functions in a generalized sense. The corresponding coercivity identity is derived and explicit sufficient conditions for the appearance and bounds for the size of the spectral gap of L are given. These techniques are applied to Glauber dynamics associated to Gibbs measure and conditions are derived extending all previous known results and, in particular, potentials with negative parts can now be treated. The high temperature regime is extended essentially and potentials with non-trivial negative part can be included. Furthermore, a special class of potentials is defined for which the size of the spectral gap is as least as large as for the free system and, surprisingly, the spectral gap is independent of the activity. This type of potentials should not show any phase transition for a given temperature at any activity.

Modeling electrocortical activity through improved local approximations of integral neural field equations

Neural field models of firing rate activity typically take the form of integral equations with space-dependent axonal delays. Under natural assumptions on the synaptic connectivity we show how one can derive an equivalent partial differential equation (PDE) model that properly treats the axonal delay terms of the integral formulation. Our analysis avoids the so-called long-wavelength approximation that has previously been used to formulate PDE models for neural activity in two spatial dimensions. Direct numerical simulations of this PDE model show instabilities of the homogeneous steady state that are in full agreement with a Turing instability analysis of the original integral model. We discuss the benefits of such a local model and its usefulness in modeling electrocortical activity. In particular, we are able to treat “patchy” connections, whereby a homogeneous and isotropic system is modulated in a spatially periodic fashion. In this case the emergence of a “lattice-directed” traveling wave predicted by a linear instability analysis is confirmed by the numerical simulation of an appropriate set of coupled PDEs.