Averaging sequences and modulated ergodic theorems for weakly almost periodic group representations

LetT be a weakly almost periodic (WAP) representation of a locally compact Σ-compact groupG by linear operators in a Banach spaceX, and letM = M(T) be its ergodic projection onto the space of fixed points (i.e.,Mx is the unique fixed point in the closed convex hull of the orbit ofx). A sequence of probabilities Μ_n is said toaverage T [weakly] if ∫T(t)x dΜ _n converges [weakly] toM(T)x for eachx ∃X. We callΜ _n [weakly]unitarily averaging if it averages [weakly] every unitary representation in a Hilbert space, and [weakly]WAPRaveraging if it averages [weakly] every WAP representation. We investigate some of the relationships of these notions, and connect them with properties of the regular representation (by translations) in the spaceWAP(G). Research partially supported by the Israel Science Foundation.     

Randomized consistent statistical inference for random processes and fields

Statistical Inference for Stochastic Processes - We propose a randomized approach to the consistent statistical analysis of random processes and fields on $${mathbb {R}}^m$$ and $${mathbb {Z}}^m,...     

The nucleolus for cooperative games with arbitrary bounds of individual rationality

We consider cooperative games with a given bound for individual rationality. We introduce the nucleolus with respect to the set of preimputations satisfying the newly defined bounds of rationality. An axiomatization of this nucleolus is given.     

On the correlation dimension of the spectral measure for the thue-morse sequence

Using the relationship between the decay rate of autocorrelation and the characteristics of singular Fourier spectra, we show that the correlation dimension of the spectral measure for the infinite Thue-Morse symbolic sequence equals 3 − log(1 + √17)/log 2=0.64298….     

System size resonance in coupled noisy systems and in the Ising model

We consider an ensemble of coupled nonlinear noisy oscillators demonstrating in the thermodynamic limit an Ising-type transition. In the ordered phase and for finite ensembles stochastic flips of the mean field are observed with the rate depending on the ensemble size. When a small periodic force acts on the ensemble, the linear response of the system has a maximum at a certain system size, similar to the stochastic resonance phenomenon. We demonstrate this effect of system size resonance for different types of noisy oscillators and for different ensembles---lattices with nearest neighbors coupling and globally coupled populations. The Ising model is also shown to demonstrate the system size resonance.     

A method for establishing upper bounds for singular perturbation problems

We present two applications of a new method for proving upper bounds for singular perturbation problems involving maps of bounded variation. The two problems are of first and second order, respectively. The first is a minimization problem, related to the question of optimal lifting for BV-maps with values in $S^1$, for which we prove a Γ-convergence result. The second problem involves the Aviles–Giga functional, $?{\int }_{\Omega }{|{\mathrm{?}}^{2}v|}^2\mathrm{d}x+\frac{1}{?}{\int }_{\Omega }{(1?{|\mathrm{?}v|}^2)}^2\mathrm{d}x$, for which we construct upper bounds via a sequence of functions whose limit has gradient in BV. To cite this article: A. Poliakovsky, C. R. Acad. Sci. Paris, Ser. I 341 (2005).     

Intermittent self-organization of scroll wave turbulence in three-dimensional excitable media

We study the asymptotic behavior of scroll wave turbulence in large three-dimensional excitable media modeled by FitzHugh-Nagumo equations. The focus is on the type of turbulence caused by negative tension of scroll wave filaments, which is considered to be one of the mechanisms of cardiac fibrillation. We discovered that the initial increase in turbulence complexity can be followed by intermittent self-organization, when complex filament tangles are replaced by a small number of relatively stable triple filament strands. The intermittency is the result of a competition between the destabilizing effect of negative tension and mutual attraction of filaments with similar orientation.     

CpRu(CO)2(BF4) and [CpFe(CO)2(THF)]+ on mesoporous silica as adsorbents for the removal of dibenzothiophenes from hydrocarbon solutions

The complexes, CpRu(CO)2(BF4) and [CpFe(CO)2(eta2-2-methylpropene)][BF4], react with dibenzothiophene (DBT) and 4,6-dimethyldibenzothiophene (4,6-Me2DBT) to give [CpRu(CO)2(DBT)][BF4] and [CpFe(CO)2(4,6-Me2DBT)][BF4], whose structures were established by X-ray diffraction studies. The same types of products are obtained when dibenzothiophenes react with CpRu(CO)2(BF4) and [CpFe(CO)2(THF)][BF4] that are adsorbed on the mesoporous silica SBA-15. DRIFT and XPS studies indicate that CpRu(CO)2(BF4) and [CpRu(CO)2(DBT)][BF4] are adsorbed on the SBA-15 by hydrogen-bonding of the BF4- anions to surface Si-O-H groups. CpRu(CO)2(BF4)/SBA-15 removes 99% of the DBT in a 45% toluene/55% hexanes simulated petroleum feedstock. This solid phase extractant is less successful for sterically-hindered 4,6-Me2DBT, as only 72% of it is removed. The results show that CpRu(CO)2(BF4) can be immobilized by adsorption on mesoporous silica and that it reacts with dibenzothiophenes in the adsorbed form, CpRu(CO)2(BF4)/SBA-15, in much the same way that it reacts in solution.     

ML-Based Analysis of Particle Distributions in High-Intensity Laser Experiments: Role of Binning Strategy

When entering the phase of big data processing and statistical inferences in experimental physics, the efficient use of machine learning methods may require optimal data preprocessing methods and, in particular, optimal balance between details and noise. In experimental studies of strong-field quantum electrodynamics with intense lasers, this balance concerns data binning for the observed distributions of particles and photons. Here we analyze the aspect of binning with respect to different machine learning methods (Support Vector Machine (SVM), Gradient Boosting Trees (GBT), Fully-Connected Neural Network (FCNN), Convolutional Neural Network (CNN)) using numerical simulations that mimic expected properties of upcoming experiments. We see that binning can crucially affect the performance of SVM and GBT, and, to a less extent, FCNN and CNN. This can be interpreted as the latter methods being able to effectively learn the optimal binning, discarding unnecessary information. Nevertheless, given limited training sets, the results indicate that the efficiency can be increased by optimizing the binning scale along with other hyperparameters. We present specific measurements of accuracy that can be useful for planning of experiments in the specified research area.