Asymptotic results for weighted means of linear combinations of independent Poisson random variables

ABSTRACT

In this paper we prove the large deviation principle for a class of weighted means of linear combinations of independent Poisson distributed random variables, which converge weakly to a normal distribution. The interest in these linear combinations is motivated by the diffusion approximation in Lansky [On approximations of Stein's neuronal model, J. Theoret. Biol. 107 (1984), pp. 631–647] of the Stein's neuronal model (see Stein [A theoretical analysis of neuronal variability, Biophys. J. 5 (1965), pp. 173–194]). We also prove an analogue result for sequences of multivariate random variables based on the diffusion approximation in Tamborrino, Sacerdote, and Jacobsen [Weak convergence of marked point processes generated by crossings of multivariate jump processes. Applications to neural network modeling, Phys. D 288 (2014), pp. 45–52]. The weighted means studied in this paper generalize the logarithmic means. We also investigate moderate deviations.     

Azido‐Substituted BODIPY Dyes for the Production of Fluorescent Carbon Nanotubes

A series of azido‐dyes were synthesized through Knoevenagel reactions of an azido‐BODIPY with aromatic aldehydes. The nature of the substituents allowed the fine tuning of their spectroscopic properties. The dyes were used to decorate oxidized multiwalled carbon nanotubes (ox‐MWCNTs), bearing terminal triple bond groups, by CuAAC reactions, affording fluorescent materials. This decoration allowed the efficient determination of the internalization of the ox‐MWCNT derivatives by different model cancer cells, such as MCF7.     

Screening Clouds and Majorana Fermions

Ken Wilson developed the Numerical Renormalization Group technique which greatly enhanced our understanding of the Kondo effect and other quantum impurity problems. Wilson’s NRG also inspired Philippe Nozières to propose the idea of a large “Kondo screening cloud”. While much theoretical evidence has accumulated for this idea it has remained somewhat controversial and has not yet been confirmed experimentally. Recently a new possibility for observing an analogous crossover length scale has emerged, involving a Majorana fermion localized at the interface between a topological superconductor quantum wire and a normal wire. We give an overview of this topic both with and without interactions included in the normal wire.     

Nonbinary convolutional codes derived from group character codes

New families of unit memory as well as multi-memory nonbinary convolutional codes are constructed algebraically in this paper. These convolutional codes are derived from the class of group character codes. The proposed codes have basic generator matrices, consequently, they are noncatastrophic. Additionally, the new code parameters are better than the ones available in the literature.     

Field Study on Mobility and Persistence of Linuron and Monolinuron in Agricultural Soil

Abstract

A field site equipped with suction cup lysimeters was installed at Treviglio (BG) to assess the migration capacity of the herbicides linuron and monolinuron from topsoil to groundwater and to verify the appearance of their relevant transformation products in soil and water samples. A constant hydraulic head was applied in order to develop water saturation conditions in the upper layers. KCl was used as a tracer to evaluate water infiltration velocity through the vertical soil profile. The constant hydraulic head accelerated infiltration rates, while herbicide concentrations reached maximum contamination because soil adsorption capacity was underdeveloped. The results indicated two main processes of pesticide transport: firstly transport due mainly to water infiltration through macropores; secondly the transport driven by matrix flow. Linuron was found to be the most mobile herbicide, while chloroanilines were found to be the major transformation products of the herbicides considered.     

Lyapunov exponent for Lipschitz maps

Nonlinear Dynamics - It is well known that the Lyapunov exponent plays a fundamental role in dynamical systems. In this note, we propose a definition of Lyapunov exponent for Lipschitz maps, which...     

Exotic states in the dynamical Casimir effect

Inhibited decoherence has been recently observed in a dissipative two-level system by increasing the strength of the coupling with the reservoir. The system is described by the spin-boson model under a perturbation approach in the delocalized phase regime occurring in weak-coupling limit at zero temperature. Within this scenario, persistence of coherence is found over long times for various low frequency structures of the bosonic environment near a band gap. Special resonances provoke transitions in the long time dynamics if the transition amplitude of the two-level system is greater than the band gap frequency or in absence of any band gap. These transitions may hinder the the loss of coherence in the spin-boson model. Limitations of the approximations are also discussed.