Autoregressive functions estimation in nonlinear bifurcating autoregressive models

Bifurcating autoregressive processes, which can be seen as an adaptation of autoregressive processes for a binary tree structure, have been extensively studied during the last decade in a parametric context. In this work we do not specify any a priori form for the two autoregressive functions and we use nonparametric techniques. We investigate both nonasymptotic and asymptotic behaviour of the Nadaraya–Watson type estimators of the autoregressive functions. We build our estimators observing the process on a finite subtree denoted by \(\mathbb {T}_n\), up to the depth n. Estimators achieve the classical rate \(|\mathbb {T}_n|^{-\beta /(2\beta +1)}\) in quadratic loss over Hölder classes of smoothness. We prove almost sure convergence, asymptotic normality giving the bias expression when choosing the optimal bandwidth. Finally, we address the question of asymmetry: we develop an asymptotic test for the equality of the two autoregressive functions which we implement both on simulated and real data.     

State-dependent importance sampling schemes via minimum cross-entropy

We present a method to obtain state- and time-dependent importance sampling estimators by repeatedly solving a minimum cross-entropy (MCE) program as the simulation progresses. This MCE-based approach lends a foundation to the natural notion to stop changing the measure when it is no longer needed. We use this method to obtain a state- and time-dependent estimator for the one-tailed probability of a light-tailed i.i.d. sum that is logarithmically efficient in general and strongly efficient when the jumps are Gaussian. We go on to construct an estimator for the two-tailed problem which is shown to be similarly efficient. We consider minor variants of the algorithm obtained via MCE, and present some numerical comparisons between our algorithms and others from the literature.     

Study of the thermal behavior of Al(III) and In(III)-diclofenac complexes in solid state

The Al and In-diclofenac compounds were prepared. Thermogravimetry (TG) and X-ray diffraction powder patterns were used to characterize these compounds. Details concerning the dehydration and thermal decomposition as well as data of kinetic parameters have been described here. The kinetic studies of these stages were evaluated from several heating rates with mass sample of 2 and 5 mg in open crucibles under nitrogen atmosphere. The results of the present study improve the knowledge on these compounds including their dehydration and thermal stability. The obtained data leads to a dependence on the sample mass, which results in two kinetic behavior patterns.     

Photodynamical simulations of cytosine: characterization of the ultrafast bi-exponential UV deactivation

Deactivation of UV-excited cytosine is investigated by non-adiabatic dynamics simulations, optimization of conical intersections, and determination of reaction paths. Quantum chemical calculations are performed up to the MR-CISD level. Dynamics simulations were performed at multiconfigurational level with the surface hopping method including four electronic states. The results show the activation of four distinct reaction pathways at two different subpicosecond time scales and involving three different conical intersections. Most trajectories relax to a minimum of the S(1) state and deactivate with a time constant of 0.69 ps mainly through a semi-planar conical intersection along the n(O)π* surface. A minor fraction deactivate along ππ* regions of the S(1) surface. Sixteen percent of trajectories do not relax to the minimum and deactivate with a time constant of only 13 fs.     

Realization of cartesian closed topological hulls

The cartesian closed topological (CCT) hull of a concrete categoryK is the smallest full CCT extension ofK. A general method for describing the CCT hulls is presented and applied to render unified proofs for the basic examples ofK: topological spaces, uniform spaces, pretopological spaces, compact T₂ spaces, metrizable spaces, and completely regular spaces.     

Two-dimensional classical representations of the partition function of the spin-1/2 chain

Starting from the Trotter formula, we derive several classical representations of the partition function of a spin-1/2 chain. We investigate the rate of convergence of the different approximants by means of exact calculations for small systems. We demonstrate that it is important to use approximants that have the same symmetry properties as the original quantum model.     

Periodische Erscheinungen bei Kaltverstreckung

Ohne Zusammenfassung     

Определение средней величины кристаллик ов кварца И графита на основани и первичной экстинкц ии

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