A Lepskiĭ-type stopping rule for the covariance estimation of multi-dimensional Lévy processes

We suppose that a Lévy process is observed at discrete time points. Starting from an asymptotically minimax family of estimators for the continuous part of the Lévy Khinchine characteristics, i.e., the covariance, we derive a data-driven parameter choice for the frequency of estimating the covariance. We investigate a Lepskiĭ-type stopping rule for the adaptive procedure. Consequently, we use a balancing principle for the best possible data-driven parameter. The adaptive estimator achieves almost the optimal rate. Numerical experiments with the proposed selection rule are also presented.

Reheating after inflation by supersymmetry breaking

We study reheating after the end of inflation in models where the inflaton is the superpartner of goldstino and is charged under a gauged U(1) R-symmetry. We consider two classes of models – one is small field characterized by an almost flat Kähler space, and the other large field characterized by a hyperbolic Kähler space SU(1, 1)/U(1), while in both cases the inflaton superpotential is linear due to the R-symmetry. The inflationary observables of our models fit within 2$$\sigma $$ σ CMB values. Upon coupling the inflaton sector to the (supersymmetric) Standard Model, we compute the MSSM parameters, mass spectrum, and decay modes of the inflaton, with the resulting reheating temperature around $$10^8$$ 10 8 GeV. We also find that both models can accommodate superheavy LSP dark matter, depending on the parameter choice.

Landweber Iterative Regularization Method for Identifying the Initial Value Problem of the Rayleigh–Stokes Equation

In this paper, we study an inverse problem to identify the initial value problem of the homogeneous Rayleigh–Stokes equation for a generalized second-grade fluid with the Riemann–Liouville fractional derivative model. This problem is ill posed; that is, the solution (if it exists) does not depend continuously on the data. We use the Landweber iterative regularization method to solve the inverse problem. Based on a conditional stability result, the convergent error estimates between the exact solution and the regularization solution by using an a priori regularization parameter choice rule and an a posteriori regularization parameter choice rule are given. Some numerical experiments are performed to illustrate the effectiveness and stability of this method.

On backward problem for fractional spherically symmetric diffusion equation with observation data of nonlocal type

The main target of this paper is to study a problem of recovering a spherically symmetric domain with fractional derivative from observed data of nonlocal type. This problem can be established as a new boundary value problem where a Cauchy condition is replaced with a prescribed time average of the solution. In this work, we set some of the results above existence and regularity of the mild solutions of the proposed problem in some suitable space. Next, we also show the ill-posedness of our problem in the sense of Hadamard. The regularized solution is given by the fractional Tikhonov method and convergence rate between the regularized solution and the exact solution under a priori parameter choice rule and under a posteriori parameter choice rule.

Maximal spaces for approximation rates in $$\ell ^1$$-regularization

We study Tikhonov regularization for possibly nonlinear inverse problems with weighted $$\ell ^1$$ ℓ 1 -penalization. The forward operator, mapping from a sequence space to an arbitrary Banach space, typically an $$L^2$$ L 2 -space, is assumed to satisfy a two-sided Lipschitz condition with respect to a weighted $$\ell ^2$$ ℓ 2 -norm and the norm of the image space. We show that in this setting approximation rates of arbitrarily high Hölder-type order in the regularization parameter can be achieved, and we characterize maximal subspaces of sequences on which these rates are attained. On these subspaces the method also converges with optimal rates in terms of the noise level with the discrepancy principle as parameter choice rule. Our analysis includes the case that the penalty term is not finite at the exact solution (’oversmoothing’). As a standard example we discuss wavelet regularization in Besov spaces $$B^r_{1,1}$$ B 1 , 1 r . In this setting we demonstrate in numerical simulations for a parameter identification problem in a differential equation that our theoretical results correctly predict improved rates of convergence for piecewise smooth unknown coefficients.

Study of the values of the social workers in Bulgaria

The purpose of this article is to study the priority motivation values of the social workers in Bulgaria and the factors influencing them. The study covers 205 social workers, participating voluntarily and anonymously. The Schwartz questionnaire: The Portrait Values Questionnaire (PVQ) was used, adapted by Karandashev (2004). The factor influences between the most significantly manifested values of the social workers and the parameters age, sex, education, improvement of the qualification, work experience, choice of profession and need for specific knowledge and skills were verified. It has been found out that only the parameter ‘choice of profession’ has an influence on the value of “benevolence”. The results of the study show that the priority values of the social workers coincide with the mission and purpose of the social work and confirm the results of other researchers.

Bootstrap Inference for Quantile Treatment Effects in Randomized Experiments with Matched Pairs

This paper examines methods of inference concerning quantile treatment effects (QTEs) in randomized experiments with matched-pairs designs (MPDs). Standard multiplier bootstrap inference fails to capture the negative dependence of observations within each pair and is therefore conservative. Analytical inference involves estimating multiple functional quantities that require several tuning parameters. Instead, this paper proposes two bootstrap methods that can consistently approximate the limit distribution of the original QTE estimator and lessen the burden of tuning parameter choice. Most especially, the inverse propensity score weighted multiplier bootstrap can be implemented without knowledge of pair identities.

Design and beam dynamics of CEPC damping ring system

A damping ring system which includes a small 1.1 GeV ring and two transport lines is introduced in CEPC linac in order to reduce the transverse emittance of positron beam at the end of linac and hence reduce the beam loss in the booster. This paper introduces the parameter choice and optics study of damping ring. The corresponding instability effect and IBS effect are also checked to make sure the design current and design emittance can be realized. Except for damping ring, two transport lines are needed to match the parameters between linac and damping ring. Both designs for energy compressor and bunch compressor including beam simulations are discussed in this paper.

IDENTIFICATION OF THE SOURCE FOR FULL PARABOLIC EQUATIONS

In this work, we consider the problem of identifying the time independent source for full parabolic equations in Rn from noisy data. This is an ill-posed problem in the sense of Hadamard. To compensate the factor that causes the instability, a family of parametric regularization operators is introduced, where the rule to select the value of the regularization parameter is included. This rule, known as regularization parameter choice rule, depends on the data noise level and the degree of smoothness that it is assumed for the source. The proof for the stability and convergence of the regularization criteria is presented and a Hölder type bound is obtained for the estimation error. Numerical examples are included to illustrate the effectiveness of this regularization approach.