On robust cross-validation for nonparametric smoothing

An essential problem in nonparametric smoothing of noisy data is a proper choice of the bandwidth or window width, which depends on a smoothing parameter $k$ . One way to choose $k$ based on the data is leave-one-out-cross-validation. The selection of the cross-validation criterion is similarly important as the choice of the smoother. Especially, when outliers are present, robust cross-validation criteria are needed. So far little is known about the behaviour of robust cross-validated smoothers in the presence of discontinuities in the regression function. We combine different smoothing procedures based on local constant fits with each of several cross-validation criteria. These combinations are compared in a simulation study under a broad variety of data situations with outliers and abrupt jumps. There is not a single overall best cross-validation criterion, but we find Boente-cross-validation to perform well in case of large percentages of outliers and the Tukey-criterion in case of data situations with jumps, even if the data are contaminated with outliers.     

Testing non-standard CP violation in neutrino propagation

Non-standard physics which can be described by effective four fermion interactions may be an additional source of CP violation in the neutrino propagation. We discuss the detectability of such a CP violation at a neutrino factory. We assume the current baseline setup of the international design study of a neutrino factory (IDS-NF) for the simulation. We find that the CP violation from certain non-standard interactions is, in principle, detectable significantly below their current bounds – even if there is no CP violation in the standard oscillation framework. Therefore, a new physics effect might be mis-interpreted as the canonical Dirac CP violation, and a possibly even more exciting effect might be missed.     

On the exterior algebra method applied to restricted set addition

In 1994 Dias da Silva and Hamidoune solved a long-standing open problem of Erd?s and Heilbronn using the structure of cyclic spaces for derivatives on Grassmannians and the representation theory of symmetric groups. They proved that for any subset A$A$ of the p$p$-element group Z/pZ$\mathbb{Z}/p\mathbb{Z}$ (where p$p$ is a prime), at least min{p,m|A|−m²+1}$min\{p,m\left|A\right|-m^2+1\}$ different elements of the group can be written as the sum of m$m$ different elements of A$A$. In this note we present an easily accessible simplified version of their proof for the case m=2$m=2$, and explain how the method can be applied to obtain the corresponding inverse theorem.     

Minkowski content and fractal curvatures of self-similar tilings and generator formulas for self-similar sets

We study Minkowski contents and fractal curvatures of arbitrary self-similar tilings (constructed on a feasible open set of an IFS) and the general relations to the corresponding functionals for self-similar sets. In particular, we characterize the situation, when these functionals coincide. In this case, the Minkowski content and the fractal curvatures of a self-similar set can be expressed completely in terms of the volume function or curvature data, respectively, of the generator of the tiling. In special cases such formulas have been obtained recently using tube formulas and complex dimensions or as a corollary to results on self-conformal sets. Our approach based on the classical Renewal Theorem is simpler and works for a much larger class of self-similar sets and tilings. In fact, generator type formulas are obtained for essentially all self-similar sets, when suitable volume functions (and curvature functions, respectively) related to the generator are used. We also strengthen known results on the Minkowski measurability of self-similar sets, in particular on the question of non-measurability in the lattice case.     

The raspberry model for protein-like particles: Ellipsoids and confinement in cylindrical pores

The study of protein mass transport via atomistic simulation requires time and length scales beyond the computational capabilities of modern computer systems. The raspberry model for colloidal particles in combination with the mesoscopic hydrodynamic method of lattice Boltzmann facilitates coarse-grained simulations that are on the order of microseconds and hundreds of nanometers for the study of diffusive transport of protein-like colloid particles. The raspberry model reproduces linearity in resistance to motion versus particle size and correct enhanced drag within cylindrical pores at off-center coordinates for spherical particles. Owing to the high aspect ratio of many proteins, ellipsoidal raspberry colloid particles were constructed and reproduced the geometric resistance factors of Perrin and of Happel and Brenner in the laboratory-frame and in the moving body-frame. Accurate body-frame rotations during diffusive motion have been captured for the first time using projections of displacements. The spatial discretization of the fluid leads to a renormalization of the hydrodynamic radius, however, the data describes a self-consistent hydrodynamic frame within this renormalized system.     

Phase transitions of nonlinear waves in quadratic waveguide arrays

We study two-color parametric nonlinear modes in waveguide arrays with a quadratic nonlinear response. We predict theoretically and observe experimentally a new type of phase transition manifested in an abrupt power-controlled change of the mode structure from unstaggered to staggered, due to the interplay of localization and synchronization in parametrically driven discrete systems.     

Optimal control of Markovian jump processes with partial information and applications to a parallel queueing model

We consider a stochastic control problem over an infinite horizon where the state process is influenced by an unobservable environment process. In particular, the Hidden-Markov-model and the Bayesian model are included. This model under partial information is transformed into an equivalent one with complete information by using the well-known filter technique. In particular, the optimal controls and the value functions of the original and the transformed problem are the same. An explicit representation of the filter process which is a piecewise-deterministic process, is also given. Then we propose two solution techniques for the transformed model. First, a generalized verification technique (with a generalized Hamilton–Jacobi–Bellman equation) is formulated where the strict differentiability of the value function is weaken to local Lipschitz continuity. Second, we present a discrete-time Markovian decision model by which we are able to compute an optimal control of our given problem. In this context we are also able to state a general existence result for optimal controls. The power of both solution techniques is finally demonstrated for a parallel queueing model with unknown service rates. In particular, the filter process is discussed in detail, the value function is explicitly computed and the optimal control is completely characterized in the symmetric case.     

Maximum likelihood estimation for stochastic volatility in mean models with heavy‐tailed distributions

In this article, we introduce a likelihood‐based estimation method for the stochastic volatility in mean (SVM) model with scale mixtures of normal (SMN) distributions. Our estimation method is based on the fact that the powerful hidden Markov model (HMM) machinery can be applied in order to evaluate an arbitrarily accurate approximation of the likelihood of an SVM model with SMN distributions. Likelihood‐based estimation of the parameters of stochastic volatility models, in general, and SVM models with SMN distributions, in particular, is usually regarded as challenging as the likelihood is a high‐dimensional multiple integral. However, the HMM approximation, which is very easy to implement, makes numerical maximum of the likelihood feasible and leads to simple formulae for forecast distributions, for computing appropriately defined residuals, and for decoding, that is, estimating the volatility of the process. Copyright © 2017 John Wiley & Sons, Ltd.