Correction to: Multivariate cluster weighted models using skewed distributions

Advances in Data Analysis and Classification - In the original publication of the article, the line after equation (5) has been published incorrectly     

Geometric Singular Perturbation Theory for Systems with Symmetry

Journal of Dynamics and Differential Equations - In this paper we focus on a class of symmetric vector fields in the context of singularly perturbed fast-slow dynamical systems. Our main question...     

Detecting and classifying outliers in big functional data

Advances in Data Analysis and Classification - We propose two new outlier detection methods, for identifying and classifying different types of outliers in (big) functional data sets. The proposed...     

Crossing VIMP and EIS for studying heterogeneous sets of copper/bronze coins

Journal of Solid State Electrochemistry - Electrochemical impedance spectroscopy (EIS) and voltammetry of immobilized particles (VIMP) measurements using air-saturated mineral water and...     

Biomedical application of VIMP: screening of malignant cells in the prostate

An electrochemical method for discriminating healthy and malignant tissues in prostate biopsies using the voltammetry of immobilized particles methodology is described. The method involves the sampling with graphite bars 0.5 mm in diameter on paraffin-impregnated cross sections of prostate tissues used in ordinary cytological evaluation after local staining with methylene blue (MB). The subsequent record of the voltammetric response of sample-modified graphite electrodes displays clearly different MB-centered features for healthy and malignant regions due to the different association of the dye to the respective cells.

     

Swendsen‐Wang dynamics for general graphs in the tree uniqueness region

The Swendsen‐Wang (SW) dynamics is a popular Markov chain for sampling from the Gibbs distribution for the ferromagnetic Ising model on a graph G = (V,E). The dynamics is conjectured to converge to equilibrium in O(|V|^1/4) steps at any (inverse) temperature β, yet there are few results providing o(|V|) upper bounds. We prove fast convergence of the SW dynamics on general graphs in the tree uniqueness region. In particular, when β < β_c(d) where β_c(d) denotes the uniqueness/nonuniqueness threshold on infinite d‐regular trees, we prove that the relaxation time (i.e., the inverse spectral gap) of the SW dynamics is Θ(1) on any graph of maximum degree d ≥ 3. Our proof utilizes a monotone version of the SW dynamics which only updates isolated vertices. We establish that this variant of the SW dynamics has mixing time and relaxation time Θ(1) on any graph of maximum degree d for all β < β_c(d). Our proof technology can be applied to general monotone Markov chains, including for example the heat‐bath block dynamics, for which we obtain new tight mixing time bounds.