A bound on the Wasserstein-2 distance between linear combinations of independent random variables

We provide a bound on a distance between finitely supported elements and general elements of the unit sphere of ${?}^2\left({\mathbb{N}}^1\right)$. We use this bound to estimate the Wasserstein-2 distance between random variables represented by linear combinations of independent random variables. Our results are expressed in terms of a discrepancy measure related to Nourdin–Peccati’s Malliavin–Stein method. The main application is towards the computation of quantitative rates of convergence to elements of the second Wiener chaos. In particular, we explicit these rates for non-central asymptotic of sequences of quadratic forms and the behavior of the generalized Rosenblatt process at extreme critical exponent.     

Optical spectra of organic quantum dots in the strong coupling regime

We analyze the emission spectrum of a single organic quantum dot coupled to a microcavity in the strong coupling regime. We take into account non-linearities arising from both exciton–exciton interactions and the Pauli exclusion principle. We apply the recently developed Pade approximation for regular truncation of Green functions to calculate the emission spectrum. We show that as the number of excitations in the quantum dot increases the Rabi doublet evolves into a more complicated triplet structure.     

On strong solutions to the compressible Hall-magnetohydrodynamic system

In this paper, we consider strong/classical solutions to the 3D compressible Hall-magnetohydrodynamic system. First, we prove the existence of local strong solutions with positive density. Then the existence of global small solutions with small initial data is proved. Optimal time decay rate is also established.     

Localization microscopy (SPDM) facilitates high precision control of lithographically produced nanostructures

Nanoscale resolution in material sciences is usually restricted to scanning electron beam microscopes. Here we present a procedure that allows single molecule resolution of the sample surface with visible light. Highlighting the performance we used electron beam lithography to generate highly regular nanostructures consisting of interconnected cubes. The samples were labeled with Alexa 647 dyes. The spatial organization of the dyes on nanostructured surfaces was localized with single molecule resolution using localization microscopy. This succeeded also in an absolute spatial calibration of the localization method applied (spectral precision distance microscopy/SPDM). The findings will contribute to the field of product control for industrial applications and long-term fluorescence imaging.     

Computing the distribution of the Robinson-Foulds distance

With the exponential growth of genome databases, the importance of phylogenetics has increased dramatically over the past years. Studying phylogenetic trees enables us not only to understand how genes, genomes, and species evolve, but also helps us predict how they might change in future. One of the crucial aspects of phylogenetics is the comparison of two or more phylogenetic trees. There are different metrics for computing the dissimilarity between a pair of trees. The Robinson-Foulds (RF) distance is one of the widely used metrics on the space of labeled trees. The distribution of the RF distance from a given tree has been studied before, but the fastest known algorithm for computing this distribution is a slow, albeit polynomial-time, O(l⁵) algorithm. In this paper, we modify the dynamic programming algorithm for computing the distribution of this distance for a given tree by leveraging the number-theoretic transform (NTT), and improve the running time from O(l⁵) to O(l³ log l), where l is the number of tips of the tree. In addition to its practical usefulness, our method represents a theoretical novelty, as it is, to our knowledge, one of the rare applications of the number-theoretic transform for solving a computational biology problem.     

Examination of Changes in 6-minute Walk Distance and Related Factors in Patients with Perioperative Peripheral Arterial Disease

Objective: This study aimed to clarify the effects of pre- and postoperative physical function on the 6-minute walking distance (6MWD) in patients with peripheral arterial disease (PAD). Method: Forty-two elderly patients with PAD who were hospitalized for revascularization and able to walk independently were included in the study. The 6MWD, ankle brachial index (ABI), weight-bearing index (WBI), gait, and intermittent claudication distance (ICD) were measured before and after the surgery, and skeletal muscle index was measured only before surgery. Analyses were performed by comparing the pre- and postoperative values of each factor using a paired t-test. In addition, multiple regression analysis was performed with 6MWD as the dependent variable before and after surgery. Results: Postoperatively, pain disappeared in 22 patients, and ABI, ICD, 6MWD, and stride length improved significantly. ICD and stride length were extracted as factors related to 6MWD before and after surgery, and ABI, WBI, and stride length were extracted as factors related to 6MWD after surgery. Conclusion: The improvement of intermittent claudication associated with revascularization suggests a stronger influence of functional aspects on postoperative 6MWD.