On the Maximum Weight of a Sparse Connected Graph of Given Order and Size

The weight of an edge of a graph is defined to be the sum of degrees of vertices incident to the edge. The weight of a graph G is the minimum of weights of edges of G. Jendrol’ and Schiermeyer (Combinatorica 21:351–359, 2001) determined the maximum weight of a graph having n vertices and m edges, thus solving a problem posed in 1990 by Erd?s. The present paper is concerned with a modification of the mentioned problem, in which involved graphs are connected and of size \(m\le \left( {\begin{array}{c}n\\ 2\end{array}}\right) -\left( {\begin{array}{c}\lceil n/2\rceil \\ 2\end{array}}\right) \).     

On the analysis of a dynamic evolutionary algorithm

Evolutionary algorithms are applied as problem-independent optimization algorithms. They are quite efficient in many situations. However, it is difficult to analyze even the behavior of simple variants of evolutionary algorithms like the (1+1) EA on rather simple functions. Nevertheless, only the analysis of the expected run time and the success probability within a given number of steps can guide the choice of the free parameters of the algorithms. Here static (1+1) EAs with a fixed mutation probability are compared with dynamic (1+1) EAs with a simple schedule for the variation of the mutation probability. The dynamic variant is first analyzed for functions typically chosen as example-functions for evolutionary algorithms. Afterwards, it is shown that it can be essential to choose the suitable variant of the (1+1) EA. More precisely, functions are presented where each static (1+1) EA has exponential expected run time while the dynamic variant has polynomial expected run time. For other functions it is shown that the dynamic (1+1) EA has exponential expected run time while a static (1+1) EA with a good choice of the mutation probability has polynomial run time with overwhelming probability.     

Correspondences of ribbon categories

Much of algebra and representation theory can be formulated in the general framework of tensor categories. The aim of this paper is to further develop this theory for braided tensor categories. Several results are established that do not have a substantial counterpart for symmetric tensor categories. In particular, we exhibit various equivalences involving categories of modules over algebras in ribbon categories. Finally, we establish a correspondence of ribbon categories that can be applied to, and is in fact motivated by, the coset construction in conformal quantum field theory.     

An Overview on Non-Ideal Vibrations

We analyze the dynamical coupling between energy sources and structural response that must not be ignored in real engineering problems, since real motors have limited output power.     

Exploring interactions in high-dimensional genomic data: an overview of Logic Regression, with applications

Logic Regression is an adaptive regression methodology mainly developed to explore high-order interactions in genomic data. Logic Regression is intended for situations where most of the covariates in the data to be analyzed are binary. The goal of Logic Regression is to find predictors that are Boolean (logical) combinations of the original predictors. In this article, we give an overview of the methodology and discuss some applications. We also describe the software for Logic Regression, which is available as an R and S-Plus package.     

Finding small somatic structural variants in exome sequencing data: a machine learning approach

Genetic variation forms the basis for diversity but can as well be harmful and cause diseases, such as tumors. Structural variants (SV) are an example of complex genetic variations that comprise of many nucleotides ranging up to several megabases. Based on recent developments in sequencing technology it has become feasable to elucidate the genetic state of a person’s genes (i.e. the exome) or even the complete genome. Here, a machine learning approach is presented to find small disease-related SVs with the help of sequencing data. The method uses differences in characteristics of mapping patterns between tumor and normal samples at a genomic locus. This way, the method aims to be directly applicable for exome sequencing data to improve detection of SVs since specific SV detection methods are currently lacking. The method has been evaluated based on a simulation study as well as with exome data of patients with acute myeloid leukemia. An implementation of the algorithm is available at https://github.com/lenz99-/svmod.     

Measurement and simulations of hollow atom X-ray spectra of solid-density relativistic plasma created by high-contrast PW optical laser pulses

K-shell spectra of solid Al excited by petawatt picosecond laser pulses have been investigated at the Vulcan PW facility. Laser pulses of ultrahigh contrast with an energy of 160 J on the target allow studies of interactions between the laser field and solid state matter at 10²⁰ W/cm². Intense X-ray emission of KK hollow atoms (atoms without n = 1 electrons) from thin aluminum foils is observed from optical laser plasma for the first time. Specifically for 1.5 μm thin foil targets the hollow atom yield dominates the resonance line emission. It is suggested that the hollow atoms are predominantly excited by the impact of X-ray photons generated by radiation friction to fast electron currents in solid-density plasma due to Thomson scattering and bremsstrahlung in the transverse plasma fields. Numerical simulations of Al hollow atom spectra using the ATOMIC code confirm that the impact of keV photons dominates the atom ionization. Our estimates demonstrate that solid-density plasma generated by relativistic optical laser pulses provide the source of a polychromatic keV range X-ray field of 10¹⁸ W/cm² intensity, and allows the study of excited matter in the radiation-dominated regime. High-resolution X-ray spectroscopy of hollow atom radiation is found to be a powerful tool to study the properties of high-energy density plasma created by intense X-ray radiation.