Tight Localizations of Feedback Sets

The classical NP-hard feedback arc set problem (FASP) and feedback vertex set problem (FVSP) ask for a minimum set of arcs $\varepsilon \subseteq E$ or vertices $\nu \subseteq V$ whose removal $G\setminus \varepsilon$, $G\setminus \nu$ makes a given multi-digraph $G=(V,E)$ acyclic, respectively. Though both problems are known to be APX-hard, approximation algorithms or proofs of inapproximability are unknown. We propose a new $\mathcal{O}(|V||E|^4)$-heuristic for the directed FASP. While a ratio of $r \approx 1.3606$ is known to be a lower bound for the APX-hardness, at least by empirical validation we achieve an approximation of $r \leq 2$. The most relevant applications, such as circuit testing, ask for solving the FASP on large sparse graphs, which can be done efficiently within tight error bounds due to our approach.Comment: manuscript submitted to AC

Impossible ecologies: Interaction networks and stability of coexistence in ecological communities

Does an ecological community allow stable coexistence? Identifying the general principles that determine the answer to this question is a central problem of theoretical ecology. Random matrix theory approaches have uncovered the general trends of the effect of competitive, mutualistic, and predator-prey interactions between species on stability of coexistence. However, an ecological community is determined not only by the counts of these different interaction types, but also by their network arrangement. This cannot be accounted for in a direct statistical description that would enable random matrix theory approaches. Here, we therefore develop a different approach, of exhaustive analysis of small ecological communities, to show that this arrangement of interactions can influence stability of coexistence more than these general trends. We analyse all interaction networks of $N\leqslant 5$ species with Lotka-Volterra dynamics by combining exact results for $N\leqslant 3$ species and numerical exploration. Surprisingly, we find that a very small subset of these networks are "impossible ecologies", in which stable coexistence is non-trivially impossible. We prove that the possibility of stable coexistence in general ecologies is determined by similarly rare "irreducible ecologies". By random sampling of interaction strengths, we then show that the probability of stable coexistence varies over many orders of magnitude even in ecologies that differ only in the network arrangement of identical ecological interactions. Finally, we demonstrate that our approach can reveal the effect of evolutionary or environmental perturbations of the interaction network. Overall, this work reveals the importance of the full structure of the network of interactions for stability of coexistence in ecological communities.Comment: 14 pages, 6 figures, 3 supplementary figure

IGraph/M: graph theory and network analysis for Mathematica

IGraph/M is an efficient general purpose graph theory and network analysis package for Mathematica. IGraph/M serves as the Wolfram Language interfaces to the igraph C library, and also provides several unique pieces of functionality not yet present in igraph, but made possible by combining its capabilities with Mathematica's. The package is designed to support both graph theoretical research as well as the analysis of large-scale empirical networks.Comment: submitted to Journal of Open Source Software on August 30, 202

igraph enables fast and robust network analysis across programming languages

Networks or graphs are widely used across the sciences to represent relationships of many kinds. igraph (https://igraph.org) is a general-purpose software library for graph construction, analysis, and visualisation, combining fast and robust performance with a low entry barrier. igraph pairs a fast core written in C with beginner-friendly interfaces in Python, R, and Mathematica. Over the last two decades, igraph has expanded substantially. It now scales to billions of edges, supports Mathematica and interactive plotting, integrates with Jupyter notebooks and other network libraries, includes new graph layouts and community detection algorithms, and has streamlined the documentation with examples and Spanish translations. Modern testing features such as continuous integration, address sanitizers, stricter typing, and memory-managed vectors have also increased robustness. Hundreds of bug reports have been fixed and a community forum has been opened to connect users and developers. Specific effort has been made to broaden use and community participation by women, non-binary people, and other demographic groups typically underrepresented in open source software.Comment: 5 pages, 4 figure

Phase transitions in non-equilibrium dynamical systems

This work is a summary of three papers (references [5, 14, 24]), which deal with modelling the hadronization and freeze-out in heavy ion collisions. There is evidence that this is a non-equilibrium process, and therefore cannot be described in a quasi-statical way, assuming local phase equilibrium. The study of dynamical phase transitions is an important subject, as it has practical applications not only in the description of nuclear collisions, but also in many other fields, e.g. in technical applications which involve high temperature detonations. Examples include gas turbines, internal combustion engines, rocket engines, etc. The correct description of some of these processes requires a relativistic approach. For example, in a rocket engine, radiation pressure has an important role in stabilizing the detonation front, therefore a relativistic description is required despite the relatively small flow velocities. Lessons learned from the study of the dynamical phase transition in heavy ion collisions can be applied to these other fields as well. The first part of the work, based on [5, 14], analyses the final stages of expansion in fluid dynamical models, taking into account the effects of numerical viscosity in computational approaches. A way to compute the thermodynamic parameters, such as temperature and entropy, is presented. These parameters are relevant for finding the location of the freeze-out surface. The second part of the work, based on [24], presents a simple model of rapid and dynamical hadronization that is capable of reproducing the constituent quark number scaling of elliptic flow, as observed in experiments

szhorvat/MaTeX v1.7.2

Better compatibility with the new documentation search in Mathematica 11.2 Better error reporting in case of Ghostscript failure Documentation improvement

Superstructure stabilization of ballast bedded railway tracks with geogrids

The paper deals with the research and development of the authors related to investigation of geogrid railway ballast reinforcement. It summarizes the theory of the geometrical deterioration of railway tracks, as well as the advantages of the use of geogrid reinforced ballast in railway superstructure. This article summarizes the results of the field tests with five different geogrid types on a Hungarian main railway line and laboratory multi-level shear box tests. It points out to future research possibilities, for example the modelling of laboratory multi-level shear box tests with discrete element method that may certify their results