27 research outputs found
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 or
vertices whose removal , makes a given multi-digraph acyclic, respectively. Though both
problems are known to be APX-hard, approximation algorithms or proofs of
inapproximability are unknown. We propose a new
-heuristic for the directed FASP. While a ratio of is known to be a lower bound for the APX-hardness, at least by
empirical validation we achieve an approximation of . 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
species with Lotka-Volterra dynamics by combining exact results for 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