Analyzing massive complex networks yields promising insights about our everyday lives. Building scalable algorithms to do so is a challenging task that requires a careful analysis and an extensive evaluation. However, engineering such algorithms is often hindered by the scarcity of publicly available datasets.Network generators serve as a tool to alleviate this problem by providing synthetic instances with controllable parameters. However, many network generators fail to provide instances on a massive scale due to their sequential nature or resource constraints. Additionally, truly scalable network generators are few and often limited in their realism.In this work, we present novel generators for a variety of network models that are frequently used as benchmarks. By making use of pseudorandomization and divide-and-conquer schemes, our generators follow a communication-free paradigm. The resulting generators are thus embarrassingly parallel and have a near optimal scaling behavior. This allows us to generate instances of up to 2 43 vertices and 2 47 edges in less than 22 minutes on 32 768 cores. Therefore, our generators allow new graph families to be used on an unprecedented scale.

Incongruence, or topological conflict, is prevalent in genome-scale data sets. Internode certainty (IC) and related measures were recently introduced to explicitly quantify the level of incongruence of a given internal branch among a set of phylogenetic trees and complement regular branch support measures (e.g., bootstrap, posterior probability) that instead assess the statistical confidence of inference. Since most phylogenomic studies contain data partitions (e.g., genes) with missing taxa and IC scores stem from the frequencies of bipartitions (or splits) on a set of trees, IC score calculation typically requires adjusting the frequencies of bipartitions from these partial gene trees. However, when the proportion of missing taxa is high, the scores yielded by current approaches that adjust bipartition frequencies in partial gene trees differ substantially from each other and tend to be overestimates. To overcome these issues, we developed three new IC measures based on the frequencies of quartets, which naturally apply to both complete and partial trees. Comparison of our new quartet-based measures to previous bipartition-based measures on simulated data shows that: (1) on complete data sets, both quartet-based and bipartition-based measures yield very similar IC scores; (2) IC scores of quartet-based measures on a given data set with and without missing taxa are more similar than the scores of bipartition-based measures; and (3) quartet-based measures are more robust to the absence of phylogenetic signal and errors in phylogenetic inference than bipartition-based measures. Additionally, the analysis of an empirical mammalian phylogenomic data set using our quartet-based measures reveals the presence of substantial levels of incongruence for numerous internal branches. An efficient open-source implementation of these quartet-based measures is freely available in the program QuartetScores (https://github.com/lutteropp/QuartetScores).

Quantum-chemical fragmentation methods offer an efficient approach for the treatment of large proteins, in particular if local target quantities such as protein–ligand interaction energies, enzymatic reaction energies, or spectroscopic properties of embedded chromophores are sought. However, the accuracy that is achievable for such local target quantities intricately depends on how the protein is partitioned into smaller fragments. While the commonly employed naı̈ve approach of using fragments with a fixed size is widely used, it can result in large and unpredictable errors when varying the fragment size. Here, we present a systematic partitioning scheme that aims at minimizing the fragmentation error of a local target quantity for a given maximum fragment size. To this end, we construct a weighted graph representation of the protein, in which the amino acids constitute the nodes. These nodes are connected by edges weighted with an estimate for the fragmentation error that is expected when cutting this edge. This allows us to employ graph partitioning algorithms provided by computer science to determine near-optimal partitions of the protein. We apply this scheme to a test set of six proteins representing various prototypical applications of quantum-chemical fragmentation methods using a simplified molecular fractionation with conjugate caps (MFCC) approach with hydrogen caps. We show that our graph-based scheme consistently improves upon the naı̈ve approach.

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Generative network models play an important role in algorithm development, scaling studies, network analysis, and realistic system benchmarks for graph data sets. The commonly used graph-based benchmark model R-MAT has some drawbacks concerning realism and the scaling behavior of network properties. A complex network model gaining considerable popularity builds random hyperbolic graphs, generated by distributing points within a disk in the hyperbolic plane and then adding edges between points whose hyperbolic distance is below a threshold. We present in this paper a fast generation algorithm for such graphs. Our experiments show that our new generator achieves speedup factors of 3-60 over the best previous implementation. One billion edges can now be generated in under one minute on a shared-memory workstation. Furthermore, we present a dynamic extension to model gradual network change, while preserving at each step the point position probabilities.