Sufficient Conditions for the Global Rigidity of Periodic Graphs

Tanigawa (2016) showed that vertex-redundant rigidity of a graph implies its global rigidity in arbitrary dimension. We extend this result to periodic frameworks under fixed lattice representations. That is, we show that if a generic periodic framework is vertex-redundantly rigid, in the sense that the deletion of a single vertex orbit under the periodicity results in a periodically rigid framework, then it is also periodically globally rigid. Our proof is similar to the one of Tanigawa, but there are some added difficulties. First, it is not known whether periodic global rigidity is a generic property in dimension $$d>2$$ d > 2 . We work around this issue by using slight modifications of recent results of Kaszanitzky et al. (2021). Secondly, while the rigidity of finite frameworks in $${\mathbb {R}}^d$$ R d on at most d vertices obviously implies their global rigidity, it is non-trivial to prove a similar result for periodic frameworks. This is accomplished by extending a result of Bezdek and Connelly (2002) on the existence of a continuous motion between two equivalent d-dimensional realisations of a single graph in $${\mathbb {R}}^{2d}$$ R 2 d to periodic frameworks. As an application of our result, we give a necessary and sufficient condition for the global rigidity of generic periodic body-bar frameworks in arbitrary dimension. This provides a periodic counterpart to a result of Connelly et al. (2013) regarding the global rigidity of generic finite body-bar frameworks.

Towards Version Controlling in RefactorErl

Static source code analyser tools are operating on an intermediate representation of the source code that is usually a tree or a graph. Those representations need to be updated according to the different versions of the source code. However, the developers might be interested in the changes or might need information about previous versions, therefore, keeping different versions of the source code analysed by the tools are required. RefactorErl is an open-source static analysis and transformation tool for Erlang that uses a graph representation to store and manipulate the source code. The aim of our research was to create an extension of the Semantic Program Graph of RefactorErl that is able to store different versions of the source code in a single graph. The new method resulted in 30% memory footprint decrease compared to the available workaround solutions.

On Turán exponents of bipartite graphs

A long-standing conjecture of Erdős and Simonovits asserts that for every rational number $r\in (1,2)$ there exists a bipartite graph H such that $\mathrm{ex}(n,H)=\Theta(n^r)$ . So far this conjecture is known to be true only for rationals of form $1+1/k$ and $2-1/k$ , for integers $k\geq 2$ . In this paper, we add a new form of rationals for which the conjecture is true: $2-2/(2k+1)$ , for $k\geq 2$ . This in turn also gives an affirmative answer to a question of Pinchasi and Sharir on cube-like graphs. Recently, a version of Erdős and Simonovits $^{\prime}$ s conjecture, where one replaces a single graph by a finite family, was confirmed by Bukh and Conlon. They proposed a construction of bipartite graphs which should satisfy Erdős and Simonovits $^{\prime}$ s conjecture. Our result can also be viewed as a first step towards verifying Bukh and Conlon $^{\prime}$ s conjecture. We also prove an upper bound on the Turán number of theta graphs in an asymmetric setting and employ this result to obtain another new rational exponent for Turán exponents: $r=7/5$ .

Visualizing the evolution of income inequality

The reporting of only relative inequalities is decreasing and other inequality invariance criteria are often being considered simultaneously. Having multiple measures with potentially different conclusions on whether inequality has increased or decreased complicates communicating what these results imply about the evolution of income inequality. To facilitate understanding this evolution, we highlight the advantage of visualizing in a single graph the relationship between changes in mean income and the development of inequality according to multiple inequality invariance criteria. Not presenting how these entities relate may mislead policy makers about the evolution of income inequality and its potential causes.

ThunderRW

As random walk is a powerful tool in many graph processing, mining and learning applications, this paper proposes an efficient in-memory random walk engine named ThunderRW. Compared with existing parallel systems on improving the performance of a single graph operation, ThunderRW supports massive parallel random walks. The core design of ThunderRW is motivated by our profiling results: common RW algorithms have as high as 73.1% CPU pipeline slots stalled due to irregular memory access, which suffers significantly more memory stalls than the conventional graph workloads such as BFS and SSSP. To improve the memory efficiency, we first design a generic step-centric programming model named Gather-Move-Update to abstract different RW algorithms. Based on the programming model, we develop the step interleaving technique to hide memory access latency by switching the executions of different random walk queries. In our experiments, we use four representative RW algorithms including PPR, DeepWalk, Node2Vec and MetaPath to demonstrate the efficiency and programming flexibility of ThunderRW. Experimental results show that ThunderRW outperforms state-of-the-art approaches by an order of magnitude, and the step interleaving technique significantly reduces the CPU pipeline stall from 73.1% to 15.0%.

Tensor Graph Convolutional Networks for Text Classification

Compared to sequential learning models, graph-based neural networks exhibit some excellent properties, such as ability capturing global information. In this paper, we investigate graph-based neural networks for text classification problem. A new framework TensorGCN (tensor graph convolutional networks), is presented for this task. A text graph tensor is firstly constructed to describe semantic, syntactic, and sequential contextual information. Then, two kinds of propagation learning perform on the text graph tensor. The first is intra-graph propagation used for aggregating information from neighborhood nodes in a single graph. The second is inter-graph propagation used for harmonizing heterogeneous information between graphs. Extensive experiments are conducted on benchmark datasets, and the results illustrate the effectiveness of our proposed framework. Our proposed TensorGCN presents an effective way to harmonize and integrate heterogeneous information from different kinds of graphs.

ViSiElse: an innovative R-package to visualize raw behavioral data over time

The scientific community encourages the use of raw data graphs to improve the reliability and transparency of the results presented in articles. However, the current methods used to visualize raw data are limited to one or two numerical variables per graph and/or small sample sizes. In the behavioral sciences, numerous variables must be plotted together in order to gain insight into the behavior in question. In this article, we present ViSiElse, an R-package offering a new approach in the visualization of raw data. ViSiElse was developed with the open-source software R to visualize behavioral observations over time based on raw time data extracted from visually recorded sessions of experimental observations. ViSiElse gives a global overview of a process by creating a visualization of the timestamps for multiple actions and all participants into a single graph; individual or group behavior can then be easily assessed. Additional features allow users to further inspect their data by including summary statistics and time constraints.

GREG—studying transcriptional regulation using integrative graph databases

A gene regulatory process is the result of the concerted action of transcription factors, co-factors, regulatory non-coding RNAs (ncRNAs) and chromatin interactions. Therefore, the combination of protein–DNA, protein–protein, ncRNA–DNA, ncRNA–protein and DNA–DNA data in a single graph database offers new possibilities regarding generation of biological hypotheses. GREG (The Gene Regulation Graph Database) is an integrative database and web resource that allows the user to visualize and explore the network of all above-mentioned interactions for a query transcription factor, long non-coding RNA, genomic range or DNA annotation, as well as extracting node and interaction information, identifying connected nodes and performing advanced graphical queries directly on the regulatory network, in a simple and efficient way. In this article, we introduce GREG together with some application examples (including exploratory research of Nanog’s regulatory landscape and the etiology of chronic obstructive pulmonary disease), which we use as a demonstration of the advantages of using graph databases in biomedical research. Database URL: https://mora-lab.github.io/projects/greg.html, www.moralab.science/GREG/