Complex Graph Research Articles

Analysing and Transforming Graph Structures: The Graph Transformation Framework

Interconnected data or, in particular, graph structures are a valuable source of information. Gaining insights and knowledge from graph structures is applied throughout a wide range of application areas, for which efficient tools are desired. In this work we present an open source Java graph transformation framework. The framework provides a simple fluent Application Programming Interface (API) to transform a provided graph structure to a desired target format and, in turn, allow further analysis. First, we provide an overview on the architecture of the framework and its core components. Second, we provide an illustrative example which shows how to use the framework’s core API for transforming and verifying graph structures. Next to that, we present an instantiation of the framework in the context of analyzing the third-party dependencies amongst open source libraries on the Android platform. The example scenario provides insights on a typical scenario in which the graph transformation framework is applied to efficiently process complex graph structures. The framework is open-source and actively developed, and we further provide information on how to obtain it from its official GitHub page.

Noise-like color pulses and domains in ring fiber lasers with an anomalous dispersion cavity

We have numerically studied a noise-like regime for the formation of color pulses and domains in dual-wavelength fiber lasers. In the established generation, each of these pulses and domains consists of two noise-radiation square fragments with different carrier frequencies. The noise radiation regime is due to the Kerr nonlinearity of the fiber making up the laser ring cavity. The spectral and temporal structures of this noise radiation have been determined. We have found the main regularities in the change of lasing regimes as the laser parameters are changed. The results obtained are of interest for understanding the nonlinear dynamics of noise-like radiation and for further development of methods for controlling laser regimes.

Comparing voxel- and feature-wise harmonization of complex graph measures from multiple sites for structural brain network investigation of aging.

Complex graph theory measures of brain structural connectomes derived from diffusion weighted images (DWI) provide insight into the network structure of the brain. Further, as the number of available DWI datasets grows, so does the ability to investigate associations in these measures with major biological factors, like age. However, one key hurdle that remains is the presence of scanner effects that can arise from different DWI datasets and confound multisite analyses. Two common approaches to correct these effects are voxel-wise and feature-wise harmonization. However, it is still unclear how to best leverage them for graph-theory analysis of an aging population. Thus, there is a need to better characterize the impact of each harmonization method and their ability to preserve age related features. We investigate this by characterizing four complex graph theory measures (modularity, characteristic path length, global efficiency, and betweenness centrality) in 48 participants aged 55 to 86 from Baltimore Longitudinal Study of Aging (BLSA) and Vanderbilt Memory and Aging Project (VMAP) before and after voxel- and feature-wise harmonization with the Null Space Deep Network (NSDN) and ComBat, respectively. First, we characterize across dataset coefficients of variation (CoV) and find the combination of NSDN and ComBat causes the greatest reduction in CoV followed by ComBat alone then NSDN alone. Second, we reproduce published associations of modularity with age after correcting for other covariates with linear models. We find that harmonization with ComBat or ComBat and NSDN together improves the significance of existing age effects, reduces model residuals, and qualitatively reduces separation between datasets. These results reinforce the efficiency of statistical harmonization on the feature-level with ComBat and suggest that harmonization on the voxel-level is synergistic but may have reduced effect after running through the multiple layers of the connectomics pipeline. Thus, we conclude that feature-wise harmonization improves statistical results, but the addition of biologically informed voxel-based harmonization offers further improvement.

AF-GCN: Attribute-Fusing Graph Convolution Network for Recommendation

Graph Convolution Networks (GCNs) are playing important role and widely used in recommendation systems. This is benefited from their capability of capturing the collaborative signals of higher-order neighbors by exploiting the graph structure. GCN-based methods have made great success in improving recommending performance, but still suffer from the severe problem of data sparsity. An effective solution to alleviate the data sparsity is to introduce attribute information. However, existing GCN-based methods hardly capture the complex attribute information of users and items and the complicated relationships between users, items, and attributes simultaneously. To address the above problems, we propose a novel attribute-fusing graph convolution network model called AF-GCN. Specifically, we first propose an attention-based attribute fusion strategy by taking account of different effects of attributes. Then, we construct a complex graph containing four kinds of nodes. Finally, we design a particular Laplacian matrix, which leverages the attribute information through graph structure to learn user and item representations better. Extensive experimental results on three real-world datasets demonstrate that the proposed AF-GCN significantly outperforms state-of-the-art methods. The source codes of this work are available at <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/xiaorui-mnaire/af-gcn</uri> .

Vertex cut of a graph and connectivity of its neighbourhood complex

We show that if a graph G satisfies certain conditions, then the connectivity of neighbourhood complex N(G) is strictly less than the vertex connectivity of G. As an application, we give a relation between the connectivity of the neighbourhood complex and the vertex connectivity for stiff chordal graphs, and for weakly triangulated graphs satisfying certain properties. Next, we consider graphs with a vertex v such that for any k-subset S of neighbours of v, there exists a vertex vS≠v such that S is subset of neighbours of vS. We prove that for any graph G with a vertex v as above, N(G−{v}) is (k−1)-connected implies that N(G) is (k−1)-connected. We use this to show that:(i) neighbourhood complexes of queen and king graphs are simply connected and (ii) if G is a non-complete stiff chordal graph, then vertex connectivity of G is n+1 if and only if Conn(N(G))=n.

Corners and simpliciality in oriented matroids and partial cubes

Building on a recent characterization of tope graphs of Complexes of Oriented Matroids (COMs), we tackle and generalize several classical problems in Oriented Matroids (OMs), Lopsided Sets (aka ample set systems), and partial cubes via Metric Graph Theory.Our first main result is that every element of an OM from a class introduced by Mandel is incident to a simplicial tope, i.e, such OMs contain no mutation-free elements. This allows us to refute a conjecture of Mandel from 1983, that would have implied the famous Las Vergnas’ simplex conjecture. Further, we show that the mutation graph of uniform OMs of order at most 9 are connected, thus confirming a stronger conjecture of Cordovil-Las Vergnas in this setting.The second main contribution is the introduction of corners of COMs as a natural generalization of corners in Lopsided Sets. Generalizing results of Bandelt and Chepoi, Tracy Hall, and Chalopin et al. we prove that realizable COMs, rank 2 COMs, as well as hypercellular graphs admit corner peelings. Using this, we confirm Las Vergnas’ conjecture for antipodal partial cubes (a class much larger than OMs) of small rank or isometric dimension.

Twisting of properads

We study T. Willwacher's twisting endofunctor tw in the category of dg prop(erad)s P under the operad of (strongly homotopy) Lie algebras, i:Lie→P. It is proven that if P is a properad under properad of Lie bialgebras Lieb, then the associated twisted properad twP becomes in general a properad under quasi-Lie bialgebras (rather than under Lieb). This result implies that the cyclic cohomology of any cyclic homotopy associative algebra has in general an induced structure of a quasi-Lie bialgebra. We show that the cohomology of the twisted properad twLieb is highly non-trivial — it contains the cohomology of the so called hairy graph complex introduced and studied recently in the context of the theory of long knots and the theory of moduli spaces Mg,n of algebraic curves of arbitrary genus g with n punctures.Using a polydifferential functor from the category of props to the category of operads, we introduce and study two new twisting endofunctors, one in the category dg prop(erad)s P under the minimal resolution of Lieb, and one for the involutive version of Lieb. We compute the cohomology of the associated deformation complexes, and discuss their applications in string topology.

A graph-based superframework for mixture model estimation using EM: an analysis of US wholesale electricity markets

A fully unsupervised graph-based superframework is proposed to handle the EM initialization problem for estimating mixture models on financial time series. Using a complex network approach that links time series and graphs, the graph-structured information derived from the observed data is exploited to produce a meaningful starting point for the EM algorithm. It is shown that structural information derived by complex graphs can definitely capture time series behavior and nonlinear relationships between different observations. The proposed methodology is employed to estimate Gaussian mixture models on US wholesale electricity market prices using two different configurations of the superframework. The obtained results show that the proposed methodology performs better than conventional initialization methods, such as K-means based techniques. The improvements are significant on the overall representation of the empirical distribution of log-returns and, in particular, on the first four moments. Moreover, this approach has a high degree of generalization and flexibility, exploiting graph manipulation and employing functional operating blocks, which can be adapted to very different empirical situations.

Issue Information

Journal of the European Academy of Dermatology and VenereologyVolume 37, Issue S4 p. 1-2 Issue InformationFree Access Issue Information First published: 30 March 2023 https://doi.org/10.1111/jdv.19023AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat No abstract is available for this article. Volume37, IssueS4Special Issue: A Precise Analysis of the Relative Contribution of UVA1 and Visible Light Colour Domains in Solar Light‐induced Skin Pigmentation. This supplement was supported by a grant from L’Oreal Research and InnovationApril 2023Pages 1-2 RelatedInformation

A precise analysis of the relative contribution of UVA1 and visible light colour domains in solar light-induced skin pigmentation.

Solar light induces or aggravates hyperpigmentation issues. The contribution of UVA1, as well as visible light (VL), especially high-energy blue-violet visible (HEV) light, is now clearly established. This work aimed at determining the relative contribution of UVA1, HEV and VL wavelength bands and their sub-domains in pigmentation induction. Two clinical studies using solar simulators equipped with specific bandpass physical filters were carried out. Volunteers (FSPT III-IV) were exposed on the back to UVA1 + HEV (350-450 nm), UVA1 (350-400 nm), HEV (400-450 nm) or part of UVA1 + HEV (370-450 nm) in Study 1 (n= 27) and to VL (400-700 nm), HEV (400-450 nm), Blue (400-500 nm), Green (500-600 nm) and Green+Red (500-700 nm) domains in Study 2 (n= 25). Pigmentation level was assessed by visual scoring and colorimetry at different time points postexposure, up to Day 43. Induced pigmentation was detected in all exposed conditions, peaking at 2h and thereafter progressively decreasing but remaining persistent up to Day 43. In Study 1, UVA1 showed an additive effect with HEV, with a significant contribution coming from the Longest UVA1 rays (370-400 nm). Study 2 demonstrated that 24 h postexposure, the Blue domain accounted for 71% of VL-induced pigmentation, the HEV one for 47%, the Green one for 37% and the Green+Red one for 36%, confirming no significant effect for Red light. Altogether, these results underline the need for UVA1 photoprotection up to 400 nm and highlight the importance of protecting the skin from solar VL wavelengths and especially from HEV, Blue and Green light, to limit induced pigmentation.

Lie graph homology model for [formula omitted

This paper develops a new chain model for the commutative graph complex GC2 which takes Lie graph homology as an input. Our main technical result is the identification of a large contractible complex of (certain) tadpoles and higher genus vertices of the Feynman transform of Lie graph homology. Using this result we identify the anti-invariants of Lie graph homology in genus 2 with relations between bracketings of conjectural generators of grt1 in depth 2 modulo depth 3, unifying two a priori disparate appearances of the space of modular cusp forms in the study of graph homology.

Deep Artificial Neural Network based Blind Color Image Watermarking in YCbCr Color Domain using statistical features

Deep Artificial Neural Network based Blind Color Image Watermarking in YCbCr Color Domain using statistical features

Extended Property-level k-vertex Cardinality Constraints Model for Graph Databases

Graph databases are nowadays considered the most appropriate solution for highly connected domains. Nevertheless, the lack of a fixed schema perplexes the implementation of business rules and inhibits the usage of graph database technology in practical use cases. To tackle this challenge, we study cardinality constraints in graph databases, as their focus is on the essential component of the property graph data model - relationships between entities. This paper presents an abstract cardinality constraints model for enforcing cardinality constraints in graph databases, which represent complex graph patterns. We extend our initial k-vertex cardinality constraints model to allow the representation of cardinality constraints between a node and a subgraph with given node and/or edge properties. Second, we implement the proposed model as procedures deployed in the Neo4j Graph Database Management System (GDBMS) to prevent adding new edges that violate k-vertex cardinality constraints to the graph database. Finally, we study the performance of the implemented approach on synthetic and real datasets and analyze its performance compared to the initial model. Overall, the query execution time (QET) of the procedure increases exponentially on larger datasets. Still, the added node/edge property-level evaluation does not show a significant performance effect on the edge insertion process.

Homomorphism complexes, reconfiguration, and homotopy for directed graphs

The neighborhood complex of a graph was introduced by Lovász to provide topological lower bounds on chromatic number. More general homomorphism complexes of graphs were further studied by Babson and Kozlov. Such ‘Hom complexes’ are also related to mixings of graph colorings and other reconfiguration problems, as well as a notion of discrete homotopy for graphs. Here we initiate the detailed study of Hom complexes for directed graphs (digraphs). For any pair of digraphs graphs G and H, we consider the polyhedral complex Hom⃗(G,H) that parametrizes the directed graph homomorphisms f:G→H. This construction can be seen as a special case of the poset structure on the set of multihomomorphisms in more general categories, as introduced by Kozlov, Matsushita, and others. Hom complexes of digraphs have applications in the study of chains in graded posets and cellular resolutions of monomial ideals.We study examples of directed Hom⃗ complexes and relate their topological properties to certain graph operations including products, adjunctions, and foldings. We introduce a notion of a neighborhood complex for a digraph and prove that its homotopy type is recovered as the Hom⃗ complex of homomorphisms from a directed edge. We establish a number of results regarding the topology of directed neighborhood complexes, including the dependence on directed bipartite subgraphs, a digraph version of the Mycielski construction, as well as vanishing theorems for higher homology. The Hom⃗ complexes of digraphs provide a natural framework for reconfiguration of homomorphisms of digraphs. Inspired by notions of directed graph colorings we study the connectivity of Hom⃗(G,Tn) for Tn a tournament, obtaining a complete answer for the case of transitive Tn. If G=Tm is also a transitive tournament, we describe a connection to mixed subdivisions of dilated simplices. Finally we use paths in the internal hom objects of digraphs to define various notions of homotopy, and discuss connections to the topology of Hom⃗ complexes.

An investigation of continuous-time quantum walk on hypercube in view of Cartesian product structure

In this paper, continuous-time quantum walk on hypercube is discussed in view of Cartesian product structure. We find that the [Formula: see text]-fold Cartesian power of the complete graph [Formula: see text] is the [Formula: see text]-dimensional hypercube, which give us new ideas for the study of quantum walk on hypercube. Combining the product structure, the spectral distribution of the graph and the quantum decomposition of the adjacency matrix, the probability amplitudes of the continuous-time quantum walker’s position at time [Formula: see text] are given, and it is discussed that the probability distribution for the continuous-time case is uniform when [Formula: see text]. The application of this product structure greatly improves the study of quantum walk on complex graphs, which has far-reaching influence and great significance.

FlexCNN: An End-to-end Framework for Composing CNN Accelerators on FPGA

With reduced data reuse and parallelism, recent convolutional neural networks (CNNs) create new challenges for FPGA acceleration. Systolic arrays (SAs) are efficient, scalable architectures for convolutional layers, but without proper optimizations, their efficiency drops dramatically for reasons: (1) the different dimensions within same-type layers, (2) the different convolution layers especially transposed and dilated convolutions, and (3) CNN’s complex dataflow graph. Furthermore, significant overheads arise when integrating FPGAs into machine learning frameworks. Therefore, we present a flexible, composable architecture called FlexCNN, which delivers high computation efficiency by employing dynamic tiling, layer fusion, and data layout optimizations. Additionally, we implement a novel versatile SA to process normal, transposed, and dilated convolutions efficiently. FlexCNN also uses a fully pipelined software-hardware integration that alleviates the software overheads. Moreover, with an automated compilation flow, FlexCNN takes a CNN in the ONNX 1 representation, performs a design space exploration, and generates an FPGA accelerator. The framework is tested using three complex CNNs: OpenPose, U-Net, and E-Net. The architecture optimizations achieve 2.3× performance improvement. Compared to a standard SA, the versatile SA achieves close-to-ideal speedups, with up to 5.98× and 13.42× for transposed and dilated convolutions, with a 6% average area overhead. The pipelined integration leads to a 5× speedup for OpenPose.

Probabilistic Coarsening for Knowledge Graph Embeddings

Knowledge graphs have risen in popularity in recent years, demonstrating their utility in applications across the spectrum of computer science. Finding their embedded representations is thus highly desirable as it makes them easily operated on and reasoned with by machines. With this in mind, we propose a simple meta-strategy for embedding knowledge graphs using probabilistic coarsening. In this approach, a knowledge graph is first coarsened before being embedded by an arbitrary embedding method. The resulting coarse embeddings are then extended down as those of the initial knowledge graph. Although straightforward, this allows for faster training by reducing knowledge graph complexity while revealing its higher-order structures. We demonstrate this empirically on four real-world datasets, which show that coarse embeddings are learned faster and are often of higher quality. We conclude that coarsening is a recommended prepossessing step regardless of the underlying embedding method used.

Using Evolutionary Algorithms to Target Complexity Levels in Game Economies

Game economies (GEs) describe how resources in games are created, transformed, or exchanged: They underpin most games and exist in different complexities. Their complexity may directly impact player difficulty. Nevertheless, neither difficulty nor complexity adjustment has been explored for GEs. Moreover, there is a lack of knowledge about complexity in GEs, how to define or assess it, and how it can be employed by automated adjustment approaches in game development to target specific complexity. We present a proof-of-concept for using evolutionary algorithms to craft targeted complexity graphs to model GEs. In a technical evaluation, we tested our first working definition of complexity in GEs. We then evaluated player-perceived complexity in a city-building game prototype through a user study and confirmed the generated GEs' complexity in an online survey. Our approach toward reliably creating GEs of specific complexity can facilitate game development and player testing but also inform and ground research on player perception of GE complexity.

Spatial–Temporal Complex Graph Convolution Network for Traffic Flow Prediction

Traffic flow prediction remains an ongoing hot topic in the field of Intelligent Transportation System. The state-of-the-art traffic flow prediction models can effectively extract both spatial and temporal features of traffic flow data, but ignore the correlation and external interference between traffic nodes. To this end, this paper proposes a novel method based on Spatial–Temporal Complex Graph Convolution Network (ST-CGCN) for traffic flow prediction. Specifically, we first constructs the distance matrix, the data correlation matrix, and the comfort measurement matrix according to the geographical locations, the historical data record, and the external interference between traffic nodes. Then, these three matrices are fused into a complex correlation matrix by introducing self-learning dynamic weights to improve the joint modeling ability of spatial–temporal features and external factors. Next, a spatial feature extraction module and a temporal feature extraction module are designed to characterize dynamic spatial–temporal features. The spatial feature extraction module consists of a graph convolution operator with a proposed complex correlation matrix and a residual unit. The temporal feature extraction module consists of a 3D convolution operator and a Long Short-Term Memory (LSTM). Experiments constructed on five real-world datasets demonstrate that the new proposed ST-CGCN is more effective than several existing deep learning based traffic flow prediction models. The key source code and data are available at https://github.com/Bounger2/ST-CGCN.

The Extension of Diagram Group over Semigroup Presentation

In this paper, we will discuss the diagram groups from union of two semigroup presentations namely 2S , =&lt; X,Y : X = Y &gt;, 3S = &lt; a,b,c : a = b, b = c,c = a, &gt; and their two complex graphs will be presented. The covering space will be determined by selecting normal subgroup from diagram group that previously obtained from 2S U3S . Finally, the number of generator and relations of the diagram group can be computed.