Graph-based Formalism Research Articles

Multi-part kinematic constraint prediction for automatic generation of CAD model assemblies using graph convolutional networks

This paper presents a machine learning-based approach to predict kinematic constraints between CAD models that have potentially never been assembled together before. During the learning phase, the algorithm is trained to predict the next-possible-constraints between a set of parts candidate to the assembly. Assemblies are represented in a new graph-based formalism that is capable of capturing features associated with parts, interfaces between parts and constraints between them. Using such a multi-level feature extraction strategy coupled to a state-by-state graph decomposition, the approach does not need to be trained on a large database. This formalism is used to model both the network input and output where the next-possible-constraints appear after evaluation. The core of the approach relies on a series of networks based on a link-prediction encoder–decoder architecture, integrating the capabilities of several convolutional networks trained in an end-to-end manner. A decision-making algorithm is added to post-process the output and drive the prediction process in finding one among the set of next-possible-constraints. This process is repeated until no more constraints can be added. The experimental results show that the proposed approach outperforms state-of-the-art methods on such assembly tasks. Although the state-by-state assembly algorithm is iterative, it still takes into account the whole set of parts as well as the whole set of constraints already predicted, and this makes it possible to handle constraint cycles, which is generally not possible when not considering multiple parts as input.

A graph-based formalism for surface codes and twists

A graph-based formalism for surface codes and twists

The corrected gene proximity map for analyzing the 3D genome organization using Hi-C data

BackgroundGenome-wide ligation-based assays such as Hi-C provide us with an unprecedented opportunity to investigate the spatial organization of the genome. Results of a typical Hi-C experiment are often summarized in a chromosomal contact map, a matrix whose elements reflect the co-location frequencies of genomic loci. To elucidate the complex structural and functional interactions between those genomic loci, networks offer a natural and powerful framework.ResultsWe propose a novel graph-theoretical framework, the Corrected Gene Proximity (CGP) map to study the effect of the 3D spatial organization of genes in transcriptional regulation. The starting point of the CGP map is a weighted network, the gene proximity map, whose weights are based on the contact frequencies between genes extracted from genome-wide Hi-C data. We derive a null model for the network based on the signal contributed by the 1D genomic distance and use it to “correct” the gene proximity for cell type 3D specific arrangements. The CGP map, therefore, provides a network framework for the 3D structure of the genome on a global scale. On human cell lines, we show that the CGP map can detect and quantify gene co-regulation and co-localization more effectively than the map obtained by raw contact frequencies. Analyzing the expression pattern of metabolic pathways of two hematopoietic cell lines, we find that the relative positioning of the genes, as captured and quantified by the CGP, is highly correlated with their expression change. We further show that the CGP map can be used to form an inter-chromosomal proximity map that allows large-scale abnormalities, such as chromosomal translocations, to be identified.ConclusionsThe Corrected Gene Proximity map is a map of the 3D structure of the genome on a global scale. It allows the simultaneous analysis of intra- and inter- chromosomal interactions and of gene co-regulation and co-localization more effectively than the map obtained by raw contact frequencies, thus revealing hidden associations between global spatial positioning and gene expression. The flexible graph-based formalism of the CGP map can be easily generalized to study any existing Hi-C datasets.

High-order tensor estimation via trains of coupled third-order CP and Tucker decompositions

In this work, equivalence relations between a Tensor Train (TT) decomposition and the Canonical Polyadic Decomposition (CPD)/Tucker Decomposition (TD) are investigated. It is shown that a Q-order tensor following a CPD/TD with Q>3 can be written using the graph-based formalism as a train of Q tensors of order at most 3 following the same decomposition as the initial Q-order tensor. This means that for any practical problem of interest involving the CPD/TD, there exists an equivalent TT-based formulation. This equivalence allows us to overcome the curse of dimensionality when dealing with the big data tensors. In this paper, it is shown that the native difficult optimization problems for CPD/TD of Q-order tensors can be efficiently solved using the TT decomposition according to flexible strategies that involve Q−2 optimization problems with 3-order tensors. This methodology hence involves a number of free parameters linear with Q, and thus allows to mitigate the exponential growth of parameters for Q-order tensors. Then, by capitalizing on the TT decomposition, we also formulate several robust and fast algorithms to accomplish Joint dImensionality Reduction And Factors rEtrieval (JIRAFE) for the CPD/TD. In particular, based on the TT-SVD algorithm, we show how to exploit the existing coupling between two successive TT-cores in the graph-based formalism. The advantages of the proposed solutions in terms of storage cost, computational complexity and factor estimation accuracy are also discussed.

HiePaCo: Scalable Hierarchical Exploration in Abstract Parallel Coordinates Under Budget Constraints

Abstract In exploratory visualization systems, interactions allow to manipulate a visual representation and thereby gain insight into its supporting data. The responsiveness of these interactions is crucial, but achieving it on common hardware becomes increasingly difficult with the ever-growing size of datasets. Moreover, the representation of a large dataset itself is challenging since screen space is limited and, past a certain size, the number of items exceeds the number of pixels available or may render the representation unhelpful. The focus of this paper is on multidimensional data and parallel coordinates. For the system to be scalable, we propose a multiscale representation based on hierarchical aggregation on the client-side and distributed computing on a horizontally scalable infrastructure on the server-side. Multiscale visualization builds on several levels of abstraction to provide interactive and incremental changes in the level of detail. Horizontal scalability refers to the ability to increase the resources of the computing infrastructure by connecting additional computers. This paper presents: (1) a graph-based formalism for describing multiscale representations of parallel coordinates and their interactions and (2) a client-server system with a focus+context representation for multiscale parallel coordinates and distributed computation on a remote data-intensive infrastructure. We leverage the proposed formalism to describe several design possibilities for usual interactions in parallel coordinates, hierarchical navigation, and edition. We illustrated the scalability and usage of the representation in a real-world case. Performance experiments demonstrate that on a 15-computer cluster, the prototype system can scale to billion-item datasets while preserving the interactivity for analysis.

Computing discrete Morse complexes from simplicial complexes

We consider the problem of efficiently computing a discrete Morse complex on simplicial complexes of arbitrary dimension and very large size. Based on a common graph-based formalism, we analyze existing data structures for simplicial complexes, and we define an efficient encoding for the discrete Morse gradient on the most compact of such representations. We theoretically compare methods based on reductions and coreductions for computing a discrete Morse gradient, proving that the combination of reductions and coreductions produces new mutually equivalent approaches. We design and implement a new algorithm for computing a discrete Morse complex on simplicial complexes. We show that our approach scales very well with the size and the dimension of the simplicial complex also through comparisons with the only existing public-domain algorithm for discrete Morse complex computation. We discuss applications to the computation of multi-parameter persistent homology and of extremum graphs for visualization of time-varying 3D scalar fields.

Mining Patterns from Change Logs to Support Reuse-Driven Evolution of Software Architectures

Modern software systems are subject to a continuous evolution under frequently varying requirements and changes in systems’ operational environments. Lehman’s law of continuing change demands for long-living and continuously evolving software to prolong its productive life and economic value by accommodating changes in existing software. Reusable knowledge and practices have proven to be successful for continuous development and evolution of the software effectively and efficiently. However, challenges such as empirical acquisition and systematic application of the reusable knowledge and practices must be addressed to enable or enhance software evolution. We investigate architecture change logs — mining histories of architecture-centric software evolution — to discover change patterns that 1) support reusability of architectural changes and 2) enhance the efficiency of the architecture evolution process. We model architecture change logs as a graph and apply graph-based formalism (i.e., graph mining techniques) to discover software architecture change patterns. We have developed a prototype that enables tool-driven automation and user decision support during software evolution. We have used the ISO-IEC-9126 model to qualitatively evaluate the proposed solution. The evaluation results suggest that the proposed solution 1) enables the reusability of frequent architectural changes and 2) enhances the efficiency of architecture-centric software evolution process. The proposed solution promotes research efforts to exploit the history of architectural changes to empirically discover knowledge that can guide architecture-centric software evolution.

Binary Partition Tree construction from multiple features for image segmentation

In the context of image analysis, the Binary Partition Tree (BPT) is a classical data structure for the hierarchical modelling of images at different scales. BPTs belong both to the families of graph-based models and morphological hierarchies. They constitute an efficient way to define sets of nested partitions of image support, that further provide knowledge-guided reduced research spaces for optimization-based segmentation procedures. Basically, a BPT is built in a mono-feature way, i.e. for one given image, and one given metric, by merging pairs of connected image regions that are similar in the induced feature space. Our goal is to design a new family of BPTs, dealing with the need to directly manage multiple features within its building process. Then, we propose a generalization of the BPT construction framework, allowing one to embed multiple features. The cornerstone of our approach relies on a collaborative strategy used to establish a consensus between different metrics, thus enabling to obtain a unified hierarchical segmentation space. In particular, this provides alternatives to the complex issue of metric construction from several —possibly non-comparable— features. To reach that goal, we first revisit the BPT construction algorithm to describe it in a graph-based formalism. Then, we present the structural and algorithmic evolutions and impacts when embedding multiple features in BPT construction. Final experiments illustrate how this multi-feature framework can be used to build BPTs from multiple metrics computed through the (potentially multiple) image content(s).

Application of distributed graph transformations to automated generation of control patterns for intelligent lighting systems

Designing a large infrastructure, such as a street lighting system, is a complex task itself especially in the context of Smart City and Smart Grid approaches. The problem is made even harder if it needs to be designed with control in mind. To facilitate a complex design process without losing fidelity, a graph-based formalism, namely General Environment Model (GEM), is proposed to be applied to model such an environment. Moreover, another graph-based model, namely Control Availability Graph or shortly CAG, is proposed to enable definition of routines for dynamic control of large-scale systems. Both of these models have been verified in practice, but the transition from GEM to CAG had been performed manually. In this paper, we propose a coherent, formal method of generating a control system from the graph-based environment description while taking into account the designer's decisions. An application of the generated CAG as a control system yields up to 34% of energy consumption reduction in a pilot deployment of over 3500 light points for the city of Krakow, Poland.

A new network representation of the metabolism to detect chemical transformation modules.

BackgroundMetabolism is generally modeled by directed networks where nodes represent reactions and/or metabolites. In order to explore metabolic pathway conservation and divergence among organisms, previous studies were based on graph alignment to find similar pathways. Few years ago, the concept of chemical transformation modules, also called reaction modules, was introduced and correspond to sequences of chemical transformations which are conserved in metabolism. We propose here a novel graph representation of the metabolic network where reactions sharing a same chemical transformation type are grouped in Reaction Molecular Signatures (RMS).ResultsRMS were automatically computed for all reactions and encode changes in atoms and bonds. A reaction network containing all available metabolic knowledge was then reduced by an aggregation of reaction nodes and edges to obtain a RMS network. Paths in this network were explored and a substantial number of conserved chemical transformation modules was detected. Furthermore, this graph-based formalism allows us to define several path scores reflecting different biological conservation meanings. These scores are significantly higher for paths corresponding to known metabolic pathways and were used conjointly to build association rules that should predict metabolic pathway types like biosynthesis or degradation.ConclusionsThis representation of metabolism in a RMS network offers new insights to capture relevant metabolic contexts. Furthermore, along with genomic context methods, it should improve the detection of gene clusters corresponding to new metabolic pathways.Electronic supplementary materialThe online version of this article (doi:10.1186/s12859-015-0809-4) contains supplementary material, which is available to authorized users.

Measuring the Complexity of a Higraph-based System Model: Formalism and Metrics

The exponential growing effort, cost and time investment of complex systems in modeling phase emphasize the need for a methodology, a framework and a environment to handle the system model complexity. For that, it is necessary to be able to measure the system model complexity. This paper highlights the requirements a model needs to fulfill to match human user expectations, presents a generic framework for designing complex systems, and suggests a graph-based formalism for modeling complex systems. Finally, a way to measure system model structural complexity based on Shannon theory of information is proposed and illustrated with an example.

Handling Complexity of a Model in System Design: Framework, Formalism and Metrics

Current systems complexity has reached a degree that requires addressing conception and design issues while taking into account all the necessary aspects. Therefore, one of the main challenges is the way complex system models are specified and designed. The exponential growing effort, cost, and time investment during the phase of modeling a complex systems emphasize the need for a paradigm, a framework, and an environment to handle the system model complexity. For that, it is necessary to understand the expectations of the human user of the model and his limits. This paper highlights the requirements a system model needs to fulfill to meet human user expectations. For that, it is necessary to be able to measure the system model complexity. This paper highlights the requirements a model needs to fulfill to match human user expectations, and suggests a graph-based formalism for modeling complex systems. Finally, a way to measure system model structural complexity based on Shannon theory of information is proposed.

Complexity issues in color-preserving graph embeddings

In the context of comparative analysis of protein–protein interaction graphs, we use a graph-based formalism to detect the preservation of a given protein complex (pattern graph) in the protein–protein interaction graph (target graph) of another species with respect to (w.r.t.) orthologous proteins. We give an efficient exponential-time randomized algorithm in case the occurrence of the pattern graph in the target graph is required to be exact. For approximate occurrences, we prove a tight inapproximability result and give four approximation algorithms that deal with bounded degree graphs, small ortholog numbers, linear forests and very simple yet hard instances, respectively.

Finding occurrences of protein complexes in protein–protein interaction graphs

In the context of comparative analysis of protein–protein interaction graphs, we use a graph-based formalism to detect the preservation of a given protein complex G in the protein–protein interaction graph H of another species with respect to (w.r.t.) orthologous proteins. Two problems are considered: the Exact- ( μ G , μ H ) - Matching problem and the Max- ( μ G , μ H ) - Matching problems, where μ G (resp. μ H ) denotes in both problems the maximum number of orthologous proteins in H (resp. G) of a protein in G (resp. H). Following [I. Fagnot, G. Lelandais, S. Vialette, Bounded list injective homomorphism for comparative analysis of protein–protein interaction graphs, Journal of Discrete Algorithms 6 (2) (2008) 178–191], the Exact- ( μ G , μ H ) - Matching problem asks for an injective homomorphism of G to H w.r.t. orthologous proteins. The optimization version is called the Max- ( μ G , μ H ) - Matching problem and is concerned with finding an injective mapping of a graph G to a graph H w.r.t. orthologous proteins that matches as many edges of G as possible. For both problems, we essentially focus on bounded degree graphs and extremal small values of parameters μ G and μ H .

Bounded list injective homomorphism for comparative analysis of protein–protein interaction graphs

Comparing genomic properties of multiple species at varying evolutionary distances is a powerful approach for studying biological and evolutionary principles. In the context of comparative analysis of protein–protein interaction graphs, we use a graph-based formalism to detect the preservation of a given protein complex. We show that the problem is polynomial-time solvable provided that each protein has at most two orthologs in the other species, but is hard for three. Also, we suggest ways to cope with hardness by proposing three translations of the problem into well-known combinatorial optimization problems, thereby allowing the use of many recent results in fast exponential-time algorithms. Motivated by the need for more accurate models, we conclude by giving and discussing three natural extensions of the problem.

A Graph-based Semantics For Object-oriented Programming Constructs

This paper presents a graph-based formalism for object-oriented class structure specifications. The formalism combines labelled graphs with partial orders, to adequately model the (single) inheritance relation among objects and the overriding relation between methods within derived classes. The semantics of system extension by inheritance and aggregation is then defined as colimits in a suitable category of object-oriented system specifications and their morphisms.

A Virtual Simulation-Based Prototype Tool for Designing Filling Lines

Filling lines are too complex to allow realistic models of them to be evaluated analytically. In this paper, the requirements for designing filling lines are analysed, and a directed graph-based modelling formalism which unifies object oriented analysis methods, and the 3D geometry and mechanism required for the simulation is proposed. A framework of a virtual simulation system is proposed, and the architecture and main modules of the prototyping tool are introduced. These provide an integrated tool for the design and optimisation of filling lines. Entire facilities and filling line can be modelled in the modelling and simulation environment to evaluate alternatives, and to identify physical bottlenecks. An example is given.

A graph-based formalism for RBAC

Role-Based Access Control (RBAC) is supported directly or in a closely related form, by a number of products. This article presents a formalization of RBAC using graph transformations that is a graphical specification technique based on a generalization of classical string grammars to nonlinear structures. The proposed formalization provides an intuitive description for the manipulation of graph structures as they occur in information systems access control and a precise specification of static and dynamic consistency conditions on graphs and graph transformations. The formalism captures the RBAC models published in the literature, and also allows a uniform treatment of user roles and administrative roles, and a detailed analysis of the decentralization of administrative roles.

Singularly Perturbed Bond Graph Models for Simulation of Multibody Systems

This paper develops a bond graph-based formalism for modeling multibody systems in a singularly perturbed formulation. As opposed to classical multibody modeling methods, the singularly perturbed formulation is explicit, which makes it suitable for modular simulation. Kinematic joints that couple rigid bodies are described by a set of differential equations with an order of magnitude smaller time scale than that of the system. Singularly perturbed models of joints can be used to investigate nonlinear properties of joints, such as clearance and friction. The main restriction of this approach is that the simulation may need to be computed using 64 bits precision because of the two-time scale nature of the solution. The formalism is based on developing bond graph models of an elementary set of graphical velocity-based constraint functions. This set can be used to construct bond graphs of any type of mechanical joint. Here, this set is used to develop bond graphs of several joints used in multibody systems and spatial mechanisms. Complex models of multibody systems may now be built by graphically concatenating bond graphs of rigid bodies and bond graphs of joints. The dynamic equations of the system are automatically generated from the resulting bond graph model. The dynamic equation derived from the bond graph are in explicit state space form, ready for numerical integration, and exclude the computationally intensive terms that arise from acceleration analysis.

G-Log: a graph-based query language

We introduce G-Log, a declarative query language based on graphs, which combines the expressive power of logic, the modeling power of complex objects with identity and the representation power of graphs. G-Log is a nondeterministic complete query language, and thus allows the expression of a large variety of queries. We compare G-Log to well-known deductive database languages, and find that it is the only nondeterministic and computationally complete language that does not suffer from the copy-elimination problem. G-Log may be used in a totally declarative way, as well as in a "more procedural" way. Thus, it provides an intuitive, flexible graph-based formalism for nonexpert database users.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>