Equivalent Graph Research Articles

Type synthesis of deployable and symmetrical single-loop mechanisms for constructing aerospace platforms

This paper presents a general synthesis method for 1-DOF single-loop mechanisms (SLMs). This method divides an SLM into two portions: one is a revolute pair and another is a branch chain consisting of several kinematic pairs. The core idea is to design several kinematic pairs in the branch chain without constraining the rotation of the revolute pair. First, the constraint line graph of this revolute pair is drawn. The constraints of the branch chain are classified according to the equivalent constraint line graph of this revolute pair. Subsequently, the synthesis schemes corresponding to these constraints are formulated. Deployable and symmetrical SLMs are constructed, which include not only novel SLMs such as RS1P1RS3RS2P2R, and Rc1Rc2PRc2′Rc1′, but also classical SLMs such as Bennett and Bricard SLMs. It verifies the feasibility and effectiveness of the method. Finally, based on the overconstrained SLMs, another approach for obtaining more deployable non-overconstrained SLMs is proposed. By this approach, some non-overconstrained 7R SLMs are also obtained. Three examples are given to illustrate the potential applications of the obtained SLMs.

Text-based automatic personality prediction using KGrAt-Net: a knowledge graph attention network classifier

Nowadays, a tremendous amount of human communications occur on Internet-based communication infrastructures, like social networks, email, forums, organizational communication platforms, etc. Indeed, the automatic prediction or assessment of individuals’ personalities through their written or exchanged text would be advantageous to ameliorate their relationships. To this end, this paper aims to propose KGrAt-Net, which is a Knowledge Graph Attention Network text classifier. For the first time, it applies the knowledge graph attention network to perform Automatic Personality Prediction (APP), according to the Big Five personality traits. After performing some preprocessing activities, it first tries to acquire a knowing-full representation of the knowledge behind the concepts in the input text by building its equivalent knowledge graph. A knowledge graph collects interlinked descriptions of concepts, entities, and relationships in a machine-readable form. Practically, it provides a machine-readable cognitive understanding of concepts and semantic relationships among them. Then, applying the attention mechanism, it attempts to pay attention to the most relevant parts of the graph to predict the personality traits of the input text. We used 2467 essays from the Essays Dataset. The results demonstrated that KGrAt-Net considerably improved personality prediction accuracies (up to 70.26% on average). Furthermore, KGrAt-Net also uses knowledge graph embedding to enrich the classification, which makes it even more accurate (on average, 72.41%) in APP.

Unsupervised Feature Selection Using Iterative Shrinking and Expansion Algorithm

In this article, we propose an unsupervised feature selection algorithm based on the recently developed shrinking and expansion algorithm (SEA). The SEA is already an established, efficient algorithm to identify dense subgraphs within a weighted graph. To conduct SEA on a weighted graph, the dataset is first mapped onto an equivalent graph notation where each vertex corresponds to a feature, and the weight of each edge represents the normalized mutual information between the associated two features that form the edge. As a result, the feature selection problem is presented as the best way to obtain several dense sub-feature spaces by using the SEA on a weighted feature graph. The proposed feature selection algorithm consists of a two-stage structure, in which the first stage is utilized to find a number of dense feature subgraphs, whereas the second stage is used to identify a representative feature from each of these feature subgraphs. The main advantage of the proposed algorithm is that the users are not required to provide the number of features to be selected, which is a major flaw in most of the existing algorithms. The current findings from the researchers' method are better than the other state-of-the-art algorithms because the feature selection process identifies approximately one-fifth to one-third of the number of original features while providing a high accuracy score. The superiority of the proposed algorithm over the other conventional methods of feature selection is established for a number of real-life datasets. In addition, the performance of the proposed feature selection algorithm is also found to be better than other algorithms in one of the innovative application areas of computational intelligence such as ambient intelligence.

LMI-based [formula omitted] boundary practical consensus control for nonlinear multi-agent systems with actuator saturation

This paper mainly addresses the practical consensus problem of nonlinear multi-agent systems modeled by reaction–diffusion equations subject to the bounded external disturbances. Different from the existing consensus control methods associated with spatiotemporal dynamics, the proposed H∞ Neumann boundary controller based on distributed measurement data can guarantee the optimal disturbance attenuation performance under the actuator saturation. Initially, a consensus spatiotemporal error model is constructed by introducing the Kronecker product and equivalent directed graph. Subsequently, a linear matrix inequalities (LMIs)-based sufficient condition is derived by combining the improved Lyapunov-based approach and H∞ norm. Then, an optimization problem is proposed by applying invariant set, such that the consensus errors can converge to a minimized bounded region in the presence of actuator saturation. Finally, comparison simulations on the synchronization of FitzHugh–Nagumo (FHN) model are given to demonstrate the effectiveness of proposed methodology.

Universal Graph Filter Design Based on Butterworth, Chebyshev, and Elliptic Functions

Graph filters are crucial tools in processing the spectrum of graph signals. In this paper, we propose to design universal IIR graph filters with low computational complexity by using three kinds of functions, which are Butterworth, Chebyshev, and elliptic functions, respectively. Specifically, inspired by the classical analog filter design method, we first derive the zeros and poles of graph frequency responses. With these zeros and poles, we construct the conjugate graph filters to design the Butterworth high-pass graph filter, Chebyshev high-pass graph filter, and elliptic high-pass graph filter, respectively. On this basis, we further propose to construct a desired graph filter of low pass, band pass, and band stop by mapping the parameters of the desired graph filter to those of the equivalent high-pass graph filter. Furthermore, we propose to set the graph filter order given the maximum passband attenuation and the minimum stopband attenuation. Our numerical results show that the proposed graph filter design methods realize the desired frequency response more accurately than the autoregressive moving average graph filter design method, the linear least-squares fitting-based graph filter design method, and the Chebyshev FIR polynomial graph filter design method.

Abacus proofs of Schur expansions of Macdonald polynomials

A famous problem in symmetric function theory is to find combinatorial formulas for Schur expansions of the Macdonald polynomials H ~ μ \tilde {H}_{\mu } . One such formula, valid for μ \mu satisfying μ 1 ≤ 3 \mu _1\leq 3 and μ 2 ≤ 2 \mu _2\leq 2 , involves Yamanouchi words weighted by Haglund’s statistics inv μ \operatorname {inv}_{\mu } and maj μ \operatorname {maj}_{\mu } . Previous proofs of this formula use the technical machinery of crystals and dual equivalence graphs. We give a new, elementary, and fully bijective proof of this formula based on the abacus model for antisymmetrized Macdonald polynomials. An extension to the Schur expansion of s ν H ~ μ s_{\nu }\tilde {H}_{\mu } is also provided.

Leveraging structural properties of source code graphs for just-in-time bug prediction

The most common use of data visualization is to minimize the complexity for proper understanding. A graph is one of the most commonly used representations for understanding relational data. It produces a simplified representation of data that is challenging to comprehend if kept in a textual format. In this study, we propose a methodology to utilize the relational properties of source code in the form of a graph to identify Just-in-Time (JIT) bug prediction in software systems during different revisions of software evolution and maintenance. We presented a method to convert the source codes of commit patches to equivalent graph representations and named it Source Code Graph (SCG). To understand and compare multiple source code graphs, we extracted several structural properties of these .graphs, such as the density, number of cycles, nodes, edges, etc. We then utilized the attribute values of those SCGs to visualize and detect buggy software commits. We process more than 246 K software commits from 12 subject systems in this investigation. Our investigation on these 12 open-source software projects written in C++ and Java programming languages shows that if we combine the features from SCG with conventional features used in similar studies, we will get the increased performance of Machine Learning (ML) based buggy commit detection models. We also find the increase of F1 Scores in predicting buggy and non-buggy commits statistically significant using the Wilcoxon Signed Rank Test. Since SCG-based feature values represent the style or structural properties of source code updates or changes in the software system, it suggests the importance of careful maintenance of source code style or structure for keeping a software system bug-free.

Global aspects of measure preserving equivalence relations and graphs

This paper is an introduction and survey of a “global” theory of measure preserving equivalence relations and graphs. In this theory one views a measure preserving equivalence relation or graph as a point in an appropriate topological space and then studies the properties of this space from a topological, descriptive set theoretic and dynamical point of view.

A Graph Theory of Rook Placements

Two boards are rook equivalent if they have the same number of non-attacking rook placements for any number of rooks. Define a rook equivalence graph on an equivalence class of Ferrers boards by specifying that two boards are connected by an edge if you can obtain one of the boards by moving squares in the other board out of one column and into a single other column. Given such a graph, we characterize which boards will yield connected graphs. We also provide some cases where common graphs will or will not be the graph for some set of rook equivalent Ferrers boards. Finally, we extend this graph definition to the m-level rook placement generalization developed by Briggs and Remmel. This yields a graph on the set of rook equivalent singleton boards, and we characterize which singleton boards give rise to a connected graph.

Robinson–Schensted correspondence for unit interval orders

The Stanley-Stembridge conjecture associates a symmetric function to each natural unit interval order $\mathcal P$. In this paper, we define relations \`a la Knuth on the symmetric group for each $\mathcal P$ and conjecture that the associated $\mathcal P$-Knuth equivalence classes are Schur-positive, refining theorems of Gasharov, Brosnan-Chow, and Guay-Paquet. The resulting equivalence graphs fit into the framework of D graphs studied by Assaf. Furthermore, we conjecture that the Schur expansion is given by column-readings of $\mathcal P$-tableaux that occur in the equivalence class. We prove these conjectures for $\mathcal P$ avoiding two specific suborders by introducing $\mathcal P$-analog of Robinson-Schensted insertion, giving an answer to a long standing question of Chow.

Optimal Task Assignment for Integrated Cloud and Edge Networks With Tree Topology

The rapid growth of mobile applications and the Internet of Things generates a huge amount of data that can hardly be processed by end devices. Recently, Integrated Cloud and Edge (ICE) networks have been proposed to support smart applications and services by leveraging both remote clouds and edge clusters. However, task assignment over ICE networks has been proved NP-hard, which makes it challenging in practice. In this work, we discover that a polynomial-time optimal solution does exist for the task assignment problem when the ICE network is organized with tree topology. Specifically, the studied problem for the ICE network with tree topology is transformed into an equivalent graph optimization problem. Theoretical analysis is then provided to find the polynomial-time optimal solution. Evaluation results demonstrate the correctness and efficiency of the discovered solution.

Rockfall susceptibility and network-ranked susceptibility along the Italian railway

Rockfalls pose a substantial threat to ground transportation, due to their rapidity, destructive potential and high probability of occurrence on steep topographies, often found along roads and railway routes. Approaches for the assessment of rockfall susceptibility range from purely phenomenological methods and statistical methods, suitable for modeling large areas, to purely deterministic ones, usually easier to use in local analyses. A common requirement is the need to locate potential detachment points, often found uphill on cliffs, and the subsequent assessment of the runout areas of rockfalls stemming from such points.Here, we apply a physically based model for the calculation of rockfall trajectories along the whole Italian railway network, within a corridor of total length of about 17,000 km and varying width. We propose a data-driven method for the location of rockfall source points based on expert mapping of potential source areas on sample representative locations. Using empirical distributions of gridded slope angle values in source areas mapped by experts, we derived probabilistic maps of rockfall sources in the proximity of the railway network, regardless of a particular trigger.Source areas act as starting points of simulated trajectories within the three-dimensional model STONE. The program provides a pixel-by-pixel trajectory count, covering 24,500 km2 and representing the largest homogeneous application of the model to date. We classified the raster map into a vector susceptibility map, analyzing the railway track as a collection of segments, for which we provide segment-wise rockfall susceptibility.Eventually, we considered an equivalent graph representation of the network, which helps classifying the segments both on the basis of rockfall susceptibility and the role of each segment in the network, resulting in a network-ranked susceptibility. Both maps are useful for subsequent hazard assessment, and to prioritize safety improvements along the railway, at national scale.

The Role of Instrumental Variables in Causal Inference Based on Independence of Cause and Mechanism.

Causal inference methods based on conditional independence construct Markov equivalent graphs and cannot be applied to bivariate cases. The approaches based on independence of cause and mechanism state, on the contrary, that causal discovery can be inferred for two observations. In our contribution, we pose a challenge to reconcile these two research directions. We study the role of latent variables such as latent instrumental variables and hidden common causes in the causal graphical structures. We show that methods based on the independence of cause and mechanism indirectly contain traces of the existence of the hidden instrumental variables. We derive a novel algorithm to infer causal relationships between two variables, and we validate the proposed method on simulated data and on a benchmark of cause-effect pairs. We illustrate by our experiments that the proposed approach is simple and extremely competitive in terms of empirical accuracy compared to the state-of-the-art methods.

Testing Piecewise Structural Equations Models in the Presence of Latent Variables and Including Correlated Errors

ABSTRACT Path models, expressed as Directed Acyclic Graphs (DAGs), and the testing of such DAGs via a d-sep test, have become popular because they can incorporate complicated data structures that are difficult or impossible to accommodate in classical structural equation modeling. However, d-sep tests cannot accommodate DAGs that include unmeasured (latent) variables. We describe (i) how to convert a DAG with latent variables into an observationally equivalent graph without latents (a Mixed Acyclic Graph, MAG), (ii) how this MAG identifies which latents can/cannot be ignored without changing the causal meaning of the original DAG, and (iii) how to perform the MAG equivalent of a d-sep test.

The Number of Matching Equivalent for the Union Graph of Vertices and Cycles

For two graphs G and H, if G and H have the same matching polynomial, then G and H are said to be matching equivalent. We denote by δ (G), the number of the matching equivalent graphs of G. In this paper, we give δ (sK1 ∪ t1C9 ∪ t2C15), which is a generation of the results of in [1].

A New Method for Type Synthesis of 2R1T and 2T1R 3-DOF Redundant Actuated Parallel Mechanisms with Closed Loop Units

The current type synthesis of the redundant actuated parallel mechanisms is adding active-actuated kinematic branches on the basis of the traditional parallel mechanisms, or using screw theory to perform multiple getting intersection and union to complete type synthesis. The number of redundant parallel mechanisms obtained by these two methods is limited. In this paper, based on Grassmann line geometry and Atlas method, a novel and effective method for type synthesis of redundant actuated parallel mechanisms (PMs) with closed-loop units is proposed. Firstly, the degree of freedom (DOF) and constraint line graph of the moving platform are determined successively, and redundant lines are added in constraint line graph to obtain the redundant constraint line graph and their equivalent line graph, and a branch constraint allocation scheme is formulated based on the allocation criteria. Secondly, a scheme is selected and redundant lines are added in the branch chains DOF graph to construct the redundant actuated branch chains with closed-loop units. Finally, the branch chains that meet the requirements of branch chains configuration criteria and F&C (degree of freedom & constraint) line graph are assembled. In this paper, two types of 2 rotational and 1 translational (2R1T) redundant actuated parallel mechanisms and one type of 2 translational and 1 rotational (2T1R) redundant actuated parallel mechanisms with few branches and closed-loop units were taken as examples, and 238, 92 and 15 new configurations were synthesized. All the mechanisms contain closed-loop units, and the mechanisms and the actuators both have good symmetry. Therefore, all the mechanisms have excellent comprehensive performance, in which the two rotational DOFs of the moving platform of 2R1T redundant actuated parallel mechanism can be independently controlled. The instantaneous analysis shows that all mechanisms are not instantaneous, which proves the feasibility and practicability of the method.

TAN modelling of HH-shape microstrip interconnect tree

This paper develops an unfamiliar modelling of printed circuit board (PCB) interconnect behaving as HH-tree. The developed model is based on the tensorial analysis of networks (TAN) formalism. The HH-tree is implemented with the equivalent LC-network based on Hammerstad-Jensen modelling. The unfamiliar TAN methodology is described by starting from the equivalent graph topology. The HH-tree TAN model is established from the branch and mesh spaces implementation of voltage, current and impedance tensorial objects. Then, the HH-tree PCB problem is reformulated with the tensorial electrical system metric. The solution of the metric problem is validated with commercial tool simulation from DC up to 2.5 GHz with a microstrip circuit proof-of-concept. As expected, computed and simulated results are in good agreement.

PP-OCQ: A distributed privacy-preserving optimal closeness query scheme for social networks

Optimal closeness query in social networks requires obtaining the social datasets from each user so that he/she finds out a shortest social distance with any target user. For example, we can make friends in terms of the most similar social relationship of family background, education level and hobbies etc. Unfortunately, social data concerning user’s attributes might reveal personal sensitive information and be exploited maliciously. Considering the above privacy-revealing issues, this paper proposes a Privacy-Preserving Optimal Closeness Query (PP-OCQ) scheme, which achieves the secure optimal closeness query in a distributed manner without revealing the users’ sensitive information. We construct an equivalent cost graph where all users’ information are encrypted by his/her public key and the data are authenticated by signature. It employs the ElGamal Cryptosystem to achieve the privacy protection in social networks, and gives an optimal closeness query protocol without leaking the users’ sensitive information on homomorphic user ciphertexts. Then it follows the routing protocol, distributed Bellman-Ford shortest-paths protocol, to query the optimal closeness through the users’ message propagation in multiple iterations. The direction of propagation is controlled by some indicators so that each user performs corresponding operations based on homomorphism property and fails to obtain other user’s information due to the masking of random numbers. Our analysis and simulations show that the proposed scheme is efficient in terms of computation cost and communication overhead.

Affine Equivalence and Saddle Connection Graphs of Half-Translation Surfaces

AbstractTo every half-translation surface, we associate a saddle connection graph, which is a subgraph of the arc graph. We prove that every isomorphism between two saddle connection graphs is induced by an affine homeomorphism between the underlying half-translation surfaces. We also investigate the automorphism group of the saddle connection graph and the corresponding quotient graph.

Mapping graph state orbits under local complementation

Graph states, and the entanglement they posses, are central to modern quantum computing and communications architectures. Local complementation – the graph operation that links all local-Clifford equivalent graph states – allows us to classify all stabiliser states by their entanglement. Here, we study the structure of the orbits generated by local complementation, mapping them up to 9 qubits and revealing a rich hidden structure. We provide programs to compute these orbits, along with our data for each of the 587 orbits up to 9 qubits and a means to visualise them. We find direct links between the connectivity of certain orbits with the entanglement properties of their component graph states. Furthermore, we observe the correlations between graph-theoretical orbit properties, such as diameter and colourability, with Schmidt measure and preparation complexity and suggest potential applications. It is well known that graph theory and quantum entanglement have strong interplay – our exploration deepens this relationship, providing new tools with which to probe the nature of entanglement.