Graph Mapping Research Articles

Contraction criteria for incremental stability of differential systems with discontinuous right-hand sides

Incremental stability analysis, which plays a crucial role in dynamical systems, especially nonlinear systems, has attracted more and more concern for its applications in real world control systems nowadays. This paper presents a constructive approach to derive sufficient conditions for incremental exponential stability of the Filippov solutions of a class of differential systems with discontinuous right-hand sides, by introducing a sequence of continuous dynamical systems which is uniformly contracting and approximating the Filippov systems in terms of the evolution map graphs. Afterwards, several applications of the derived theoretical results are explored. Some specific classes of control dynamical systems with discontinuous right-hand sides are studied and relative detailed conditions are presented to show the power of the present approach to investigate the stability of switched dynamical systems, Hopfield neural network with discontinuous activations and sliding mode control.

Birkhoff centre and backward limit points

We suggest one complete and one partial solution to the selected problems presented in the recently published article On Backward Attractors of Interval Maps (Hantáková and Roth (2021) [15]). Specifically we prove a conjecture proposing a characterisation of sets of β-limit points (i.e. limit points of all accumulation points of backward orbit branches of a specific point) for graph maps. We show that β-limit sets coincide with Birkhoff centre Rec(f)‾ and that the condition for a point to belong to its β-limit set is equivalent to belonging to the β-limit set of an other point.In the second part of the paper we deal with genericity of having all sα-limit sets closed and we prove that maps with not all sα-limit sets closed are dense in C0([0,1]), which partially solves an open problem also suggested in the aforementioned article.

GMOM: An Offloading Method of Dependent Tasks Based on Deep Reinforcement Learning

Mobile edge computing (MEC) is considered as an effective solution to delay-sensitive services, and computing offloading, the central technology in MEC, can expand the capacity of resource-constrained mobile terminals (MTs). However, because of the interdependency among applications, and the dynamically changing and complex nature of the MEC environment, offloading decision making turns out to be an NP-hard problem. In the present work, a graph mapping offloading model (GMOM) based on deep reinforcement learning (DRL) is proposed to address the offloading problem of dependent tasks in MEC. Specifically, the MT application is first modeled into a directed acyclic graph (DAG), which is called a DAG task. Then, the DAG task is transformed into a subtask sequence vector according to the predefined order of priorities to facilitate processing. Finally, the sequence vector is input into an encoding-decoding framework based on the attention mechanism to obtain the offloading strategy vector. The GMOM is trained using the advanced proximal policy optimization (PPO) algorithm to minimize the comprehensive cost function including delay and energy consumption. Experiments show that the proposed model has good decision-making performance, with verified effectiveness in convergence, delay, and energy consumption.

Trends in research related to menopausal hormone therapy from 2000 to 2021: A bibliometric analysis

We conducted the present bibliometric analysis to explore menopausal hormone therapy (MHT)-related research trends between 2000 and 2021. The Web of Science database was systematically searched from 2000 to 2021 to retrieve MHT-related publications. Visualization mapping and keyword cluster graphs were utilized to illustrate the research topics and hotpots. We included 11,616 MHT-related publications for this bibliometric analysis. The results showed that (1) MHT-related research had a very slow increase in the past 22 years, and the trend fluctuated. Sum of times cited and average citations per item had the same trend: a sharp decline from 2002 to 2003, and a rapid increase from 2003 to 2006, reaching the peak in 2006, then following a downward trend. The average H-index was 57, peaking in 2001; (2) the USA, the League of European Research Universities, and Dr. JoAann Manson from Harvard University contributed the most; (3) Menopause: The Journal of The North American Menopause Society had the most significant number of MHT-related publications; (4) the research hotpots primarily focused on MHT for treating menopausal symptoms and the impact of MHT on women's health. According to previous studies, MHT was the most effective treatment for managing vasomotor symptoms of menopause, but results from the clinical trials and observational studies regarding MHT adverse events remain inconsistent. Mechanisms are fundamental when clinical studies give conflicting results. Therefore, future studies should focus on adverse events and their mechanisms.

Directed Graph Mapping for Ventricular Tachycardia: A Comparison to Established Mapping Techniques

BackgroundUnderstanding underlying mechanism(s) and identifying critical circuit components are fundamental to successful ventricular tachycardia (VT) ablation. Directed graph mapping (DGM) offers a novel technique to identify the mechanism and critical components of a VT circuit. ObjectivesThis study sought to evaluate the accuracy of DGM in VT ablation compared with traditional mapping techniques and a commercially available automated conduction velocity mapping (ACVM) tool. MethodsPatients with structural heart disease who had undergone a VT ablation with entrainment-proven critical isthmus and a high-density electroanatomical activation map were included. Traditional mapping (TM) consisted of a combination of local activation time and entrainment mapping and was considered the gold standard for determining the VT mechanism, circuit, and isthmus location. The same local activation time values were then processed using DGM and a commercially available ACVM (Coherent Mapping, Biosense Webster) tool. The aim of this study was to compare TM vs DGM and ACVM in their ability to identify the VT mechanism, characterize the VT circuit, and locate the critical isthmus. ResultsThirty-five cases were identified. TM classified the VT mechanism as focal in 7 patients and re-entrant in 28 patients. TM classified 11 VTs as single-loop re-entry, 15 as dual-loop re-entry, 1 as complex, and 1 case was indeterminant. The overall agreement between DGM and TM for determining VT mechanism and circuit type was strong (kappa value = 0.79; P < 0.01), as was the agreement between ACVM and TM (kappa value = 0.66; P < 0.01). Both DGM and ACVM identified the putative VT isthmus in 25 (89%) of the re-entrant cases. Focal activation was correctly identified by both techniques in all cases. ConclusionsDGM is a rapid automated algorithm that has a strong level of agreement with TM for manually re-annotated VT maps.

Improved product structure for graphs on surfaces

Dujmovi\'c, Joret, Micek, Morin, Ueckerdt and Wood [J. ACM 2020] proved that for every graph $G$ with Euler genus $g$ there is a graph $H$ with treewidth at most 4 and a path $P$ such that $G\subseteq H \boxtimes P \boxtimes K_{\max\{2g,3\}}$. We improve this result by replacing "4" by "3" and with $H$ planar. We in fact prove a more general result in terms of so-called framed graphs. This implies that every $(g,d)$-map graph is contained in $ H \boxtimes P\boxtimes K_\ell$, for some planar graph $H$ with treewidth $3$, where $\ell=\max\{2g\lfloor \frac{d}{2} \rfloor,d+3\lfloor\frac{d}{2}\rfloor-3\}$. It also implies that every $(g,1)$-planar graph (that is, graphs that can be drawn in a surface of Euler genus $g$ with at most one crossing per edge) is contained in $H\boxtimes P\boxtimes K_{\max\{4g,7\}}$, for some planar graph $H$ with treewidth $3$.

Decay‐like fracture diagnosis of composite insulator based on small sample virtual expansion and radar graph mapping

AbstractDue to the complexity of test procedures and the high cost of measurements, the mechanism of the decay‐like fracture is unclear, which brings hard concepts and the small sample problem. Therefore, it is intractable to establish accurate data‐driven models. To solve the above mentioned problems, this paper proposes a data‐driven modeling method based on radar graph mapping models and virtual sample generation (Radar‐VSG). The main idea of the proposed method is to construct and select the most appropriate input features by using radar graph mapping, and to generate virtual samples by using the local outlier factor based on the isometric feature mapping algorithm (Isomap‐LOF). To verify the effectiveness of our approach, a set of 27 training samples and 127 testing samples from China Southern Power Grid was applied. Experimental results suggested the accuracy was up to 100% after adding more than 27 virtual samples, with a 4.75% improvement. And the model has the best generalisation ability for 270 virtual samples, with the root mean square error of 0.018. Compared with support vector machine and four advanced VSG methods, the proposed Radar‐VSG can achieve better performance.

Clique-Based Separators for Geometric Intersection Graphs

Let F be a set of n objects in the plane and let mathcal {G}^{times }(F) be its intersection graph. A balanced clique-based separator of mathcal {G}^{times }(F) is a set mathcal {mathcal {S}} consisting of cliques whose removal partitions mathcal {G}^{times }(F) into components of size at most delta n, for some fixed constant delta <1. The weight of a clique-based separator is defined as sum _{Cin mathcal {mathcal {S}}}log (|C|+1). Recently De Berg et al. (SIAM J. Comput. 49: 1291-1331. 2020) proved that if S consists of convex fat objects, then mathcal {G}^{times }(F) admits a balanced clique-based separator of weight O(sqrt{n}). We extend this result in several directions, obtaining the following results. (i) Map graphs admit a balanced clique-based separator of weight O(sqrt{n}), which is tight in the worst case. (ii) Intersection graphs of pseudo-disks admit a balanced clique-based separator of weight O(n^{2/3}log n). If the pseudo-disks are polygonal and of total complexity O(n) then the weight of the separator improves to O(sqrt{n}log n). (iii) Intersection graphs of geodesic disks inside a simple polygon admit a balanced clique-based separator of weight O(n^{2/3}log n). (iv) Visibility-restricted unit-disk graphs in a polygonal domain with r reflex vertices admit a balanced clique-based separator of weight O(sqrt{n}+rlog (n/r)), which is tight in the worst case. These results immediately imply sub-exponential algorithms for Maximum Independent Set (and, hence, Vertex Cover), for Feedback Vertex Set, and for q-Coloring for constant q in these graph classes.

Optimization of first-order Nicoletti boundary value problem with discrete and differential inclusions and duality

This paper is devoted to optimal control of the first-order Nicoletti boundary value problem (BVP) with discrete and differential inclusions (DFIs) and duality. First, we define Nicoletti-type problem with discrete inclusions, formulate optimality conditions for it and, based on the concept of infimal convolution, dual problems. Then, using the auxiliary discrete-approximate problem, we construct dual problems for Nicoletti DFIs and prove the duality theorems. Here, for the transition to the continuous problem, some results on the equivalence of locally adjoint mappings and support functions to the graph of set-valued mapping are proved. It turns out that the Euler–Lagrange type inclusions are ‘duality relations’ for both primal and dual problems, which means that a pair consisting of solutions to the primal and dual problems satisfies this extremal relation and vice versa. Finally, as an appication of the results obtained, we consider the first-order Nicoletti BVP with polyhedral DFIs.

Power monitoring network security situation awareness system based on Knowledge Map

When selecting network security indicators, the conventional security situational awareness system ignores the impact of operation and maintenance index and assets on network security, resulting in a small number of attack events perceived by the system when network nodes are attacked. In order to solve this problem, this research designs a power monitoring network security situational awareness system based on knowledge map. In terms of system hardware, the overall system architecture is composed of data layer, function layer and interface layer, and the data collector is used to collect network security risk data; In terms of system software, the knowledge map graph is used to describe the network security risk data. After calculating the network security vulnerability index, assets, security event compensation and operation and maintenance index, the calculation results are used as the network security index to obtain the network security situation value. The test results show that the system can reflect the attack events in all attack stages, and the number of perceived attack events is significantly more than that of the conventional system, indicating that the system can effectively perceive the security situation of the power monitoring network.

Multi-view clustering with orthogonal mapping and binary graph

The multi-view clustering problem has attracted considerable attention over recent years for the remarkable clustering performance due to exploiting complementary information from multiple views. Most existing related research work processes data in the decimal real value space that is not the most compatible space for computers. Binary code learning, also known as hashing technology, is well-known for fast Hamming distance computation, less storage requirement and accurate calculation results. The Hamming space is most enjoyed by computers because of binary/hash codes. Several studies combine multi-view clustering with binary code learning for improving clustering performance. However, there is much redundant information contained in the learned binary codes, which negatively affects the clustering performance, but these studies ignore eliminating redundant information for learning compact codes. In addition, they don’t give a unified (one-step) clustering framework with binary graph structure, which doesn’t lead to the optimal clustering result due to the information loss during the two-step process. In this paper, to cope with the two issues, we propose an orthogonal mapping binary graph method (OMBG) for the multi-view clustering problem, which makes the mapping matrix of every view orthogonalize for eliminating redundant information and embeds a binary graph structure into the unified binary multi-view clustering framework for extracting local geometric structure information of binary codes and achieving the optimal clustering result. Furthermore, we design an effective optimization algorithm based on alternating direction minimization to solve the model of OMBG. Extensive experiments performed on four frequently-used benchmark multi-view datasets illustrate the superiority of OMBG which is compared with some state-of-the-art clustering baselines.

Resource and delay aware fine-grained service offloading in collaborative edge computing

Fine-grained service offloading in collaborative edge computing can realize full use of the limited resources of edge nodes to achieve efficient parallel computing. The existing research mainly focuses on service delay but pays insufficient attention to the network status, which will easily cause unbalanced resource utilization. Therefore, we propose a resource and delay aware fine-grained service offloading mechanism. First, we propose a novel network-adaptive service graph reconstruction algorithm to reduce the complexity of service offloading and the transmission delay, which includes service graph partition, dependency conflict detection and elimination, and service graph re-creation. Next, to better balance link and node resource utilization respectively, we propose original graph-based and association graph-based service graph mapping algorithms based on graph neural networks. A goal-directed affinity-based loss function is explored for them, which aims to address the difficulty of label generation in supervised learning. We conduct extensive simulation experiments with different numbers of subtasks, edge nodes and service requests under different network resource statuses. The experimental results show that the proposed service graph reconstruction method can balance network resource utilization, while reducing the service transmission delay and algorithm execution time for complex services. Moreover, the service graph mapping algorithms can improve the resource utilization balance degree while satisfying service constraints with start-end node location, resources and delay in various scenarios, especially in the case of unbalanced user distribution. Generally, our fine-grained service offloading mechanism enables short execution time and strong scalability, and is applicable to dynamic edge networks.

Generic Structure Extraction with Bi-Level Optimization for Graph Structure Learning

Currently, most Graph Structure Learning (GSL) methods, as a means of learning graph structure, improve the robustness of GNN merely from a local view by considering the local information related to each edge and indiscriminately applying the mechanism across edges, which may suffer from the local structure heterogeneity of the graph (i.e., the uneven distribution of inter-class connections over nodes). To overcome the drawbacks, we extract the graph structure as a learnable parameter and jointly learn the structure and common parameters of GNN from the global view. Excitingly, the common parameters contain the global information for nodes features mapping, which is also crucial for structure optimization (i.e., optimizing the structure relies on global mapping information). Mathematically, we apply a generic structure extractor to abstract the graph structure and transform GNNs in the form of learning structure and common parameters. Then, we model the learning process as a novel bi-level optimization, i.e., Generic Structure Extraction with Bi-level Optimization for Graph Structure Learning (GSEBO), which optimizes GNN parameters in the upper level to obtain the global mapping information and graph structure is optimized in the lower level with the global information learned from the upper level. We instantiate the proposed GSEBO on classical GNNs and compare it with the state-of-the-art GSL methods. Extensive experiments validate the effectiveness of the proposed GSEBO on four real-world datasets.

Graphs of Stable Gauss Maps and Quine’s Theorem for Oriented 2-Manifolds

In this paper we will study the topology of the singular set of stable Gauss maps from closed orientable surfaces immersed in the 3-space from a global point of view and we will obtain a relationship between the Euler Characteristic of the regular components and the signs of the cusps.

Long-term object search using incremental scene graph updating

AbstractEffective searching for target objects in indoor scenes is essential for household robots to perform daily tasks. With the establishment of a precise map, the robot can navigate to a fixed static target. However, it is difficult for mobile robots to find movable objects like cups. To address this problem, we establish an object search framework that combines navigation map, semantic map, and scene graph. The robot updates the scene graph to achieve a long-term target search. Considering the different start positions of the robots, we weigh the distance the robot walks and the probability of finding objects to achieve global path planning. The robot can continuously update the scene graph in a dynamic environment to memorize the position relation of objects in the scene. This method has been realized in both simulation and real-world environments. The experimental results show the feasibility and effectiveness of this method.

KONFIGURASI RUANG KAWASAN PASAR HONGKONG DENGAN METODE SPACE SYNTAX

This research is based on the phenomenon of the importance of urban service spaces for tourist areas and users in them. For example, the Singkawang City service area that has been developed and is crowded with visitors is the Hongkong Market area. This area is a tourist destination in the form of a row of commercial and culinary buildings along Jl. Budi Utomo, Jl. Setia Budi and the surrounding streets. Seeing the importance of the city service space for tourist areas, it is necessary to optimize the city service space which is relatively easy for the community to cross. The purpose of this study is to find out the potential and problems of user distribution as seen from the spatial configuration of the Hongkong Market area. This study uses the space syntax to determine the achievement of the movement of visitors in the circulation space. The data analyzed by the space syntax first with the depthmapX 0.50. The results obtained from the space syntax are in the form of circulation data to determine the tendency of people to choose routes using axial map and visual graph mapping (VGA). The calculation analysis technique uses connectivity, integration, choice, step depth and intelligibility. Analysis space syntax is in the form of proposed findings by adding culinary facilities to the Traditional Area alley and Jalan Muslimin Ismail.

Asynchronous simulated annealing on the placement problem: A beneficial race condition

Race conditions, which occur when compute workers do not synchronise correctly, are considered undesirable in parallel computing, as they introduce often-unintended stochastic behaviour. This study presents an asynchronous parallel algorithm with a race condition, and demonstrates that it reaches a superior solution faster than the equivalent synchronous algorithm without the race condition. Specifically, a parallel simulated annealing algorithm that solves a graph mapping problem (placement) is used to explore this. This paper illustrates how problem size and degree of parallelism affects both the collision rate caused by the race condition, and convergence time. The asynchronous approach reaches a superior solution in half the time of the equivalent synchronous approach. The solver presented here can be applied to application deployment in distributed systems, and the concept can be applied to problems solvable by global optimisation methods, where fitness errors can be tolerated in exchange for faster execution.

Identifying Feasible and Impactful Approaches to Implementing Telehealth in Rural Washington Communities: Group Concept Mapping Study

Background The expansion of telehealth use during the COVID-19 pandemic increased access to health care services for many US residents. This is particularly true for provider-to-patient telehealth communication. In rural communities, telehealth can increase access to health care services that would otherwise be limited due to geographic and distance barriers. The adoption of telehealth in rural communities, however, has been hindered by technology barriers, lack of community awareness, and lack of provider buy-in. The purpose of this study was to explore community-identified approaches to improving telehealth access in rural North Central Washington. Objective The aim of this study was to identify, group, and rate approaches to expanding and integrating telehealth in rural communities in North Central Washington. Methods We used group concept mapping, a participant-engaged, mixed method approach, to explore participant perspectives and preferences. Purposively sampled participants were community leaders and stakeholders in rural North Central Washington. Participants brainstormed strategies for implementing and expanding community telehealth access in their community and sorted them into conceptually similar groups. Strategies were then rated by participants in terms of potential impact, feasibility, and the cost of implementation. Quantitative analyses included multidimensional scaling and hierarchical cluster analysis to produce a cluster map and pattern match graph for interpreting the community members’ ideas and preferences. Results Participant brainstorming yielded 70 strategies for implementing telehealth in rural North Central Washington. Strategies were individually sorted into groups (point map stress value 0.21), producing a 6-cluster solution. The clusters were “Community infrastructure,” “Ensuring access to telehealth technology,” “Technology infrastructure for telehealth,” “Training/awareness of telehealth,” “State- and policy-level considerations,” and “Health care systems engagement and delivery.” Participants rated “Training/awareness of telehealth” and “Health care systems engagement and delivery” to be highly impactful and feasible approaches. The “Training/awareness of telehealth” cluster included strategies such as educating community members that telehealth is an easy, reliable, convenient, and private way to access health care and providing community training on how to access health care remotely. The latter cluster, “Health care systems engagement and delivery,” included approaches that were ranked as highly feasible and impactful, such as engaging with clinics and providers on overcoming barriers to implementing telehealth services or ensuring that local health clinic staff is on board with telehealth as an alternative platform to provide services. Conclusions Strategies identified and rated by participants incorporate the importance of community engagement in telehealth implementation, including educating community members about telehealth and engaging with community health clinics to facilitate use by providers. Community partners in North Central Washington will use these findings, along with additional community survey data, broadband speed test data, and provider input, to increase access to telehealth in their rural and remote communities. Conflicts of Interest None declared.

Transfinite diameter on the graph of a polynomial mapping and the DeMarco–Rumely formula

We study Chebyshev constants and transfinite diameter on the graph of a polynomial mapping f:{{mathbb {C}}}^2rightarrow {{mathbb {C}}}^2. We show that two transfinite diameters of a compact subset of the graph (i.e., defined with respect to two different collections of monomials) are equal when the set has a certain symmetry. As a consequence, we give a new proof in {{mathbb {C}}}^2 of a pullback formula for transfinite diameter due to DeMarco and Rumely that involves a homogeneous resultant.

RRL-GAT: Graph Attention Network-Driven Multilabel Image Robust Representation Learning

Exploring the characterization laws of image data and improving the efficiency of image data characterization knowledge is essential to promote the development of the Internet of Things technology. Considering that images in the real world usually contain multiple objects, and the objects are closely dependent. For these reasons, it brings great challenges to the robust representation learning of multilabel images. In general, researchers model the relationship between objects based on a class activation map and use graph convolution to mine the dependencies between objects. However, graph structure data often contain noise, which means that the edges between nodes are sometimes not so reliable, and the relative importance of neighbors is also different. Based on this, our goal is to reduce noisy connections and false connections between objects, eliminate multilabel image representation bias, and learn robust representations. Therefore, we propose a robust representation learning method for multilabel images driven by graph attention network (RRL-GAT). Specifically, to reduce the accidental false connection of objects in the image, we propose the class attention graph convolution module (C-GAT) to mine the strong association structure between categories. Besides, for the dynamic correlation between objects in the image, we propose an adaptive graph attention convolution module (A-GAT) to capture the subtle dynamic dependencies in the image. The results on two authoritative data sets show that our method is significantly better than all current state-of-the-art methods. Besides, the visualization results show that RRL-GAT can capture the semantic relationship of a specific input image and has sufficient recognizability.