Graph Mapping Research Articles

On the L 1-relaxed area of graphs of BV piecewise constant maps taking three values

Abstract Given a bounded open connected set Ω ⊂ ℝ 2 {\Omega\subset\mathbb{R}^{2}} with Lipschitz boundary, we consider the class of piecewise constant maps u taking three fixed values α , β , γ ∈ ℝ 2 {\alpha,\beta,\gamma\in\mathbb{R}^{2}} , vertices of an equilateral triangle; for any u in this class, using a weak notion of Jacobian determinant valid for BV functions, we give a precise description of Det ⁡ ( ∇ ⁡ u ) {\operatorname{Det}(\nabla\kern 0.569055ptu)} and show that the relaxed graph area of u is bounded from above by a quantity related to the flat norm of Det ⁡ ( ∇ ⁡ u ) {\operatorname{Det}(\nabla\kern 0.569055ptu)} . The provided upper bound allows to show the validity of a De Giorgi conjecture regarding the relaxed area functional when one restricts to this class of piecewise constant functions.

GCFExplainer: Global Counterfactual Explainer for Graph Neural Networks

Graph neural networks (GNNs) find applications in various domains such as computational biology, natural language processing, and computer security. Owing to their popularity, there is an increasing need to explain GNN predictions since GNNs are black-box machine learning models. One way to address this issue involves using counterfactual reasoning where the objective is to alter the GNN prediction by minimal changes in the input graph. Existing methods for counterfactual explanation of GNNs are limited to instance-specific local reasoning. This approach has two major limitations of not being able to offer global recourse policies and overloading human cognitive ability with too much information. In this work, we study the global explainability of GNNs through global counterfactual reasoning. Specifically, we want to find a small set of representative counterfactual graphs that explains all input graphs. Towards this goal, we propose GCF Explainer , a novel algorithm powered by vertex-reinforced random walks on an edit map of graphs with a greedy summary . Extensive experiments on real graph datasets show that the global explanation from GCF Explainer provides important high-level insights of the model behavior and achieves a 46.9% gain in recourse coverage, a 9.5% reduction in recourse cost compared to the state-of-the-art local counterfactual explainers. We also demonstrate that GCF Explainer generates explanations that are more consistent with input dataset characteristics, and is robust under adversarial attacks. In addition, K-GCF Explainer , which incorporates a graph clustering component into GCF Explainer , is introduced as a more competitive extension for datasets with a clustering structure, leading to superior performance in three out of four datasets in the experiments and better scalability.

Dynamic community detection algorithm based on hyperbolic graph convolution

PurposeCommunity detection is a key factor in analyzing the structural features of complex networks. However, traditional dynamic community detection methods often fail to effectively solve the problems of deep network information loss and computational complexity in hyperbolic space. To address this challenge, a hyperbolic space-based dynamic graph neural network community detection model (HSDCDM) is proposed.Design/methodology/approachHSDCDM first projects the node features into the hyperbolic space and then utilizes the hyperbolic graph convolution module on the Poincaré and Lorentz models to realize feature fusion and information transfer. In addition, the parallel optimized temporal memory module ensures fast and accurate capture of time domain information over extended periods. Finally, the community clustering module divides the community structure by combining the node characteristics of the space domain and the time domain. To evaluate the performance of HSDCDM, experiments are conducted on both artificial and real datasets.FindingsExperimental results on complex networks demonstrate that HSDCDM significantly enhances the quality of community detection in hierarchical networks. It shows an average improvement of 7.29% in NMI and a 9.07% increase in ARI across datasets compared to traditional methods. For complex networks with non-Euclidean geometric structures, the HSDCDM model incorporating hyperbolic geometry can better handle the discontinuity of the metric space, provides a more compact embedding that preserves the data structure, and offers advantages over methods based on Euclidean geometry methods.Originality/valueThis model aggregates the potential information of nodes in space through manifold-preserving distribution mapping and hyperbolic graph topology modules. Moreover, it optimizes the Simple Recurrent Unit (SRU) on the hyperbolic space Lorentz model to effectively extract time series data in hyperbolic space, thereby enhancing computing efficiency by eliminating the reliance on tangent space.

Shortcut to multipartite entanglement generation: A graph approach to boson subtractions

We propose a graph method for systematically searching for schemes that can generate multipartite entanglement in linear bosonic systems with heralding. While heralded entanglement generation offers more tolerable schemes for quantum tasks than postselected ones, it is generally more challenging to find appropriate circuits for multipartite systems. We show that our graph mapping from boson subtractions provides handy tactics to overcome the limitations in circuit designs. Within our graph framework, we identify enhanced schemes for qubit N-partite GHZ, W, and the superposition of N = 3 GHZ and W states. Furthermore, we have found a qudit N-partite GHZ state generation scheme, which requires substantially fewer particles than previous proposals. These results demonstrate the power of our approach in discovering optimized solutions for the generation of intricate heralded entangled states. We expect our method to serve as a promising tool in generating diverse entanglement.

O-221 An interpretable deep learning model for predicting the number of mature oocytes retrieved after ovarian hyperstimulation

Abstract Study question Can an interpretable deep learning model successfully predict the number of mature oocytes retrieved after ovarian hyperstimulation and provide the rationale for these predictions? Summary answer An interpretable deep learning model can successfully predict the number of mature oocytes retrieved and provide a rationale for these predictions. What is known already A number of recent studies have used classical machine learning models in order to predict the number of mature oocytes retrieved in IVF cycles, including XGBoost, RandomForests and even basic deep learning models such as feed forward networks. Although these studies predicted the number of mature oocytes with a relatively high performance, the employed methods lack insights into the rationale governing their predictions. This lack of interpretability poses an important limitation when applying these models in a clinical setting. Study design, size, duration This study was a retrospective analysis of a dataset of 6,430 ovarian stimulation cycles performed at a single center in the USA, aimed at building a deep learning based, interpretable model to predict the number of mature oocytes retrieved after ovarian hyperstimulation. Participants/materials, setting, methods An interpretable deep learning model was developed to predict the number of mature oocytes retrieved. The model was evaluated on an out-of-sample test set and compared to baseline models used in prior studies such as XGBoost and Linear Regression. Main results and the role of chance The model successfully predicted the retrieved oocyte count, with a mean absolute error (MAE) deviation of ± 3.14 oocytes from the ground truth. The model outperformed the performance of models used in previous studies such as XGBoost and Linear Regression which achieved a MAE of ± 3.16 and ±3.2 oocytes respectively on the test dataset. Parameter significance was measured by calculating how much parameters aided in the final prediction. The parameters found to be most significant in predicting the number of retrieved mature oocytes were (in order): total number of follicles, number of follicles size 12mm-15mm and number of follicles size 16-17mm. Parameters that were found to be of lower significance but still indicative were follicles larger than 18 mm and estradiol on trigger day. Surprisingly, age and basal FSH were of little significance. Most notably, the number of follicles in the 12mm -15mm bin were much more indicative than larger follicles of size 16-17mm and much more than follicles larger than 18mm. Furthermore, the model generates a transparent breakdown of the prediction for each patient, including a heat map and bar graph highlighting the factors influencing the decision making process at every step, creating a completely transparent prediction process. Limitations, reasons for caution The model was developed on training data from a single clinic, therefore requiring further data collection from diverse global locations to ensure the model’s ability to generalize. Wider implications of the findings This study demonstrates better oocyte prediction accuracy and transparency in the prediction process, surpassing previous models while also building trust. These advancements not only improve the safety of Artificial Intelligence tools for optimizing stimulation protocols but also contribute to reducing regulatory concerns surrounding their deployment in clinical settings. Trial registration number not applicable

Multiscale knowledge distillation with attention based fusion for robust human activity recognition

Knowledge distillation is an effective approach for training robust multi-modal machine learning models when synchronous multimodal data are unavailable. However, traditional knowledge distillation techniques have limitations in comprehensively transferring knowledge across modalities and models. This paper proposes a multiscale knowledge distillation framework to address these limitations. Specifically, we introduce a multiscale semantic graph mapping (SGM) loss function to enable more comprehensive knowledge transfer between teacher and student networks at multiple feature scales. We also design a fusion and tuning (FT) module to fully utilize correlations within and between different data types of the same modality when training teacher networks. Furthermore, we adopt transformer-based backbones to improve feature learning compared to traditional convolutional neural networks. We apply the proposed techniques to multimodal human activity recognition and compared with the baseline method, it improved by 2.31% and 0.29% on the MMAct and UTD-MHAD datasets. Ablation studies validate the necessity of each component.

Visual analysis of trustworthiness studies: based on the Web of Science database

Trustworthiness is the most significant predictor of trust and has a significant impact on people’s levels of trust. Most trustworthiness–related research is empirical, and while it has a long history, it is challenging for academics to get insights that are applicable to their fields of study and to successfully transfer fragmented results into practice. In order to grasp their dynamic development processes through the mapping of network knowledge graphs, this paper is based on the Web of Science database and uses CiteSpace (6.2.R4) software to compile and visualize the 1,463 publications on trustworthy studies over the past 10 years. This paper aims to provide valuable references to theoretical research and the practice of Trustworthiness. The findings demonstrate that: over the past 10 years, trustworthiness-related research has generally increased in volume; trustworthiness research is concentrated in industrialized Europe and America, with American research findings having a bigger global impact; The University of California System, Harvard University, and Yale University are among the high-production institutions; the leading figures are represented by Alexander Todorov, Marco Brambilla, Bastian Jaeger, and others; the core authors are distinguished university scholars; however, the level of cooperation of the core author needs to be improved. The primary journal for publishing research on trustworthiness is the Journal of Personality and Social Psychology and Biology Letters. In addition, the study focuses on three distinct domains, involving social perception, facial clues, and artificial intelligence.

Generalized relative interiors and generalized convexity in infinite-dimensional spaces

This paper focuses on investigating generalized relative interior notions for sets in locally convex topological vector spaces with particular attentions to graphs of set-valued mappings and epigraphs of extended-real-valued functions. We introduce, study, and utilize a novel notion of quasi-near convexity of sets that is an infinite-dimensional extension of the widely acknowledged notion of near convexity. Quasi-near convexity is associated with the quasi-relative interior of sets, which is investigated in the paper together with other generalized relative interior notions for sets, not necessarily convex. In this way, we obtain new results on generalized relative interiors for graphs of set-valued mappings in convexity and generalized convexity settings.

Global structure graph mapping for multimodal change detection

ABSTRACT Multimodal change detection (MCD) combines multiple remote sensing data sources to realize surface change monitoring, which is essential for disaster evaluation and environmental monitoring. However, due to the ‘incomparable’ features in multimodal data, traditional change detection methods for unimodal (homogenous) data no longer apply. To address this issue, this paper proposes a novel MCD method with global structure graph mapping (GSGM) which extracts the ‘comparable’ structural features between multimodal datasets and constructs a global structure graph (GSG) to express the structure information for each of the multi-temporal images, which are then cross-mapped to the other data domain. The change intensity (CI) is determined by measuring the change of GSGs after mapping and the differences between GSGs and mapped GSGs. The forward and backward CI maps (CIMs) are then fused with the latent low-rank representation method (LLRR), and the change map (CM) is obtained by threshold segmentation. Experiments on five multimodal and four unimodal datasets demonstrate the effectiveness and robustness of the proposed method (source code is made available at https://github.com/rshante0426/GSGM).

Stability mapping of bipartite tight-binding graphs with losses and gain: PTPT-symmetry and beyond.

We consider bipartite tight-binding graphs composed by N nodes split into two sets of equal size: one set containing nodes with on-site loss, the other set having nodes with on-site gain. The nodes are connected randomly with probability p. Specifically, we measure the connectivity between the two sets with the parameter α, which is the ratio of current adjacent pairs over the total number of possible adjacent pairs between the sets. For general undirected-graph setups, the non-Hermitian Hamiltonian H(γ,α,N) of this model presents pseudo-Hermiticity, where γ is the loss/gain strength. However, we show that for a given graph setup H(γ,α,N) becomes PT-symmetric. In both scenarios (pseudo-Hermiticity and PT-symmetric), depending on the parameter combination, the spectra of H(γ,α,N) can be real even when it is non-Hermitian. Then we demonstrate, for both setups, that there is a well-defined sector of the γα-plane (which grows with N) where the spectrum of H(γ,α,N) is predominantly real.

Information-integration-based optimal coverage path planning of agricultural unmanned systems formations: From theory to practice

Industrial information integration engineering (IIIE) is an innovative research subject for analyzing complicated and large-scale systems. Autonomous and efficient path coverage of unmanned systems formations is an important subject of intelligent industrial agriculture. As one typical kind of complicated systems, agricultural unmanned systems formations are urgently required to optimize their operating trajectories. In this paper, an IIIE design for coverage path planning of the agricultural unmanned systems formations is presented as an IIIE application to verify the entire performances with considering the couplings between the formations and the working environment. In this design, one key concept of field-state iteration for information coupling integration is inherited and introduced in detail. Furthermore, its simulation models were developed based on structure (unmanned system agent structure and formation structure), geometry (map model and graph theory), dynamics (unmanned system agent model and formation model), and control (formation coverage path planning, formation control and trajectory recurrence) in the practice environments. The practice results were analyzed to validate the effectiveness of the proposed information integration design. Further, this paper puts forward a coverage path planning scheme for unmanned systems formations based on the rotating beam and improved probability roadmap algorithms, which can maintain 99.8% coverage rate, 0.08% repetition rate, and 0.007% redundant coverage rate while ensuring the optimal time. Then, two types of three-dimensional practice platform software including CarSim and Gazebo, are selected to graft the proposed algorithm into agricultural tractors formation and plant protection UAVs formation respectively, and the feasibility of the algorithm is verified under the condition closest to the real environment. Multiple experimentalresults demonstrate that the algorithm proposed in this paper has superior feasibility for engineering practice.

On planarity of graphs in homotopy type theory

AbstractIn this paper, we present a constructive and proof-relevant development of graph theory, including the notion of maps, their faces and maps of graphs embedded in the sphere, in homotopy type theory (HoTT). This allows us to provide an elementary characterisation of planarity for locally directed finite and connected multigraphs that takes inspiration from topological graph theory, particularly from combinatorial embeddings of graphs into surfaces. A graph is planar if it has a map and an outer face with which any walk in the embedded graph is walk-homotopic to another. A result is that this type of planar maps forms a homotopy set for a graph. As a way to construct examples of planar graphs inductively, extensions of planar maps are introduced. We formalise the essential parts of this work in the proof assistant Agda with support for HoTT.

Metals pre–enrichment during the syn–sedimentary period of Mengxing Pb–Zn Deposit, western Yunnan, SW China: Evidence on LA–ICP–MS trace elements and S isotopes of lamellar sphalerite

The Mengxing Pb–Zn deposit, which contains up to 1.02 Mt of Pb + Zn metal with an average Pb + Zn grade of ca. 12.13 %, is a representative of sedimentary–reworked deposit in western Yunnan. The orebodies, which are strata–bound and veined, occur in the Silurian Shangrenheqiao formation. The mineralization process has been divided into sedimentary stage and hydrothermal stage. Previous research has primarily focused on the economic ores enriched during the hydrothermal stage. However, the formation of syn–sedimentary ore, responsible for metal pre–enrichment, has been largely ignored. To solve the issue above, the in–situ trace elements and mapping, as well as in–situ S isotopes analyses, were conducted on lamellar sphalerite ore, which retains the characteristics of the syn–sedimentary ore. Analysis of the trace elements revealed that the sphalerite at Mengxing are rich in Ge, Cd, As, Sb and poor in Fe, Mn, In, Sn and Co overall, suggesting a metallogenic environment of medium–low temperature. The LA–ICP–MS trace elemental mapping graph indicated that colloidal sphalerite exhibits the obvious oscillation belts. The dark zonal band of sphalerite is more enriched in Fe, Mn, Cu, Ge, As, Ag, Sb, and Pb, and depleted in Ga, Cd, and Sn, compared to the light zonal band, suggesting the various formation temperature. Based on the equation of the first principal component (PC1*) relating trace elements to mineral formation temperature, it is estimated that ore in the sedimentary stage occurred at relatively lower temperatures (174.74℃ – 203.18℃), while that of the hydrothermal stage occurred at higher temperatures (209.78℃ – 240.18℃). The S isotopic composition of sphalerite indicated a significant distinction between the sedimentary stage (δ34SVCDT = 13.29 ‰ – 37.06 ‰, with an average value of 27.97 ‰) and the hydrothermal stage (δ34SVCDT = −6.45 ‰ – 31.57 ‰, with an average of 9.01 ‰). It is hypothesized that sulfur during the early stage originated primarily from thermochemical sulfate reduction (TSR) of seawater sulfate, while sulfur during the hydrothermal stage was likely influenced by hydrothermal fluid from the deep. In conclusion, the early lamellar ores formed during the Silurian period exhibit characteristics consistent with SEDEX type mineralization, leading to initial metal pre–enrichment, followed by further enrichment of ore grade by superimposed fluid during the hydrothermal stage.

Mengukur Indeks Kepuasan Mahasiswa Fakultas Ekonomi Universitas 45 Surabaya Terhadap Variabel Layanan Akademik

This research aims to determine the quality of service at the Faculty of Economics, University 45 Surabaya. The population used as subjects in this research was 300 students from the Faculty of Economics, University 45 Surabaya. Determining the sample in this study used probability sampling with proportional sample strata. The results of the analysis using the Importance Performance Analysis (IPA) method show that the services that occur are not running effectively. In the results of the science map graph, there are variables that the faculty should pay special attention to, namely the physical evidence variable. This variable is considered important and is highly expected by students, but the performance shown is low. The variable whose performance must be maintained is the guarantee variable. The variables of responsiveness, reliability and empathy are variables with a low level of hope/importance but the existing performance has been running very well. The author's suggestion is that the faculty continue to maintain the performance of the assurance variable, concentrate more on improving the performance of the physical evidence variable and the responsiveness, reliability and empathy variables which are already running well.

GIS TOOLS IN THE CONSERVATION AND SUSTAINABLE DEVELOPMENT NATIONAL PARKS, FORESTS AND RURAL AREAS

The problem of optimising the location of crops/plots in protected areas, national parks, farmland or forests involves trying to reconcile their proper functioning with nature conservation, the preservation of unique ecosystems or sustainable development. Such areas are crucial for the preservation of biodiversity and wildlife. This paper examines and discusses the impact of land consolidation in rural areas using GIS (Geographic Information System) tools. It performs a series of network analyses to determine the real distances (following the road network) and linear distances (rectilinear distances) between habitats and farmland. A tool was also developed to automate this process. The results obtained were visualised using map compositions, tables and graphs. The implemented project had a significant beneficial effect on the change in the land structure in the analysed village. The number of registered plots decreased by 40% (from 1,189 to 711) due to the consolidation process.

DGAMDA: Predicting miRNA-disease association based on dynamic graph attention network.

MiRNA (microRNA)-disease association prediction has essential applications for early disease screening. The process of traditional biological experimental validation is both time-consuming and expensive. However, as artificial intelligence technology continues to advance, computational methods have become efficient tools for predicting miRNA-disease associations. These methods often rely on the combination of multiple sources of association data and require improved feature mining. This study proposes a dynamic graph attention-based association prediction model, DGAMDA, which combines feature mapping and dynamic graph attention mechanisms through feature mining on a single miRNA-disease association network. DGAMDA effectively solves the problems of feature heterogeneity and inadequate feature mining by previous static graph attention mechanisms and achieves high-precision feature mining and association scoring prediction. We conducted a five-fold cross-validation experiment and obtained the mean values of Accuracy, Precision, Recall, and F1-score, which were .8986, .8869, .9115, and .8984, respectively. Our proposed model outperforms other advanced models in terms of experimental results, demonstrating its effectiveness in feature mining and association prediction based on a single association network. In addition, our model can also be used to predict miRNAs associated with unknown diseases.

A mechanistic approach to weighting edge-effects in landscape connectivity assessments

ContextUnderstanding landscape functional connectivity is critical for nature conservation in fragmented landscapes. Spatially explicit graph-theoretical approaches to assessing landscape connectivity have provided a promising framework for capturing functional components driving connectivity at the landscape scale. However, existing weighting schemes used to parameterise functional connectivity in graph theory-based methods are limited with respect to their ability to capture patch-level characteristics relevant to habitat use such as edge-effects.ObjectivesWe set out to develop a new approach to weighting habitat connectivity as a function of edge-effects exerted by non-habitat patches through better delineation of edge-interior habitat transitions at the patch-level and parameterization of intra-patch movement cost at the landscape scale.MethodsWe leverage the use of raster surfaces and area-weighted exponential kernels to operationalize a mechanistic approach to computing spatially explicit edge surfaces. We integrate map algebra, graph theory and landscape resistance methods to capture connectivity for a range of species specialisms on the edge-interior spectrum. We implement our method through a set of functions in the R statistical environment.ResultThrough a real-world case study, we demonstrate that our approach, drawing on these behaviours, outperforms competing metrics when evaluating potential functional connectivity in a typically fragmented agricultural landscape. We highlight options for the optimal parameterization of graph-theoretical models.ConclusionOur method offers increased flexibility, being tuneable for interior-edge habitat transitions. This therefore represents a key opportunity that can help to re-align the fields of landscape ecology and conservation biology by reconciling patch-versus-landscape methodological stances.

Weak Graph Map Homotopy and Its Applications

Weak Graph Map Homotopy and Its Applications

Mapping Graph Homology to $$K$$-Theory of Roe Algebras

Mapping Graph Homology to $$K$$-Theory of Roe Algebras

No effects of the theta-frequency transcranial electrical stimulation for recall, attention control, and relation integration in working memory.

Recent studies have suggested that transcranial alternating current stimulation (tACS), and especially the theta-frequency tACS, can improve human performance on working memory tasks. However, evidence to date is mixed. Moreover, the two WM tasks applied most frequently, namely the n-back and change-detection tasks, might not constitute canonical measures of WM capacity. In a relatively large sample of young healthy participants (N = 62), we administered a more canonical WM task that required stimuli recall, as well as we applied two WM tasks tapping into other key WM functions: attention control (the antisaccade task) and relational integration (the graph mapping task). The participants performed these three tasks three times: during the left frontal 5.5-Hz and the left parietal 5.5-Hz tACS session as well as during the sham session, with a random order of sessions. Attentional vigilance and subjective experience were monitored. For each task administered, we observed significant gains in accuracy neither for the frontal tACS session nor for the parietal tACS session, as compared to the sham session. By contrast, the scores on each task positively inter-correlated across the three sessions. The results suggest that canonical measures of WM capacity are strongly stable in time and hardly affected by theta-frequency tACS. Either the tACS effects observed in the n-back and change detection tasks do not generalize onto other WM tasks, or the tACS method has limited effectiveness with regard to WM, and might require further methodological advancements.