Representations Of Edges Research Articles

Egocentric neural representation of geometric vertex in the retrosplenial cortex

Egocentric neural representations of environmental features, such as edges and vertices, are important for constructing a geometrically detailed egocentric cognitive map for goal-directed navigation and episodic memory. While egocentric neural representations of edges like egocentric boundary/border cells exist, those that selectively represent vertices egocentrically are yet unknown. Here we report that granular retrosplenial cortex (RSC) neurons in male mice generate spatial receptive fields exclusively near the vertices of environmental geometries during free exploration, termed vertex cells. Their spatial receptive fields occurred at a specific orientation and distance relative to the heading direction of mice, indicating egocentric vector coding of vertex. Removing physical boundaries defining the environmental geometry abolished the egocentric vector coding of vertex, and goal-directed navigation strengthened the egocentric vector coding at the goal-located vertex. Our findings suggest that egocentric vector coding of vertex by granular RSC neurons helps construct an egocentric cognitive map that guides goal-directed navigation.

Past and future of the Arctic sea ice in High-Resolution Model Intercomparison Project (HighResMIP) climate models

Abstract. We examine the past and projected changes in Arctic sea ice properties in six climate models participating in the High-Resolution Model Intercomparison Project (HighResMIP) in the Coupled Model Intercomparison Project Phase 6 (CMIP6). Within HighResMIP, each of the experiments is run using a reference resolution configuration (consistent with typical CMIP6 runs) and using higher-resolution configurations. The role of horizontal grid resolution in both the atmosphere model component and the ocean model component in reproducing past and future changes in the Arctic sea ice cover is analysed. Model outputs from the coupled historical (hist-1950) and future (highres-future) runs are used to describe the multi-model, multi-resolution representation of the Arctic sea ice and to evaluate the systematic differences (if any) that resolution enhancement causes. Our results indicate that there is not a strong relationship between the representation of sea ice cover and the ocean/atmosphere grids; the impact of horizontal resolution depends rather on the sea ice characteristic examined and the model used. However, the refinement of the ocean grid has a more prominent effect compared to the refinement of the atmospheric one, with eddy-permitting ocean configurations generally providing more realistic representations of sea ice area and sea ice edges. All models project substantial sea ice shrinking: the Arctic loses nearly 95 % of sea ice volume from 1950 to 2050. The model selection based on historical performance potentially improves the accuracy of the model projections and predicts that the Arctic will turn ice-free as early as 2047. Along with the overall sea ice loss, changes in the spatial structure of the total sea ice and its partition in ice classes are noticed: the marginal ice zone (MIZ) will dominate the ice cover by 2050, suggesting a shift to a new sea ice regime much closer to the current Antarctic sea ice conditions. The MIZ-dominated Arctic might drive development and modification of model physics and parameterizations in the new generation of general circulation models (GCMs).

Using network science to examine audio-visual speech perception with a multi-layer graph.

To examine visual speech perception (i.e., lip-reading), we created a multi-layer network (the AV-net) that contained: (1) an auditory layer with nodes representing phonological word-forms and edges connecting words that were phonologically related, and (2) a visual layer with nodes representing the viseme representations of words and edges connecting viseme representations that differed by a single viseme (and additional edges to connect related nodes in the two layers). The results of several computer simulations (in which activation diffused across the network to simulate word identification) are reported and compared to the performance of human participants who identified the same words in a condition in which audio and visual information were both presented (Simulation 1), in an audio-only presentation condition (Simulation 2), and a visual-only presentation condition (Simulation 3). Another simulation (Simulation 4) examined the influence of phonological information on visual speech perception by comparing performance in the multi-layer AV-net to a single-layer network that contained only a visual layer with nodes representing the viseme representations of words and edges connecting viseme representations that differed by a single viseme. We also report the results of several analyses of the errors made by human participants in the visual-only presentation condition. The results of our analyses have implications for future research and training of lip-reading, and for the development of automatic lip-reading devices and software for individuals with certain developmental or acquired disorders or for listeners with normal hearing in noisy conditions.

Metric based resolvability of cycle related graphs

<abstract><p>If a subset of vertices of a graph, designed in such a way that the remaining vertices have unique identification (usually called representations) with respect to the selected subset, then this subset is named as a metric basis (or resolving set). The minimum count of the elements of this subset is called as metric dimension. This concept opens the gate for different new parameters, like fault-tolerant metric dimension, in which the failure of any member of the designed subset is tolerated and the remaining subset fulfills the requirements of the resolving set. In the pattern of the resolving sets, a concept was introduced where the representations of edges must be unique instead of vertices. This concept was called the edge metric dimension, and this as well as the previously mentioned concepts belong to the idea of resolvability parameters in graph theory. In this paper, we find all the above resolving parametric sets of a convex polytope $ {F}_{♃} $ and compare their cardinalities.</p></abstract>

Simplicial Complex Neural Networks.

Graph-structured data, where nodes exhibit either pair-wise or high-order relations, are ubiquitous and essential in graph learning. Despite the great achievement made by existing graph learning models, these models use the direct information (edges or hyperedges) from graphs and do not adopt the underlying indirect information (hidden pair-wise or high-order relations). To address this issue, in this paper, we propose a general framework named Simplicial Complex Neural (SCN) network, in which we construct a simplicial complex based on the direct and indirect graph information from a graph so that all information can be employed in the complex network learning. Specifically, we learn representations of simplices by aggregating and integrating information from all the simplices together via layer-by-layer simplicial complex propagation. In consequence, the representations of nodes, edges, and other high-order simplices are obtained simultaneously and can be used for learning purposes. By making use of block matrix properties, we derive the theoretical bound of the simplicial complex filter learnt by the propagation and establish the generalization error bound of the proposed simplicial complex network. We perform extensive experiments on node (0-simplex), edge (1-simplex), and triangle (2-simplex) classifications, and promising results demonstrate the performance of the proposed method is better than that of existing graph and hypergraph network approaches.

Boundary fusion multi-scale enhanced network for gland segmentation in colon histology images

Morphological features of glands serve as essential diagnostic criteria for colon cancer, and physicians must accurately segment glands in histopathological sections to grade the cancer. However, owing to the diverse gland morphologies and blurred edges of malignant glands, the contextual representations of edges have received limited attention in current segmentation methods, leading to less-than-ideal segmentation results, particularly in malignant cases. We present an edge-based multi-scale enhanced network (BFMSE-Net) for gland segmentation to address these issues. This network is based on U-net and fuses an edge fusion module (BFM) and a multi-scale enhancement module (MSEM). The BFM extracts detailed edge features, fuses edge information, and enhances edge pixel values, which effectively facilitates the segmentation of glands with blurred edges and adhesions. MSEM can handle complex scenarios where gland size and shape significantly change because it adaptively gathers information from various receptive fields in the region of interest. The method applied to evaluate this proposed network was to compare it to current methods through experiments, applying the gland segmentation (GlaS) and colorectal adenocarcinoma gland (CRAG) datasets. The experimental results demonstrate that our proposed method achieves clear gland segmentation, with shape similarity indices of 72.617 and 69.792 on the GlaS and CRAG datasets, respectively. These results show an improvement of 20.627 and 76.978, respectively, over current state-of-the-art methods. In conclusion, BFMSE-Net, which clearly focuses on edge representation, can accurately segment various types of glands.

A Spatio-Temporal Task Allocation Model in Mobile Crowdsensing Based on Knowledge Graph

With the increasing popularity of wireless networks and the development of smart cities, the Mobile Crowdsourcing System (MCS) has emerged as a framework for automatically assigning spatiotemporal tasks to workers. The study of mobile crowdsourcing makes a valuable research contribution to community service and urban route planning. However, previous algorithms have faced challenges in effectively addressing task allocation issues with massive spatial data. In this paper, we propose a novel solution to the spatiotemporal task allocation problem using a knowledge graph. Firstly, we construct a robust spatiotemporal knowledge graph (STKG) and employ a knowledge graph embedding algorithm to learn the representations of nodes and edges. Next, we utilize these representations to build a task transition graph, which is a weighted and learning-based graph that highlights important neighbors for each task. We then apply a simplified Graph Convolutional Network (GCN) and an RNN-based model to enhance task representations and capture sequential transition patterns on the task transition graph. Furthermore, we design a similarity function to facilitate personalized task allocation. Through experimental results, we demonstrate that our solution achieves higher accuracy compared to existing approaches when tested on three real datasets. These research findings are significant as they contribute to an 18.01% improvement in spatiotemporal task allocation accuracy.

SCLMnet: A dual-branch guided network for lung and lung lobe segmentation

Lung and lung lobe segmentation are two crucial techniques for lung imaging analysis that interact in clinical settings. Lung segmentation assists physicians in comparing different images to select the most appropriate surgical plan, while lobe segmentation provides precise anatomical information to help plan surgical procedures. However, inaccurate lung segmentation edges, mis-segmented lobe boundaries, and tiny targets pose challenges. Therefore, we propose a dual-branch guided convolutional neural network, SCLMnet, for lung and lung lobe segmentation. To completely leverage the semantic information of feature maps, the first branch adds a spatial linkage module (SLM) to focus on low-level features at different spatial levels, highlighting feature representations of lung edges and lung lobe boundaries. A channel linkage module (CLM) is added by matrix inner product to model channel relations, emphasizing the relevance and similarity of feature maps and capturing the interdependency of high-level feature channels to highlight feature representations of the entire lung lobe region. Transmodal synaptic linkage (TSL) and multi-scale fusion strategy guide the feature information of the CLM and SLM and the deep features extracted by the second branch ResUNet to jointly explore useful information in chest computer tomography (CT) images. To evaluate the performance of the state-of-the-art model, we use three publicly available datasets: LUNA16, COVID-19-CT-Seg, and VESSEL12. Compared to the existing methods, SCLMnet achieves average Dice scores of 92.17%, 97.80%, and 99.12%, respectively, demonstrating remarkable performance, which suggests that lung and lung lobe segmentation using CT images with SCLMnet can play an essential role in clinical research.

Revisiting lithic edge characterization with microCT: multiscale study of edge curvature, re-entrant features, and profile geometry on Olduvai Gorge quartzite flakes

The angle and shape of lithic tool edges have long been used as a method of inferring prehistoric tool function. However, accurately measuring and characterizing edge angles of lithic tools is notoriously difficult. Studies using goniometers, calipers, or morphometrics often rely on two-dimensional representations of edges. Furthermore, there have been limited attempts to quantitatively document stone tool edges based on surface metrology, most notably edge curvature. In this study, we use microCT to capture models of the complex geometry, or ‘freeform’ surfaces, of experimental quartzite flakes from Olduvai Gorge (Tanzania) to document and mathematically calculate edge curvature using multiscalar length-scale analysis. Through this analysis, we also explore the quantification of re-entrant (overhang) features on lithic edge cross-sections. On lithic tools, especially coarse-grained rocks with complex surface topographies, such as quartzite, traditional techniques for edge angle measurement are incapable of capturing re-entrant features on edge profiles. Here we present the first archaeological study that addresses the measurement of these re-entrant features, using novel length-scale and curvature analysis methods of calculating edge angles for complex freeform surfaces. With these new methods for measuring edge angles, we can consider the impact of complex geometry, including re-entrant features, on the function of lithic tools in the past.

Automated 3D tree-ring detection and measurement from X-ray computed tomography

Tree ring analysis is essential to reveal the environmental information encoded in the wood structure. It provides quantitative data on the anatomical structure which can be used, for example, to measure the impact of the fluctuating environment on the tree growth, to support global vegetation models and for the dendrochronological analysis of archaeological wooden artefacts. Currently, several imaging-based methods for tree-ring detection and tree-ring feature estimation exist. However, despite advances in computer vision and edge recognition algorithms, detection of tree-rings is mostly limited to two-dimensional (2D) datasets and performed manually in some cases. This paper describes a new approach to estimate the three-dimensional (3D) structure of tree rings and their width automatically from X-ray computed tomography data. This approach relies on a modified Canny edge detection algorithm, which is capable of detecting fully connected tree-ring edges throughout the image stack. Our results show that this approach performs well on six tree species having conifer, ring-porous and diffuse-porous ring boundary structures. In our study, image denoising proved to be a critical step to achieve accurate results. A major advantage of this procedure is that it requires very little to no user interaction rendering it a reproducible procedure for tree-ring width measurements. As it also provides 3D representations of the ring edges, it also may be used in the future for the inspection of anatomical features.

Biological applications of knowledge graph embedding models.

Complex biological systems are traditionally modelled as graphs of interconnected biological entities. These graphs, i.e. biological knowledge graphs, are then processed using graph exploratory approaches to perform different types of analytical and predictive tasks. Despite the high predictive accuracy of these approaches, they have limited scalability due to their dependency on time-consuming path exploratory procedures. In recent years, owing to the rapid advances of computational technologies, new approaches for modelling graphs and mining them with high accuracy and scalability have emerged. These approaches, i.e. knowledge graph embedding (KGE) models, operate by learning low-rank vector representations of graph nodes and edges that preserve the graph's inherent structure. These approaches were used to analyse knowledge graphs from different domains where they showed superior performance and accuracy compared to previous graph exploratory approaches. In this work, we study this class of models in the context of biological knowledge graphs and their different applications. We then show how KGE models can be a natural fit for representing complex biological knowledge modelled as graphs. We also discuss their predictive and analytical capabilities in different biology applications. In this regard, we present two example case studies that demonstrate the capabilities of KGE models: prediction of drug-target interactions and polypharmacy side effects. Finally, we analyse different practical considerations for KGEs, and we discuss possible opportunities and challenges related to adopting them for modelling biological systems.

An evolutionary approach to generalized biobjective traveling salesperson problem

We consider the generalized biobjective traveling salesperson problem, where there are a number of nodes to be visited and each node pair is connected by a set of edges. The final route requires finding the order in which the nodes are visited (tours) and finding edges to follow between the consecutive nodes of the tour. We exploit the characteristics of the problem to develop an evolutionary algorithm for generating an approximation of nondominated points. For this, we approximate the efficient tours using approximate representations of the efficient edges between node pairs in the objective function space. We test the algorithm on several randomly-generated problem instances and our experiments show that the evolutionary algorithm approximates the nondominated set well.

Understanding mid-level representations in visual processing.

It is clear that early visual processing provides an image-based representation of the visual scene: Neurons in Striate cortex (V1) encode nothing about the meaning of a scene, but they do provide a great deal of information about the image features within it. The mechanisms of these "low-level" visual processes are relatively well understood. We can construct plausible models for how neurons, up to and including those in V1, build their representations from preceding inputs down to the level of photoreceptors. It is also clear that at some point we have a semantic, "high-level" representation of the visual scene because we can describe verbally the objects that we are viewing and their meaning to us. A huge number of studies are examining these "high-level" visual processes each year. Less well studied are the processes of "mid-level" vision, which presumably provide the bridge between these "low-level" representations of edges, colors, and lights and the "high-level" semantic representations of objects, faces, and scenes. This article and the special issue of papers in which it is published consider the nature of "mid-level" visual processing and some of the reasons why we might not have made as much progress in this domain as we would like.

Consistent treatment of boundaries with mortar contact formulations using dual Lagrange multipliers

Computational modelling of contact problems raises two basic questions: Which method should be used to enforce the contact conditions and how should this method be discretised? The most popular enforcement methods are the Lagrange multiplier method, the penalty method and combinations of these two. A frequently used discretisation method is the so called node-to-segment approach. However, this approach might lead to problems like jumps in contact forces, loss of convergence or failure to pass the patch test. Thus in the last few years, several segment-to-segment contact algorithms based on the mortar method were proposed. Combination of a mortar discretisation with a penalty based enforcement of the contact conditions leads to unphysical penetrations. On the other hand, a Lagrange multiplier mortar method requires additional unknowns. Hence, condensation of the Lagrange multipliers is desirable to preserve the initial size of the system of equations. This can be achieved by interpolating the Lagrange multipliers with so-called dual shape functions. Discretising two contacting bodies leads to opposed contact surface representations of finite element edges, called slave and master elements, respectively. In current versions of dual Lagrange multiplier mortar formulations an inconsistency at the boundary appears when only a part of a slave element (instead of the entire element) belongs to the contact area. We present a modified definition of the dual shape functions in such slave elements. The basic idea is to construct dual shape functions that fulfill the so-called biorthogonality condition within the contact area. This leads to consistent mortar matrices also in the boundary region. To avoid ill-conditioning of the stiffness matrix, the modified mortar matrices are weighted with appropriate weighting factors. In doing so, the corresponding modified Lagrange multiplier nodal values are of the same order as the unmodified ones. Various examples demonstrate the performance of the modified mortar contact algorithm.

Controlling Presentation Speed, Labels, and Tooltips in Interactive Animations

The experiment investigated whether controlling presentation speed as well as labels, which display the names of the currently presented nodes in interactive dynamic graphs, affects comprehension performance. Dynamic graphs are animated graphical representations of nodes and edges representing mathematical structures used to model relations between different objects over time. After being tested on spatial imagination and linguistic thinking, 111 students had to answer twelve multiple choice comprehension questions about six interactive dynamic graphs while working with them. For each question, participants were randomly assigned to one cell of a 2 (with or without a scrollbar to adjust the presentation speed of the visualization) × 2 (with labels displaying all names of the currently presented nodes in the dynamic graphs or with tooltips displaying only one node name if the mouse cursor hovers over this node) factorial design. Scrollbars, which allow adjusting the presentation speed, were rarely used and did not foster learners’ comprehension performance. Labels displaying all names of the currently presented nodes fostered learners’ comprehension performance compared to tooltips. The higher the ability for linguistic thinking of the participants, the more their comprehension performance benefited from labels. These results are consistent with the cognitive-affective theory of learning with media.

Brain responses to auditory and visual stimulus offset: Shared representations of temporal edges

Edges are crucial for the formation of coherent objects from sequential sensory inputs within a single modality. Moreover, temporally coincident boundaries of perceptual objects across different sensory modalities facilitate crossmodal integration. Here, we used functional magnetic resonance imaging in order to examine the neural basis of temporal edge detection across modalities. Onsets of sensory inputs are not only related to the detection of an edge but also to the processing of novel sensory inputs. Thus, we used transitions from input to rest (offsets) as convenient stimuli for studying the neural underpinnings of visual and acoustic edge detection per se. We found, besides modality-specific patterns, shared visual and auditory offset-related activity in the superior temporal sulcus and insula of the right hemisphere. Our data suggest that right hemispheric regions known to be involved in multisensory processing are crucial for detection of edges in the temporal domain across both visual and auditory modalities. This operation is likely to facilitate cross-modal object feature binding based on temporal coincidence.

Singularity and corner effects in a boundary element model for a short, linearly magnetic conducting cylinder

An impedance boundary condition, boundary integral equation formulation is presented for the eddy currents induced in a magnetically linear conducting body having rotational symmetry. The treatment of kernel singularities and the representations of sharp edges are examined. A numerical treatment based on Chiba’s method is outlined. This method can be used to estimate correct values for the singular terms that can occur in the boundary integral equations. Two different representations of sharp edges are compared. The recommended representation is one in which well-defined normal directions are obtained everywhere on the conductor boundary. Numerical results are presented for the case of a short, conducting disk in a uniform, axially directed, time harmonic source field. It is shown that when the sharp edge is inadequately handled, the computed current density and power loss can be significantly in error.

Polar-vector representations of edges in pictures

By representing an edge in a picture by a sequence of polar vectors, we obtain a compact and versatile description that readily lends itself to a variety of picture processing operations, including edge smoothing, finding the convex hull, measuring area and perimeter and skeletonising/grassfire algorithms.