Internal Edges Research Articles

Research on construction method of command and control network model based on complex network theory

AbstractThe command and control (C2) network is a complete organizational system that connects operational units at all levels based on command relationships. Its purpose is to ensure that the C2 system can fully perform its command functions, achieving high precision and efficiency in decision‐making. As warfare models evolve rapidly from network‐centric warfare to multi‐domain operations, traditional C2 networks, which utilize a tree structure for connectivity, exhibit only a single hierarchical relationship, making it challenging for different operational units at the same level to interconnect. Furthermore, with the diversification of warfare, the three types of nodes in traditional C2 network models are insufficient to encompass all operational units. In response, this paper proposes a method for edge weighting in C2 networks based on a combination of node attributes and network attributes described by complex network theory. The node attributes mainly include node information transmission capacity, task coordination ability between nodes, node distance, and response time. The network attributes are primarily represented by hierarchy and betweenness centrality. Additionally, the traditional C2 network model's three types of nodes are expanded to five types of nodes. Based on the edge weighting method, internal command edges, inter‐network collaborative edges, and cross‐level command edges are generated within the C2 network. Simulation results demonstrate that the constructed C2 network model's characteristic parameters are superior to those of traditional C2 networks and collaborative C2 networks. This improvement enhances command and coordination abilities, aligns more closely with real‐world scenarios, and effectively improves network command and control efficiency.

The conjecture on distance-balancedness of generalized Petersen graphs holds when internal edges have jumps 3 or 4

The conjecture on distance-balancedness of generalized Petersen graphs holds when internal edges have jumps 3 or 4

Effect of Ultraviolet-C Light Exposure Time on the Dimensional Stability of Addition Silicone Dental Impressions: An In Vitro Study.

To compare the effect of different ultraviolet-C (UV-C) light exposure times on the dimensional stability of addition silicone dental impressions. The dimensional stability of the addition silicone dental impressions was assessed by measuring specific dimensions on dental casts that were recovered from an upper acrylic resin model of dental implants. The impressions were reproduced using a customized tray adapted in a three-point simplex dental articulator permitting only opening and closing movements. Addition silicone dental impressions were divided into five groups (N = 12) according to the UV-C light exposure time. Group A was untreated; group B received 10 minutes; group C, 20 minutes; group D, 30 minutes; and group E, 40 minutes. All the impressions were poured with type IV dental stone and the internal edges of the upper silicone retainers of impression copings were used as five reference points (E, D, C, B, and A) to determine six linear measurements between ED, CB, EA, AD, EB, and CD points using a traveling microscope of 0.001 mm accuracy. One-way analysis of variance (ANOVA) was used for the statistical analysis (p < 0.05). Expansion and contraction were noted among ED, CB, EA, and EB measurements, whereas only expansion was noted among AD and CD measurements. The ANOVA analysis showed there was no significant difference in the arithmetic means for the measurements between and within group A and the other groups (p > 0.05). The UV-C light exposure time of 10, 20, 30, and 40 minutes did not have any negative effect on the dimensional stability of the addition silicone dental impressions evaluated. In the daily routine dental practice, dental impressions need to be washed and disinfected immediately after making to prevent cross-infections. The UV-C light has been proposed as a promising method for disinfection, but only a few studies have been published about its effect on the dimensional stability of dental silicones. How to cite this article: Bravo-Cueto AG, Tinedo-López PL, Malpartida-Carrillo V. Effect of Ultraviolet-C Light Exposure Time on the Dimensional Stability of Addition Silicone Dental Impressions: An In Vitro Study. J Contemp Dent Pract 2024;25(6):507-513.

Chromatic symmetric functions and polynomial invariants of trees

AbstractStanley asked whether a tree is determined up to isomorphism by its chromatic symmetric function. We approach Stanley's problem by studying the relationship between the chromatic symmetric function and other invariants. First, we prove Crew's conjecture that the chromatic symmetric function of a tree determines its generalized degree sequence, which enumerates vertex subsets by cardinality and the numbers of internal and external edges. Second, we prove that the restriction of the generalized degree sequence to subtrees contains exactly the same information as the subtree polynomial, which enumerates subtrees by cardinality and number of leaves. Third, we construct arbitrarily large families of trees sharing the same subtree polynomial, proving and generalizing a conjecture of Eisenstat and Gordon.

One-loop integrals from volumes of orthoschemes

Recently in arXiv:2012.05599 Rudenko presented a formula for the volume of hyperbolic orthoschemes in terms of alternating polylogarithms. We use this result to provide an explicit analytic result for the one-loop scalar n-gon Feynman integral in n dimensions, for even n, with massless or massive internal and external edges. Furthermore, we evaluate the general six-dimensional hexagon integral in terms of classical polylogarithms.

Collaborative Multi-Metadata Fusion to Improve the Classification of Lumbar Disc Herniation.

Computed tomography (CT) images are the most commonly used radiographic imaging modality for detecting and diagnosing lumbar diseases. Despite many outstanding advances, computer-aided diagnosis (CAD) of lumbar disc disease remains challenging due to the complexity of pathological abnormalities and poor discrimination between different lesions. Therefore, we propose a Collaborative Multi-Metadata Fusion classification network (CMMF-Net) to address these challenges. The network consists of a feature selection model and a classification model. We propose a novel Multi-scale Feature Fusion (MFF) module that can improve the edge learning ability of the network region of interest (ROI) by fusing features of different scales and dimensions. We also propose a new loss function to improve the convergence of the network to the internal and external edges of the intervertebral disc. Subsequently, we use the ROI bounding box from the feature selection model to crop the original image and calculate the distance features matrix. We then concatenate the cropped CT images, multiscale fusion features, and distance feature matrices and input them into the classification network. Next, the model outputs the classification results and the class activation map (CAM). Finally, the CAM of the original image size is returned to the feature selection network during the upsampling process to achieve collaborative model training. Extensive experiments demonstrate the effectiveness of our method. The model achieved 91.32% accuracy in the lumbar spine disease classification task. In the labelled lumbar disc segmentation task, the Dice coefficient reaches 94.39%. The classification accuracy in the Lung Image Database Consortium and Image Database Resource Initiative (LIDC-IDRI) reaches 91.82%.

Theory of nonlinear corner states in photonic fractal lattices

AbstractWe study linear and nonlinear higher-order topological insulators (HOTIs) based on waveguide arrays arranged into Sierpiński gasket and Sierpiński carpet structures, both of which have non-integer effective Hausdorff dimensionality. Such fractal structures possess different discrete rotational symmetries, but both lack transverse periodicity. Their characteristic feature is the existence of multiple internal edges and corners in their optical potential landscape, and the formal absence of an insulating bulk. Nevertheless, we show that a systematic geometric shift of the waveguides in the first generation of such fractal arrays, which affects the coupling strengths between sites of this building block as well as in subsequent structure generations, enables the formation of corner states of topological origin at the outer corners of the array. We find that, in contrast to HOTIs based on periodic arrays, Sierpiński gasket arrays always support topological corner states, irrespective of the direction of the shift of the waveguides, while in Sierpiński carpet structures, corner states emerge only for one direction of the waveguide shift. We also find families of corner solitons bifurcating from linear corner states of fractal structures that remain stable practically in the entire gap in which they form. These corner states can be efficiently excited by injecting Gaussian beams into the outer corner sites of the fractal arrays. Our results pave the way toward the investigation of nonlinear effects in topological insulators with non-integer dimensionality and enrich the variety of higher-order topological states.

Comparative Studies of Graphene and Phosphorene Zigzag Edge Nanoribbons with Antidots

Recently, there is much interest in narrow graphene‐like nanoribbons in view of their exceptional electronic and magnetic properties. Of special interest are ultranarrow zigzag edge nanoribbons because they can have magnetic moments at the edges. Of course, it is also well known that if there are antidots (nanopores) in a system, its physical properties are strongly affected, too. In this letter, the comparative studies of graphene and phosphorene nanoribbons are presented, with emphasis on edge as well as antidot effects. It is shown that phosphorene has quite large magnetic moments on both external and internal zigzag edges and it is a half‐metal for certain electron concentrations. So phosphorene is a very attractive material for spintronic applications.

Shape reconstruction for undetectable regions of abdominal organs based on a graph convolutional network

Although computed tomography (CT) and magnetic resonance imaging (MRI) produce high-resolution images, during surgery or radiotherapy, only low-resolution cone-beam CT and low-dimensional X-ray images are usually obtained. Furthermore, because the duodenum and stomach are filled with air, it may be hard to accurately segment their contours, even on high-resolution images. Although denoising and image enhancement can be used to assist in the segmentation and reconstruction of 3D images, some regions of organs may remain difficult to detect. To approach this issue, we propose a graph convolutional network (GCN) to reconstruct organs that are hard to detect on medical images. The method uses a framework to transform an initial template into an estimated shape of the patient’s organs based on previous information attainted from different detectable organs from different patients. To overcome the inaccurate estimation results of triangular surface mesh data with the GCN, we propose a method to add internal vertices and edges, which has the effect of improving the calculation accuracy by enhancing the topological structure of the mesh data. In this study, the organ data of 124 patients who underwent pancreatic tumor treatment were used to verify the predictive effect of the proposed method. The 3D organ contours were defined by board-certified radiation oncologists and used as the ground truth surface meshes. For 100 randomly selected detectable feature vertices, the average Euclidean distance error of the liver was 3.72 mm. The topological enhancement proposed in this study reduced the prediction error of the liver by an average of 0.84 mm.

Bananas: multi-edge graphs and their Feynman integrals

We consider multi-edge or banana graphs b_n on n internal edges e_i with different masses m_i. We focus on the cut banana graphs Im (Phi _R(b_n)) from which the full result Phi _R(b_n) can be derived through dispersion. We give a recursive definition of Im (Phi _R(b_n)) through iterated integrals. We discuss the structure of this iterated integral in detail. A discussion of accompanying differential equations, of monodromy and of a basis of master integrals is included.

Effective and efficient core computation in signed networks

With the proliferation of mobile technology and IT development, people can use social network services anywhere and anytime. Among many social network mining problems, identifying cohesive subgraphs has attracted extensive attention from different fields due to its numerous applications. The most widely used among many cohesive subgraph models is k-core, because of its simple and intuitive structure. In this paper, we formulate (p,n)-core in signed networks by extending the k-core model. (p,n)-core is designed to guarantee sufficient internal positive edges and deficient internal negative edges. We formally prove that finding an exact (p,n)-core is NP-hard. Hence, we propose three efficient and effective algorithms to find a solution. We demonstrate the superiority of our proposed algorithms using real-world and synthetic networks.

Evaluation of the Relative Performance of the Subflattenings Method for Phylogenetic Inference

The algebraic properties of flattenings and subflattenings provide direct methods for identifying edges in the true phylogeny—and by extension the complete tree—using pattern counts from a sequence alignment. The relatively small number of possible internal edges among a set of taxa (compared to the number of binary trees) makes these methods attractive; however, more could be done to evaluate their effectiveness for inferring phylogenetic trees. This is the case particularly for subflattenings, and the work we present here makes progress in this area. We introduce software for constructing and evaluating subflattenings for splits, utilising a number of methods to make computing subflattenings more tractable. We then present the results of simulations we have performed in order to compare the effectiveness of subflattenings to that of flattenings in terms of split score distributions, and susceptibility to possible biases. We find that subflattenings perform similarly to flattenings in terms of the distribution of split scores on the trees we examined, but may be less affected by bias arising from both split size/balance and long branch attraction. These insights are useful for developing effective algorithms to utilise these tools for the purpose of inferring phylogenetic trees.

Exploring novel disease-disease associations based on multi-view fusion network

Established taxonomy system based on disease symptom and tissue characteristics have provided an important basis for physicians to correctly identify diseases and treat them successfully. However, these classifications tend to be based on phenotypic observations, lacking a molecular biological foundation. Therefore, there is an urgent to integrate multi-dimensional molecular biological information or multi-omics data to redefine disease classification in order to provide a powerful perspective for understanding the molecular structure of diseases. Therefore, we offer a flexible disease classification that integrates the biological process, gene expression, and symptom phenotype of diseases, and propose a disease-disease association network based on multi-view fusion. We applied the fusion approach to 223 diseases and divided them into 24 disease clusters. The contribution of internal and external edges of disease clusters were analyzed. The results of the fusion model were compared with Medical Subject Headings, a traditional and commonly used disease taxonomy. Then, experimental results of model performance comparison show that our approach performs better than other integration methods. As it was observed, the obtained clusters provided more interesting and novel disease-disease associations. This multi-view human disease association network describes relationships between diseases based on multiple molecular levels, thus breaking through the limitation of the disease classification system based on tissues and organs. This approach which motivates clinicians and researchers to reposition the understanding of diseases and explore diagnosis and therapy strategies, extends the existing disease taxonomy. Availability of data and materialsThe preprocessed dataset and source code supporting the conclusions of this article are available at GitHub repository https://github.com/yangxiaoxi89/mvHDN.

Perceptually Optimizing Color Look-up Tables.

The quality of ICC profiles with embedded look-up tables (LUTs) depends on multiple factors: 1. the accuracy of the optical printer model, 2. the exploitation of the available gamut combined with the quality of the gamut mapping approach encoded in the B2A-LUTs (backwards LUTs) and 3. the tonal smoothness as well color accuracy of the backwards LUTs. It can be shown that optimizing the smoothness of the LUTs comes at the expense of color accuracy and requires gamut reduction because of internal tonal edges. We present a method to optimize backwards LUTs of existing ICC profiles w.r.t accuracy, smoothness, gamut exploitation and mapping, which can be extended beyond color, e.g. to joint color and translucency backward LUTs. The approach is based on a perceptual difference metric that is used to optimize the LUT's tonal smoothness constrained to preserve both the accuracy of and the relationship between colors.

Graph complexes and Feynman rules

We investigate Feynman graphs and their Feynman rules from the viewpoint of graph complexes. We focus on graph homology and on the appearance of cubical complexes when either reducing internal edges or when removing them by putting them on the massshell.

A split–merge clustering algorithm based on the k-nearest neighbor graph

Numerous graph-based clustering algorithms relying on k-nearest neighbor (KNN) have been proposed. However, the performance of these algorithms tends to be affected by many factors such as cluster shape, cluster density and outliers. To address these issues, we present a split–merge clustering algorithm based on the KNN graph (SMKNN), which is based on the idea that two adjacent clusters can be merged if the data points located in the connection layers of the two clusters tend to be consistent in distribution. In Stage 1, a KNN graph is constructed. In Stage 2, the subgraphs are obtained by removing the pivot points from the KNN graph, in which the pivot points are determined by the size of local distance ratio of data points. In Stage 3, the adjacent cluster pairs satisfying the maximum similarity are merged, in which the similarity measure of two clusters is designed with two concepts including external connection edges and internal connection edges. By the experiments on ten synthetic data sets and eight real data sets, we compared SMKNN with two traditional algorithms, two density-based algorithms, nine graph-based algorithms and four neural network based algorithms in accuracy. The experimental results demonstrate a good performance of the proposed clustering method.

Quadri-algebras, preLie algebras, and the Catalan family of Lie idempotents

We compute the expansion of the Catalan family of Lie idempotents introduced in [Menous et al., Adv. Applied Math. 51 (2013), 177-22] on the PBW basis of the Lie module. It is found that the coefficient of a tree depends only on its number of left and right internal edges. In particular, the Catalan idempotents belong to a preLie algebra based on naked binary trees, of which we identify several Lie and preLie subalgebras.

Inside the coupling of ladybird beetle elytra: elastic setae can facilitate swift deployment.

The ladybird beetle (Coccinella septempunctata) is known for swift deployment of its elytra, an action that requires considerable power. However, actuation by thoracic muscles alone may be insufficient to deploy elytra at high speed because the maximum mechanical power that elytral muscles can produce is only 70% of that required for initiation of deployment. Nevertheless, the elytra open rapidly, within 3 ms in the initial phase, at a maximum angular velocity of 66.49±21.29 rad s-1, rivaling the strike velocity of ant lion (Myrmeleon crudelis) mandibles (65±21 rad s-1). Here, we hypothesize that elytra coupling may function as an energy storage mechanism that facilitates rapid opening by releasing elastic strain energy upon deployment. To test this hypothesis and better understand the biomechanics of elytra deployment, we combined micro-computed tomography and scanning electron microscopy to examine the microstructure of the coupling of paired elytra. We found that two rows of setae on the internal edges of the elytra coupling structure undergo elastic deformation when the elytra are locked together. Kinematics observations and mathematical modeling suggest that the elastic potential energy stored in the compressed setae generates 40% of the power required for deployment of elytra. Our findings broaden insights into how ladybirds actuate elytra opening by a strategy of using both muscles and elastic microstructures, and demonstrate a distributed pattern of actuation that adapts to geometrical constraints in elytra locking.

Edge vectors on plabic networks in the disk and amalgamation of totally non-negative Grassmannians

The amalgamation of cluster varieties introduced by Fock and Goncharov in [21] plays a relevant role both in mathematical and physical problems. In particular, amalgamation in the totally non-negative part of positroid varieties is explicitly described as gluing of several copies of small positive Grassmannians, GrTP(1,3) and GrTP(2,3), has important topological implications [53] and naturally appears in the computation of amplitude scatterings in N=4 SYM theory [9,10]. Lam [44] has proposed to represent amalgamation in positroid varieties by equivalence classes of relations on bipartite graphs and to identify total non-negativity via appropriate edge signatures. In this paper we provide an explicit geometric characterization of such signatures in the setting of the planar bicolored trivalent directed perfect networks in the disk introduced in [52] to parametrize positroid cells SMTNN⊂GrTNN(k,n) using systems of relations for n-vectors.More precisely, to any such graph G, we associate a geometric signature satisfying both the full rank condition and the total non–negativity property on the full positroid cell. Such signature is uniquely identified by geometric indices (local winding and intersection number) ruled by the orientation O and gauge ray direction l on G.The principal result is the enrichment of Postnikov's construction in [52] by associating measurements not only to boundary edges or vertices, but to internal edges as well. Indeed we generalize prior results by Postnikov [52] and Talaska [61] providing an explicit representation of the solution to the system of geometric relations on the network (N,O,l) of graph G and positive weights. At this aim, we assign canonical basis vectors in Rn at the boundary sinks and define the vectors components at the edge e as (finite or infinite) summations over the directed paths from e to the given boundary sink. Such edge vectors have the following properties:1) They solve the geometric system of relations on (N,O,l);2) Their components are rational in the weights with subtraction–free denominators, and have explicit expressions in terms of the conservative and edge flows of [61]. At the boundary sources they coincide with the entries of the boundary measurement matrix defined in [52]. If N is acyclically orientable, all components are subtraction–free rational expressions in the weights with respect to a convenient basis. Null edge vectors may occur on reducible networks not acyclically orientable;3) We provide explicit formulas both for the transformation rules of the edge vectors with respect to the orientation and the several gauges of the given network, and for their transformations due to moves and reductions of networks.Finally, we associate a Kasteleyn orientation to the graph following [17]. If the graph is bipartite, it is known that the partition functions of dimer configurations on the graph with given boundary conditions coincide with the Plucker coordinates of the corresponding point of the totally non-negative Grassmannian [54,44,60,1,8]. In the case of plabic graphs which are not bipartite we show that the partition function for a given boundary condition is not a multiple of the corresponding minor of the boundary measurement matrix. Therefore, in this case a statistical mechanical interpretation of the boundary measurement map remains open.

A network analysis to identify lung cancer comorbid diseases

Cancer patients with comorbidities face various life problems, health costs, and quality of life. Therefore, determining comorbid diseases would significantly affect the treatment of cancer patients. Because cancer disease is very complex, we can represent the relationship between cancer and its comorbidities as a network. Furthermore, the network analysis can be employed to determine comorbidities as a community detection problem because the relationship between cancer and its comorbidities forms a community. This study investigates which community detection algorithms are more appropriate to determine the comorbid of cancer. Given different community findings, this study attempted to analyze the modularity generated by the algorithm to decide the significant comorbid diseases. We retrieved lung cancer comorbid data on the basis of text mining manuscripts in PubMed, searched through disease ontologies, and calculated disease similarity. We investigate 20 algorithms using five modularity metrics and 16 fitness function evaluations to determine the significant comorbid diseases. The results show the five best modularity algorithms, namely label propagation, spinglass, Chinese whispers, Louvain, RB Pots. These five algorithms found significant comorbidities: blood vessels, immune system, bone, pancreas, and metabolic disorders, atrial cardiac septal defect, atrial fibrillation respiratory system, interstitial lung, and diabetes mellitus. The fitness function justifies the results of the community algorithm, and the ones that have a significant effect are average internal degree, size, and edges inside. This study contributes to more comprehensive knowledge and management of diseases in the healthcare context.