Edge Contraction Research Articles

Distinct cellular and junctional dynamics independently regulate the rotation and elongation of the embryonic gut in Drosophila.

Complex organ structures are formed with high reproducibility. To achieve such intricate morphologies, the responsible epithelium undergoes multiple simultaneous shape changes, such as elongation and folding. However, these changes have typically been assessed separately. In this study, we revealed how distinct shape changes are controlled during internal organ morphogenesis. The Drosophila embryonic hindgut undergoes left-right asymmetric rotation and anteroposterior elongation in a tissue-autonomous manner driven by cell sliding and convergent extension, respectively, in the hindgut epithelia. However, the regulation of these processes remains unclear. Through genetic analysis and live imaging, we demonstrated that cell sliding and convergent extension are independently regulated by Myosin1D and E-cadherin, and Par-3, respectively, whereas both require MyosinII activity. Using a mathematical model, we demonstrated that independently regulated cellular dynamics can simultaneously cause shape changes in a single mechanical system using anisotropic edge contraction. Our findings indicate that distinct cellular dynamics sharing a common apparatus can be independently and simultaneously controlled to form complex organ shapes. This suggests that such a mechanism may be a general strategy during complex tissue morphogenesis.

Parameterized complexity of vertex splitting to pathwidth at most 1

Motivated by the planarization of 2-layered straight-line drawings, we consider the problem of modifying a graph such that the resulting graph has pathwidth at most 1. The problem Pathwidth-One Vertex Explosion (POVE) asks whether such a graph can be obtained using at most k vertex explosions, where a vertex explosion replaces a vertex v by deg⁡(v) degree-1 vertices, each incident to exactly one edge that was originally incident to v. For POVE, we give an FPT algorithm with running time O(4k⋅m) and an O(k2) kernel, thereby improving over the O(k6)-kernel by Ahmed et al. [2] in a more general setting. Similarly, a vertex split replaces a vertex v by two distinct vertices v1 and v2 and distributes the edges originally incident to v arbitrarily to v1 and v2. Analogously to POVE, we define the problem variant Pathwidth-One Vertex Splitting (POVS) that uses the split operation instead of vertex explosions. Here we obtain a linear kernel and an algorithm with running time O((6k+12)k⋅m). This answers an open question by Ahmed et al. [2].Finally, we consider the problem Π-VertexSplitting (Π-VS), which generalizes the problem POVS and asks whether a given graph can be turned into a graph of a specific graph class Π using at most k vertex splits. For graph classes Π that can be defined in monadic second-order graph logic (MSO2), we show that the problem Π-VS can be expressed as an MSO2 formula, resulting in an FPT algorithm for Π-VS parameterized by k if Π additionally has bounded treewidth. We obtain the same result for the problem variant using vertex explosions.

Understanding a new wrinkling behavior of annular grooved panel during flexible free incremental sheet forming

Wrinkling behavior of sheet metal by inappropriate process parameters and the resultant variation of thickness and microstructure during incremental sheet forming (ISF) have significant impact on forming stability and geometric profile. The wrinkling-related mechanism is yet to be well understood, which make it difficult to effectively control wrinkling defects during ISF. In the present work, the wrinkling behavior and related mechanism of a typical annular grooved panel are investigated during a novel flexible free ISF process. Experiments demonstrate that during this ISF process, the sheet material sequentially undergoes 4 deformation modes: contacting state under plane strain condition, contracting state with only elastic deflection, thickening state under uniaxial compression condition, and wrinkling state where the circumferential compressive stress exceeds the critical wrinkling stress. The evolution of these deformation modes is dominantly caused by the increasing of edge contraction and circumferential stress, which are induced by the bending moment from the forming tool and auxiliary sheets. Based on the mechanism, an analytical model is developed to predict the wrinkling behavior, by which the corresponded sheet thickness, bending moment, circumferential compressive stress and critical wrinkling stress during the wrinkling process could be comprehensively calculated. Experimental results validate that the analytical model can accurately predict the wrinkling behavior under different process parameters, material properties and auxiliary sheet materials. Through microstructural characterization, numerical simulation and analytical modeling, the influence of process parameter and material property on wrinkling behavior is systematically investigated, along with the variation of sheet thickness and microstructure under different wrinkling modes. This work enhance a deep understanding of wrinkling behavior during ISF process, thereby providing effective methods for process optimization and quality improvement.

Splitting Plane Graphs to Outerplanarity

Vertex splitting replaces a vertex by two copies and partitions its incident edges amongst the copies. This problem has been studied as a graph editing operation to achieve desired properties with as few splits as possible, most often planarity, for which the problem is NP-hard.Here we study how to minimize the number of splits to turn a plane graph into an outerplane one. We tackle this problem by establishing a direct connection between splitting a plane graph to outerplanarity, finding a connected face cover, and finding a feedback vertex set in its dual. We prove NP-completeness for plane biconnected graphs, while we show that a polynomial-time algorithm exists for maximal planar graphs. Additionally, we show upper and lower bounds for certain families of maximal planar graphs. Finally, we provide a SAT formulation for the problem, and evaluate it on a small benchmark.

Topology of Edge Contracted Möbius Ladder: Indices and Dimension

Assigning numbers to graphs serves as a fundamental tool in graph theory and enables various analytical, computational, and visualization techniques for studying and understanding graph structures and properties. Edge Contraction is a process that separates edges from the graph while also joining the two previously linked vertices. In this paper, we study metric dimension and degree-based topological indices of Möbius Ladder and edge contracted Möbius Ladder like first Zagreb index, second Zagreb index, first Zagreb Hyper index, second Zagreb Hyper index, Augmented Zagreb index, Randic index, general Randic index, and Harmonic index.

Multivalued nonlinear dominated mappings on a closed ball and associated numerical illustrations with applications to nonlinear integral and fractional operators

In the context of complete strong b-metric-like spaces, we prove new multi-fixed point solutions for the pair of multivalued, dominated operators that fulfill the generalized nonlinear contractions on a closed ball. We employ a mix of two different types of mappings in our approach: one is a class of multi-dominated mappings, while the other is a weaker class of strictly increasing mappings. Additionally, some new fixed-point results concerning the multi-graph-dominated structure in graph contraction are presented. To validate the hypothesis of acquired results, a few sample cases are presented. A numerical experiment has been carried out to approximate the fixed point. In addition, to demonstrate the originality of our findings, we proposed simple and efficient solutions to the system of fractional differential equations and nonlinear Volterra-type integral equations.

Hecke algebras and edge contractions

We establish an embedding from the Hecke algebra associated with the edge contraction of a Coxeter system along an edge to the Hecke algebra associated with the original Coxeter system.

On the difference of mean subtree orders under edge contraction

Given a tree T of order n, one can contract any edge and obtain a new tree T⁎ of order n−1. In 1983, Jamison made a conjecture that the mean subtree order, i.e., the average order of all subtrees, decreases at least 13 in contracting an edge of a tree. In 2023, Luo, Xu, Wagner and Wang proved the case when the edge to be contracted is a pendant edge. In this article, we prove that the conjecture is true in general.

On the Dominant of the Multicut Polytope

Given a graph G=(V,E)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$G=(V,E)$$\\end{document} and a set S⊆V2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$S \\subseteq \\left( {\\begin{array}{c}V\\\\ 2\\end{array}}\\right) $$\\end{document} of terminal pairs, the minimum multicut problem asks for a minimum edge set δ⊆E\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\delta \\subseteq E$$\\end{document} such that there is no s-t-path in G-δ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$G -\\delta $$\\end{document} for any {s,t}∈S\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\{s,t\\}\\in S$$\\end{document}. For |S|=1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$|S|=1$$\\end{document} this is the well known s-t-cut problem, but in general the minimum multicut problem is NP-complete, even if the input graph is a tree. The multicut polytope MULTC□(G,S)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extsc {MultC}^\\square (G,S)$$\\end{document} is the convex hull of all multicuts in G; the multicut dominant is given by MULTC(G,S)=MULTC□(G,S)+R≥0E\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extsc {MultC}(G,S)=\ extsc {MultC}^\\square (G,S)+\\mathbb {R}^E_{{\\ge 0}}$$\\end{document}. The latter is the relevant object for the minimization problem. While polyhedra associated to several cut problems have been studied intensively there is only little knowledge for multicut. We investigate properties of the multicut dominant and in particular derive results on liftings of facet-defining inequalities. This yields a classification of all facet-defining path- and edge inequalities. Moreover, we investigate the effect of graph operations such as node splitting, edge subdivisions, and edge contractions on the multicut-dominant and its facet-defining inequalities. In addition, we introduce facet-defining inequalities supported on stars, trees, and cycles and show that the former two can be separated in polynomial time when the input graph is a tree.

Digger: A Graph Contraction Algorithm for Patrolling Games

Digger: A Graph Contraction Algorithm for Patrolling Games

Confinement induces internal flows in adherent cell aggregates.

During mesenchymal migration, F-actin protrusion at the leading edge and actomyosin contraction determine the retrograde flow of F-actin within the lamella. The coupling of this flow to integrin-based adhesions determines the force transmitted to the extracellular matrix and the net motion of the cell. In tissues, motion may also arise from convection, driven by gradients in tissue-scale surface tensions and pressures. However, how migration coordinates with convection to determine the net motion of cellular ensembles is unclear. To explore this, we study the spreading of cell aggregates on adhesive micropatterns on compliant substrates. During spreading, a cell monolayer expands from the aggregate towards the adhesive boundary. However, cells are unable to stabilize the protrusion beyond the adhesive boundary, resulting in retraction of the protrusion and detachment of cells from the matrix. Subsequently, the cells move upwards and rearwards, yielding a bulk convective flow towards the centre of the aggregate. The process is cyclic, yielding a steady-state balance between outward (protrusive) migration along the surface, and 'retrograde' (contractile) flows above the surface. Modelling the cell aggregates as confined active droplets, we demonstrate that the interplay between surface tension-driven flows within the aggregate, radially outward monolayer flow and conservation of mass leads to an internal circulation.

A structure theorem for homology 4-manifolds with g2 ≤ 5

Numerous structural findings of homology manifolds have been derived in various ways in relation to g2-values. The homology 4-manifolds with g2≤5 are characterized combinatorially in this article. It is well-known that all homology 4-manifolds for g2≤2 are polytopal spheres. We demonstrate that homology 4-manifolds with g2≤5 are triangulated spheres and are derived from triangulated 4-spheres with g2≤2 by a series of connected sum, bistellar 1- and 2-moves, edge contraction, edge expansion, and edge flipping operations. We establish that the above inequality is optimally attainable, i.e., it cannot be extended to g2=6.

A Continuous Non-Invasive Blood Pressure Prediction Method Based on Deep Sparse Residual U-Net Combined with Improved Squeeze and Excitation Skip Connections.

Arterial blood pressure (ABP) serves as a pivotal clinical metric in cardiovascular health assessments, with the precise forecasting of continuous blood pressure assuming a critical role in both preventing and treating cardiovascular diseases. This study proposes a novel continuous non-invasive blood pressure prediction model, DSRUnet, based on deep sparse residual U-net combined with improved SE skip connections, which aim to enhance the accuracy of using photoplethysmography (PPG) signals for continuous blood pressure prediction. The model first introduces a sparse residual connection approach for path contraction and expansion, facilitating richer information fusion and feature expansion to better capture subtle variations in the original PPG signals, thereby enhancing the network's representational capacity and predictive performance and mitigating potential degradation in the network performance. Furthermore, an enhanced SE-GRU module was embedded in the skip connections to model and weight global information using an attention mechanism, capturing the temporal features of the PPG pulse signals through GRU layers to improve the quality of the transferred feature information and reduce redundant feature learning. Finally, a deep supervision mechanism was incorporated into the decoder module to guide the lower-level network to learn effective feature representations, alleviating the problem of gradient vanishing and facilitating effective training of the network. The proposed DSRUnet model was trained and tested on the publicly available UCI-BP dataset, with the average absolute errors for predicting systolic blood pressure (SBP), diastolic blood pressure (DBP), and mean blood pressure (MBP) being 3.36 ± 6.61 mmHg, 2.35 ± 4.54 mmHg, and 2.21 ± 4.36 mmHg, respectively, meeting the standards set by the Association for the Advancement of Medical Instrumentation (AAMI), and achieving Grade A according to the British Hypertension Society (BHS) Standard for SBP and DBP predictions. Through ablation experiments and comparisons with other state-of-the-art methods, the effectiveness of DSRUnet in blood pressure prediction tasks, particularly for SBP, which generally yields poor prediction results, was significantly higher. The experimental results demonstrate that the DSRUnet model can accurately utilize PPG signals for real-time continuous blood pressure prediction and obtain high-quality and high-precision blood pressure prediction waveforms. Due to its non-invasiveness, continuity, and clinical relevance, the model may have significant implications for clinical applications in hospitals and research on wearable devices in daily life.

In Vivo Wound-Healing and Anti-Inflammatory Activities of Honey Produced by Melipona beecheii Bees

Background: Honey produced by the Melipona beecheii bees has been highly prized in Mexico since pre-Hispanic times for its therapeutic properties, particularly in wound healing. Objectives: The aim of this study was to assess the in vivo wound-healing and anti-inflammatory effects of M. beecheii honey using an animal model. Methods: Honey samples were collected from the state of Yucatan, Mexico. Male albino mice were utilized to test the wound-healing and anti-inflammatory properties of the honey, with pirfenidone (KitosCell®) and indomethacin (1 and 30 mg/mL) serving as positive controls, respectively. Results: From day one, enhancements in wound healing, granulation tissue formation, and continuous contraction of the wound edges were observed. In terms of anti-inflammatory activity, the honey dose was capable of reducing edema comparably to the control group receiving 1 mg/mL of indomethacin. However, differences were noted when compared to the 30 mg/mL indomethacin control group in three of the groups. Conclusions: It can be concluded that M. beecheii honey exhibits wound-healing and anti-inflammatory effects comparable to those of the positive controls used in this study. Therefore, it offers a viable alternative for the topical treatment of wounds.

Learning long- and short-term dependencies for improving drug-target binding affinity prediction using transformer and edge contraction pooling.

The accurate identification of drug-target affinity (DTA) is crucial for advancements in drug discovery and development. Many deep learning-based approaches have been devised to predict drug-target binding affinity accurately, exhibiting notable improvements in performance. However, the existing prediction methods often fall short of capturing the global features of proteins. In this study, we proposed a novel model called ETransDTA, specifically designed for predicting drug-target binding affinity. ETransDTA combines convolutional layers and transformer, allowing for the simultaneous extraction of both global and local features of target proteins. Additionally, we have integrated a new graph pooling mechanism into the topology adaptive graph convolutional network (TAGCN) to enhance its capacity for learning feature representations of chemical compounds. The proposed ETransDTA model has been evaluated using the Davis and Kinase Inhibitor BioActivity (KIBA) datasets, consistently outperforming other baseline methods. The evaluation results on the KIBA dataset reveal that our model achieves the lowest mean square error (MSE) of 0.125, representing a 0.6% reduction compared to the lowest-performing baseline method. Furthermore, the incorporation of queries, keys and values produced by the stacked convolutional neural network (CNN) enables our model to better integrate the local and global context of protein representation, leading to further improvements in the accuracy of DTA prediction.

Block-and-Hole Graphs: Constructibility and (3,0)-Sparsity

Abstract: We show that minimally 3-rigid block-and-hole graphs with one block are characterised as those that are constructible from K 3 by vertex splitting, and also as those having associated looped face graphs that are (3, 0)-tight. This latter property can be verified in polynomial time by a form of pebble game algorithm. We also indicate an application to graph rigidity in 3-dimensional normed spaces that are smooth and strictly convex.

Efficient Pooling Operator for 3D Morphable Models.

Learning the latent representation of three-dimensional (3D) morphable geometry is useful for several tasks, such as 3D face tracking, human motion analysis, and character generation and animation. For unstructured surface meshes, previous state-of-the-art methods focus on designing convolution operators and share the same pooling and unpooling operations to encode neighborhood information. Previous models use a mesh pooling operation based on edge contraction, which is based on the euclidean distance of vertices rather than the actual topology. In this study, we investigated whether such a pooling operation can be improved, introducing an improved pooling layer that combines the vertex normals and adjacent faces area. Furthermore, to prevent template overfitting, we increased the receptive field and improved low-resolution projection in the unpooling stage. This increase did not affect processing efficiency because the operation was implemented once on the mesh. We performed experiments to evaluate the proposed method, whose results indicated that the proposed operations outperformed Neural3DMM with 14% lower reconstruction errors and outperformed CoMA by 15% by modifying the pooling and unpooling matrices.

Deep Graph Reinforcement Learning for Solving Multicut Problem.

The multicut problem, also known as correlation clustering, is a classic combinatorial optimization problem that aims to optimize graph partitioning given only node (dis)similarities on edges. It serves as an elegant generalization for several graph partitioning problems and has found successful applications in various areas such as data mining and computer vision. However, the multicut problem with an exponentially large number of cycle constraints proves to be NP-hard, and existing solvers either suffer from exponential complexity or often give unsatisfactory solutions due to inflexible heuristics driven by hand-designed mechanisms. In this article, we propose a deep graph reinforcement learning method to solve the multicut problem within a combinatorial decision framework involving sequential edge contractions. The customized subgraph neural network adapts to the dynamically edge-contracted graph environment by extracting bilevel connected features from both contracted and original graphs. Our method can learn to infer feasible multicut solutions end-to-end toward optimization of the multicut objective in a data-driven manner. More specifically, by exploring the decision space adaptively, it implicitly gains heuristic knowledge from topological patterns of instances and thereby generates more targeted heuristics overcoming the short-sightedness inherent in the hand-designed ones. During testing, the learned heuristics iteratively contract graphs to construct high-quality solutions within polynomial time. Extensive experiments on synthetic and real-world multicut instances show the superiority of our method over existing combinatorial solvers, while also maintaining a certain level of out-of-distribution generalization ability.

Distance-Preserving Graph Compression Techniques

We study the problem of distance-preserving graph compression for weighted paths and trees. The problem entails a weighted graph $G = (V, E)$ with non-negative weights and a subset of edges $E^{\prime} \subset E$, which needs to be removed from G (with their endpoints merged as a supernode). The goal is to redistribute the weights of the deleted edges in a way that minimizes the error. The error is defined as the sum of the absolute differences of the shortest path lengths between different pairs of nodes before and after contracting $E^{\prime}$. Based on this error function, we propose optimal approaches for merging any subset of edges in a path and a single edge in a tree. Previous works on graph compression techniques aimed at preserving different graph properties (such as the chromatic number) or solely focused on identifying the optimal set of edges to contract. However, our focus in this paper is on achieving optimal edge contraction (when the contracted edges are provided as input), specifically for weighted trees and paths.

Derivation of high-contracted topology graphs for the type synthesis of complex closed robotic mechanisms with more mechanical advantages

AbstractChallenges/shortages of existing research: Both a topology graph TG and a contracted graph CG are the important tool for the type synthesis of mechanisms and have been studied. Let (b, t, q, p, h) be (binary, ternary, quaternary, pentagonal, hexagonal) link, respectively. Existing TG may include (b, t, q, p, h, …), and existing CG may include (t, q, p, h, …) and exclude b. Therefore, their derivation and isomorphism identification are quite complicated.The significance of this research: A novel high-contracted topology graph Gj/i including n (q, p, h, …) is proposed in this paper. Since Gj/i excludes (b, t), Gj/i must be more simple than complex TG and CG, and the derivation and isomorphism identification of various Gj/i must be more easily than that of the complex TG and CG.This paper focuses on the derivation and isomorphism identification of various Gj/i for deriving TG and type synthesis of the complex closed robotic mechanisms with more mechanical advantages and useful functions. First, the conceptions for deriving Gj/i and the relations between Gj/i and the basic links are explained, the relative rules are determined for representing Gj/i and reducing isomorphism of Gj/i using the character strings and the digit groups, and many different Gj/i are represented based on determined rules. Second, many different Gj/i (j = 0, …, 17) are constructed using a circle, several composite curves, and vertex points on the circle based on the character strings and the digit groups. Third, a condition for identifying isomorphism Gj/i is discovered and proved using the composite curves and their connections in Gj/i. Some isomorphism Gj/i are identified from constructed different Gj/i. Finally, different Gj/i (G7/7, G11/11) are illustrated to derive TGs, several complex closed robotic mechanisms are synthesized using derived TGs for creating robotic gripper, a long-stroke robotic pumping unit, and a tunnel robotic excavator.