Vertex Groups Research Articles

Strong Embeddability for Groups Acting on Metric Spaces

The strong embeddability is a notion of metric geometry, which is an intermediate property lying between coarse embeddability and property A. In this paper, the permanence properties of strong embeddability for groups acting on metric spaces are studied. The authors show that a finitely generated group acting on a finitely asymptotic dimension metric space by isometries whose K-stabilizers are strongly embeddable is strongly embeddable. Moreover, they prove that the fundamental group of a graph of groups with strongly embeddable vertex groups is also strongly embeddable.

An adaptive large neighbourhood search algorithm for the orienteering problem

We propose a new heuristic algorithm for the well-known Orienteering Problem, which aims at maximising the prize collected at vertices of a graph, visiting them through a simple closed tour whose length (also known as travel time) is limited by an upper bound. The algorithm is based on the Adaptive Large Neighbourhood Search metaheuristic paradigm, and uses a clustering of the graph to operate on groups of nearby vertices. Extensive computational results show that the proposed algorithm is able to find very good solutions (it produced 27 new best known solutions on a set of benchmark instances) and that it fares favourably compared with other state-of-the-art heuristics when tested with both long and short computation time budgets.

New and Simple Algorithms for Stable Flow Problems

Stable flows generalize the well-known concept of stable matchings to markets in which transactions may involve several agents, forwarding flow from one to another. An instance of the problem consists of a capacitated directed network in which vertices express their preferences over their incident edges. A network flow is stable if there is no group of vertices that all could benefit from rerouting the flow along a walk. Fleiner (Algorithms 7:1–14, 2014) established that a stable flow always exists by reducing it to the stable allocation problem. We present an augmenting path algorithm for computing a stable flow, the first algorithm that achieves polynomial running time for this problem without using stable allocations as a black-box subroutine. We further consider the problem of finding a stable flow such that the flow value on every edge is within a given interval. For this problem, we present an elegant graph transformation and based on this, we devise a simple and fast algorithm, which also can be used to find a solution to the stable marriage problem with forced and forbidden edges. Finally, we study the stable multicommodity flow model introduced by Kiraly and Pap (Algorithms 6:161–168, 2013). The original model is highly involved and allows for commodity-dependent preference lists at the vertices and commodity-specific edge capacities. We present several graph-based reductions that show equivalence to a significantly simpler model. We further show that it is $${\textsf {NP}}$$ -complete to decide whether an integral solution exists.

Detecting a subclass of torsion-generated groups

We classify the groups quasi-isometric to a group generated by finite-order elements within the class of one-ended hyperbolic groups which are not Fuchsian and whose JSJ decomposition over two-ended subgroups does not contain rigid vertex groups. To do this, we characterize which JSJ trees of a group in this class admit a cocompact group action with quotient a tree. The conditions are stated in terms of two graphs we associate to the degree refinement of a group in this class. We prove there is a group in this class which is quasi-isometric to a Coxeter group but is not abstractly commensurable to a group generated by finite-order elements. Consequently, the subclass of groups in this class generated by finite-order elements is not quasi-isometrically rigid. We provide necessary conditions for two groups in this class to be abstractly commensurable. We use these conditions to prove there are infinitely many abstract commensurability classes within each quasi-isometry class within this class that contains a group generated by finite-order elements.

A Distributed Evolutionary algorithm for detecting minimum vertex cuts for wireless ad hoc and sensor networks

A minimum vertex cut (MVC) of a graph G is the smallest subset of vertices whose removal creates at least two disconnected group of other vertices. Detecting nodes in MVCs in wireless ad hoc and sensor networks (WASNs) provides valuable information about their robustness and critical parts. There is a wide variety of central algorithms that find or estimate MVCs of graphs, but to the best of our knowledge the existing distributed algorithms can only estimate the cardinality of MVCs, or k, from local neighborhood information. Regardless of the fact that MVCs remain unknown in these algorithms, local estimation of k may produce wrong values, far from the real k. We propose a distributed algorithm, which uses an adapted meta heuristic method, to detect the nodes in MVCs. In the proposed algorithm, all nodes find their available paths to the sink (root node) and determine the minimum subset of nodes that their failure disconnects all detected paths. The smallest detected sets by the nodes will be MVCs of the WASN. Besides finding the union of MVCs with up to 89% average accuracy, the testbed and simulation results show that the correct detection ratio of k in the proposed algorithm is up to 37% more than the existing distributed algorithms.

Hydrophobic Nature of Methacrylate-POSS in Combination with 2-(Methacryloyloxy)ethyl Phosphorylcholine for Enhanced Solubility and Controlled Release of Paclitaxel.

Amphiphilic copolymers consisting of 2-(methacryloyloxy)ethyl phosphorylcholine (MPC) and hydrophobic monomers are known as biomaterials for the administration of poorly water-soluble drugs such as paclitaxel (PTX). However, the hydrophobic monomers to be copolymerized with MPC have not been optimized for PTX solubilization and its dosage forms. Here, we show the enhanced PTX solubility by only an MPC-based amphiphilic copolymer using a polyhedral oligomeric silsesquioxane (POSS) methacrylate (MA) bearing an ethyl (C2H5) group as a vertex group. MPC was copolymerized with POSS methacrylates bearing different vertex groups of ethyl (C2H5), hexyl (C6H13), and octyl (C8H17) via radical polymerization. We found that the strong interaction between C2H5-POSS and PTX contributed to the slow release of PTX without any burst release. The C2H5-POSS-MA MPC copolymer was internalized into the cultured HeLa cells, which was confirmed by using a fluorescein-4-isothiocyanate (FITC)-labeled PTX, and the PTX-dissolved copolymer induced cell death. We anticipate that the C2H5-POSS-MA MPC copolymer is a good solubilizer bearing a controlled release function for PTX.

Deciding isomorphy using Dehn fillings, the splitting case

We solve Dehn's isomorphism problem for virtually torsion-free relatively hyperbolic groups with nilpotent parabolic subgroups. We do so by reducing the isomorphism problem to three algorithmic problems in the parabolic subgroups, namely the isomorphism problem, separation of torsion (in their outer automorphism groups) by congruences, and the mixed Whitehead problem, an automorphism group orbit problem. The first step of the reduction is to compute canonical JSJ decompositions. Dehn fillings and the given solutions of the algorithmic problems in the parabolic groups are then used to decide if the graphs of groups have isomorphic vertex groups and, if so, whether a global isomorphism can be assembled. For the class of finitely generated nilpotent groups, we give solutions to these algorithmic problems by using the arithmetic nature of these groups and of their automorphism groups.

Location- and relation-based clustering on privacy-preserving social networks

Graph clustering has a long-standing problem in that it is difficult to identify all the groups of vertices that are cohesively connected along their internal edges but only sparsely connected along their external edges. Apart from structural information in social networks, the quality of the location-information clustering has been improved by identifying clusters in the graph that are closely connected and spatially compact. However, in real-world scenarios, the location information of some users may be unavailable for privacy reasons, which renders existing solutions ineffective. In this paper, we investigate the clustering problem of privacy-preserving social networks, and propose an algorithm that uses a prediction-and-clustering approach. First, the location of each invisible user is predicted with a probability distribution. Then, each user is iteratively assigned to different clusters. The experimental results verify the effectiveness and efficiency of our method, and our proposed algorithm exhibits high scalability on large social networks.

A centrality measure for cycles and subgraphs II

In a recent work we introduced a measure of importance for groups of vertices in a complex network. This centrality for groups is always between 0 and 1 and induces the eigenvector centrality over vertices. Furthermore, its value over any group is the fraction of all network flows intercepted by this group. Here we provide the rigorous mathematical constructions underpinning these results via a semi-commutative extension of a number theoretic sieve. We then established further relations between the eigenvector centrality and the centrality proposed here, showing that the latter is a proper extension of the former to groups of nodes. We finish by comparing the centrality proposed here with the notion of group-centrality introduced by Everett and Borgatti on two real-world networks: the Wolfe’s dataset and the protein-protein interaction network of the yeast Saccharomyces cerevisiae. In this latter case, we demonstrate that the centrality is able to distinguish protein complexes

Voting Simulation based Agglomerative Hierarchical Method for Network Community Detection

Community detection has been paid much attention in many fields in recent years, and a great deal of community-detection methods have been proposed. But the time consumption of some of them is heavy, limiting them from being applied to large-scale networks. On the contrary, there exist some lower-time-complexity methods. But most of them are non-deterministic, meaning that running the same method many times may yield different results from the same network, which reduces their practical utility greatly in real-world applications. To solve these problems, we propose a community-detection method in this paper, which takes both the quality of the results and the efficiency of the detecting procedure into account. Moreover, it is a deterministic method which can extract definite community structures from networks. The proposed method is inspired by the voting behaviours in election activities in the social society, in which we first simulate the voting procedure on the network. Every vertex votes for the nominated candidates following the proposed voting principles, densely connected groups of vertices can quickly reach a consensus on their candidates. At the end of this procedure, candidates and their own voters form a group of clusters. Then, we take the clusters as initial communities, and agglomerate some of them into larger ones with high efficiency to obtain the resulting community structures. We conducted extensive experiments on some artificial networks and real-world networks, the experimental results show that our proposed method can efficiently extract high-quality community structures from networks, and outperform the comparison algorithms significantly.

Impact of the mode of delivery on maternal and neonatal outcome in spontaneous-onset breech labor at 32+0–36+6 weeks of gestation: A retrospective cohort study

ObjectiveTo compare neonatal and maternal outcomes in spontaneously onset preterm breech deliveries after trial of labor (BTOL) and intended cesarean section (BCS), and between BTOL and vertex control deliveries, in singleton fetuses at 32+0–36+6 weeks of gestation. Study designRetrospective single center cohort study in a Finnish University Hospital including all spontaneous-onset preterm breech deliveries with 32 completed gestational weeks in 2003–2015. The study population comprised a total of 176 preterm breech and 103 vertex control deliveries, matched by gestational age and whether the mother had given birth vaginally before or not. Infants with severe malformations and antepartum fetal distress were excluded. Subgroup analyses were made in two cohorts according to gestational age. Main outcome measures were maternal and neonatal mortality and morbidity, low cord pH and Apgar score. ResultsNo mortality was observed, and severe morbidity was rare. No difference in incidence of low cord pH or five-minute Apgar score was observed between the groups. Apgar scores at the age of one minute were comparable in the breech groups but more often low in the BTOL group compared to the vertex control group. 16.5% of neonates in the BTOL group, 23.3% in the BCS group and 7.8% in the vertex group needed intensive care. In logistic regression analysis, lower gestational age and being small for gestational age were associated with the need for neonatal intensive care. Being allowed a trial of labor was not associated with the need for neonatal intensive care. Maternal morbidity was similar across the groups, but median blood loss was more pronounced in the BCS group compared to the BTOL group. ConclusionIn breech deliveries at 32+0–36+6 gestational weeks, trial of labor did not increase neonatal morbidity compared to intended cesarean delivery. Infants born after a trial of labor in breech presentation display low one-minute Apgar score and need intensive care more often compared to vertex controls.

Faster computation of successive bounds on the group betweenness centrality

We propose a method that computes bounds on the group betweenness centrality (GBC) of groups of vertices of a network. Once certain quantities related to the network are computed in the preprocessing step that takes time, where n is the number of vertices in the network, our method can compute bounds on the GBC of any number of groups of vertices successively, for each group requiring a running time proportional to the square of its size. Our method is an improvement of the method of Kolaczyk et al. [Social Networks, 31, 3 (2009)], which has to be restarted for each group making it less efficient for the successive GBC computations. In addition, the bounds used in our method are stronger and/or faster to compute. Our computational experiments show that in the search for a group of a certain size with the highest GBC value, our method reduces the number of candidate groups substantially and in some cases the optimal group can be found without exactly computing the GBC values which is computationally more demanding.

Complex Networks: Theory Building for Integrated Healthcare Research in Rural of China

Introduction: The three tiered healthcare networks（county, township and village) in rural area of China undertakes health service needs of 0.8 billion rural residents. Multiple researches in this area indicates the healthcare system in rural area is suffering from lacking integrated networkss not only among healthcare institutions, but also among all the participants from different interest related parties, this current situation causes numerous issues in rural healthcare system including huge waste of healthcare resources, overuse and misuse of medication between different tiered institutions and gaps of medical information transferring and sharing during the referral processes, etc. However, the traditional models and methods for healthcare system analysis usually not enough to elaborate the specific networkss among all of participants in this system and to monitor the changing of the overall networkss. We introduced the Complex networks theory into this area and try to build a new analysis aspect for future study of integrated healthcare researches. Method: This study simulated and analyzed the characteristics of Complex networks system in rural area of China by introducing the Small world and Community structure theories from System Science. We designed a hypothetic complex networks environment of rural healthcare system with participants (Nodes=200), connectivity (K=15, means the average number of edges connected to a node), and s=0.15 which indicates the possibility of connection of each participant. Result: In simulated environment of healthcare system in rural area, the Clustering coefficient (which measures the density of triangles in a networks) is high and the Scale-free Property (which refers to any functional form f(x) that remains unchanged to within a multiplicative factor under a rescaling of the independent variable x) is quite obvious (Graph 1.). Furthermore, the result also indicates that the networkss of rural healthcare system shows the “Community structure” which means the groups of vertices that have a high density of edges within them, with a lower density of edges between groups. (Graph.2.) Graph.1. The small world effect and Scale-free Property Graph.2. The Community structure Conclusions: We presume thatthe small world Effect, Scale-free Property and the Community structure does exist in interpersonal networkss in rural healthcare system, it indicates that in an actual environment of rural healthcare system, the providers and users consisted millions of nodes, and most of these nodes only contact with their neighbors or acquaintances. At the same time, most of rural areas in China has no initial diagnosis or “Gate keeper”-General practice system at present, so service users could freely reach to any providers who has high professional position or good reputation in that area. Discussion: This study was inspired by the innovative works in complex theory studies in recent years. We could use the theories from complex networkss such as Small world and Community structure to simulate and to analyze the healthcare networkss in rural China in order to find more specific characteristics among the integrated networkss in rural area. For example, by analyzing the actual networkss based on Small world theory, we could locate the high density “community” (it could be an institution or a physician) in networkss and precisely change the healthcare resource structure to make the system more integrated. Lessons learned: The Complex Networks theory is rarely used in the area of Integrated Healthcare studies, we learned that when building the model of Small world by Matlab, it should be very carefully to avoid the characteristic difference between the healthcare networks and other networkss. Limitation: Because of data limitation, we could not use the actual interpersonal networks data for modeling, just simulated the modeling process to report the practical significance for using this theory to analyze the integrated healthcare system in rural area. Suggestion for future research: This study is trying to introduce an essential theory into integrated healthcare networks study. However, the stage for now is just in the process of simulating a hypothetical environment. Actually, at present, our research team launched a big data healthcare research project in Yichang, Hubei province, China. We are trying to analyzing the networks of Yichang region which contains millions of resident information by using Complex networks theory which mentioned in this paper.

Complexity volumes of splittable groups

Using graph of groups decompositions of finitely generated groups, we define Euler characteristic type invariants which are non-zero in many interesting classes of hyperbolic, limit and CSA groups, including elementarily free groups and one-ended torsion-free hyperbolic groups whose JSJ decomposition contains a maximal hanging Fuchsian vertex group.

Tuned Surface and Mechanical Properties of Polymeric Film Prepared by Random Copolymers Consisting of Methacrylate‐POSS and 2‐(Methacryloyloxy)ethyl Phosphorylcholine

AbstractPoly(2‐(methacryloyloxy)ethyl phosphorylcholine) (PMPC) is known as a biocompatible polymers. Copolymerization of 2‐(methacryloyloxy)ethyl phosphorylcholine (MPC) and hydrophobic monomers is a general approach that gives bioinert functions to solid materials via the surface coating. However, due to the amorphous nature and super hydrophilicity of the MPC‐based copolymers, both the surface and the mechanical properties are not controlled for biomedical applications. Here, the modulated mechanical property and the surface wettability of the MPC‐based copolymers are shown by using a polyhedral oligomeric silsesquioxane (POSS) methacrylate. MPC is copolymerized with POSS methacrylates bearing different vertex groups of ethyl (C2H5), hexayl (C6H13), and octayl (C8H17) via radical polymerization. It is found that only the C2H5‐POSS induces the increased mechanical strength, low surface wettability, and cellular attachment, suggesting that the C2H5‐POSS moiety restricts the motion of PMPC chain. The finding is anticipated to be tuned for both surface and bulk functions of PMPC for biomedical applications.

Geometry of the word problem for 3-manifold groups

We provide an algorithm to solve the word problem in all fundamental groups of 3-manifolds that are either closed, or compact with (finitely many) boundary components consisting of incompressible tori, by showing that these groups are autostackable. In particular, this gives a common framework to solve the word problem in these 3-manifold groups using finite state automata.We also introduce the notion of a group which is autostackable respecting a subgroup, and show that a fundamental group of a graph of groups whose vertex groups are autostackable respecting any edge group is autostackable. A group that is strongly coset automatic over an autostackable subgroup, using a prefix-closed transversal, is also shown to be autostackable respecting that subgroup. Building on work by Antolin and Ciobanu, we show that a finitely generated group that is hyperbolic relative to a collection of abelian subgroups is also strongly coset automatic relative to each subgroup in the collection. Finally, we show that fundamental groups of compact geometric 3-manifolds, with boundary consisting of (finitely many) incompressible torus components, are autostackable respecting any choice of peripheral subgroup.

Transitivity Model on Signed Graphs

In this paper, we generalize the already established iterated local transitivity model for online social networks in signed networks. In this model, at each time step t and for already existing vertex x, a new vertex(clone) x′ is added which joins to the neighbors of x. The sign of new edge xx′ is the marking on x. We also discuss the properties such as balance, clusterability, sign-compatibility and consistency. The signed networks focus on the type of relations (friendship and enmity) between the vertices(members of online social network). The ILT model for signed network gives an insight on how the network reacts to the addition of clone vertex. Also the properties like balance and clusterability helps establish a natural balance in society by providing a possible formation of group of vertices in society for a peaceful co-existence and smooth functioning of social system.

Efficient Detection of Communities in Biological Bipartite Networks.

Methods to efficiently uncover and extract community structures are required in a number of biological applications where networked data and their interactions can be modeled as graphs, and observing tightly-knit groups of vertices ("communities") can offer insights into the structural and functional building blocks of the underlying network. Classical applications of community detection have largely focused on unipartite networks - i.e., graphs built out of a single type of objects. However, due to increased availability of biological data from various sources, there is now an increasing need for handling heterogeneous networks which are built out of multiple types of objects. In this paper, we address the problem of identifying communities from biological bipartite networks - i.e., networks where interactions are observed between two different types of objects (e.g., genes and diseases, drugs and protein complexes, plants and pollinators, and hosts and pathogens). Toward detecting communities in such bipartite networks, we make the following contributions: i) (metric) we propose a variant of bipartite modularity; ii) (algorithms) we present an efficient algorithm called biLouvain that implements a set of heuristics toward fast and precise community detection in bipartite networks (https://github.com/paolapesantez/biLouvain); and iii) (experiments) we present a thorough experimental evaluation of our algorithm including comparison to other state-of-the-art methods to identify communities in bipartite networks. Experimental results show that our biLouvain algorithm identifies communities that have a comparable or better quality (as measured by bipartite modularity) than existing methods, while significantly reducing the time-to-solution between one and four orders of magnitude.

Scattering diagrams, Hall algebras and stability conditions

With any quiver with relations, we associate a consistent scattering diagram taking values in the motivic Hall algebra of its category of representations. We show that the chamber structure of this scattering diagram coincides with the natural chamber struc- ture in an open subset of the space of stability conditions on the associated triangulated category. In the three-dimensional Calabi–Yau situation, when the relations arise from a potential, we can apply an integration map to give a consistent scattering diagram taking values in a tropical vertex group.

Scattering diagrams, Hall algebras and stability conditions

To any quiver with relations we associate a consistent scattering diagram taking values in the motivic Hall algebra of its category of representations. We show that the chamber structure of this scattering diagram coincides with the natural chamber structure in an open subset of the space of stability conditions on the associated triangulated category. In the three-dimensional Calabi-Yau situation, when the relations arise from a potential, we can apply an integration map to give a consistent scattering diagram taking values in a tropical vertex group.