Articulation Points Research Articles

On the residual closeness of graphs with cut vertices

On the residual closeness of graphs with cut vertices

Block symmetries in graph coloring reconfiguration systems

In this paper, we study reconfiguration systems for proper graph colorings modified by single-vertex recolorings. Applying a general construction of Ghrist and Peterson [15] to the graph coloring problem, we consider cubical complexes in which cubes represent recolorings of independent sets of vertices. For any choice of base graph and number of colors, the 0-skeleton of the associated coloring state complex is the set of proper colorings, and the 1-skeleton is the transition graph.Appealing to symmetries induced by color permutation, we give two main results regarding the organization of the biconnected components (blocks) of coloring transition graphs and the colorings within those blocks. First, the 1-skeleton of any connected coloring state complex has a unique block whose vertex set is the union of entire classes of isomorphic colorings. We call this block the nucleus. Second, the nucleus of the state complex of any non-empty graph contains a non-trivial cycle. This implies that although the state complex for any reconfiguration system is locally CAT(0) [15], only the very simplest coloring state complexes are globally CAT(0).

ВЛИЯНИЕ ЖЕСТКОСТИ НАВЕСНОЙ СИСТЕМЫ НА УСТОЙЧИВОСТЬ КРИВОЛИНЕЙНОГО ДВИЖЕНИЯ МАШИННО-ТРАКТОРНОГО АГРЕГАТА

The search for constructive solutions to reduce the influence of inertial forces on the process of curved movement of a machine-tractor unit during curved movement is an urgent problem associated not only with reducing dynamic loads on the tractor and equipment aggregated with it, but with maintaining the stability of movement. A circular loop-free turn was chosen as the object of research. An experimental hinged system is designed to solve the tasks set in the work. It differs from the basic one in that between the hinged frame of the Belarus-1221.2 tractor and the hinged frame of the STV-12 seeder, an elastic element made of polyurethane is installed, which has the most suitable physical and mechanical properties. Nonlinear approximation of the array of abscissas and ordinates of the turn entry trajectory curve, calculated using the parametric form of equations for a circle of constant radius of the steady turn section, made it possible to describe the two considered stages of the theoretical turn trajectory by explicit non-linear functions. Analysis of arrays of theoretical and experimental values of the coordinates of the curves of the trajectories gave a constant value of the shift coefficient of the theoretical trajectory for the studied operating conditions of the unit 1.12, multiplying by which the explicit theoretical function obtained a parametric function of the actual trajectory of rotation. The comparison of trajectories showed the expediency of using elastic elements at the points of articulation of the tractor with the equipment, the use of polyurethane leads to the preservation of the trajectory, since the deviation of the actual trajectory from the theoretical one with the basic configuration in the height of the turning strip is 1.6... 2.25 m, and with the experimental one – 0.6 ... 1.13 m, the length of the theoretical curves is 8.21...10.82 m, and valid: with a base hitch of 11,223...12,792 m, with an experimental one – 9,652 ...11,854 m. A comparison of the results of theoretical studies with experimental data showed that their greatest difference does not exceed 4%, which allows us to conclude that they are correct.

Impact of 3-dimensional anatomical changes secondary to orthognathic surgery on voice resonance and articulatory function: a prospective study

An evaluation was made of the impact of orthognathic surgery (OS) on speech, addressing in particular the effects of skeletal and airway changes on voice resonance characteristics and articulatory function. A prospective study was carried out involving 29 consecutive patientssubjected to OS. Preoperative, and short and long-term postoperative evaluations were made of anatomical changes (skeletal and airway measurements), speech evolution (assessed objectively by acoustic analysis: fundamental frequency, local jitter, local shimmer of each vowel, and formants F1 and F2 of vowel /a/), and articulatory function (use of compensatory musculature, point of articulation, and speech intelligibility). These were also assessed subjectively by means of a visual analogue scale. Articulatory function after OS showed immediate improvement and had further progressed at one year of follow up. This improvement significantly correlated with the anatomical changes, and was also notably perceived by the patient. On the other hand, although a slight modification in vocal resonance was reported and seen to correlate with anatomical changes of the tongue, hyoid bone, and airway, it was not subjectively perceived by the patients. In conclusion, the results demonstrated that OS had beneficial effects on articulatory function and imperceptible subjective changes in a patient’s voice. Patients subjected to OS, apart from benefitting from improved articulatory function, should not be afraid that they will not recognise their voice after treatment.

Territorial planning and sustainable development—case study: Protected areas in the territory of the Aspiring West Geopark, Portugal

Introduction: The holistic concept of the sustainable development of United Nations Educational, Scientific and Cultural Organization (UNESCO) Global Geoparks encompasses the promotion of connected protected areas and activities that link geological heritage with other aspects of natural and cultural heritage. This case study aims to identify points of articulation and/or to identify conflicts in the overlap between protected areas and UNESCO World Geoparks in Portugal, and to provide information to improve the interrelation of these designations.Methods: The methodological procedures in analysing the organisational structures of different classified areas from the respective management documents. The technical procedure consisted of document consultation and on-site activities carried out between September 2020 and November 2021.Results: The study resulted in the identification of points of natural objects that can be held together by protected natural spaces and aspiring Oeste Geopark. A proposal for synergistic action was presented, with the main pillars of integration in the territory. The different designations for sustainable territorial management in complementary to the conservation of natural heritage. The results of the analyses indicate that the overlap of the different designations of areas and territories studied here can act both in a joint and complementary way to conserve natural heritage.Discussion: This reinforcement study, which has different designations of areas and/or territories for sustainable territorial planning at the local, regional, national, and international levels, is fundamental for nature conservation, lacking more in terms of efficient management and integration of the social component.

Fault tolerability analysis of folded crossed cubes based on g-component and g-good neighbor fault pattern

As data center networks and network-on-chip are developing rapidly, many graph invariants have been proposed to measure the reliability and fault tolerance of the network so that the multiprocessor systems can be ensured to operate efficiently and smoothly. The g-component connectivity of a graph G, denoted by cκg(G), is the minimum size of vertex cut such that G has at least g components. The g-good neighbor connectivity of a graph G, represented by κg(G), is the minimum size of vertex cut such that each vertex has at least g fault-free neighbors. Motivated by the conditional connectivities above, the g-component diagnosability (ctg(G)) and g-good neighbor diagnosability (tg(G)) of graph G have been suggested to evaluate the fault diagnostic capability of multiprocessor systems successively. In this paper, we determine the (g+1)-component connectivity of folded crossed cubes FCQn, i.e., cκg+1(FCQn)=ng−g22+g2+1 for 1≤g≤⌊n2⌋, and (g+1)-component diagnosability of FCQn under the PMC model and MM⁎ model, i.e., ctg+1(FCQn)=ng+n−g22−g2+1. Moreover, we establish the g-good neighbor connectivity of FCQn, i.e., κg(FCQn)=(n+1−g)2g for 0≤g≤n−5, and g-good neighbor diagnosability of FCQn under the PMC model and MM⁎ model, i.e., tg(FCQn)=(n+2−g)2g−1.

Faster Edge‐Path Bundling through Graph Spanners

AbstractEdge‐Path bundling is a recent edge bundling approach that does not incur ambiguities caused by bundling disconnected edges together. Although the approach produces less ambiguous bundlings, it suffers from high computational cost. In this paper, we present a new Edge‐Path bundling approach that increases the computational speed of the algorithm without reducing the quality of the bundling. First, we demonstrate that biconnected components can be processed separately in an Edge‐Path bundling of a graph without changing the result. Then, we present a new edge bundling algorithm that is based on observing and exploiting a strong relationship between Edge‐Path bundling and graph spanners. Although the worst case complexity of the approach is the same as of the original Edge‐Path bundling algorithm, we conduct experiments to demonstrate that the new approach is 5–256 times faster than Edge‐Path bundling depending on the dataset, which brings its practical running time more in line with traditional edge bundling algorithms.

Generative Design of Soft Robot Actuators Using ESP

Soft robotics is an emerging field that leverages the compliant nature of materials to control shape and behaviour. However, designing soft robots presents a challenge, as they do not have discrete points of articulation and instead articulate through deformation in whole regions of the robot. This results in a vast, unexplored design space with few established design methods. This paper presents a practical generative design process that combines the Encapsulation, Syllabus, and Pandamonium method with a reduced-order model to produce results comparable to the existing state-of-the-art in reduced design time while including the human designer meaningfully in the design process and facilitating the inclusion of other numerical techniques such as Markov chain Monte Carlo methods. Using a combination of reduced-order models, L-systems, MCMC, curve matching, and optimisation, we demonstrate that our method can produce functional 2D articulating soft robot designs in less than 1 s, a significant reduction in design time compared to monolithic methods, which can take several days. Additionally, we qualitatively show how to extend our approach to produce more complex 3D robots, such as an articulating tentacle with multiple grippers.

Vertex cut of a graph and connectivity of its neighbourhood complex

We show that if a graph G satisfies certain conditions, then the connectivity of neighbourhood complex N(G) is strictly less than the vertex connectivity of G. As an application, we give a relation between the connectivity of the neighbourhood complex and the vertex connectivity for stiff chordal graphs, and for weakly triangulated graphs satisfying certain properties. Next, we consider graphs with a vertex v such that for any k-subset S of neighbours of v, there exists a vertex vS≠v such that S is subset of neighbours of vS. We prove that for any graph G with a vertex v as above, N(G−{v}) is (k−1)-connected implies that N(G) is (k−1)-connected. We use this to show that:(i) neighbourhood complexes of queen and king graphs are simply connected and (ii) if G is a non-complete stiff chordal graph, then vertex connectivity of G is n+1 if and only if Conn(N(G))=n.

ADA-PC: An asynchronous distributed algorithm for minimizing pairwise connectivity in wireless multi-hop networks

Reliability analysis is of great significance to designing and maintaining wireless multi-hop networks (WMhNs). In WMhNs, several reasons can cause a node to be inoperable, such as hardware failure, software errors, and battery drain. Failure of some critical nodes may partition networks into disconnected segments. The presence of such critical nodes may also reduce the network lifetime since they consume more energy for packet forwarding. Therefore, it is crucial to identify the critical nodes of the networks and strengthen them by adding more nodes surrounding those or creating alternate pathways connecting other nodes to ensure connectivity maintenance in WMhNs. One of the most common approaches in direction is detecting the cut nodes of the networks. However, although finding cut nodes provide helpful information, it may be insufficient for precise reliability analysis since finding cut nodes only does not consider the remaining network. Critical Node Problem (CNP) aims to detect the most important nodes of the network whose removal minimizes the pairwise connectivity (the total number of node pairs connected by at least one path). In other words, the CNP tries to identify a set of nodes whose absence partitions the network into several disconnected segments of similar size. Detecting critical nodes for pairwise connectivity reveals the weak points and bottlenecks of the networks and may help to increase the fault tolerance and lifetime of WMhNs. This paper proposes an Asynchronous Distributed Algorithm for minimizing Pairwise Connectivity (ADA-PC) in WMhNs. To the best of our knowledge, this is the first distributed algorithm for the targeted problem in the network literature. The proposed algorithm uses a distributed Breadth-First Search (BFS) tree which limits bit complexity to O(n.m.log2n) and space complexity to O(d), where d is the network’s diameter. The experimental study on both testbed experiment and simulation reveals that the proposed algorithm is capable of finding the most critical nodes with up to 60% lower sent bytes than the existing central algorithms.

Morphometric examination of hind limb and foot bones and fibre type composition of crus region muscles in quail and pigeon.

In this study, the foot and hind limb bones of pigeons and quails were measured morphometrically. Additionally, microscopic classifications of the muscles affecting the foot and digit joints were made. For the macroscopic inspection, 40 birds were used, including 20 adult quails (10 males, 10 females) and 20 adult pigeons (10 males, 10 females). Diethyl ether was inhaled to anaesthetize the animals. The poultry animals were put under anaesthesia, and radiographic pictures of their left feet were obtained individually. DAP measurements were performed separately from the images taken with the Image J program. Then, they were euthanized by cervical dislocation under diethyl ether anaesthesia. The right legs of the euthanized animals were preserved in a 10% neutral formalin solution for histology procedures just after the legs were dissected from the trunk. Morphometric measurements of bone lengths were made in accordance with the measurement points specified by von den Driesch. After fixation for histological examination, routine tissue follow-up was performed and the tissues were embedded in paraffin. The presence of SO-type I, FG-type IIb and FOG-type IIa in 4-5μ sections taken from paraffin blocks was demonstrated using the indirect streptavidin-biotin-complex method from immunohistochemical methods. The result of our study was statistically evaluated at p < 0.05 and p < 0.001 levels. The length of the hallux, the articulation point to the TMT and the fibre arrangements in the two flexor group muscles showed that the hind limbs and feet of the pigeons had a more favourable anatomical and histological structure for the perching movement.

Generalized network dismantling via a novel spectral partition algorithm

Network dismantling problem aims to find a node subset whose removal from a network results in the fragmentation of the network into subcritical connected components at the minimal overall cost. People have always been more interested in the unweighted case where each node has the same cost, while there are few results for the weighted case when nodes have different costs. It is a much more challenging problem in network science. In this paper, we present a novel strategy for this generalized network dismantling problem by characterizing the relationship between blocks and cut nodes. We firstly construct an auxiliary block-cut tree T from the original network G, where the nodes in the tree T have two types which correspond to either blocks or cut nodes of G, and edges of T only exist between two different type of nodes. Then we transform the problem of partitioning G by removing nodes to the problem of partitioning T by removing edges, both at a minimum overall cost. Finally partitioning T can be solved by a weighted spectral clustering algorithm. When we apply this new strategy on real-world networks, it performs equally or even better than the current state-of-the-art methods.

Coordinated network partition detection and bi-connected inter-partition topology creation in damaged sensor networks using multiple UAVs

Reliable connectivity restoration mechanism is essential for retaining the prolonged network functioning of Wireless Sensor and Actor Networks (WSANs). WSANs operate in harsh or inhospitable environments and are susceptible to multiple node failures that may fragment the fully connected network into disparate fragments. The well-known network recovery techniques deploy new relay nodes for recovery and introduce more cut vertices in the network that generates the resulting network topology vulnerable to further partitioning. Therefore, it is advantageous to identify the network partitions in less time and establish a fault-tolerant topology during the network restoration. This paper provides a new coordinated network partition detection and Bi-connected Inter-partition Topology creation solution in damaged sensor networks using multiple UAVs (UAV-BITS) that operates in different phases. UAV-BITS employs multiple UAVs to identify the network partitions and engages network nodes to self-identify their partitions by creating Connected Component Sets (CCSs) iteratively. During the network recovery process, UAV-BITS creates two-vertex disjoint paths between the network partitions to make the recovered network topology fault-tolerant. UAV-BITS is assessed according to various parameters like the number of deployed relay nodes, the number of messages transmitted during detection and recovery phases, network partition detection and recovery time, and distance traveled by UAVs. The performance of CCS based partition detection mechanism is also compared with a similar UAVs-assisted partition detection approach. The working of existing bi-connected topology creation algorithms that employ representative nodes is also analyzed and compared with the proposed recovery algorithm. The simulation results illustrate that UAV-BITS provides a better fault-tolerant network topology than already proposed solutions. The algorithm also reduces the travel distance of UAVs and detection time.

Time-optimal construction of overlay networks

This article shows how to construct an overlay network of constant degree and diameter O(log n) in O(log n) time starting from an arbitrary weakly connected graph. We assume a synchronous communication network in which nodes can send messages to nodes they know the identifier of, and new connections can be established by sending node identifiers. Suppose the initial network’s graph is weakly connected and has constant degree. In that case, our algorithm constructs the desired topology with each node sending and receiving only O(log n) messages in each round in O(log n) time w.h.p., which beats the currently best O(log ^{3/2} n) time algorithm of Götte et al. (International colloquium on structural information and communication complexity (SIROCCO), Springer, 2019). Since the problem cannot be solved faster than by using pointer jumping for O(log n) rounds (which would even require each node to communicate Omega (n) bits), our algorithm is asymptotically optimal. We achieve this speedup by using short random walks to repeatedly establish random connections between the nodes that quickly reduce the conductance of the graph using an observation of Kwok and Lau (Approximation, randomization, and combinatorial optimization. Algorithms and techniques (APPROX/RANDOM 2014), Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, 2014). Additionally, we show how our algorithm can be used to efficiently solve graph problems in hybrid networks (Augustine et al. in Proceedings of the fourteenth annual ACM-SIAM symposium on discrete algorithms, SIAM, 2020). Motivated by the idea that nodes possess two different modes of communication, we assume that communication of the initial edges is unrestricted, whereas only polylogarithmically many messages can be sent over edges that have been established throughout an algorithm’s execution. For an (undirected) graph G with arbitrary degree, we show how to compute connected components, a spanning tree, and biconnected components in O(log n) time w.h.p. Furthermore, we show how to compute an MIS in O(log d + log log n) time w.h.p., where d is the initial degree of G.

Parsimony and the rank of a flattening matrix

The standard models of sequence evolution on a tree determine probabilities for every character or site pattern. A flattening is an arrangement of these probabilities into a matrix, with rows corresponding to all possible site patterns for one set A of taxa and columns corresponding to all site patterns for another set B of taxa. Flattenings have been used to prove difficult results relating to phylogenetic invariants and consistency and also form the basis of several methods of phylogenetic inference. We prove that the rank of the flattening equals r^{nu _T(A|B)}, where r is the number of states and nu _T(A|B) is the minimum size of a vertex cut separating A from B. When T is binary the rank of the flattening equals r^{ell _T(A|B)} where ell _T(A|B) equals the parsimony length of the binary character separating A and B. We provide a direct proof that requires little more than undergraduate algebra, but note that the formula could also be derived from work by Casanellas and Fernández-Sánchez (2011) on phylogenetic invariants.

THE PHONOLOGICAL PROBLEMS AMONG NON-ARABIC SPEAKING STUDENTS OF HAUSA AND METHODS OF SOLVING THEM

This article aims to study the pronunciation problems related to the phonetic aspect that non-Arabic-speaking students of Hausa suffer from, and the study adopted the descriptive analytical approach and the contrastive approach. The significance of this study comes from the fact that it seeks to study the most important branch among the linguistic branches, which is the phonetics. It also acquires its importance in that it is based on analyzing the difficulties experienced by Hausa students when pronouncing some Arabic sounds, and shows the reason for these difficulties, while drawing methods to overcome them and putting steps to solve these problems. The study concluded that pronouncing some Arabic sounds is one of the biggest linguistic problems that most Hausa students suffer from, due to the difference of their mother tongue (Hausa) from the Arabic language in sound pattern, points of articulation, manners and the pronunciation habits of the Arabic native speakers. The finding also revealed that the majority of these students face Great difficulty in pronouncing Arabic sounds that do not exist in Hausa Language, such as: (Өث , ḥح , ḫخ , ’ع , ṣص , ḍض , ḏذ , d⸮ظ ) and we also found that, the pronunciation of the dark sounds correctly, is one of the big problem to them.

On Whitehead’s cut vertex lemma

Abstract One version of Whitehead’s famous cut vertex lemma says that if an element of a free group is part of a free basis, then a certain graph associated to its conjugacy class that we call the star graph is either disconnected or has a cut vertex. We state and prove a version of this lemma for conjugacy classes of elements and convex-cocompact subgroups of groups acting cocompactly on trees with finitely generated edge stabilizers.

Total eccentricity index of graphs with fixed number of pendant or cut vertices

The total eccentricity index of a connected graph is defined as sum of the eccentricities of all its vertices. In this paper, we give the sharp upper bound on the total eccentricity index over graphs with fixed number of pendant vertices and the sharp lower bound on the same over graphs with fixed number of cut vertices. We also provide the sharp upper bounds on the total eccentricity index over graphs with s cut vertices for \(s=0, 1, n-3, n-2\) and propose a conjecture for \(2\le s\le n-4\).

Gangguan Perkembangan Bahasa pada Anak Usia 5 Tahun (Observasi pada Kasus Ahmad Djiat) Desa Moutong, Kecamatan Tilongkabila

This study aims to describe the condition of speech disorders experienced by children aged 5 years. Technical data collection is done through observation and interviews with children who are the object of research. The results of observations and analyzes carried out refer to psycholinguistic studies related to language disorders. It was found that the speech disorder experienced by Djiat was caused by a disturbance in his nervous system which was triggered by an injury or trauma during the prenatal period. Speech disorders are also caused by the lack of a good stimulus from the environment. Thus, children who experience difficulties in transformation really need communication activities. One of the symptoms in children with language and speech disorders is that there are pronunciation errors, both in the mechanism of the movement of the points of articulation and in the pronunciation. Handling that can be done for children who experience language and speech disorders is to do speech therapy, oral motor, and melodic intonation

New results on imbalance graphic graphs

An edge imbalance provides a local measure of how irregular a given graph is. In this paper, we study graphs with graphic imbalance sequences. We give a new proof of imbalance graphicness for trees and use the new idea to prove that the same holds for unicyclic graphs. We then show that antiregular graphs are imbalance graphic and consider the join operation on graphs as well as the double graph operation. Our main results are concerning imbalance graphicness of three classes of block graphs: block graphs having all cut vertices in a single block; block graphs in which the subgraph induced by the cut vertices is either a star or a path. In the end, we discuss open questions and conjectures regarding imbalance graphic graphs.