An efficient method to improve the quality of tetrahedron mesh with MFRC

In this paper, we proposed a novel operation to reconstruction tetrahedrons within a certain region, which we call MFRC (Multi-face reconstruction). During the existing tetrahedral mesh improvement methods, the flip operation is one of the very important components. However, due to the limited area affected by the flip, the improvement of the mesh quality by the flip operation is also very limited. The proposed MFRC algorithm solves this problem. MFRC can reconstruct the local mesh in a larger range and can find the optimal tetrahedron division in the target area within acceptable time complexity. Therefore, based on the MFRC algorithm, we combined other operations including smoothing, edge removal, face removal, and vertex insertion/deletion to develop an effective mesh quality improvement method. Numerical experiments of dozens of meshes show that the algorithm can effectively improve the low-quality elements in the tetrahedral mesh, and can effectively reduce the running time, which has important significance for the quality improvement of large-scale mesh.

Hogyan befolyásolja a villamosenergia-hálózatról rendelkezésre álló információ a fizikai támadások által okozott sérülékenységről alkotott képet?

Összefoglaló. A villamosenergia-rendszerek fizikai támadásokkal szembeni ellenálló képessége a közelmúltban világszerte történt események ismeretében egyre nagyobb hangsúlyt kap a tématerület kutatásaiban. Az ilyen eseményekre való megfelelő felkészüléshez elengedhetetlen az üzemeltetett infrastruktúrának, elsősorban annak gyengeségeinek pontos ismerete. A cikkben Magyarország villamosenergia-hálózatának adatai alapján készített súlyozatlan és súlyozott gráfokon végzünk vizsgálatokat, hogy megértsük a különböző stratégia mentén kiválasztott célpontok elleni támadások milyen mértékben csökkentik a topológiai hatékonyságot. A cikk célja egyben a magyar hálózat sérülékenységének általános bemutatása is, mely hasznos bemeneti információ lehet a kockázati tervek elkészítésekor. Summary. Tolerance of the power grid against physical intrusions has gained importance in the light of various attacks that have taken place around the world. To adequately prepare for such events, grid operators have to possess a deep understanding of their infrastructure, more specifically, of its weaknesses. A graph representation of the Hungarian power grid was created in a way that the vertices are generators, transformers, and substations and the edges are high-voltage transmission lines. All transmission and sub-transmission elements were considered, including the 132 kV network as well. The network is subjected to various types of single and double element attacks, objects of which are selected according to different aspects. The vulnerability of the network is measured as a relative drop in efficiency when a vertex or an edge is removed from the network. Efficiency is a measure of the network’s performance, assuming that the efficiency for transmitting electricity between vertices i and j is proportional to the reciprocal of their distance. In this paper, simultaneous removals were considered, arranged into two scenarios (single or double element removal) and a total of 5 cases were carried out (single vertex removal, single edge removal, double vertex removal, double edge removal, single vertex and single edge removal). During the examinations, all possible removal combinations were simulated, thus the 5 cases represent 385, 504, 73920, 128271 and 193797 runs, respectively. After all runs were performed, damage values were determined for random and targeted attacks, and attacks causing maximal damage were also identified. In all cases, damage was calculated for unweighted and weighted networks as well, to enable the comparison of those two models. The aims of this paper are threefold: to perform a general assessment on the vulnerability of the Hungarian power grid against random and targeted attacks; to compare the damage caused by different attack strategies; and to highlight the differences between using unweighted and weighted graphs representations. Random removal of a single vertex or a single edge caused 0.3–0.4% drop in efficiency, respectively, which indicates a high tolerance against such attacks. Damage for random double attacks was still only in the range of 0.6–0.8%, which is acceptable. It was shown that if targets are selected by the attacker based on the betweenness rank of the element, damage would be below the maximal possible values. Comparison of the damage measured in the unweighted and the weighted network representations has shown that damage to the weighted network tends to be bigger for vertex attacks, but the contrary is observed for edge attacks. Numerical differences between the two representations do not show any trend that could be generalised, but in the case of the most vulnerable elements significant differences were found in damage measures, which underlines the importance of using weighted models.

Qualitative Regionalization of Bay of Bengal

Clustering is an essential statistical technique to find subgroups within a dataset. Clustering helps to uncover hidden relationships among the observational variables in the data. Many researchers have applied clustering techniques across a number of knowledge domains with success. Here we focus on application to ocean science, more particularly to the north region of the Indian Ocean, i.e., the Bay of Bengal. In this article, Regionalization is carried out for the Bay of Bengal to group the regions with similar characteristics using a graph-based clustering technique called SKATER (Spatial ‘K’luster Analysis by Tree Edge Removal). These subgroups are consistent with observations that characterize the near-surface features of the Bay of Bengal.

Critical concepts of restrained domination in signed graphs

A signed graph [Formula: see text] is a simple undirected graph in which each edge is either positive or negative. Restrained dominating set [Formula: see text] in [Formula: see text] is a restrained dominating set of the underlying graph [Formula: see text] where the subgraph induced by the edges across [Formula: see text] and within [Formula: see text] is balanced. The minimum cardinality of a restrained dominating set of [Formula: see text] is called the restrained domination number, denoted by [Formula: see text]. In this paper, we initiate the study on various critical concepts to investigate the effect of edge removal or edge addition on restrained domination number in signed graphs.

Election Manipulation on Social Networks: Seeding, Edge Removal, Edge Addition

We focus on the election manipulation problem through social influence, where a manipulator exploits a social network to make her most preferred candidate win an election. Influence is due to information in favor of and/or against one or multiple candidates, sent by seeds and spreading through the network according to the independent cascade model. We provide a comprehensive theoretical study of the election control problem, investigating two forms of manipulations: seeding to buy influencers given a social network and removing or adding edges in the social network given the set of the seeds and the information sent. In particular, we study a wide range of cases distinguishing in the number of candidates or the kind of information spread over the network. Our main result shows that the election manipulation problem is not affordable in the worst-case, even when one accepts to get an approximation of the optimal margin of victory, except for the case of seeding when the number of hard-to-manipulate voters is not too large, and the number of uncertain voters is not too small, where we say that a voter that does not vote for the manipulator's candidate is hard-to-manipulate if there is no way to make her vote for this candidate, and uncertain otherwise. We also provide some results showing the hardness of the problems in special cases. More precisely, in the case of seeding, we show that the manipulation is hard even if the graph is a line and that a large class of algorithms, including most of the approaches recently adopted for social-influence problems (e.g., greedy, degree centrality, PageRank, VoteRank), fails to compute a bounded approximation even on elementary networks, such as undirected graphs with every node having a degree at most two or directed trees. In the case of edge removal or addition, our hardness results also apply to election manipulation when the manipulator has an unlimited budget, being allowed to remove or add an arbitrary number of edges, and to the basic case of social influence maximization/minimization in the restricted case of finite budget. Interestingly, our hardness results for seeding and edge removal/addition still hold in a re-optimization variant, where the manipulator already knows an optimal solution to the problem and computes a new solution once a local modification occurs, e.g., the removal/addition of a single edge.

Criminal networks analysis in missing data scenarios through graph distances

Data collected in criminal investigations may suffer from issues like: (i) incompleteness, due to the covert nature of criminal organizations; (ii) incorrectness, caused by either unintentional data collection errors or intentional deception by criminals; (iii) inconsistency, when the same information is collected into law enforcement databases multiple times, or in different formats. In this paper we analyze nine real criminal networks of different nature (i.e., Mafia networks, criminal street gangs and terrorist organizations) in order to quantify the impact of incomplete data, and to determine which network type is most affected by it. The networks are firstly pruned using two specific methods: (i) random edge removal, simulating the scenario in which the Law Enforcement Agencies fail to intercept some calls, or to spot sporadic meetings among suspects; (ii) node removal, modeling the situation in which some suspects cannot be intercepted or investigated. Finally we compute spectral distances (i.e., Adjacency, Laplacian and normalized Laplacian Spectral Distances) and matrix distances (i.e., Root Euclidean Distance) between the complete and pruned networks, which we compare using statistical analysis. Our investigation identifies two main features: first, the overall understanding of the criminal networks remains high even with incomplete data on criminal interactions (i.e., when 10% of edges are removed); second, removing even a small fraction of suspects not investigated (i.e., 2% of nodes are removed) may lead to significant misinterpretation of the overall network.