Search Results (13)

To understand the spread of the pine wood nematode Bursaphelenchus xylophilus (Steiner and Buhrer, 1934; Nickle, 1970) and identify infected trees, the dispersal ability of insects was examined. In this study, the effects of sex, adult age, and morphological traits on the flight performance (such as flight distance, time, and speed) of Monochamus alternatus (Hope, 1843) were investigated using flight mills. Over a period of 8 weeks, a total of 42 newly emerged adult beetles were tethered to flight mills once a week. Flight distance and time were recorded for 2 h during each session. The total flight distance of individuals that flew more than 100 m during each session was calculated. The results showed that females flew an average of 6.65 km, for 59.6 min, while males flew an average of 9.89 km, for 85.8 min. In a single flight experimental session, both sexes could fly up to approximately 2 km and were found to fly at an average speed of 1.9 m s⁻¹. In our principal component analysis (PCA), the first and second principal components were found to be highly correlated with the sex, morphological traits, and flight performances of M. alternatus. This study demonstrates that the flight ability of M. alternatus varies significantly according to body size and sex, which is fundamental and crucial for understanding the dispersal patterns of pine wilt disease. Full article

Steiner $(k,k^{\prime })$-eccentricity on a given fixed $k^{\prime }$-subset in a graph G is the maximum Steiner distance over all k-subsets of $V\left(G\right)$ which contain the fixed $k^{\prime }$-set, where the Steiner distance of a set is the size of a minimum Steiner tree on this set in a graph. Let $R\subseteq V\left(T\right)$ be the given fixed $k^{\prime }$-subset in a tree T. Let $k_1$ and $k_2$ be two integers such that $k_1\ge k_2\ge k^{\prime }$. We prove that, in a tree, every optimal solution of Steiner $(k_1,k^{\prime })$-eccentricity on R takes some optimal solution of Steiner $(k_2,k^{\prime })$-eccentricity on R as a partial solution. On the other hand, every optimal solution of Steiner $(k_2,k^{\prime })$-eccentricity on R is part of some optimal solution of Steiner $(k_1,k^{\prime })$-eccentricity on the set R in a tree. Finally, we present an $O\left(kn\right)$-time algorithm to solve Steiner $(k,k^{\prime })$-eccentricity on a given fixed $k^{\prime }$-set in trees. Full article

Multi-Agent Systems (MAS) are widely deployed in smart factory environments, where efficient task assignment and path planning for agents can greatly enhance production efficiency. Existing algorithms usually ignore resource constraints, overly simplify the geometric shape of agents, and perform poorly in large-scale scenarios. In this paper, we propose a Multi-Factor Task Assignment and Adaptive Window Enhanced Conflict-Based Search (MTA-AWECBS) algorithm to solve these problems, which considers the resource constraints and volume of agents, improving the algorithm’s scalability and adaptability. In task assignment, a novel scheme is designed by considering distance cost, maximum travel distances, and maximum number of executable tasks. In path planning, we first propose a new mathematical description of global traffic congestion level. Based on this, an adaptive window is proposed to dynamically adjust the time horizon in the WECBS algorithm, improving search efficiency and solving the deadlock issue. Additionally, based on experimental observations, two optimization strategies are proposed to further improve operation efficiency. The experimental results show that MTA-AWECBS outperforms Token Passing (TP), Token Passing with Task Swaps (TPTSs), and Conflict-Based Steiner Search (CBSS) in handling a large number of tasks and agents, achieving an average $39\%$ reduction in timestep cost and an average $22\%$ reduction in total path cost. Full article

In this paper, we primarily investigate and establish several properties of spherical Steiner symmetrizations, along with the isoperimetric property of the spherical cap in ${\mathbb{S}}^n$. Specifically, we study the monotonically decreasing property of the measure of the symmetric difference of two spherical compact sets, the monotonically decreasing property of the spherical diameter of a spherical compact set, the convergence of iterative spherical Steiner symmetrizations, and so on. In particular, we prove that the sequence of iterative spherical Steiner symmetrizations of $K\subset {\mathbb{S}}^n$, which follow sequences selected from a finite set of directions, converges to a spherical cap with the same measure as K, extending the result from ${\mathbb{R}}^n$ to ${\mathbb{S}}^n$ on Steiner symmetrizations. It provides us with valuable insights for studying the relevant applications and conclusions of spherical Steiner symmetrizations. Full article

With the increasing demand for online shopping and home delivery services, optimizing the routing of electric delivery vehicles in urban areas is crucial to reduce environmental pollution and improve operational efficiency. To address this opportunity, we optimize the Steiner Traveling Salesman Problem (STSP) for electric vehicles (EVs) in urban areas by combining city graphs with topographic and traffic information. The STSP is a variant of the traditional Traveling Salesman Problem (TSP) where it is not mandatory to visit all the nodes present in the graph. We train an artificial neural network (ANN) model to estimate electric consumption between nodes in the route using synthetic data generated with historical traffic simulation and topographical data. This allows us to generate smaller-weighted graphs that transform the problem from an STSP to a normal TSP where the 2-opt optimization algorithm is used to solve it with a Nearest Neighbor (NN) initialization. Compared to the approach of optimizing routes based on distance, our proposed algorithm offers a fast solution to the STSP for EVs (EV-STSP) with routes that consume 17.34% less energy for the test instances generated. Full article

In 1994, Dobrynin and Kochetova introduced the concept of degree distance $DD(\Gamma )$ of a connected graph $\Gamma$. Let $d_{\Gamma }\left(S\right)$ be the Steiner k-distance of $S\subseteq V(\Gamma )$. The Steiner Wiener k-index or k-center Steiner Wiener index${SW}_k(\Gamma )$ of $\Gamma$ is defined by ${SW}_k(\Gamma )={\sum }_{\stackrel{S\subseteq V(\Gamma )}{\left|S\right|=k}}{d}_{\Gamma }\left(S\right).$ The k-center Steiner degree distance${SDD}_k(\Gamma )$ of a connected graph $\Gamma$ is defined by ${SDD}_k(\Gamma )={\sum }_{\stackrel{S\subseteq V(\Gamma )}{\left|S\right|=k}}\left[{\sum }_{v\in S}de{g}_{\Gamma }\left(v\right)\right]d_{\Gamma }\left(S\right)$, where $de{g}_{\Gamma }\left(v\right)$ is the degree of the vertex v in $\Gamma$. In this paper, we consider the Nordhaus–Gaddum-type results for ${SW}_k(\Gamma )$ and ${SDD}_k(\Gamma )$. Upper bounds on ${SW}_k(\Gamma )+{SW}_k\left(\overline{\Gamma }\right)$ and ${SW}_k(\Gamma )·{SW}_k\left(\overline{\Gamma }\right)$ are obtained for a connected graph $\Gamma$ and compared with previous bounds. We present sharp upper and lower bounds of ${SDD}_k(\Gamma )+{SDD}_k\left(\overline{\Gamma }\right)$ and ${SDD}_k(\Gamma )·{SDD}_k\left(\overline{\Gamma }\right)$ for a connected graph $\Gamma$ of order n with maximum degree $\Delta$ and minimum degree $\delta$. Some graph classes attaining these bounds are also given. Full article

The aim of this study was to evaluate the relationship between skeletal sagittal nasal profile morphology and sagittal skeletal malocclusions. Regarding lateral cephalometric films, the study was conducted in a total of 135 individuals without any prior orthodontic treatment (mean age of 17.91 ± 1.91), including 49 males (mean age 17.91 ± 1.16) and 86 females (mean age 17.78 ± 1.91 years). The groups were divided into two groups as male and female according to gender, and three groups as skeletal Class 1, Class 2, and Class 3 according to the Steiner’s ANB angle. In addition, skeletal groups were compared within groups by dividing into two groups of male and female. A total of eight parameters, three skeletal sagittal angular (SNA, SNB, and ANB angles), four nasal linear (R-A, N-A, N-ANS, and N-R distances) and one nasal angular (N1-N2/N2-R angle), were measured on each cephalometric film. The arithmetic mean and standard deviation of all measured nasal parameters were calculated. For statistical analysis, independent sample t-test and one-way analysis of variance (One-Way ANOVA) were used for normally distributed data, and Mann Whitney U and Kruskal Wallis tests were used for data that did not show normal distribution. For statistical analysis, p < 0.05 was considered significant. R-A, N-A, and N-ANS linear nasal parameters differed significantly between the male and female groups, which were evaluated regardless of the skeletal groups, with a higher rate in males (p < 0.05). N-R linear nasal parameter showed a statistically significant difference between skeletal malocclusion groups, which were evaluated regardless of gender. N-R distance was found to be significantly longer in skeletal Class 3 individuals than in Class 1 and 2 individuals (p < 0.05). There was no statistically significant difference in nasal bone concavity angle in all groups (p > 0.05). R-A and N-A linear nasal parameters showed statistically significant differences between male and female sex groups in all skeletal malocclusion classes (p < 0.05). At first, results showed that males had longer measurements than females in all linear nasal parameters. Second, longer measurements were found in all linear nasal parameters in skeletal Class 3 individuals than those in skeletal Class 1 and Class 2 individuals. Third, the nasal bone concavity angle was greater in skeletal Class 2 individuals than the others. Full article

In 1989, Chartrand, Oellermann, Tian and Zou introduced the Steiner distance for graphs. This is a natural generalization of the classical graph distance concept. Let $\Gamma$ be a connected graph of order at least 2, and $S\backslash V(\Gamma )$. Then, the minimum size among all the connected subgraphs whose vertex sets contain S is the Steiner distance$d_{\Gamma }\left(S\right)$ among the vertices of S. The Steiner k-eccentricity $e_k\left(v\right)$ of a vertex v of $\Gamma$ is defined by $e_k\left(v\right)=max\{d_{\Gamma }\left(S\right)|S\backslash V(\Gamma ),|S|=k,andv\in S\}$, where n and k are two integers, with $2\le k\le n$, and the Steiner k-diameter of $\Gamma$ is defined by ${sdiam}_k(\Gamma )=max\left\{e_k\left(v\right)\right|v\in V(\Gamma )\}$. In this paper, we present an algorithm to derive the Steiner distance of a graph; in addition, we obtain a relationship between the Steiner k-diameter of a graph and its line graph. We study various properties of the Steiner diameter through a combinatorial approach. Moreover, we characterize graph $\Gamma$ when ${sdiam}_k(\Gamma )$ is given, and we determine ${sdiam}_k(\Gamma )$ for some special graphs. We also discuss some of the applications of Steiner diameter, including one in education networks. Full article

In this study, we examine the dual expression of Valeontis’ concept of parallel p-equidistant ruled surfaces well known in Euclidean 3-space, according to the Study mapping. Furthermore, we show that the dual part of the dual angle on the unit dual sphere corresponds to the p-distance. We call these ruled surfaces we obtained “dual parallel equidistant ruled surfaces” and we briefly denote them with “DPERS”. Furthermore, we find the Blaschke vectors, the Blaschke invariants and the striction curves of these DPERS and we give the relationships between these elements. Moreover, we show the relationships between the Darboux screws, the instantaneous screw axes, the instantaneous dual Pfaff vectors and dual Steiner rotation vectors of these surfaces. Finally, we give an example, which we reinforce this article, and we explain all of these features with the figures on the example. Furthermore, we see that the corresponding dual curves on the dual unit sphere to these DPERS are such that one of them is symmetric with respect to the imaginary symmetry axis of the other. Full article

In this paper, the fluctuation properties of the number of energy levels (mode fluctuation) are studied in the mixed-type lemon billiards at high lying energies. The boundary of the lemon billiards is defined by the intersection of two circles of equal unit radius with the distance $2B$ between the centers, as introduced by Heller and Tomsovic. In this paper, the case of two billiards, defined by $B=0.1953,0.083$, is studied. It is shown that the fluctuation of the number of energy levels follows the Gaussian distribution quite accurately, even though the relative fraction of the chaotic part of the phase space is only 0.28 and 0.16, respectively. The theoretical description of spectral fluctuations in the Berry–Robnik picture is discussed. Also, the (golden mean) integrable rectangular billiard is studied and an almost Gaussian distribution is obtained, in contrast to theory expectations. However, the variance as a function of energy, E, behaves as $\sqrt{E}$, in agreement with the theoretical prediction by Steiner. Full article

We studied paraxial light beams, obtained by a continuous superposition of off-axis Gaussian beams with their phases chosen so that the whole superposition is invariant to free-space propagation, i.e., does not change its transverse intensity shape. Solving a system of five nonlinear equations for such superpositions, we obtained an analytical expression for a propagation-invariant off-axis elliptic Gaussian beam. For such an elliptic beam, an analytical expression was derived for the orbital angular momentum, which was shown to consist of two terms. The first one is intrinsic and describes the momentum with respect to the beam center and is shown to grow with the beam ellipticity. The second term depends parabolically on the distance between the beam center and the optical axis (similar to the Steiner theorem in mechanics). It is shown that the ellipse orientation in the transverse plane does not affect the normalized orbital angular momentum. Such elliptic beams can be used in wireless optical communications, since their superpositions do not interfere in space, if they do not interfere in the initial plane. Full article

Building upon the notion of the Gutman index $SGut\left(G\right)$, Mao and Das recently introduced the Steiner Gutman index by incorporating Steiner distance for a connected graph G. The Steiner Gutman k-index ${SGut}_k\left(G\right)$ of G is defined by ${SGut}_k\left(G\right)$$={\sum }_{S\subseteq V\left(G\right),\left|S\right|=k}\left({\prod }_{v\in S}de{g}_G\left(v\right)\right)d_G\left(S\right)$, in which $d_G\left(S\right)$ is the Steiner distance of S and $de{g}_G\left(v\right)$ is the degree of v in G. In this paper, we derive new sharp upper and lower bounds on ${SGut}_k$, and then investigate the Nordhaus-Gaddum-type results for the parameter ${SGut}_k$. We obtain sharp upper and lower bounds of ${SGut}_k\left(G\right)+{SGut}_k\left(\overline{G}\right)$ and ${SGut}_k\left(G\right)·{SGut}_k\left(\overline{G}\right)$ for a connected graph G of order n, m edges, maximum degree $\Delta$ and minimum degree $\delta$. Full article

Connectivity has significance in both of data collection and aggregation for Wireless Sensor Networks (WSNs). Once the connectivity is lost, relay nodes are deployed to build a Steiner Minimal Tree (SMT) such that the inter-component connection is reestablished. In recent years, there has been a growing interest in connectivity restoration problems. In previous works, the deployment area of a WSN is assumed to be flat without obstacles. However, such an assumption is not realistic. In addition, most of the existing strategies chose the representative of each component, which serves as the starting point of relay node deployment during the connectivity restoration, either in a random way or in the shortest-distance based manner. In fact, both ways of representative selection could potentially increase the length of the SMT such that more relay nodes are required. In this paper, a novel connectivity restoration strategy is proposed—Obstacle–Avoid connectivity restoration strategy based on Straight Skeletons (OASS), which employs both the polygon based representative selection with the presence of obstacles and the straight skeleton based SMT establishment. The OASS is proved to be a 3- $opt$ approximation algorithm with the complexity of $O(nlogn)$ , and the approximation ratio can reduce to $\frac{3\sqrt{3}}{2}$ while it satisfies a certain condition. The theoretical analysis and simulations show that the performance of the OASS is better than other strategies in terms of the relay count and the quality of the established topology (i.e., distances between components, delivery latency and balanced traffic load) as well. Full article