Analysis on the Status Quo and Paths of Informatization Teaching Ability of Teachers in Rural Primary and Middle Schools in Hotan Area

This study conducted an in-depth analysis of the informatization teaching ability of teachers in rural primary and secondary schools in Hotan area through the literature method and questionnaire survey method. The investigation is mainly conducted in the aspects of teachers’ informatization awareness, teachers’ informatization ability, informatization application status, and existing problems, etc., analyzing the constraints existing in the informatization teaching of rural elementary and middle schools teachers, and making targeted improvements Strategies for teachers’ informatization teaching ability in rural elementary and middle schools: raising awareness of informatization teaching; informatization teaching training; informatization evaluation system; establishing a systematic and complete management system

The complexity of determining the rainbow vertex-connection of graphs

A vertex-colored graph is {\it rainbow vertex-connected} if any two vertices are connected by a path whose internal vertices have distinct colors, which was introduced by Krivelevich and Yuster. The {\it rainbow vertex-connection} of a connected graph $G$, denoted by $rvc(G)$, is the smallest number of colors that are needed in order to make $G$ rainbow vertex-connected. In this paper, we study the computational complexity of vertex-rainbow connection of graphs and prove that computing $rvc(G)$ is NP-Hard. Moreover, we show that it is already NP-Complete to decide whether $rvc(G)=2$. We also prove that the following problem is NP-Complete: given a vertex-colored graph $G$, check whether the given coloring makes $G$ rainbow vertex-connected.Comment: 7 page

Convergence and stability of Galerkin finite element method for hyperbolic partial differential equation with piecewise continuous arguments of advanced type

This paper deals with the convergence and stability of Galerkin finite element method for a hyperbolic partial differential equations with piecewise continuous arguments of advanced type. First of all, we obtain the expression of analytic solution by the method of separation variable, then the sufficient conditions for stability are obtained. Semidiscrete and fully discrete schemes are derived by Galerkin finite element method, and their convergence are both analyzed in L2-norm. Moreover, the stability of the two schemes are investigated. The semidiscrete scheme can achieve unconditionally stability. The sufficient conditions of stability for fully discrete scheme are derived under which the analytic solution is asymptotically stable. Finally, some numerical experiments are presented to illustrate the theoretical results

Toward Measuring Network Aesthetics Based on Symmetry

In this exploratory paper, we discuss quantitative graph-theoretical measures of network aesthetics. Related work in this area has typically focused on geometrical features (e.g., line crossings or edge bendiness) of drawings or visual representations of graphs which purportedly affect an observer’s perception. Here we take a very different approach, abandoning reliance on geometrical properties, and apply information-theoretic measures to abstract graphs and networks directly (rather than to their visual representaions) as a means of capturing classical appreciation of structural symmetry. Examples are used solely to motivate the approach to measurement, and to elucidate our symmetry-based mathematical theory of network aesthetics

A Two-stage Flow-based Intrusion Detection Model ForNext-generation Networks

The next-generation network provides state-of-the-art access-independent services over converged mobile and fixed networks. Security in the converged network environment is a major challenge. Traditional packet and protocol-based intrusion detection techniques cannot be used in next-generation networks due to slow throughput, low accuracy and their inability to inspect encrypted payload. An alternative solution for protection of next-generation networks is to use network flow records for detection of malicious activity in the network traffic. The network flow records are independent of access networks and user applications. In this paper, we propose a two-stage flow-based intrusion detection system for next-generation networks. The first stage uses an enhanced unsupervised one-class support vector machine which separates malicious flows from normal network traffic. The second stage uses a self-organizing map which automatically groups malicious flows into different alert clusters. We validated the proposed approach on two flow-based datasets and obtained promising results

An Examination of Not-For-Profit Stakeholder Networks for Relationship Management: A Small-Scale Analysis on Social Media

Using a small-scale descriptive network analysis approach, this study highlights the importance of stakeholder networks for identifying valuable stakeholders and the management of existing stakeholders in the context of mental health not-for-profit services. We extract network data from the social media brand pages of three health service organizations from the U.S., U.K., and Australia, to visually map networks of 579 social media brand pages (represented by nodes), connected by 5,600 edges. This network data is analyzed using a collection of popular graph analysis techniques to assess the differences in the way each of the service organizations manage stakeholder networks. We also compare node meta-information against basic topology measures to emphasize the importance of effectively managing relationships with stakeholders who have large external audiences. Implications and future research directions are also discussed

The maximal matching energy of tricyclic graphs

Abstract Gutman and Wagner proposed the concept of the matching energy (M E) and pointed out that the chemical applications of M E go back to the 1970s. Let G be a simple graph of order n and µ 1 , µ 2 , . . . , µ n be the roots of its matching polynomial. The matching energy of G is defined to be the sum of the absolute values of µ i (i = 1, 2, . . . , n). Gutman and Cvetković determined the tricyclic graphs on n vertices with maximal number of matchings by a computer search for small values of n and by an induction argument for the rest. Based on this result, in this paper, we characterize the graphs with the maximal value of matching energy among all tricyclic graphs, and completely determine the tricyclic graphs with the maximal matching energy. We prove our result by using Coulson-type integral formula of matching energy, which is similar as the method to comparing the energies of two quasi-order incomparable graphs

A Note on Distance-based Graph Entropies

A variety of problems in, e.g., discrete mathematics, computer science, information theory, statistics, chemistry, biology, etc., deal with inferring and characterizing relational structures by using graph measures. In this sense, it has been proven that information-theoretic quantities representing graph entropies possess useful properties such as a meaningful structural interpretation and uniqueness. As classical work, many distance-based graph entropies, e.g., the ones due to Bonchev et al. and related quantities have been proposed and studied. Our contribution is to explore graph entropies that are based on a novel information functional, which is the number of vertices with distance (k) to a given vertex. In particular, we investigate some properties thereof leading to a better understanding of this new information-theoretic quantity