Abstract:
The problem addressed in this paper is the detection of defects on atomic structures. The procedure proposed is in two steps. At first a tessellation is built starting from the atoms. It consists of a partition of the space into cells, and is used to define the neighbourhood relationships between the atoms. Then, the local contribution to a topological parameter, namely the Euler-Poincare characteristic, is defined and measured for each cell. Within a regular tessellation, made of identical cells, this local contribution is equal to zero. Any local deviation from regularity corresponds to a tessellation containing cells with non-zero contributions. This allows us to locate the defects from a topological criterion and opens the way to a fully automatic detection of interfaces at atomic scale. The procedure is applied in 2D space for the detection of edge dislocations, grain boundaries and twins from HREM models and images. A 3D example is also given to illustrate its generality.

Abstract:
According to the research progress of software networks in these years, the software structural networks show the same characteristics with complex networks and the software topological structure has an effect on the quality characteristics of software systems. The research work begins with the statistics analysis of three characteristic values, which can reflect the efficiency, complexity and orderliness of software systems separately, of 500 open source software systems. Then D(AP), D(AD) and D(E) are presented for measuring the quality characteristics of software systems refer to the definition of deviation of characteristic value and quality characteristics relative to software scale. By testing on seven Linux kernels of different versions, the metrics on software networks based on deviation of characteristic values is validated effective.

Abstract:
We evolve topology of a network of N fully-coupled nodes that interact according to repulsion-attractiondynamics within a confining wall. The dynamics portrays each node’s tendency to keep distance from itscompetitors while maintaining a lighter tendency to resist relative isolation. Each node is characterizedby two parameters: an intrinsic mobility μ and a preferred neighboring distance ρ. Onset of clustering isfound to occur at a critical variance in mobility, σμ2 = 1, and in preferred neighboring distance, σμ2 = 10.This result implies that small-world behavior manifested in clustering can be triggered by the diversity ofnode population.

Abstract:
Sampling bias caused by few points was first present,and by increasing the measurement points can reduce the omission of network edge.Based on the giant data samples authorized by CAIDA,the distribution of network nodes was analyzed respectively.The distribution of frequency-degree presents that the nodes of network follows power-law,and the distribution of network nodes exists heterogeneity confirmed by the degree-rank distribution.Cumulative function indicates that Weibull distribution may be more suitabl...

Abstract:
Abstract problems about attainability in topological spaces are considered. Some nonsequential version of the Warga approximate solutions is investigated: we use filters and ultrafilters of measurable spaces. Attrac- tion sets are constructed. AMS (MOS) subject classification. 46A, 49 K 40.

Abstract:
A detailed understanding of the structural properties of Internet topology will benefit the further design and development of the Internet. It seems infeasible to study the whole Internet at router level due to its extremely large size and the difficulty in obtaining a whole topology at this level. Studying each national or continental Internet service provider (ISP) topology individually becomes an alternative method for this goal. In this paper, the measured China Education and Research Network topology, a nationwide ISP topology, is basically taken as an example. The results of mapping the topology from multiple vantage points are briefly presented. The properties of the degree distribution, large eigenvalues, and the spectral density of the measured topology graphs are analyzed. The characteristics of the signless Laplacian spectra (SLS), the normalized Laplacian spectra (NLS), and the clustering coefficients of the measured graphs are also presented. The results suggest that some power laws indeed hold in some large-scale ISP topologies; in contrast to the case of autonomous system level topologies, the power law fit is not the best choice for some ISP topologies in terms of the complementary cumulative distribution function of the degree; some real ISP topologies are a kind of scale-free graphs which are not consistent with the Barabási-Albert (BA) growth model; router level topologies are distinguishable in terms of the SLS or the NLS; router level Internet topology may have developed over time following a different set of growth processes from those of the BA model.

Rough set theory is
a powerful tool for dealing with uncertainty, granularity, and incompleteness
of knowledge in information systems. In addition, digital topology deals with
properties and features of two-dimensional or three-dimensional digital
images that correspond to topological properties of objects. So, we try to describe
the relationship between rough sets and digital topology. Firstly, we will
study the classifications of topologies in rough sets. Secondly, we will use
the upper approximation operator to span the digital line, which is the basic
building block of the digital spaces.

Abstract:
This paper considers fuzzifying topologies, a special case of I-fuzzy topologies (bifuzzy topologies), introduced by Ying. It investigates topological notions defined by means of -open sets when these are planted into the frame-work of Ying’s fuzzifying topological spaces (by Lukasiewicz logic in [0, 1]). In this paper we introduce some sorts of operations, called general fuzzifying operations from P(X) to , where (X, τ) is a fuzzifying topological space. By making use of them we contract neighborhood structures, derived sets, closure operations and interior operations.

Abstract:
Background: Implant-associated infections are a result of bacterial adhesion to an implant surface and subsequent biofilm formation at the implantation site. This study compares different magnesium materials based on their ability to resist bacterial adhesion as well as further biofilm formation. Material and Methods: The surfaces of four magnesium-based materials (Mg2Ag, Mg10Gd, WE43 and 99.99% pure Mg) were characterized using atomic force microscope. In addition, the samples were tested for their ability to resist biofilm formation. Planktonic bacteria of either S. epidermidis or E. faecalis were allowed to adhere to the magnesium surfaces for two hour followed by rinsing and, for S. epidermidis, further incubation of 24, 72 and 168 h was carried out. Results: E. faecalis had a significantly stronger adhesion to all magnesium surfaces compared to S. epidermidis (p = 0.001). Biofilm growth of S. epidermidis was different on various magnesium materials: the amount of bacteria increased up to 72 h but interestingly a significant decrease was seen at 168 h on Mg2Ag and WE43 surfaces. For pure Mg and Mg10Gd the biofilm formation reached plateau at 72 h. Surface characteristics of resorbable magnesium materials were changing over time, and the surface was generally less rough at 168 h compared to earlier time points. No correlation was found between the surface topology and the amount of adherent bacteria. Conclusion: In early stages of biofilm adhesion, no differences between magnesium materials were observed. However, after 72 h Mg2Ag and WE43 had the best ability to suppress S. epidermidis’ biofilm formation. Also, bacterial adhesion to magnesium materials was not dependent on samples’ surface topology.

Abstract:
Aiming at the problem of the interval partition of satellite network topology updating, put forword a method of the updating period estimate of satellite network topology based on the characteristic of link. First, put forword three models to fulfill the modeling of updating period of satellite network topology, the models were as follows: the model of the coverage time of satellite, the model of the characteristic of link and the model of the updating period estimate of satellite network topology, then the simulation of the satellite of different constellations was done to validate the method, achieved the updating period estimate of satellite network topology by the synthetic research of coverage time, time delay skip and the characteristic of link, provided the view of research from the characteristic of link to network topology and routing computing, and through network topology, connected the characteristic of link and routing computing with each other integrally, which had direction for the effective design of satellite network.