View Of Topology Research Articles

A topological view of ordered groups

We show how to use topological ideas, such as compactness, to establish orderability properties of infinite groups. A new application is to provide a left-ordering for the group of PL homeomorphisms of a connected surface with boundary which are fixed on at least one boundary component. This has been extended in recent joint work by the author and D. Calegari.

Detecting events in the dynamics of ego-centred measurements of the Internet topology

Detecting events such as major routing changes or congestions in the dynamics of the Internet topology is an important but challenging task. We explore here an empirical approach based on a notion of statistically significant events. It consists in identifying properties of graph dynamics which exhibit a homogeneous distribution with outliers, corresponding to events. We apply this approach to ego-centred measurements of the Internet topology (views obtained from a single monitor) and show that it succeeds in detecting meaningful events. Finally, we give some hints for the interpretation of detected events in terms of network operations.

A paradigm for development of novel PTP 1B inhibitors: Pharmacophore modelling, atom-based 3D-QSAR and docking studies

Inhibitors of protein tyrosine phosphatase 1B (PTP 1B) are of great interest for the development of newer therapeutics for the management of type 2 diabetes mellitus (T2DM). In order to understand structural requirement of molecules to act as PTP 1B inhibitors, ligand-based pharmacophore model, atom-based 3D-QSAR and structure-based drug design studies have been performed on a series of thiophene derivatives to correlate their molecular architecture with PTP 1B inhibitory activity. A five-point pharmacophore hypothesis with one hydrogen acceptor (A), two negative ionic (N), and two aromatic rings (R) as pharmacophoric features were developed using PHASE module of Schrodinger suite. The pharmacophore hypothesis was characterized by good PLS statistics (survival score = 3.894, the best cross validated r2 (Q2) = 0.737, regression coefficient r2 = 0.968, Pearson-R = 0.887 and F value = 253.3). Docking studies demonstrated binding orientations of ligands in dataset with bidentate binding pockets of the enzyme and importance of hydrophobic groups. Taken together, Partial least square (PLS) generated 3D-QSAR pharmacophore and regression cubes along with structure based drug design provided a three dimensional topological view of active site that can be used for rational modification of ligands for optimal PTP 1B inhibitory activity.

The Campbell–Hausdorff near-ring over [formula omitted]—A topological view

The famous Baker–Campbell–Hausdorff series defines a group composition on the set of the so called grouplike elements of a completed free Lie algebra as we can find in P. Cartier’s paper on the Campbell–Hausdorff formula in 1956. According to A. Baider and R.C. Churchill, we call this group the Campbell–Hausdorff group over the alphabetX of the free Lie algebra. By a certain coproduct and certain bialgebra endomorphisms of the free associative algebra over a set X which should be at most countably infinite, we get an alternative realisation of this Campbell–Hausdorff group. This realisation is much more comfortable to deal with than the classical one. The usual composition of endomorphisms gives a near-ring structure to this group. In this paper we consider a metric on the Campbell–Hausdorff near-ring over the alphabet N and the compatibility of this metric with the near-ring compositions and we make some topological remarks.

Review on the Technology of on Board DC/DC Conversion for EV Application

The paper gives a systemic classification to the common electric vehicle (EV). The technology of low power converter using as auxiliary power supply and high power converter using for traction system has been deeply discussed from the view of topology, control strategy and devices. Finally, the development tendency of on board DC conversion technology is prospected.

Coordination polymers (NiII and CoII) based on the rigid bridging ligand, 4,4′-bis(imidazol-1-yl)biphenyl, with (46) topology

Two coordination polymers, {[Ni0.5(4,4′-bib)Cl][(4,4′-bib)0.5]·H2O} n (1) and {[Co(4,4′-bib)3(H2O)2][NO3]2·H2O} n (2) (4,4′-bib = 4,4′-bis(imidazol-1-yl)biphenyl) have been hydrothermally synthesized. Their structures have been determined by single-crystal X-ray diffraction analyses and are further characterized by elemental analyses, IR, thermogravimetric analyses, and powder X-ray diffraction. In 1, each NiII is linked by four μ 2–4,4′-bib ligands in 2-D (4,4)-networks, which are further connected through host–guest interaction to form a 3-D packing diagram with 1-D channels. In 2, each CoII is linked by two μ 2–4,4′-bib and two μ 1–4,4′-bib ligands in a 1-D zigzag chain, further connected through non-covalent interactions (including O–HN, O–HO, C–Hπ, and ππ interactions) to form a 3-D supramolecular structure. 4,4′-bib exhibits μ 2-, μ 1-, and μ 0-coordination during the construction of 1 and 2. From the topological view, the overall structures of 1 and 2 possess (46) topology.

Semi-uniform sub-additive ergodic theorems for discontinuous skew-product transformations

In this paper we will establish some semi-uniform ergodic theorems for skew-product transformations with discontinuity from the point of view of topology. The main assumptions are that the discontinuity sets of transformations are neglected in some measure-theoretical sense. The theorems have extended the classical results which have been established for continuous dynamical systems.

Topological approach to multigranulation rough sets

For further studying the theory of multigranulation rough sets, we attempt to investigate a new theory on multigranulation rough sets from the topological view in this paper. We firstly explore multigranulation topological rough space and its topological properties by giving some new definitions and theorems. Then, topological granularity and topological entropy are proposed to characterize the uncertainty of a multigranulation topological rough space. Finally, based on the invariance of interior and closure operators of a target concept, a granulation selection algorithm is introduced to deal with the granularity selection issue in the multigranulation rough data analysis.

A new view of flow topology and conditional statistics in turbulence

By partitioning a turbulent flow field into relative simple units, the original complex system may be better understood from studying decomposed structures. In this paper, some general principles for identifying geometrical decomposition are discussed. Logically, to make analysis more objective and quantitative, the decomposed units need to be non-arbitrarily defined and space filling. Following this vein, we introduced two topological approaches satisfying these prerequisites and the relevant work is reviewed. For a given scalar variable, dissipation elements are defined as the spatial regions that the gradient trajectories of this scalar can share the same pair of scalar extremums (one maximum and one minimum), whereas for the general vector variables, vector tube segments are the part of vector tubes bounded by adjacent extremums of the magnitude of the given vector. Both structures can be characterized by representative shape parameters: the length scale and the extremum difference. On the basis of direct numerical simulation data, the statistics of the shape parameters have been studied. Physically, those structures reveal the 'nature' topology of turbulence, and thus their characteristic parameters reflect the flow properties. For instance, when the vector tube segment approach is applied to the velocity case, the negative skewness of the velocity derivative can be explained by the asymmetry of the joint probability density function of the shape parameters of streamtube segments. Conditional statistics based on these newly defined structures identify finer flow physics and are believed helpful for modelling improvement. Application examples illustrate that, in principle, these methods can generally be applied to different flow cases under different situations.

Topological view of the thermal stability of nanotwinned copper

Sputter deposited nanotwinned copper (nt-Cu) foils typically exhibit strong {111} fiber textures and have grain boundary networks (GBN) consisting of high-angle and a small fraction of low-angle columnar boundaries interspersed with crystallographically special boundaries. Using a transmission electron microscope based orientation mapping system with sub-nanometer resolution, we have statistically analyzed the GBN in as-deposited and annealed nt-Cu foils. From the observed grain boundary characteristics and network evolution during thermal annealing, we infer that triple junctions are ineffective pinning sites and that the microstructure readily coarsens through thermal-activated motion of incoherent twin segments followed by lateral motion of high-angle columnar boundaries.

A multipath routing strategy to prevent flooding disruption attacks in link state routing protocols for MANETs

Multipath routing has been proposed to increase resilience against network failures or improve security in Mobile Ad Hoc Networks (MANETs). The Optimized Link State Routing (OLSR) protocol has been adopted by several multipath routing strategies. They implement Multipoint Relay (MPR) nodes as a flooding mechanism for distributing control information. Ideally, the construction of multiple disjoint paths helps to increase resilience against network failures or malicious attacks. However, this is not always possible. In OLSR networks, partial link-state information is generated and flooded exclusively by the MPRs. Therefore, the nodes only obtain a partial view of the network topology. Additionally, flooding disruption attacks may affect either the selection of the MPRs or the propagation of control traffic information. As a consequence, the chances of constructing multiple disjoint paths are reduced. We present a strategy to compute multiple strictly disjoint paths between any two nodes in OLSR-based networks. We provide mechanisms to improve the view of the network topology by the nodes, as well as handling potential flooding disruption attacks to the multipath construction mechanism in OLSR-based networks. We conduct simulations that confirm our claims.

The construction of Cu(i)/Cu(ii) coordination polymers based on pyrazine–carboxylate: Structural diversity tuned by in situ hydrolysis reaction

The reaction of a new ligand, N,N′-(5,7-dihydro-1,3,5,7-tetraoxobenzo[1,2-c:4,5-c′]dipyrrole-2,6(1H,3H)-diyl)bis-(9CI)-3-pyrazinecarboxamide (L), with CuCl2·2H2O, CuI, or Cu(ClO4)·2H2O yields five coordination polymers. Among these polymers are three new coordination polymers, [CuII2(μ3-pzc)2(μ1-Cl)2]n (1), [CuICuII(μ2-pzc)2(μ2-Cl)(H2O)]n (2a), and {[CuI2CuII(μ2-pzc)2(μ3-I)2(H2O)]·H2O}n (3), as well as two previously reported coordination compounds, [CuICuII(μ2-pzc)2(μ2-Cl)(H2O)]n (2b) and [CuII(pzc)2] (4), in which 2-pyrazinecarboxylate (Hpzc) was obtained from in situ hydrolysis of the L ligand. Compound 1 is a two-dimensional (2D) double-layer structure, which can be viewed as a binodal (3,3)-connected network with the Schläfli symbol of (62·10) (6·102). Compounds 2a and 2b are two supramolecular isomers, both of them are (4,4) nets in topological view but showing different packing modes. Compound 3 has a 3D open framework constructed from the linkages of 1D sawtooth chains of iodide copper(I) clusters with [CuII(μ2-pzc)] subunits. Compound 4 is a mononuclear complex. Interestingly, except for compounds 2b and 4, all the other compounds cannot be directly synthesized using Hpzc and the corresponding Cu ions as initial reactants under the same reaction conditions. This finding indicates that the structural diversity of this system is tuned by the in situ hydrolysis reactions.

Heterogeneity playing key role

Heterogeneities (heterogeneous characteristics) are intrinsic in dynamic and autonomous networks, and may be caused by the following factors: finite nodes, structured network graph, mutation of node's strategy and topological view, and dynamic linking, and so on. However, few works systematically investigate the effect of the intrinsic heterogeneities on the evolutionary dynamics of incentive mechanisms in autonomous networks. In this article, we thoroughly discuss this interesting problem. Specifically, this article respectively models the pairwise interaction between peers as PD (prisoner's dilemma)-like game and multiple peers' interactions as public-goods game, proposes a general analytical framework for dynamics in evolutionary game theory (EGT)-based incentive mechanisms, and draws the following conclusions. First, for explicit incentive mechanisms, due to heterogeneity, it is impossible to get the static equilibrium of absolutely-full-cooperation (or state that provides service to the networks—so-called reciprocation), but, on the other hand, heterogeneity can facilitate reciprocation evolution, and drive the whole system into almost-full-reciprocation state, that is, most of the system time would be occupied by the full reciprocation state. Second, even without any explicit incentive mechanisms, simultaneous coevolution between dynamic linking and peers' rational strategies can not only facilitate the cooperation evolution, but drive the network structure into the desirable small-world structure. The philosophical implication of our work is that simplicity and homogeneity are too idealized for incentive mechanisms in autonomous networks—diversity and heterogeneity are intrinsic for any incentive mechanism that is compatible with the essence of our real society. Diversity is everywhere.

One novel multidimensional organic–inorganic hybrid based on polyoxometalates and copper chlorine coordination polymers with 4,4′-bipyridine ligands

Abstract One novel organic–inorganic hybrid materials with 4,4′-bipy ligands and copper chlorine coordination polymers as linkers, with new topology, {[Cu I (4,4′-bipy)] 10 Cl 2 (SiW 12 O 40 ) 2 }·6H 2 O ( 1 ) (4,4′-bipy = 4,4′-bipyridine), has been hydrothermally synthesized. The single crystal X-ray structural analysis reveals that the structure of 1 is constructed from classical Keggin anions and [Cu I (4,4′-bipy)] cations into a novel, three-dimensional (3D) polyoxometalates (POMs)based network. From the topological view, compound 1 is a novel (3.4 4 .5 2 .6 3 )(3 2 .4 4 .5 6 .6 9 ) topology. The electrochemical and photocatalysis properties of 1 have been investigated in details.

Using Sol–Gel Replications to Assess the Porosity of Block-Copolymer Derived Thin Films

In this paper, we report the use of a sol–gel replication method to prepare high fidelity SiO2 replicas of porous thin films obtained from microphase separated block-copolymer systems as an easy, robust, and rapid way to investigate their inner morphology. The cylinder-forming poly(styrene)-b-poly(lactide) (PS-b-PLA) block copolymer, containing a sacrificial block (PLA), was used to produce porous thin films with thicknesses above one periodical distance and bearing various internal organizations and orientations of the cylinders. The porosity was first infiltrated by silica precursors using a chemical solution deposition process, before being exposed to a brief thermal treatment to provoke inorganic condensation and elimination of the PS template. SEM observations of the obtained replica gave three-dimensional view of the internal topology of the porosity, which were then compared to structural characterizations obtained directly by AFM, SEM, or GISAXS on the parent block-copolymer films. It is shown that the replication provides an ideal tool to characterize the topology of porous networks in supported polymer thin films. This method can be generalized to any type of porous polymer media, offering a unique mode of visualization of the internal topology with valuable details at the substrate interface.

Generalizations of Rough Functions in Topological Spaces by Using Pre-Open Sets

Functions are a means to link or transport from a world to another world may be similarly or completely different from the other world. In this paper we addressed the issue of rough functions and the possibility of transfer it from the real line to the topological abstract view that can be applied to intelligent information systems. The rough function approach has not been studied much specially from a topological point of view. Here we developed a new type of topological generalizations of rough functions with reference to how it is used in medical applications. Considering that the function is in the original a relation can be based on a review of all circular functions from the perspective of relations. Accordingly, the dream that the generalizations of rough functions are transferred to all papers prior to a comprehensive computer application.

Performance evaluation of lifetime‐driven admission control for infrastructure‐less clustered wireless networks

SUMMARYClassical call admission control schemes focus on QoS enhancements because radio bandwidth will be allocated for mobile communications. Both of radio bandwidth and lifetime duration of mobile node are very important and precious for resources allocation in wireless networks. In this paper, we present a novel admission control for infrastructure‐less clustered wireless networks. The proposed admission control is based on QoS constraints and the lifetime duration of mobile nodes, including speed and power consumption parameters. Some new schemes are introduced, QoS parameters are negotiated during the admission procedure, and a forced handover technique is developed instead of reject flows, using a centralized view of topology. The performance of the proposed scheme was analyzed and evaluated with respect to throughput and call blocking probability, using different classes of traffic. Furthermore, simulation results confirmed the effectiveness of the admission control schemes. Copyright © 2011 John Wiley & Sons, Ltd.

A New 5-Connected Cu(II) Complex with 5-Bromoisophthalic Acid: Synthesis, Crystal Structure, and Properties

A new coordination polymer, {[Cu(Brip)(1,4-btb)1.5]·2H2O}n, (H2Brip = 5-bromoisophthalic acid, 1,4-btb = 1,4-bis(triazol) butane) was prepared under hydrothermal condition by the reactions of Cu(II) acetate with H2Brip and 1,4-btb. The title complex was determined by single-crystal X-ray diffraction analysis and further characterized by elemental analysis and IR spectroscopy. Complex 1 has a 3D network extended by both H2Brip and 1,4-btb ligands that employ the same bis-monodentate bridging coordination modes. From the view of topology, the structure of 1 could be described as a 5-connected (44·66)-nov net. Two of such nets penetrate with each other to generate a 2-fold interpenetrating 3D network. In addition, the thermal stability of the title complex was briefly investigated.

Topological view on magnetic adatoms in graphene

We study theoretically the physical properties of a magnetic impurity in graphene. Within the Anderson model for a very strong Coulomb interaction on the impurity, we start from the Slave-Boson method and introduce a topological picture consisting of a degree of a map and a winding number (WN) to analyze the phase shift and the occupation on the impurity. The occupation is linked to WN. For a generic normal metal we find a fractional WN. In contrast, the winding is accelerated by the relativistic dispersion of graphene at half-filling leading to an integer occupation. We show that the renormalization parameter that shifts the impurity level is insufficient to invert the sign of the energy level. Consequently, the state at half-filling is stable unless a gate voltage is tuned such that the Fermi level touches the edge of the broadened impurity level. Only in this case the zero field susceptibility is finite and shows a pronounced peak structure with the gate voltage.

Cobweb: a Java applet for network exploration and visualisation

Cobweb is a Java applet for real-time network visualization; its strength lies in enabling the interactive exploration of networks. Therefore, it allows new nodes to be interactively added to a network by querying a database on a server. The network constantly rearranges to provide the most meaningful topological view. Cobweb is available under the GPLv3 and may be freely downloaded at http://bioinformatics.charite.de/cobweb.