A 2D coordination polymer with brick-wall network topology based on the [Cu(NCS)(2)(pn)] monomer

The new complex [Cu(NCS)(2)(pn)] (1) (pn = 1,3-propanediamine) has been synthesized and characterized by elemental analysis, infrared and electronic spectroscopy. Single crystal X-ray diffraction studies revealed that complex 1 is made up of neutral [Cu(NCS)(2)(pn)] units which are connected by mu-1,3,3-thiocyanato groups to yield a 2D metal-organic framework with a brick-wall network topology. Intermolecular hydrogen bonds of the type NH...SCN and NH...NCS are also responsible for the stabilization of the crystal structure. (c) 2007 Elsevier B.V. All rights reserved.

BERRY PHASE, AHARONOV-BOHM EFFECT AND TOPOLOGY

The Berry phase for an electron in a one-dimensional box rotated around a magnetic flux line has contributions from the geometry and the magnetic flux, which gives an Aharonov-Bohm effect. For a circular box enclosing the magnetic flux, the Berry phase depends on the boundary conditions.

Effects of self-assembly process of latex spheres on the final topology of macroporous silica

This paper surveys the topology of macroporous silica prepared using latex templates covering the submicrometric range (0.1-0.7 mu m). The behavior of latex spheres in aqueous dispersion has been analyzed by dynamic light scattering (DLS) measurement indicating the most appropriate conditions to form well-defined cubic arrays. The optical behavior of latex spheres has been analyzed by transmittance and reflectance measurements in order to determine their diameter and filling factor when they were assembled in bidimensional arrays. Macroscopic templates have been obtained by a centrifugation process and their crystalline ordering has been confirmed by porosimetry and scanning electron microscopy. These self-assembled structures have been used to produce macroporous silica, whose final topology depends on the pore size distribution of the original template. It has been seen that latex spheres are ordered in a predominant fcc arrangement with slipping of tetragonal pores due to the action of attractive electrostatic interactions. The main effect is to change the spherical shape of voids in macroporous silica into a hexagonal configuration with possible applications to fabricate photonic devices with novel optical properties. (c) 2005 Elsevier B.V. All rights reserved.

Some integrals occurring in a topology change problem

In a paper presented a few years ago, de Lorenci et al. showed, in the context of canonical quantum cosmology, a model which allowed space topology changes. The purpose of this present work is to go a step further in that model, by performing some calculations only estimated there for several compact manifolds of constant negative curvature, such as the Weeks and Thurston spaces and the icosahedral hyperbolic space (Best space). ©2000 The American Physical Society.

Quantum topology change and large-N gauge theories

We study a model for dynamical localization of topology using ideas from non-commutative geometry and topology in quantum mechanics. We consider a collection X of N one-dimensional manifolds and the corresponding set of boundary conditions (self-adjoint extensions) of the Dirac operator D. The set of boundary conditions encodes the topology and is parameterized by unitary matrices g. A particular geometry is described by a spectral triple x(g) = (A X, script H sign X, D(g)). We define a partition function for the sum over all g. In this model topology fluctuates but the dimension is kept fixed. We use the spectral principle to obtain an action for the set of boundary conditions. Together with invariance principles the procedure fixes the partition function for fluctuating topologies. The model has one free-parameter β and it is equivalent to a one plaquette gauge theory. We argue that topology becomes localized at β = ∞ for any value of N. Moreover, the system undergoes a third-order phase transition at β = 1 for large-N. We give a topological interpretation of the phase transition by looking how it affects the topology. © SISSA/ISAS 2004.

Prediction of Oncogenic Interactions and Cancer-Related Signaling Networks Based on Network Topology

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

The influence of self-weight of elastic 2D structures in topology optimization via numerical technique Smooth Evolutionary Structural Optimization (SESO)

This paper deals with topology optimization in plane elastic-linear problems considering the influence of the self weight in efforts in structural elements. For this purpose it is used a numerical technique called SESO (Smooth ESO), which is based on the procedure for progressive decrease of the inefficient stiffness element contribution at lower stresses until he has no more influence. The SESO is applied with the finite element method and is utilized a triangular finite element and high order. This paper extends the technique SESO for application its self weight where the program, in computing the volume and specific weight, automatically generates a concentrated equivalent force to each node of the element. The evaluation is finalized with the definition of a model of strut-and-tie resulting in regions of stress concentration. Examples are presented with optimum topology structures obtaining optimal settings. (C) 2012 CIMNE (Universitat Politecnica de Catalunya). Published by Elsevier Espana, S.L.U. All rights reserved.

Controllability of control systems on complex simple lie groups and the topology of flag manifolds

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Virtual Topology Reconfiguration of Wavelength-routed Optical WDM Networks

The bandwidth requirements of the Internet are increasing every day and there are newer and more bandwidth-thirsty applications emerging on the horizon. Wavelength division multiplexing (WDM) is the next step towards leveraging the capabilities of the optical fiber, especially for wide-area backbone networks. The ability to switch a signal at intermediate nodes in a WDM network based on their wavelengths is known as wavelength-routing. One of the greatest advantages of using wavelength-routing WDM is the ability to create a virtual topology different from the physical topology of the underlying network. This virtual topology can be reconfigured when necessary, to improve performance. We discuss the previous work done on virtual topology design and also discuss and propose different reconfiguration algorithms applicable under different scenarios.

Survivable Virtual Topology Routing under Shared Risk Link Groups in WDM Networks

Network survivability is one of the most important issues in the design of optical WDM networks. In this work we study the problem of survivable routing of a virtual topology on a physical topology with Shared Risk Link Groups (SRLG). The survivable virtual topology routing problem against single-link failures in the physical topology is proved to be NP-complete in [1]. We prove that survivable virtual topology routing problem against SRLG/node failures is also NP-complete. We present an improved integer linear programming (ILP) formulation (in comparison to [1]) for computing the survivable routing under SRLG/node failures. Using an ILP solver, we computed the survivable virtual topology routing against link and SRLG failures for small and medium sized networks efficiently. As even our improved ILP formulation becomes intractable for large networks, we present a congestion-based heuristic and a tabu search heuristic (which uses the congestion-based heuristic solution as the initial solution) for computing survivable routing of a virtual topology. Our experimental results show that tabu search heuristic coupled with the congestion based heuristic (used as initial solution) provides fast and near-optimal solutions.

An Analytical Model for Virtual Topology Reconfiguration in Optical Networks and A Case Study

An analytical model for Virtual Topology Reconfiguration (VTR) in optical networks is developed. It aims at the optical networks with a circuit-based data plane and an IPlike control plane. By identifying and analyzing the important factors impacting the network performance due to VTR operations on both planes, we can compare the benefits and penalties of different VTR algorithms and policies. The best VTR scenario can be adaptively chosen from a set of such algorithms and policies according to the real-time network situations. For this purpose, a cost model integrating all these factors is created to provide a comparison criterion independent of any specific VTR algorithm and policy. A case study based on simulation experiments is conducted to illustrate the application of our models.

Class Notes for Math 871: General Topology, Instructor Jamie Radcliffe

Topics include: Topological space and continuous functions (bases, the product topology, the box topology, the subspace topology, the quotient topology, the metric topology), connectedness (path connected, locally connected), compactness, completeness, countability, filters, and the fundamental group.

Selection of Switching Sites in All-Optical Nework Topology Design

In this paper, we consider the problem of topology design for optical networks. We investigate the problem of selecting switching sites to minimize total cost of the optical network. The cost of an optical network can be expressed as a sum of three main factors: the site cost, the link cost, and the switch cost. To the best of our knowledge, this problem has not been studied in its general form as investigated in this paper. We present a mixed integer quadratic programming (MIQP) formulation of the problem to find the optimal value of the total network cost. We also present an efficient heuristic to approximate the solution in polynomial time. The experimental results show good performance of the heuristic. The value of the total network cost computed by the heuristic varies within 2% to 21% of its optimal value in the experiments with 10 nodes. The total network cost computed by the heuristic for 51% of the experiments with 10 node network topologies varies within 8% of its optimal value. We also discuss the insight gained from our experiments.

Topology Verification for Isosurface Extraction

The broad goals of verifiable visualization rely on correct algorithmic implementations. We extend a framework for verification of isosurfacing implementations to check topological properties. Specifically, we use stratified Morse theory and digital topology to design algorithms which verify topological invariants. Our extended framework reveals unexpected behavior and coding mistakes in popular publicly available isosurface codes.

TOPOLOGY OF SINPLE SINGULARITIES OF RULED SURFACES IN R-p

In this work we compare the simple singularities of germs from R-2 to R-p with multiplicity 2 or 3 with the singularities appearing in the set of 2-ruled surfaces. We also study the topological type of all finitely determined singularities by studying generic projections of these singularities in R-3. (C) 2011 Elsevier B.V. All rights reserved.