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.

Electroluminescence of phenylene-vinylene random copolymers with different conjugation lengths

PPV random derivates were synthesized and characterized. Polymer light emitting diodes (PLEDs) were assembled using the random copolymers as emissive layer and showed EL in the blue-green region in function of the method of preparation. The increase in the average conjugation degree in the polymer chain led to the reduction of the turn-on voltage of the device. The addition of Alq3 as ETL increased tenfold the luminescence efficiency. (C) 2009 Elsevier B.V. All rights reserved.

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.

Predicting epidemic outbreak from individual features of the spreaders

Knowing which individuals can be more efficient in spreading a pathogen throughout a determinate environment is a fundamental question in disease control. Indeed, over recent years the spread of epidemic diseases and its relationship with the topology of the involved system have been a recurrent topic in complex network theory, taking into account both network models and real-world data. In this paper we explore possible correlations between the heterogeneous spread of an epidemic disease governed by the susceptible-infected-recovered (SIR) model, and several attributes of the originating vertices, considering Erdos-Renyi (ER), Barabasi-Albert (BA) and random geometric graphs (RGG), as well as a real case study, the US air transportation network, which comprises the 500 busiest airports in the US along with inter-connections. Initially, the heterogeneity of the spreading is achieved by considering the RGG networks, in which we analytically derive an expression for the distribution of the spreading rates among the established contacts, by assuming that such rates decay exponentially with the distance that separates the individuals. Such a distribution is also considered for the ER and BA models, where we observe topological effects on the correlations. In the case of the airport network, the spreading rates are empirically defined, assumed to be directly proportional to the seat availability. Among both the theoretical and real networks considered, we observe a high correlation between the total epidemic prevalence and the degree, as well as the strength and the accessibility of the epidemic sources. For attributes such as the betweenness centrality and the k-shell index, however, the correlation depends on the topology considered.

Discriminating Different Classes of Biological Networks by Analyzing the Graphs Spectra Distribution

The brain's structural and functional systems, protein-protein interaction, and gene networks are examples of biological systems that share some features of complex networks, such as highly connected nodes, modularity, and small-world topology. Recent studies indicate that some pathologies present topological network alterations relative to norms seen in the general population. Therefore, methods to discriminate the processes that generate the different classes of networks (e. g., normal and disease) might be crucial for the diagnosis, prognosis, and treatment of the disease. It is known that several topological properties of a network (graph) can be described by the distribution of the spectrum of its adjacency matrix. Moreover, large networks generated by the same random process have the same spectrum distribution, allowing us to use it as a "fingerprint". Based on this relationship, we introduce and propose the entropy of a graph spectrum to measure the "uncertainty" of a random graph and the Kullback-Leibler and Jensen-Shannon divergences between graph spectra to compare networks. We also introduce general methods for model selection and network model parameter estimation, as well as a statistical procedure to test the nullity of divergence between two classes of complex networks. Finally, we demonstrate the usefulness of the proposed methods by applying them to (1) protein-protein interaction networks of different species and (2) on networks derived from children diagnosed with Attention Deficit Hyperactivity Disorder (ADHD) and typically developing children. We conclude that scale-free networks best describe all the protein-protein interactions. Also, we show that our proposed measures succeeded in the identification of topological changes in the network while other commonly used measures (number of edges, clustering coefficient, average path length) failed.

Partially Observed Markov Random Fields Are Variable Neighborhood Random Fields

The present paper has two goals. First to present a natural example of a new class of random fields which are the variable neighborhood random fields. The example we consider is a partially observed nearest neighbor binary Markov random field. The second goal is to establish sufficient conditions ensuring that the variable neighborhoods are almost surely finite. We discuss the relationship between the almost sure finiteness of the interaction neighborhoods and the presence/absence of phase transition of the underlying Markov random field. In the case where the underlying random field has no phase transition we show that the finiteness of neighborhoods depends on a specific relation between the noise level and the minimum values of the one-point specification of the Markov random field. The case in which there is phase transition is addressed in the frame of the ferromagnetic Ising model. We prove that the existence of infinite interaction neighborhoods depends on the phase.

Anderson-like Transition for a Class of Random Sparse Models in d >= 2 Dimensions

We show that the Kronecker sum of d >= 2 copies of a random one-dimensional sparse model displays a spectral transition of the type predicted by Anderson, from absolutely continuous around the center of the band to pure point around the boundaries. Possible applications to physics and open problems are discussed briefly.

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.

Design-based random permutation models with auxiliary information

We extend the random permutation model to obtain the best linear unbiased estimator of a finite population mean accounting for auxiliary variables under simple random sampling without replacement (SRS) or stratified SRS. The proposed method provides a systematic design-based justification for well-known results involving common estimators derived under minimal assumptions that do not require specification of a functional relationship between the response and the auxiliary variables.

Dissipation effects in random transverse-field Ising chains

We study the effects of Ohmic, super-Ohmic, and sub-Ohmic dissipation on the zero-temperature quantum phase transition in the random transverse-field Ising chain by means of an (asymptotically exact) analytical strong-disorder renormalization-group approach. We find that Ohmic damping destabilizes the infinite-randomness critical point and the associated quantum Griffiths singularities of the dissipationless system. The quantum dynamics of large magnetic clusters freezes completely, which destroys the sharp phase transition by smearing. The effects of sub-Ohmic dissipation are similar and also lead to a smeared transition. In contrast, super-Ohmic damping is an irrelevant perturbation; the critical behavior is thus identical to that of the dissipationless system. We discuss the resulting phase diagrams, the behavior of various observables, and the implications to higher dimensions and experiments.

A Note on Large Deviations for the Stable Marriage of Poisson and Lebesgue with Random Appetites

Let IaS,a"e (d) be a set of centers chosen according to a Poisson point process in a"e (d) . Let psi be an allocation of a"e (d) to I in the sense of the Gale-Shapley marriage problem, with the additional feature that every center xi aI has an appetite given by a nonnegative random variable alpha. Generalizing some previous results, we study large deviations for the distance of a typical point xaa"e (d) to its center psi(x)aI, subject to some restrictions on the moments of alpha.

Influence of pattern gradation on the design of piezocomposite energy harvesting devices using topology optimization

Piezoelectric materials can be used to convert oscillatory mechanical energy into electrical energy. Energy harvesting devices are designed to capture the ambient energy surrounding the electronics and convert it into usable electrical energy. The design of energy harvesting devices is not obvious, requiring optimization procedures. This paper investigates the influence of pattern gradation using topology optimization on the design of piezocomposite energy harvesting devices based on bending behavior. The objective function consists of maximizing the electric power generated in a load resistor. A projection scheme is employed to compute the element densities from design variables and control the length scale of the material density. Examples of two-dimensional piezocomposite energy harvesting devices are presented and discussed using the proposed method. The numerical results illustrate that pattern gradation constraints help to increase the electric power generated in a load resistor and guides the problem toward a more stable solution. (C) 2012 Elsevier Ltd. All rights reserved.