Speeding up Martins' algorithm for multiple objective shortest path problems

The latest transportation systems require the best routes in a large network with respect to multiple objectives simultaneously to be calculated in a very short time. The label setting algorithm of Martins efficiently finds this set of Pareto optimal paths, but sometimes tends to be slow, especially for large networks such as transportation networks. In this article we investigate a number of speedup measures, resulting in new algorithms. It is shown that the calculation time to find the Pareto optimal set can be reduced considerably. Moreover, it is mathematically proven that these algorithms still produce the Pareto optimal set of paths

The Index-Based Subgraph Matching Algorithm (ISMA): Fast Subgraph Enumeration in Large Networks Using Optimized Search Trees

Subgraph matching algorithms are designed to find all instances of predefined subgraphs in a large graph or network and play an important role in the discovery and analysis of so-called network motifs, subgraph patterns which occur more often than expected by chance. We present the index-based subgraph matching algorithm (ISMA), a novel tree-based algorithm. ISMA realizes a speedup compared to existing algorithms by carefully selecting the order in which the nodes of a query subgraph are investigated. In order to achieve this, we developed a number of data structures and maximally exploited symmetry characteristics of the subgraph. We compared ISMA to a naive recursive tree-based algorithm and to a number of well-known subgraph matching algorithms. Our algorithm outperforms the other algorithms, especially on large networks and with large query subgraphs. An implementation of ISMA in Java is freely available at http://sourceforge.net/projects/isma

Strong fluorescence suppression in polymer inverse opals

Modern demands for high speed telecommunication and data processing have created the need for advanced materials that allow active manipulation of light waves. Subsequent research has shown that photonic crystals provide excellent candidates to accommodate these needs. Photonic crystals are a relatively new class of materials in which the refractive index is periodic in 1, 2 or 3 dimensions. This periodicity gives rise to a photonic band gap which in turn provides selective reflection of certain wavelengths of light. Another interesting property of photonic crystals is the anomalous dispersion that occurs close to the photonic band gap (i.e. at the band edge). The anomalous dispersion causes the group velocity of light to decrease considerably, allowing stronger interactions between the travelling light and the material of which the photonic crystal consistsstatus: publishe

Engineering of colloidal magneto-photonic crystals by infiltration with superparamagnetic magnetite nanoparticles

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A Sandwich Approach towards Inverse Opals with Linear and Nonlinear Optical Functionalities

Three-dimensionally ordered macroporous materials have unique structural and optical properties, making them useful for numerous applications in catalysis, membrane science and optics. Accessible and economic fabrication of these materials is essential to fully explore the many possibilities that these materials present. A new templating method to fabricate three-dimensionally ordered macroporous materials without overlayers is presented. The resulting structures are freestanding inverse opals with large-area uniformity. The versatility and power of our fabrication method is demonstrated by synthesizing inverse opals displaying fluorescence, chirality, upconversion, second harmonic generation and third harmonic generation. This economical and versatile fabrication method will facilitate research on inverse opals in general and on linear and nonlinear optical effects in 3D photonic crystals in specific. The relative ease of synthesis and wide variety of resulting materials will help the characterization and improvement of existing anomalous dispersion effects in these structures, while providing a platform for the discovery and demonstration of novel effects.status: publishe

Reflection symmetry.

<p>Enumeration of all possibilities to map 5 network nodes on 2 reflection symmetric motif nodes. The squares represent motif nodes, the circles represent network nodes. Once a network node has been mapped on a motif node that is part of a reflection symmetry, it will never be mapped on one of the other nodes of the symmetry.</p

The calculation time multiplicators (CTM) of the ISMA algorithm compared to other algorithms for a number of non-biological networks.

<p>The last column shows the search tree reduction factors (STRF), i.e. the ratio of the number of nodes in the search tree of the RSMA algorithm to the search tree of the ISMA algorithm.</p

Search tree.

<p>The search tree of the ISMA algorithm (left) and the standard recursive algorithm (right) applied to the example network. A search tree indicates which network nodes have been mapped on the motif nodes.</p

Example motif and network.

<p>The motif (left) which is searched for in the example network (right). Links of type A or B are directed; links of type C are undirected.</p