Trip-Based Public Transit Routing

We study the problem of computing all Pareto-optimal journeys in a public transit network regarding the two criteria of arrival time and number of transfers taken. We take a novel approach, focusing on trips and transfers between them, allowing fine-grained modeling. Our experiments on the metropolitan network of London show that the algorithm computes full 24-hour profiles in 70 ms after a preprocessing phase of 30 s, allowing fast queries in dynamic scenarios.Comment: Minor corrections, no substantial changes. To be presented at ESA 201

Molecular dynamics of ion transport through the open conformation of a bacterial voltage-gated sodium channel

The crystal structure of the open conformation of a bacterial voltage-gated sodium channel pore from Magnetococcus sp. (NaVMs) has provided the basis for a molecular dynamics study defining the channel’s full ion translocation pathway and conductance process, selectivity, electrophysiological characteristics, and ion-binding sites. Microsecond molecular dynamics simulations permitted a complete time-course characterization of the protein in a membrane system, capturing the plethora of conductance events and revealing a complex mixture of single and multi-ion phenomena with decoupled rapid bidirectional water transport. The simulations suggest specific localization sites for the sodium ions, which correspond with experimentally determined electron density found in the selectivity filter of the crystal structure. These studies have also allowed us to identify the ion conductance mechanism and its relation to water movement for the NavMs channel pore and to make realistic predictions of its conductance properties. The calculated single-channel conductance and selectivity ratio correspond closely with the electrophysiology measurements of the NavMs channel expressed in HEK 293 cells. The ion translocation process seen in this voltage-gated sodium channel is clearly different from that exhibited by members of the closely related family of voltage-gated potassium channels and also differs considerably from existing proposals for the conductance process in sodium channels. These studies simulate sodium channel conductance based on an experimentally determined structure of a sodium channel pore that has a completely open transmembrane pathway and activation gate

Distance Oracles for Time-Dependent Networks

We present the first approximate distance oracle for sparse directed networks with time-dependent arc-travel-times determined by continuous, piecewise linear, positive functions possessing the FIFO property. Our approach precomputes $(1+\epsilon)-$approximate distance summaries from selected landmark vertices to all other vertices in the network. Our oracle uses subquadratic space and time preprocessing, and provides two sublinear-time query algorithms that deliver constant and $(1+\sigma)-$approximate shortest-travel-times, respectively, for arbitrary origin-destination pairs in the network, for any constant $\sigma > \epsilon$. Our oracle is based only on the sparsity of the network, along with two quite natural assumptions about travel-time functions which allow the smooth transition towards asymmetric and time-dependent distance metrics.Comment: A preliminary version appeared as Technical Report ECOMPASS-TR-025 of EU funded research project eCOMPASS (http://www.ecompass-project.eu/). An extended abstract also appeared in the 41st International Colloquium on Automata, Languages, and Programming (ICALP 2014, track-A

Tractable Pathfinding for the Stochastic On-Time Arrival Problem

We present a new and more efficient technique for computing the route that maximizes the probability of on-time arrival in stochastic networks, also known as the path-based stochastic on-time arrival (SOTA) problem. Our primary contribution is a pathfinding algorithm that uses the solution to the policy-based SOTA problem---which is of pseudo-polynomial-time complexity in the time budget of the journey---as a search heuristic for the optimal path. In particular, we show that this heuristic can be exceptionally efficient in practice, effectively making it possible to solve the path-based SOTA problem as quickly as the policy-based SOTA problem. Our secondary contribution is the extension of policy-based preprocessing to path-based preprocessing for the SOTA problem. In the process, we also introduce Arc-Potentials, a more efficient generalization of Stochastic Arc-Flags that can be used for both policy- and path-based SOTA. After developing the pathfinding and preprocessing algorithms, we evaluate their performance on two different real-world networks. To the best of our knowledge, these techniques provide the most efficient computation strategy for the path-based SOTA problem for general probability distributions, both with and without preprocessing.Comment: Submission accepted by the International Symposium on Experimental Algorithms 2016 and published by Springer in the Lecture Notes in Computer Science series on June 1, 2016. Includes typographical corrections and modifications to pre-processing made after the initial submission to SODA'15 (July 7, 2014

Size reduction of complex networks preserving modularity

The ubiquity of modular structure in real-world complex networks is being the focus of attention in many trials to understand the interplay between network topology and functionality. The best approaches to the identification of modular structure are based on the optimization of a quality function known as modularity. However this optimization is a hard task provided that the computational complexity of the problem is in the NP-hard class. Here we propose an exact method for reducing the size of weighted (directed and undirected) complex networks while maintaining invariant its modularity. This size reduction allows the heuristic algorithms that optimize modularity for a better exploration of the modularity landscape. We compare the modularity obtained in several real complex-networks by using the Extremal Optimization algorithm, before and after the size reduction, showing the improvement obtained. We speculate that the proposed analytical size reduction could be extended to an exact coarse graining of the network in the scope of real-space renormalization.Comment: 14 pages, 2 figure

Enhance the Efficiency of Heuristic Algorithm for Maximizing Modularity Q

Modularity Q is an important function for identifying community structure in complex networks. In this paper, we prove that the modularity maximization problem is equivalent to a nonconvex quadratic programming problem. This result provide us a simple way to improve the efficiency of heuristic algorithms for maximizing modularity Q. Many numerical results demonstrate that it is very effective.Comment: 9 pages, 3 figure

Distribution of shortest cycle lengths in random networks

We present analytical results for the distribution of shortest cycle lengths (DSCL) in random networks. The approach is based on the relation between the DSCL and the distribution of shortest path lengths (DSPL). We apply this approach to configuration model networks, for which analytical results for the DSPL were obtained before. We first calculate the fraction of nodes in the network which reside on at least one cycle. Conditioning on being on a cycle, we provide the DSCL over ensembles of configuration model networks with degree distributions which follow a Poisson distribution (Erdos-R\'enyi network), degenerate distribution (random regular graph) and a power-law distribution (scale-free network). The mean and variance of the DSCL are calculated. The analytical results are found to be in very good agreement with the results of computer simulations.Comment: 44 pages, 11 figure

Changes in trabecular bone, hematopoiesis and bone marrow vessels in aplastic anemia, primary osteoporosis, and old age

Retrospective histologic analyses of bone biopsies and of post mortem samples from normal persons of different age groups, and of bone biopsies of age- and sex-matched groups of patients with primary osteoporosis and aplastic anemia show characteristic age dependent as well as pathologic changes including atrophy of osseous trabeculae and of hematopoiesis, and changes in the sinusoidal and arterial capillary compartments. These results indicate the possible role of a microvascular defect in the pathogenesis of osteoporosis and aplastic anemia

Separating Hierarchical and General Hub Labelings

In the context of distance oracles, a labeling algorithm computes vertex labels during preprocessing. An $s,t$ query computes the corresponding distance from the labels of $s$ and $t$ only, without looking at the input graph. Hub labels is a class of labels that has been extensively studied. Performance of the hub label query depends on the label size. Hierarchical labels are a natural special kind of hub labels. These labels are related to other problems and can be computed more efficiently. This brings up a natural question of the quality of hierarchical labels. We show that there is a gap: optimal hierarchical labels can be polynomially bigger than the general hub labels. To prove this result, we give tight upper and lower bounds on the size of hierarchical and general labels for hypercubes.Comment: 11 pages, minor corrections, MFCS 201

Recent Advances in Graph Partitioning

We survey recent trends in practical algorithms for balanced graph partitioning together with applications and future research directions