Scaling up Group Closeness Maximization

Closeness is a widely-used centrality measure in social network analysis. For a node it indicates the inverse average shortest-path distance to the other nodes of the network. While the identification of the k nodes with highest closeness received significant attention, many applications are actually interested in finding a group of nodes that is central as a whole. For this problem, only recently a greedy algorithm with approximation ratio (1−1/e) has been proposed [Chen et al., ADC 2016]. Since this algorithm’s running time is still expensive for large networks, a heuristic without approximation guarantee has also been proposed in the same paper. In the present paper we develop new techniques to speed up the greedy algorithm without losing its theoretical guarantee. Compared to a straightforward implementation, our approach is orders of magnitude faster and, compared to the heuristic proposed by Chen et al., we always find a solution with better quality in a comparable running time in our experiments. Our method Greedy++ allows us to approximate the group with maximum closeness on networks with up to hundreds of millions of edges in minutes or at most a few hours. To have the same theoretical guarantee, the greedy approach by [Chen et al., ADC 2016] would take several days already on networks with hundreds of thousands of edges. In a comparison with the optimum, our experiments show that the solution found by Greedy++ is actually much better than the theoretical guarantee. Over all tested networks, the empirical approximation ratio is never lower than 0.97. Finally, we study for the first time the correlation between the top-k nodes with highest closeness and an approximation of the most central group in large complex networks and show that the overlap between the two is relatively small

A Group-Theoretic Approach to the WSSUS Pulse Design Problem

We consider the pulse design problem in multicarrier transmission where the pulse shapes are adapted to the second order statistics of the WSSUS channel. Even though the problem has been addressed by many authors analytical insights are rather limited. First we show that the problem is equivalent to the pure state channel fidelity in quantum information theory. Next we present a new approach where the original optimization functional is related to an eigenvalue problem for a pseudo differential operator by utilizing unitary representations of the Weyl--Heisenberg group.A local approximation of the operator for underspread channels is derived which implicitly covers the concepts of pulse scaling and optimal phase space displacement. The problem is reformulated as a differential equation and the optimal pulses occur as eigenstates of the harmonic oscillator Hamiltonian. Furthermore this operator--algebraic approach is extended to provide exact solutions for different classes of scattering environments.Comment: 5 pages, final version for 2005 IEEE International Symposium on Information Theory; added references for section 2; corrected some typos; added more detailed discussion on the relations to quantum information theory; added some more references; added additional calculations as an appendix; corrected typo in III.

A survey on Human Mobility and its applications

Human Mobility has attracted attentions from different fields of studies such as epidemic modeling, traffic engineering, traffic prediction and urban planning. In this survey we review major characteristics of human mobility studies including from trajectory-based studies to studies using graph and network theory. In trajectory-based studies statistical measures such as jump length distribution and radius of gyration are analyzed in order to investigate how people move in their daily life, and if it is possible to model this individual movements and make prediction based on them. Using graph in mobility studies, helps to investigate the dynamic behavior of the system, such as diffusion and flow in the network and makes it easier to estimate how much one part of the network influences another by using metrics like centrality measures. We aim to study population flow in transportation networks using mobility data to derive models and patterns, and to develop new applications in predicting phenomena such as congestion. Human Mobility studies with the new generation of mobility data provided by cellular phone networks, arise new challenges such as data storing, data representation, data analysis and computation complexity. A comparative review of different data types used in current tools and applications of Human Mobility studies leads us to new approaches for dealing with mentioned challenges

Community Detection in Quantum Complex Networks

Determining community structure is a central topic in the study of complex networks, be it technological, social, biological or chemical, in static or interacting systems. In this paper, we extend the concept of community detection from classical to quantum systems---a crucial missing component of a theory of complex networks based on quantum mechanics. We demonstrate that certain quantum mechanical effects cannot be captured using current classical complex network tools and provide new methods that overcome these problems. Our approaches are based on defining closeness measures between nodes, and then maximizing modularity with hierarchical clustering. Our closeness functions are based on quantum transport probability and state fidelity, two important quantities in quantum information theory. To illustrate the effectiveness of our approach in detecting community structure in quantum systems, we provide several examples, including a naturally occurring light-harvesting complex, LHCII. The prediction of our simplest algorithm, semiclassical in nature, mostly agrees with a proposed partitioning for the LHCII found in quantum chemistry literature, whereas our fully quantum treatment of the problem uncovers a new, consistent, and appropriately quantum community structure.Comment: 16 pages, 4 figures, 1 tabl

Exponential and power laws in public procurement markets

For the first time ever, we analyze a unique public procurement database, which includes information about a number of bidders for a contract, a final price, an identification of a winner and an identification of a contracting authority for each of more than 40,000 public procurements in the Czech Republic between 2006 and 2011, focusing on the distributional properties of the variables of interest. We uncover several scaling laws -- the exponential law for the number of bidders, and the power laws for the total revenues and total spendings of the participating companies, which even follows the Zipf's law for the 100 most spending institutions. We propose an analogy between extensive and non-extensive systems in physics and the public procurement market situations. Through an entropy maximization, such the analogy yields some interesting results and policy implications with respect to the Maxwell-Boltzmann and Pareto distributions in the analyzed quantities.Comment: 6 pages, 3 figure