Evaluating links through spectral decomposition

Spectral decomposition has been rarely used to investigate complex networks. In this work we apply this concept in order to define two types of link-directed attacks while quantifying their respective effects on the topology. Several other types of more traditional attacks are also adopted and compared. These attacks had substantially diverse effects, depending on each specific network (models and real-world structures). It is also showed that the spectral-based attacks have special effect in affecting the transitivity of the networks

Evaluating Overfit and Underfit in Models of Network Community Structure

A common data mining task on networks is community detection, which seeks an unsupervised decomposition of a network into structural groups based on statistical regularities in the network's connectivity. Although many methods exist, the No Free Lunch theorem for community detection implies that each makes some kind of tradeoff, and no algorithm can be optimal on all inputs. Thus, different algorithms will over or underfit on different inputs, finding more, fewer, or just different communities than is optimal, and evaluation methods that use a metadata partition as a ground truth will produce misleading conclusions about general accuracy. Here, we present a broad evaluation of over and underfitting in community detection, comparing the behavior of 16 state-of-the-art community detection algorithms on a novel and structurally diverse corpus of 406 real-world networks. We find that (i) algorithms vary widely both in the number of communities they find and in their corresponding composition, given the same input, (ii) algorithms can be clustered into distinct high-level groups based on similarities of their outputs on real-world networks, and (iii) these differences induce wide variation in accuracy on link prediction and link description tasks. We introduce a new diagnostic for evaluating overfitting and underfitting in practice, and use it to roughly divide community detection methods into general and specialized learning algorithms. Across methods and inputs, Bayesian techniques based on the stochastic block model and a minimum description length approach to regularization represent the best general learning approach, but can be outperformed under specific circumstances. These results introduce both a theoretically principled approach to evaluate over and underfitting in models of network community structure and a realistic benchmark by which new methods may be evaluated and compared.Comment: 22 pages, 13 figures, 3 table

Detecting communities of triangles in complex networks using spectral optimization

The study of the sub-structure of complex networks is of major importance to relate topology and functionality. Many efforts have been devoted to the analysis of the modular structure of networks using the quality function known as modularity. However, generally speaking, the relation between topological modules and functional groups is still unknown, and depends on the semantic of the links. Sometimes, we know in advance that many connections are transitive and, as a consequence, triangles have a specific meaning. Here we propose the study of the modular structure of networks considering triangles as the building blocks of modules. The method generalizes the standard modularity and uses spectral optimization to find its maximum. We compare the partitions obtained with those resulting from the optimization of the standard modularity in several real networks. The results show that the information reported by the analysis of modules of triangles complements the information of the classical modularity analysis.Comment: Computer Communications (in press

Semiclassical approach to discrete symmetries in quantum chaos

We use semiclassical methods to evaluate the spectral two-point correlation function of quantum chaotic systems with discrete geometrical symmetries. The energy spectra of these systems can be divided into subspectra that are associated to irreducible representations of the corresponding symmetry group. We show that for (spinless) time reversal invariant systems the statistics inside these subspectra depend on the type of irreducible representation. For real representations the spectral statistics agree with those of the Gaussian Orthogonal Ensemble (GOE) of Random Matrix Theory (RMT), whereas complex representations correspond to the Gaussian Unitary Ensemble (GUE). For systems without time reversal invariance all subspectra show GUE statistics. There are no correlations between non-degenerate subspectra. Our techniques generalize recent developments in the semiclassical approach to quantum chaos allowing one to obtain full agreement with the two-point correlation function predicted by RMT, including oscillatory contributions.Comment: 26 pages, 8 Figure

Improving Entity Retrieval on Structured Data

The increasing amount of data on the Web, in particular of Linked Data, has led to a diverse landscape of datasets, which make entity retrieval a challenging task. Explicit cross-dataset links, for instance to indicate co-references or related entities can significantly improve entity retrieval. However, only a small fraction of entities are interlinked through explicit statements. In this paper, we propose a two-fold entity retrieval approach. In a first, offline preprocessing step, we cluster entities based on the \emph{x--means} and \emph{spectral} clustering algorithms. In the second step, we propose an optimized retrieval model which takes advantage of our precomputed clusters. For a given set of entities retrieved by the BM25F retrieval approach and a given user query, we further expand the result set with relevant entities by considering features of the queries, entities and the precomputed clusters. Finally, we re-rank the expanded result set with respect to the relevance to the query. We perform a thorough experimental evaluation on the Billions Triple Challenge (BTC12) dataset. The proposed approach shows significant improvements compared to the baseline and state of the art approaches

Mayer expansion of the Nekrasov pre potential: the subleading ϵ2\epsilon_2-order

The Mayer cluster expansion technique is applied to the Nekrasov instanton partition function of $\mathcal{N}=2$ $SU(N_c)$ super Yang-Mills. The subleading small $\epsilon_2$-correction to the Nekrasov-Shatashvili limiting value of the prepotential is determined by a detailed analysis of all the one-loop diagrams. Indeed, several types of contributions can be distinguished according to their origin: long range interaction or potential expansion, clusters self-energy, internal structure, one-loop cyclic diagrams, etc.. The field theory result derived more efficiently in [1], under some minor technical assumptions, receives here definite confirmation thanks to several remarkable cancellations: in this way, we may infer the validity of these assumptions for further computations in the field theoretical approach.Comment: 29 pages, 9 figure

Opportunistic Third-Party Backhaul for Cellular Wireless Networks

With high capacity air interfaces and large numbers of small cells, backhaul -- the wired connectivity to base stations -- is increasingly becoming the cost driver in cellular wireless networks. One reason for the high cost of backhaul is that capacity is often purchased on leased lines with guaranteed rates provisioned to peak loads. In this paper, we present an alternate \emph{opportunistic backhaul} model where third parties provide base stations and backhaul connections and lease out excess capacity in their networks to the cellular provider when available, presumably at significantly lower costs than guaranteed connections. We describe a scalable architecture for such deployments using open access femtocells, which are small plug-and-play base stations that operate in the carrier's spectrum but can connect directly into the third party provider's wired network. Within the proposed architecture, we present a general user association optimization algorithm that enables the cellular provider to dynamically determine which mobiles should be assigned to the third-party femtocells based on the traffic demands, interference and channel conditions and third-party access pricing. Although the optimization is non-convex, the algorithm uses a computationally efficient method for finding approximate solutions via dual decomposition. Simulations of the deployment model based on actual base station locations are presented that show that large capacity gains are achievable if adoption of third-party, open access femtocells can reach even a small fraction of the current market penetration of WiFi access points.Comment: 9 pages, 6 figure

Eigenvalus of Casimir Invariants for Type-I Quantum Superalgebras

We present the eigenvalues of the Casimir invariants for the type I quantum superalgebras on any irreducible highest weight module.Comment: 13 pages, AmsTex file; to appear in Lett. Math. Phy