Finding community structure in networks using the eigenvectors of matrices

We consider the problem of detecting communities or modules in networks, groups of vertices with a higher-than-average density of edges connecting them. Previous work indicates that a robust approach to this problem is the maximization of the benefit function known as "modularity" over possible divisions of a network. Here we show that this maximization process can be written in terms of the eigenspectrum of a matrix we call the modularity matrix, which plays a role in community detection similar to that played by the graph Laplacian in graph partitioning calculations. This result leads us to a number of possible algorithms for detecting community structure, as well as several other results, including a spectral measure of bipartite structure in networks and a new centrality measure that identifies those vertices that occupy central positions within the communities to which they belong. The algorithms and measures proposed are illustrated with applications to a variety of real-world complex networks.Comment: 22 pages, 8 figures, minor corrections in this versio

Achieving Low-Complexity Maximum-Likelihood Detection for the 3D MIMO Code

The 3D MIMO code is a robust and efficient space-time block code (STBC) for the distributed MIMO broadcasting but suffers from high maximum-likelihood (ML) decoding complexity. In this paper, we first analyze some properties of the 3D MIMO code to show that the 3D MIMO code is fast-decodable. It is proved that the ML decoding performance can be achieved with a complexity of O(M^{4.5}) instead of O(M^8) in quasi static channel with M-ary square QAM modulations. Consequently, we propose a simplified ML decoder exploiting the unique properties of 3D MIMO code. Simulation results show that the proposed simplified ML decoder can achieve much lower processing time latency compared to the classical sphere decoder with Schnorr-Euchner enumeration

Large-Scale MIMO Detection for 3GPP LTE: Algorithms and FPGA Implementations

Large-scale (or massive) multiple-input multiple-output (MIMO) is expected to be one of the key technologies in next-generation multi-user cellular systems, based on the upcoming 3GPP LTE Release 12 standard, for example. In this work, we propose - to the best of our knowledge - the first VLSI design enabling high-throughput data detection in single-carrier frequency-division multiple access (SC-FDMA)-based large-scale MIMO systems. We propose a new approximate matrix inversion algorithm relying on a Neumann series expansion, which substantially reduces the complexity of linear data detection. We analyze the associated error, and we compare its performance and complexity to those of an exact linear detector. We present corresponding VLSI architectures, which perform exact and approximate soft-output detection for large-scale MIMO systems with various antenna/user configurations. Reference implementation results for a Xilinx Virtex-7 XC7VX980T FPGA show that our designs are able to achieve more than 600 Mb/s for a 128 antenna, 8 user 3GPP LTE-based large-scale MIMO system. We finally provide a performance/complexity trade-off comparison using the presented FPGA designs, which reveals that the detector circuit of choice is determined by the ratio between BS antennas and users, as well as the desired error-rate performance.Comment: To appear in the IEEE Journal of Selected Topics in Signal Processin

Developmental trajectory of Caenorhabditis elegans nervous system governs its structural organization

A central problem of neuroscience involves uncovering the principles governing the organization of nervous systems which ensure robustness in brain development. The nematode Caenorhabditis elegans provides us with a model organism for studying this question. In this paper, we focus on the invariant connection structure and spatial arrangement of the neurons comprising the somatic neuronal network of this organism to understand the key developmental constraints underlying its design. We observe that neurons with certain shared characteristics - such as, neural process lengths, birth time cohort, lineage and bilateral symmetry - exhibit a preference for connecting to each other. Recognizing the existence of such homophily helps in connecting the physical location and morphology of neurons with the topological organization of the network. Further, the functional identities of neurons appear to dictate the temporal hierarchy of their appearance during the course of development. Providing crucial insights into principles that may be common across many organisms, our study shows how the trajectory in the developmental landscape constrains the eventual spatial and network topological organization of a nervous system.Comment: 25 pages, 8 figures + 24 pages supplementary materia

Grand Design and Flocculent Spirals in the Spitzer Survey of Stellar Structure in Galaxies (S4G)

Spiral arm properties of 46 galaxies in the Spitzer Survey of Stellar Structure in Galaxies (S4G) were measured at 3.6mu, where extinction is small and the old stars dominate. The sample includes flocculent, multiple arm, and grand design types with a wide range of Hubble and bar types. We find that most optically flocculent galaxies are also flocculent in the mid-IR because of star formation uncorrelated with stellar density waves, whereas multiple arm and grand design galaxies have underlying stellar waves. Arm-interarm contrasts increase from flocculent to multiple arm to grand design galaxies and with later Hubble types. Structure can be traced further out in the disk than in previous surveys. Some spirals peak at mid-radius while others continuously rise or fall, depending on Hubble and bar type. We find evidence for regular and symmetric modulations of the arm strength in NGC 4321. Bars tend to be long, high amplitude, and flat-profiled in early type spirals, with arm contrasts that decrease with radius beyond the end of the bar, and they tend to be short, low amplitude, and exponential-profiled in late Hubble types, with arm contrasts that are constant or increase with radius. Longer bars tend to have larger amplitudes and stronger arms.Comment: 31 pages, 14 figures, ApJ in pres

Trading Goods versus Sharing Money - An Experiment Testing Wether Fairness and Efficiency are Frame Dependent

Systematic experiments with distribution games (for a survey, see Roth, 1995) have shown that participants are strongly motivated by fairness and efficiency considerations. This evidence, however, results mainly from experimental designs asking directly for sharing monetary rewards. But even when not just one kind of monetary tokens is distributed efficiency and fairness are less influential. We investigate and confirm this frame dependency more systematically by comparing net-trade-proposals and payoff-proposals for the same exchange economy with two traders, two commodities and multi-period-negotiations.