Clustering and community structure is crucial for many network systems and the related dynamic processes. It has been shown that communities are usually overlapping and hierarchical. However, previous methods investigate these two properties of community structure separately. This paper proposes an algorithm (EAGLE) to detect both the overlapping and hierarchical properties of complex community structure together. This algorithm deals with the set of maximal cliques and adopts an agglomerative framework. The quality function of modularity is extended to evaluate the goodness of a cover. The examples of application to real world networks give excellent results.Comment: 7 pages, 5 figure

This paper presents a fully three-dimensional radiative hydrodymanics simulation with realistic opacities for a gravitationally unstable 0.07 M disk around a 0.5 M star. We address the following aspects of disk evolution: the strength of gravitational instabilities under realistic cooling, mass transport in the disk that arises from GIs, comparisons between the gravitational and Reynolds stresses measured in the disk and those expected in an -disk, and comparisons between the SED derived for the disk and SEDs derived from observationally determined parameters. The mass transport in this disk is dominated by global modes, and the cooling times are too long to permit fragmentation for all radii. Moreover, our results suggest a plausible explanation for the FU Ori outburst phenomenon.

In order to investigate mass transport and planet formation by gravitational instabilities (GI's), we have extended our 3-D hydrodynamic simulations of protoplanetary disks from a previous paper. Our goal is to determine the asymptotic behavior of GI's and how it is affected by different constant cooling times. Initially, R disk = 40 AU, M disk = 0.07 M § , M * = 0.5 M § , and Q min = 1.8. Sustained cooling, with t cool = 2 orps (outer rotation periods, 1 orp ≈ 250 yrs), drives the disk to instability in ~ 4 orps. This calculation is followed for 23.5 orps. After 12 orps, the disk settles into a quasi-steady state with sustained nonlinear instabilities, an average Q = 1.44 over the outer disk, a well-defined power-law S(r), and a roughly steady †The transport is driven by global low-order spiral modes. We restart the calculation at 11.2 orps with t cool = 1 and 1/4 orp. The latter case is also run at high azimuthal resolution. We find that shorter cooling times lead to increased † ˙ M 's, denser and thinner spiral structures, and more violent dynamic behavior. The asymptotic total internal energy and the azimuthally averaged Q(r) are insensitive to t cool . Fragmentation occurs only in the high-resolution t cool = 1/4 orp case; however, none of the fragments survive for even a quarter of an orbit. Ring-like density enhancements appear and grow near the boundary between GI active and inactive regions. We discuss the possible implications of these rings for gas giant planet formation.

We study the average consensus problem of multi-agent systems for general network topologies with unidirectional information flow. We propose two (linear) distributed algorithms, deterministic and gossip, respectively for the cases where the inter-agent communication is synchronous and asynchronous. Our contribution is that in both cases, the developed algorithms guarantee state averaging on arbitrary strongly connected digraphs; in particular, this graphical condition does not require that the network be balanced or symmetric, thereby extending many previous results in the literature. The key novelty of our approach is to augment an additional variable for each agent, called "surplus", whose function is to locally record individual state updates. For convergence analysis, we employ graph-theoretic and nonnegative matrix tools, with the eigenvalue perturbation theory playing a crucial role.

We study distributed control design for discrete-event systems (DES) in the framework of supervisory control theory. Our DES comprise multiple agents, acting independently except for specifications on 'global' behavior. The central problem investigated is how to synthesize 'local' controllers for individual agents such that the resultant controlled behavior is identical with that achieved by global supervision.The investigation is carried out with both language-and state-based models. In the language-based setting, a supervisor localization algorithm is developed that solves the problem in a top-down fashion: first, compute a global supervisor, then decompose it into local controllers. For large-scale DES where a global supervisor might not be feasibly computable owing to state explosion, a decomposition-aggregation solution procedure is established. In the state-based setting, specifically that of 'state tree structures' (STS), a counterpart supervisor localization algorithm is developed having potential to exploit the known efficiency of STS for large-DES control design.ii Acknowledgements It is my great honour and pleasure to study under the supervision of Professor W.M.Wonham, to whom I would like to express my deepest gratitude for his patient guidance and inspiring comments throughout the course of study. Learning closely from him, I have begun to understand and appreciate the rigorous attitude and systematic methodology toward research, the far-reaching value being unmeasurable in terms of the amount of knowledge. In addition, I am grateful to him and his wife, Anne, for their warm care and help in life.

Observational studies show that the probability of finding gas giant planets around a star increases with the star's metallicity. Our latest simulations of disks undergoing gravitational instabilities (GIs) with realistic radiative cooling indicate that protoplanetary disks with lower metallicity generally cool faster and thus show stronger overall GI activity. More importantly, the global cooling times in our simulations are too long for disk fragmentation to occur, and the disks do not fragment into dense protoplanetary clumps. Our results suggest that direct gas giant planet formation via disk instabilities is unlikely to be the mechanism that produced most observed planets. Nevertheless, GIs may still play an important role in a hybrid scenario, compatible with the observed metallicity trend, where structure created by GIs accelerates planet formation by core accretion.

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It is generally thought that protoplanetary disks embedded in envelopes are more massive and thus more susceptible to gravitational instabilities (GIs) than exposed disks.We present three-dimensional radiative hydrodynamics simulations of protoplanetary disks with the presence of envelope irradiation. For a disk with a radius of 40 AU and a mass of 0.07 M  around a young star of 0.5 M  , envelope irradiation tends to weaken and even suppress GIs as the irradiating flux is increased. The global mass transport induced by GIs is dominated by lower-order modes, and irradiation preferentially suppresses higher-order modes. As a result, gravitational torques and mass inflow rates are actually increased by mild irradiation. None of the simulations produce dense clumps or rapid cooling by convection, arguing against direct formation of giant planets by disk instability, at least in irradiated disks. However, dense gas rings and radial mass concentrations are produced, and these might be conducive to accelerated planetary core formation. Preliminary results from a simulation of a massive embedded disk with physical characteristics similar to one of the disks in the embedded source L1551 IRS5 indicate a long radiative cooling time and no fragmentation. The GIs in this disk are dominated by global two and three-armed modes.