434,817 research outputs found

    The competition number of a graph and the dimension of its hole space

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    The competition graph of a digraph D is a (simple undirected) graph which has the same vertex set as D and has an edge between x and y if and only if there exists a vertex v in D such that (x,v) and (y,v) are arcs of D. For any graph G, G together with sufficiently many isolated vertices is the competition graph of some acyclic digraph. The competition number k(G) of G is the smallest number of such isolated vertices. In general, it is hard to compute the competition number k(G) for a graph G and it has been one of important research problems in the study of competition graphs to characterize a graph by its competition number. Recently, the relationship between the competition number and the number of holes of a graph is being studied. A hole of a graph is a cycle of length at least 4 as an induced subgraph. In this paper, we conjecture that the dimension of the hole space of a graph is no smaller than the competition number of the graph. We verify this conjecture for various kinds of graphs and show that our conjectured inequality is indeed an equality for connected triangle-free graphs.Comment: 6 pages, 3 figure

    Type II Anyon Superconductivity

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    Assuming that the superconductivity which is described by the low energy effective action of the anyon system may be type II, we discuss its characteristics. We also study physical properties of the Chern-Simons vortices, which may be formed as the external magnetic field is applied to the system, such as their statistics, the free energy of single vortex and the interaction energy between two vortices.Comment: 12 pages, REVTEX, no figure

    Adaptive Duty Cycling MAC Protocols Using Closed-Loop Control for Wireless Sensor Networks

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    The fundamental design goal of wireless sensor MAC protocols is to minimize unnecessary power consumption of the sensor nodes, because of its stringent resource constraints and ultra-power limitation. In existing MAC protocols in wireless sensor networks (WSNs), duty cycling, in which each node periodically cycles between the active and sleep states, has been introduced to reduce unnecessary energy consumption. Existing MAC schemes, however, use a fixed duty cycling regardless of multi-hop communication and traffic fluctuations. On the other hand, there is a tradeoff between energy efficiency and delay caused by duty cycling mechanism in multi-hop communication and existing MAC approaches only tend to improve energy efficiency with sacrificing data delivery delay. In this paper, we propose two different MAC schemes (ADS-MAC and ELA-MAC) using closed-loop control in order to achieve both energy savings and minimal delay in wireless sensor networks. The two proposed MAC schemes, which are synchronous and asynchronous approaches, respectively, utilize an adaptive timer and a successive preload frame with closed-loop control for adaptive duty cycling. As a result, the analysis and the simulation results show that our schemes outperform existing schemes in terms of energy efficiency and delivery delay
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