The number of spanning trees in a (di-)graph (network) is an important, well-studied quantity. Most research about the number of spanning trees is devoted to determining exact formulae for the number of spanning trees...
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The number of spanning trees in a (di-)graph (network) is an important, well-studied quantity. Most research about the number of spanning trees is devoted to determining exact formulae for the number of spanning trees in many kinds of special graphs. In this thesis, we start by stating the general methods for counting the number of spanning trees in (di-)graphs. We then discuss our new results. We show that the number of spanning trees in the circulant graph [special characters omitted] always satisfies a recurrence relation and describe how to derive this relation. The asymptotic behavior of these quantities are also derived. Boesch and Prodinger have shown how to use Chebyshev polynomials to derive closed formulae for the number of spanning trees of graphs in certain classes. This work has been extended to develop new techniques for the evaluation of the number of spanning trees in circulant graphs and graphs related to circulant graphs. We end by describing a method of counting the number of spanning trees in one class of double fixed-step loop networks.
The development of intelligent transportation systems (ITS) and the resulting need for the solution of a variety of dynamic traffic network models and management problems require faster-than-real-time computation of s...
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The development of intelligent transportation systems (ITS) and the resulting need for the solution of a variety of dynamic traffic network models and management problems require faster-than-real-time computation of shortest path problems in dynamic networks. Recently, a sequential algorithm was developed to compute shortest paths in discrete time dynamic networks from all nodes and all departure times to one destination node. The algorithm is known as algorithm DOT and has an optimal worst-case running-time complexity. This implies that no algorithm with a better worst-case computational complexity can be discovered. Consequently, in order to derive algorithms to solve all-to-one shortest path problems in dynamic networks, one would need to explore avenues other than the design of sequential solution algorithms only. The use of commercially-available high-performance computing platforms to develop parallel implementations of sequential algorithms is an example of such avenue. This paper reports on the design, implementation, and computational testing of parallel dynamic shortest path algorithms. We develop two shared-memory and two message-passing dynamic shortest path algorithm implementations, which are derived from algorithm DOT using the following parallelization strategies: decomposition by destination and decomposition by transportation network topology. The algorithms are coded using two types of parallel computing environments: a message-passing environment based on the parallel virtual machine (PVM) library and a multi-threading environment based on the SUN Microsystems Multi-Threads (MT) library. We also develop a time-based parallel version of algorithm DOT for the case of minimum time paths in FIFO networks, and a theoretical parallelization of algorithm DOT on an ‘ideal’ theoretical parallel machine. Performances of the implementations are analyzed and evaluated using large transportation networks, and two types of parallel computing platforms: a distr
We have developed an improved algorithm that allows us to enumerate the number of site animals on the square lattice LIP to size 46. We also calculate the number of lattice trees up to size 44 and the radius of gyrati...
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We have developed an improved algorithm that allows us to enumerate the number of site animals on the square lattice LIP to size 46. We also calculate the number of lattice trees up to size 44 and the radius of gyration of both lattice animals and trees up to size 42. Analysis of the resulting series yields an improved estimate, lambda =4.062570(8), for the growth constant of lattice animals, and, lambda (0)=3.795254(8), for the growth constant of trees, and confirms to a very high degree of certainty that both the animal and tree generating Functions have a logarithmic divergence. Analysis of the radius of gyration series yields the estimate, nu =0.64115(5), for the size exponent.
We have developed a transfer matrix algorithm for the enumeration of compact self-avoiding walks on rectangular strips of the square lattice. The algorithm is easily adapted to other shapes or generalized to problems ...
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We have developed a transfer matrix algorithm for the enumeration of compact self-avoiding walks on rectangular strips of the square lattice. The algorithm is easily adapted to other shapes or generalized to problems such as interacting walks. These models are relevant in the study of globular proteins. (C) 2001 Elsevier Science B.V. All rights reserved.
In this paper we will describe our recent results related to the design of hybrid on-line Failure Detection and Identification (FDI) and Adaptive Reconfigurable Control (ARC) algorithms for aerial and space vehicles. ...
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ISBN:
(纸本)0780367332
In this paper we will describe our recent results related to the design of hybrid on-line Failure Detection and Identification (FDI) and Adaptive Reconfigurable Control (ARC) algorithms for aerial and space vehicles. Our approach is based on the Multiple Models, Switching and Tuning (MMST) methodology and its extensions, and has been demonstrated as an efficient tool for hybrid fault tolerant control under subsystem and component failures and structural damage.
We have developed a transfer matrix algorithm for the enumeration of compact self-avoiding walks on rectangular strips of the square lattice. The algorithm is easily adapted to other shapes or generalized to problems ...
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We have developed a transfer matrix algorithm for the enumeration of compact self-avoiding walks on rectangular strips of the square lattice. The algorithm is easily adapted to other shapes or generalized to problems such as interacting walks. These models are relevant in the study of globular proteins. (C) 2001 Elsevier Science B.V. All rights reserved.
Partially Observable Markov Decision Process (POMDP) is a general sequential decision-making model where the effects of actions are nondeterministic and only partial information about world states is available. Howeve...
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Partially Observable Markov Decision Process (POMDP) is a general sequential decision-making model where the effects of actions are nondeterministic and only partial information about world states is available. However, finding near optimal solutions for POMDPs is computationally difficult. Value iteration is a standard algorithm for solving POMDPs. It conducts a sequence of dynamic programming (DP) updates to improve value functions. Value iteration is inefficient for two reasons. First, a DP update is expensive due to the need of accounting for all belief states in a continuous belief space. Second, value iteration needs to conduct a large number of DP updates before its convergence. This thesis investigates two ways to accelerate value iteration. The work presented centers around the idea of conducting DP updates and therefore value iteration over a belief subspace, a subset of belief space. The first use of belief subspace is to reduce the number of DP updates for value iteration to converge. We design a computationally cheap procedure considering a belief subspace which consists of a finite number of belief states. It is used as an additional step for improving value functions. Due to additional improvements by the procedure, value iteration conducts fewer DP updates and therefore is more efficient. The second use of belief subspace is to reduce the complexity of DP updates. We establish a framework on how to carry out value iteration over a belief subspace determined by a POMDP model. Whether the belief subspace is smaller than the belief space is model dependent. If this is true for a POMDP, value iteration over the belief subspace is expected to be more efficient. Based on this framework, we study three POMDP classes with special problem characteristics and propose different value iteration algorithms for them. (1) An informative POMDP assumes that an agent always has a good idea about the world states. The subspace determined by the model is much smaller th
The throughput results for file transfers using file sizes ranging from 1 Kbytes through 1 Mbytes using both the standard TCP/IP and SCPS protocol stacks over a PPP link are reported. Channel properties were simulated...
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ISBN:
(纸本)0780365992
The throughput results for file transfers using file sizes ranging from 1 Kbytes through 1 Mbytes using both the standard TCP/IP and SCPS protocol stacks over a PPP link are reported. Channel properties were simulated using a space channel simulator with a range of balanced and unbalanced link speeds and channel error rates. The throughput results will show the effects of link configuration and channel error rate on file transfer time. The host computer configuration options for the protocols are factored into the comparison. The throughput reporting shows the effects of header compression and selection of congestion algorithm upon the results. The TCP/IP ftp and SCPS-FP using VJ congestion control algorithm results give similar results and better results than SCPS-FP with the Vegas congestion control algorithm in these experiments. No noticeable delay effects were noted with links delays corresponding to GEO orbits with file transfers of 1 Mbytes.
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