Results on the convergence with probability one of stochastic approximation algorithms of the form θ n+1 = θ n − γ n+1 h(θ n ) + u n+1 are given, where the θ's belong to some Banach space and { u n } is a sto...
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Results on the convergence with probability one of stochastic approximation algorithms of the form θ n+1 = θ n − γ n+1 h(θ n ) + u n+1 are given, where the θ's belong to some Banach space and { u n } is a stochastic process. Using this extension of results of Kushner and Clark [10], conditions are given for the convergence of the linear algorithm K n+1 = K n − 1 n X n ∘[K n X n − Y n ] . Several applications of the linear algorithm to problems of identification of (possibly distributed) systems and optimization are given. The applicability of these conditions is demonstrated via an example. The systems considered here are more general than those considered by Kushner and Shwartz [12].
We introduce two new classes of graphs which we call convex-round, respectively concave-round graphs. Convex-round (concave-round) graphs are those graphs whose vertices can be circularly enumerated so that the (close...
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We introduce two new classes of graphs which we call convex-round, respectively concave-round graphs. Convex-round (concave-round) graphs are those graphs whose vertices can be circularly enumerated so that the (closed) neighborhood of each vertex forms an interval in the enumeration. Hence the two classes transform into each other by taking complements. We show that both classes of graphs have nice structural properties. We observe that the class of concave-round graphs properly contains the class of proper circular arc graphs and, by a result of Tucker [Pacific J. Math., 39 (1971), pp. 535-545] is properly contained in the class of general circular arc graphs. We point out that convex-round and concave-round graphs can be recognized in O(n + m) time (here n denotes the number of vertices and m the number of edges of the graph in question). We show that the chromatic number of a graph which is convex-round (concave-round) can be found in time O(n + m) (O(n(2))). We describe optimal O(n + m) time algorithms for finding a maximum clique, a maximum matching, and a Hamiltonian cycle (if one exists) for the class of convex-round graphs. Finally, we pose a number of open problems and conjectures concerning the structure and algorithmic properties of the two new classes and a related third class of graphs.
We investigate classes of graphs and posets that admit decompositions to obtain or disprove finiteness results for obstruction sets. To do so we develop a theory of minimal infinite antichains that allows us to charac...
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We investigate classes of graphs and posets that admit decompositions to obtain or disprove finiteness results for obstruction sets. To do so we develop a theory of minimal infinite antichains that allows us to characterize such antichains by means of the set of elements below it. In particular we show that the following classes have infinite antichains with respect to the induced subgraph/poset relation: interval graphs and orders, N-free orders, orders with bounded decomposition width. On the other hand for orders with bounded decomposition diameter finiteness of all antichains is shown. As a consequence those classes with infinite antichains have undecidable hereditary properties whereas those with finite antichains have fast algorithms for all such properties.
Efficient Image processing can lead to complex algorithms. In Embedded context resources are limited and the approach of linear algorithm does not allow to decrease complexity regarding the variations of these resourc...
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Worst-case analysis of system identification by means of the linear algorithms such as least squares is considered. Estimates for worst-case and average errors are provided, showing that worst-case robust convergence ...
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Worst-case analysis of system identification by means of the linear algorithms such as least squares is considered. Estimates for worst-case and average errors are provided, showing that worst-case robust convergence cannot occur in the l 1 identification problem. The case of periodic inputs is also analysed. Finally pseu-dorandomness assumptions are introduced which allow more powerful convergence results in a deterministic framework.
Cloud computing is widely accepted as the best computing and storage model for low cost and high resource utilization. User requests from public can be run in data centers of large datacenters whey they are idle. This...
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ISBN:
(纸本)9781467367257
Cloud computing is widely accepted as the best computing and storage model for low cost and high resource utilization. User requests from public can be run in data centers of large datacenters whey they are idle. This brings in high profit for cloud providers and low cost for cloud users. The profit and response time can be improved by an optimal scheduling policy. This paper does a survey on various classes of existing cloudlet scheduling algorithms. Researchers have proposed linear algorithms, genetic algorithms and swarm intelligence algorithms. The merits and demerits of these classes of algorithms are analyzed in this paper.
Feature extraction refers to the groups of techniques that, when applied to large dimensional and redundant data result in significant dimensionality reduction while preserving or even enhancing the information conten...
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ISBN:
(纸本)9781424413010
Feature extraction refers to the groups of techniques that, when applied to large dimensional and redundant data result in significant dimensionality reduction while preserving or even enhancing the information content. Among various techniques investigated for feature extraction, of new interest is Nonnegative Matrix Factorization (NMF). In NMF, it is assumed that the data is formed as a linear nonnegative combination of positive sources and the NMF solution recovers the original sources and the mixing matrix. In this paper, we first look at ways NMF can be applied for feature extraction in hyperspectral imagery a data known for large sizes and redundancy. While some of the associations are natural to linear mixing model (LMM - that assumes that hyperspectral images are formed as a linear mixture of endmember information), we also show NMF to be a slow method. To counter this, we investigate alternative solutions such as projected NMF approaches and provide an insight to how parallel implementations would contribute to speedup. Experimental results on various data show projected NMF outperforming regular NMF with parallel implementations providing a promising speedup advantage.
A packet-switched network is universally stable if, for any greedy protocol and any adversary of injection rate less than 1, the number of packets in the network remains bounded at all times. A natural question that a...
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ISBN:
(数字)9783540778912
ISBN:
(纸本)9783540778905
A packet-switched network is universally stable if, for any greedy protocol and any adversary of injection rate less than 1, the number of packets in the network remains bounded at all times. A natural question that arises is whether there is a fast way to detect if a network is universally stable based on the network's structure. In this work, we study this question in the context of Adversarial Queueing Theory which assumes that an adversary controls the locations and rates of packet injections and determines packet paths. Within this framework, we present optimal algorithms for detecting the universal stability (packet paths do not contain repeated edges but may contain repeated vertices) and the simple-path universal stability (paths contain neither repeated vertices nor repeated edges) of a network. Additionally, we describe an algorithm which decides in constant time whether the addition of a link in a universally stable network leads it to instability;such an algorithm could be useful in detecting intrusion attacks.
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