45408024
Star Extremal Circulant Graphs
A graph is called star extremal if its fractional chromatic number is equal to its circular chromatic number (also known as the star chromatic number). We prove that members of a certain family of circulant graphs are star extremal. The result generalizes some known theorems of Sidorenko [Discrete Math., 91 (1991), pp. 215--217] and Gao and Zhu [Discrete Math., 152 (1996), pp. 147--156]. We show relations between circulant graphs and distance graphs and discuss their star extremality. Furthermore, we give counterexamples to two conjectures of Collins [SIAM J. Discrete Math., 11 (1998), pp. 330--339] on asymptotic independence ratios of circulant graphs.
16699960
Circular chromatic number for iterated Mycielski graphs
Abstract For a graph G , let M( G ) denote the Mycielski graph of G . The t th iterated Mycielski graph of G , M t ( G ), is defined recursively by M 0 ( G )= G , and M t ( G )=M(M t −1 ( G )) for t ⩾1. Let χ c ( G ) denote the circular chromatic number of G . We prove two main results: (1) If G has a universal vertex x , then χ c (M( G ))= χ (M( G )) if χ c (G−x)>χ(G)− 1 2 and G is not a star, otherwise χ c ( M (G))=χ( M (G))− 1 2 ; and (2) χ c (M t ( K m ))= χ (M t ( K m )) if m ⩾2 t −1 +2 t −2 and t ⩾2.
17515399
Sizes of Graphs with Fixed Orders and Spans for Circular-Distance-Two Labelings
A k-circular-distance-two labeling (or k-c-labeling) of a simple graph G is a vertex-labeling, using the labels 0, 1, 2, · · · , k − 1, such that the “circular difference” (mod k) of the labels for adjacent vertices is at least two, and for vertices of distance-two apart is at least one. The σ-number, σ(G), of a graph G is the minimum k of a k-c-labeling of G. For any given positive integers n and k, let G(n, k) denote the set of graphs G on n vertices and σ(G) = k. We determine the maximum size (number of edges) and the minimum size of a graph G ∈ G(n, k). Furthermore, we prove that for any value p between the maximum and the minimum size, there exists a graph G ∈ G(n, k) of size p. These results are analogues of the ones by Georges and Mauro [4] on distance-two labelings.
84347
Latent Layout Analysis for Discovering Objects in Images
Latent layout analysis (LLA) is a novel unsupervised learning technique to discover objects in unseen images using a set of un-annotated training images. LLA defines a generative model that associates latent aspects to local appearances. The dependency between aspects and position is captured by a spatial sensitive aspect model. This dependency distinguishes LLA from probabilistic latent semantic analysis (PLSA). The latent aspects together with the latent layout constitute a compact scene representation. We demonstrate that the proposed LLA significantly outperforms probabilistic latent semantic analysis in two tasks: object discovery (detection) and object localization
36089150
Hamiltonicity and circular distance two labellings
Abstract A k -circular distance two labelling (or k -c-labelling) of a graph G is a vertex-labelling such that the circular difference ( mod k ) of the labels is at least two for adjacent vertices, and at least one for vertices at distance two. Given G , denote σ(G) the minimum k for which there exists a k -c-labelling of G . Suppose G has n vertices, we prove σ(G)⩽n if G c is Hamiltonian; and σ(G)=n+p v (G c ) otherwise, where p v (G) is the path covering number of G . We give exact values of σ(G) for some families of graphs such that G c is Hamiltonian, and discuss injective k -c-labellings especially for joins and unions of graphs.
915132
On Randomized Broadcasting and Gossiping in Radio Networks
This paper has two parts. In the first part we give an alternative (and much simpler) proof for the best known lower bound of ?(Dlog (N/D)) time-steps for randomized broadcasting in radio networks with unknown topology. In the second part we give an O(N log3N)- time randomized algorithm for gossiping in such radio networks. This is an improvement over the fastest previously known algorithm that works in time O(N log4 N).
215202
Neural network-based model reference adaptive control system
In this paper, an approach to model reference adaptive control based on neural networks is proposed and analyzed for a class of first-order continuous-time nonlinear dynamical systems. The controller structure can employ either a radial basis function network or a feedforward neural network to compensate adaptively the nonlinearities in the plant. A stable controller-parameter adjustment mechanism, which is determined using the Lyapunov theory, is constructed using a sigma-modification-type updating law. The evaluation of control error in terms of the neural network learning error is performed. That is, the control error converges asymptotically to a neighborhood of zero, whose size is evaluated and depends on the approximation error of the neural network. In the design and analysis of neural network-based control systems, it is important to take into account the neural network learning error and its influence on the control error of the plant. Simulation results showing the feasibility and performance of the proposed approach are given.
41350051
Language engineering for the Semantic Web: a digital library for endangered languages