206570728
On Book-Complete Graph Ramsey Numbers
It is shown that a graph of orderNand average degreedthat does not contain the bookBm=K1+K1, mas a subgraph has independence number at leastNf(d), wheref(x)~(logx/x)(x?∞). From this result we find that the book-complete graph Ramsey number satisfiesr(Bm, Kn)?mn2/log(n/e). It is also shown that for every treeTmwithmedges,r(K1+Tm,Kn)?(2m?1)n2/log(n/e).
5363430
Differential Methods for Finding Independent Sets in Hypergraphs
It is shown by using differential methods that if ${\cal H}$ is a double linear, $r$-uniform hypergraph with degree sequence $\{d_v\}$ such that any subhypergraph induced by a neighborhood has maximum degree less than $m$, then its independence number is at least $\sum_{v}f_{r,m}(d_v)$, where $f_{r,m}(x)$ is a convex function satisfying $f_{r,m}(x)\sim (\log x)/x$ if $r=2$ and $c/x^{1/(r-1)}$ if $r \ge 3$, as $x\to\infty$, and $c=c(r,m)>0$ is a constant. The proof yields a polynomial-time algorithm for finding such an independent set in ${\cal H}$.
1087466
Independence numbers of hypergraphs with sparse neighborhoods
Let H be a hypergraph with N vertices and average degree d. Suppose that the neighborhoods of H are sparse, then its independence number is at least cN(log d/d), where c > 0 is a constant. In particular, let integers r ≥ 3 and n ≥ 1 be fixed, and let H be r-uniform, triangle-free and linear, then its independence number is at least cN logn d/d for all sufficiently large d.
2702895
Single-image reflectance estimation for relighting by iterative soft grouping
Reflectance values for image-based relighting are often estimated from grouped pixels with similar reflectance, but such groupings are difficult to compute with certainty for sparse image data. To address this problem, we propose an iterative method that aggregates BRDF data in a single image with known geometry and lighting by soft grouping, where pixels contribute to one another's estimate according to their degree of reflectance similarity. Estimation of specular reflectance is further improved by albedo-independent soft grouping of pixels based on shape continuity. With recovered reflectances, we demonstrate realistic relighting for synthetic and real scenes, including surfaces with spatially-varying reflectance.
24660543
A note on the lower bounds of signed domination number of a graph
Abstract Let G = (V, E) be a graph. For a function f : V → {−1, 1}, the weight of f is w(f) = Σv ∈ V f(v). For a vertex v in V, we define f[v] = Σu∈N[v] f(u). A signed dominating function of G is a function f : V → {−1, 1} such that f[v] ⩾ 1 for all v ∈ V. The signed domination number γs(G) of G is the minimum weight of a signed dominating function on G. A signed dominating function of a weight γs(G) we call a γs-function of G. In this paper, we study the signed domination problem of general graph, and obtain some lower bounds of the signed domination number of a graph, and show that these lower bounds are sharp, and extend a result in Dunbar et al. (1995).
15872257
Independent component analysis of complex-valued functional magnetic resonance imaging data by complex nonlinearities
Independent component analysis (ICA) for separating complex-valued sources is needed for convolutive source-separation in the frequency domain, or for performing source separation on complex-valued data. Functional magnetic resonance imaging (fMRI) is a technique that produces complex-valued data; however the vast majority of fMRI analyses utilize only magnitude images due in large part to the difficulty of developing a temporal phase model. We have successfully applied ICA to complex fMRI data but there is a need to further optimize the complex ICA. We recently proposed a number of complex nonlinear functions for ICA of complex valued data. We apply two of these functions to fMRI data and examine the properties of these nonlinearities and their efficiency in generating the higher order statistics needed for ICA. We show that the complex infomax using these efficient nonlinearities demonstrates superior performance compared to analysis of the magnitude data with either ICA or linear regression. Complex ICA thus provides a potentially powerful method for the analysis of fMRI data.
5296800
Adaptive box-based efficient fault-tolerant routing in 3D torus
In this paper, we propose efficient fault-tolerant routing algorithms for 3D torus with possible large number of faulty nodes. There is no any presumption on the number and the distribution of faulty nodes. The proposed algorithms find a fault-free path between any two nonfaulty nodes with high probability in linear time by using only the local faulty information of the network. The results of our empirical analysis through simulations show that the algorithms can find a fault-free path between any two nonfaulty nodes with a probability higher than 90% in a 3D torus with the number of faulty nodes up to 30%.
8036895
The case for multipath multimedia transport over wireless ad hoc networks
Real-time multimedia transport has stringent bandwidth, delay, and loss requirements. Supporting this application in current wireless ad hoc networks is a challenge. Such networks are characterized with frequent link failures, as well as congestion. Consequently, data packets are dropped when a link fails or congestion occurs, resulting in low received quality. In addition, a realtime multimedia service may be unavailable when a particular server is unreachable. In this article, we make the case for using multipath transport for realtime multimedia services in wireless ad hoc networks, which provides a unified solution to the above problems. We review existing work on multipath multimedia transport, and discuss the advantages, as well as related issues, of using multipath transport for realtime multimedia transport.