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 ${\cal H}$.
206964202
Asymptotic Upper Bounds for Ramsey Functions
Abstract. We show that for any graph G with N vertices and average degree d, if the average degree of any neighborhood induced subgraph is at most a, then the independence number of G is at least Nfa+1(d), where fa+1(d)=∫01(((1−t)1/(a+1))/(a+1+(d−a−1)t))dt. Based on this result, we prove that for any fixed k and l, there holds r(Kk+l,Kn)≤ (l+o(1))nk/(logn)k−1. In particular, r(Kk, Kn)≤(1+o(1))nk−1/(log n)k−2.
34644814
The Independence Number of Graphs with a Forbidden Cycle and Ramsey Numbers
Let k ≥ 5 be a fixed integer and let m = ⌊(k − 1)/2⌋. It is shown that the independence number of a Ck-free graph is at least c1[∑ d(v)1/(m − 1)](m − 1)/m and that, for odd k, the Ramsey number r(Ck, Kn) is at most c2(nm + 1/log n)1/m, where c1 = c1(m) > 0 and c2 = c2(m) > 0.
2037433
An upper bound for ramsey numbers
Let G″ be a graph obtained from G by deleting two vertices. It is shown that r(G, H) ⩽ A + B + 2 + 2 (A2 + AB + B2)3 where A = r(G″, H) and B = r(G,H″).
43234278
A Ramsey Goodness Result for Graphs with Many Pendant Edges
17658871
On generalized Ramsey numbers
Abstract Let f 1 and f 2 be graph parameters. The Ramsey number r ( f 1 ⩾ m ; f 2 ⩾ n ) is defined as the minimum integer N such that any graph G on N vertices, either f 1 ( G )⩾ m or f 2 ( G )⩾n . A general existence condition is given and a general upper bound is shown in this paper. In addition, suppose the number of triangles in G is denoted by t ( G ). We verify that (1−o(1))(24 n ) 1/3 ⩽ r ( t ⩾ n ; t ⩾ n )⩽(1+o(1))(48 n ) 1/3 as n →∞.
6040880
Rupture degree of graphs
We introduce a new graph parameter, the rupture degree. The rupture degree for a complete graph K n is defined as 1−n, and the rupture degree for an incomplete connected graph G is defined by r(G)=max{ω(G−X)−|X|−m(G−X):X⊂V(G), ω(G−X)>1}, where ω(G−X) is the number of components of G−X and m(G−X) is the order of a largest component of G−X. It is shown that this parameter can be used to measure the vulnerability of networks. Rupture degrees of several specific classes of graphs are determined. Formulas for the rupture degree of join graphs and some bounds of the rupture degree are given. We also obtain some Nordhaus–Gaddum type results for the rupture degree.
15691197
Verifying OWL and ORL Ontologies in PVS
The Semantic Web vision is being realized to reach the full potential of the Web. Semantic data modeling is the foundation of the Semantic Web. The Web Ontology Language (OWL) and OWL Rules Language (ORL) provides basic machinery to the semantic mark-up for data. However, there is limited tool support for OWL and no tool support currently for ORL. In this paper, we propose to model OWL and ORL language semantics in PVS specification language so that OWL and ORL ontologies can be transformed and verified in the Prototype Verification System (PVS). PVS user-defined proof strategies are also developed to automate the proof process.
8278906
A Hybrid Method of Unsupervised Feature Selection Based on Ranking
Feature selection is a key problem to pattern recognition. So far, most methods of feature selection focus on sample data where class information is available. For sample data without class labels, however, the related methods for feature selection are few. This paper proposes a new way of unsupervised feature selection. Our method is a hybrid approach based on ranking the features according to their relevance to clustering using a new ranking index which belongs to exponential entropy. Firstly a candidate feature subset is selected using a modified fuzzy feature evaluation index (FFEI) with a new method to calculate the feature weight, which makes the algorithm to be robust and independent of domain knowledge. Then a wrapper method is used to select compact feature subset from the candidate feature set based on the clustering performance. Experimental results on benchmark data sets indicate the effectiveness of the proposed method
10585568
Deriving Private Information from Perturbed Data Using IQR Based Approach
Several randomized techniques have been proposed for privacy preserving data mining of continuous data. These approaches generally attempt to hide the sensitive data by randomly modifying the data values using some additive noise and aim to reconstruct the original distribution closely at an aggregate level. However, one challenge here is whether the reconstructed distribution can be exploited by attackers or snoopers to derive sensitive individual data. This paper presents one simple attack using Inter-Quantile Range on reconstructed distribution. The experimental results show that current random perturbation-based privacy preserving data mining techniques may need a careful scrutiny in order to prevent privacy breaches through this model based inference.
5628621
A context-aware infrastructure for supporting applications with pen-based interaction
Pen-based user interfaces which leverage the affordances of the pen provide users with more flexibility and natural interaction. However, it is difficult to construct usable pen-based user interfaces because of the lack of support for their development. Toolkit-level support has been exploited to solve this problem, but this approach makes it hard to gain platform independence, easy maintenance and easy extension. In this paper a context-aware infrastructure is created, called WEAVER, to provide pen interaction services for both novel pen-based applications and legacy GUI-based applications. WEAVER aims to support the pen as another standard interactive device along with the keyboard and mouse and present a high-level access interface to pen input. It employs application context to tailor its service to different applications. By modeling the application context and registering the relevant action adapters, WEAVER can offer services, such as gesture recognition, continuous handwriting and other fundamental ink manipulations, to appropriate applications. One of the distinct features of WEAVER is that off-the-shelf GUI-based software packages can be easily enhanced with pen interaction without modifying the existing code. In this paper, the architecture and components of WEAVER are described. In addition, examples and feedbacks of its use are presented.