Known complexity facts: the decision problem of the existence of a kernel in a digraph G = (V; E) is NP-complete; if all of the cycles of G have even length, then G has a kernel; and the question of the number of kernels is #P-complete even for this restricted class of digraphs. In the opposite direction, we construct game theory tools, of independent interest, concerning strategies in the pres...

where K is the kernel of the integral. Given the input signal X , Y represents the output signal. The smoothness of the output depends on the smoothness of the kernel. We assume the kernel to be unimodal and isotropic. When the kernel is isotropic, it has radial symmetry and should be invariant under rotation. So it has the form K(t, s) = f(‖t− s‖) for some smooth function f . Since the kernel ...

We present new kernelization results for the s-cycle transversal problem for s > 3. In particular, we show a 6k kernel for 4-cycle transversal and a O(k) kernel for s-cycle transversal when s > 4. We prove the NP-completeness of s-cycle transversal on planar graphs and obtain a 74k kernel for 4-cycle transversal on planar graphs. We also give several kernelization results for a related problem ...

Let G be a directed graph. Its vertex-set will be denoted by X, and its arcs (or ‘directed edges’) are a subset of the Cartesian product X x X. A kernel of G is a subset S of X which is ‘stable’ (independent, i.e.: a vertex in S has no successor in S) and ‘absorbant’ (dominating, i.e. a vertex not in S has a successor in S). This concept has found many applications, for instance in cooperative ...

A set S of vertices in a digraph D = (V,A) is a kernel if S is independent and every vertex in V −S has an out-neighbor in S. We show that there exist O(n2 √ k +n)time and O(2 √ k + n)-time algorithms for checking whether a planar digraph D of order n has a kernel with at most k vertices. Moreover, if D has a kernel of size at most k, the algorithms find such a kernel of minimal size.

This paper points out that many search relevance models in information retrieval, such as the Vector Space Model, BM25 and Language Models for Information Retrieval, can be viewed as a similarity function between pairs of objects of different types, referred to as an S-function. An S-function is specifically defined as the dot product between the images of two objects in a Hilbert space mapped ...

A kernel N of a digraph D is an independent set of vertices of D such that for every w ∈ V (D)− N there exists an arc from w to N . If every induced subdigraph of D has a kernel, D is said to be a kernel perfect digraph. D is called a critical kernel imperfect digraph when D has no kernel but every proper induced subdigraph of D has a kernel. If F is a set of arcs of D, a semikernel modulo F of...

Fuzzy clustering is an important tool for analyzing microarray data. A major problem in applying fuzzy clustering method to microarray gene expression data is the choice of parameters with cluster number and centers. This paper proposes a new approach to fuzzy kernel clustering analysis (FKCA) that identifies desired cluster number and obtains more steady results for gene expression data. First...

lead to continuing effects for increasing extensive of yield by means of advanced agronomic operations and selection of high yielding resistant genotypes. there fore, due to evaluation and determination of best effective traits in improvement of yield and grain quality of local populations of winter wheat, an experiment was carried out in uremia agricultural research station, on 30 local popula...

peanuts, an oilseed crop, contain about 46% oil. the peanut shell can be used as fuel or pallets and its dry matter as feedstuff. the whole pods consist of 1-6 kernels. shelling is done at harvest time when the pod moisture content is 5-10%. in this research, a peanut sheller was designed and developed to separate the shell from the pod. the sheller included a hopper, sheller cylinder, concave,...