To resolve the online detection difficulty of some important state variables in fermentation process with traditional instruments, a soft sensing modeling method based on relevance vector machine (RVM) with a hybrid kernel function is presented. Based on the characteristic analysis of two commonly-used kernel functions, that is, local Gaussian kernel function and global polynomial kernel functi...

Abstract In Directed Feedback Arc Set ( DFAS ) we search for a set of at most k arcs which intersect every cycle in the input digraph. It is well-known open problem parameterized complexity to decide if admits kernel polynomial size. We consider $$\mathcal {C}$$ C - Deletion ADS ), variant where want remove f...

A graph is distance-hereditary if for any pair of vertices, their distance in every connected induced subgraph containing both vertices the same as original graph. The Distance-Hereditary Vertex Deletion problem asks, given a G on n and an integer k, whether there set S at most k such that $$G-S$$ distance-hereditary. This important due to its connection parameter rank-width because graphs are ...

Polynomial kernel regression is one of the standard and state-of-the-art learning strategies. However, as is well known, the choices of the degree of polynomial kernel and the regularization parameter are still open in the realm of model selection. The first aim of this paper is to develop a strategy to select these parameters. On one hand, based on the worst-case learning rate analysis, we sho...

We prove a number of results around kernelization of problems parameterized by the size of a given vertex cover of the input graph. We provide three sets of simple general conditions characterizing problems admitting kernels of polynomial size. Our characterizations not only give generic explanations for the existence of many known polynomial kernels for problems like q-Coloring, Odd Cycle Tran...

In parameterized complexity each problem instance comes with a parameter k, and a parameterized problem is said to admit a polynomial kernel if there are polynomial time preprocessing rules that reduce the input instance to an instance with size polynomial in k. Many problems have been shown to admit polynomial kernels, but it is only recently that a framework for showing the non-existence of p...

In parameterized complexity each problem instance comes with a parameter k and the parameterized problem is said to admit a polynomial kernel if there are polynomial time preprocessing rules that reduce the input instance down to an instance with size polynomial in k. Many problems have been shown to admit polynomial kernels, but it is only recently that a framework for showing the non-existenc...