Fuzzification of support vector machine has been utilized to deal with outlier and noise problem. This importance is achieved, by the means of fuzzy membership function, which is generally built based on the distance of the points to the class centroid. The focus of this research is twofold. Firstly, by taking the advantage of robust statistics in the fuzzy SVM, more emphasis on reducing the im...

We show that the Double Coset Membership problem for permutation groups possesses perfect zero-knowledge proofs.

The complexity of the polynomial ideal membership problem over arbitrary fields within the framework of arithmetic networks is investigated. We prove that the parallel complexity of this problem is single exponential over any infinite field. Our lower bound is obtained by combining a modification of Mayr and Meyer's (1982) key construction with an elementary degree bound. 1998 Academic Press, Inc.

Abstract In this paper, we prove a general result saying that under certain hypothesis an embedding of affine vertex algebra into $W$–algebra is conformal if and only their central charges coincide. This extends our previous obtained in the case minimal $W$-algebras [ 3]. We also find sufficient condition showing levels are collapsing. new enables us to some $k$ where $W_{k}(sl(N), x, f )$ coll...

There exists a complete atomless Boolean algebra that has no proper atomless complete subalgebra. An atomless complete Boolean algebra B is simple [5] if it has no atomless complete subalgebra A such that A 6= B. The question whether such an algebra B exists was first raised in [8] where it was proved that B has no proper atomless complete subalgebra if and only if B is rigid andminimal. For mo...

Not every quasihereditary algebra $(A,\Phi,\unlhd)$ has an exact Borel subalgebra. A theorem by Koenig, K\"ulshammer and Ovsienko asserts that there always exists a Morita equivalent to $A$ regular subalgebra, but characterisation of such representative is not directly obtainable from their work. This paper gives criterion decide whether contains subalgebra provides method compute all the repre...

Many algorithmic problems, which are used to prove the security of a cryptographic system, are shown to be characterized as the subgroup membership problem. We then apply the subgroup membership problem to private information retrieval schemes following the method by Kushilevitz and Ostrovsky. The resulting scheme has the same communication complexity as that of Kushilevitz and Ostrovsky. 1 Pri...

Fix a finite semigroup S and let a1, . . . , ak , b be tuples in a direct power S. The subpower membership problem (SMP) for S asks whether b can be generated by a1, . . . , ak. For combinatorial Rees matrix semigroups we establish a dichotomy result: if the corresponding matrix is of a certain form, then the SMP is in P; otherwise it is NP-complete. For combinatorial Rees matrix semigroups wit...