On the Complexity of Real Equation Solving by Bernd Bank, Humboldt–Universität zu Berlin The first part of the speech deals with the particular case of integer points in a semi-algebraic set described by quasi-convex polynomial inequalities in the n–dimensional real space. The simply exponential bounds are “optimal” with respect to the dense codification of the polynomials. Without changing the...

We present a new approach to mining patterns from symbolic interval data that extends previous approaches by allowing semi-intervals and partially ordered patterns. The mining algorithm combines and adapts efficient algorithms from sequential pattern and itemset mining for discovery of the new semi-interval patterns. The semi-interval patterns and semi-interval partial order patterns are more f...

We present a general derivation of semi-fermionic representation for spin operators in terms of a bilinear combination of fermions in real and imaginary time formalisms. The constraint on fermionic occupation numbers is fulfilled by means of imaginary Lagrange multipliers resulting in special shape of quasiparticle distribution functions. We show how Schwinger-Keldysh technique for spin operato...

In this paper we deal with the problem of computing Lyapunov functions for stability verification of differential systems. We concern on symbolic methods and start the discussion with a classical quantifier elimination model for computing Lyapunov functions in a given polynomial form, especially in quadratic forms. Then we propose a new semi-algebraic method by making advantage of the local pro...

This paper proposes a reference signal extraction method for a semi-adaptive sound reproduction system based on semi-blind source separation (semi-BSS) under a noisy environment. Since the fluctuation of room transfer functions degrades the reproduced sound, we have proposed a semi-adaptive sound reproduction system that updates the inverse filters. However, in a noisy environment, it is diffic...

semi-regular locales are extensions of the classical semiregularspaces. we investigate the conditions such that semi-regularizationis a functor. we also investigate the conditions such that semi-regularizationis a reflection or coreflection.

Let R be a real closed field. The problem of obtaining tight bounds on the Betti numbers of semi-algebraic subsets of R in terms of the number and degrees of the defining polynomials has been an important problem in real algebraic geometry with the first results due to Olĕınik and Petrovskĭı, Thom and Milnor. These bounds are all exponential in the number of variables k. Motivated by several ap...

Semi-supervised learning tries to employ a large collection of unlabeled data and a few labeled examples for improving generalization performance, which has been proved meaningful in real-world applications. The bottleneck of exiting semi-supervised approaches lies in over long training time due to the large scale unlabeled data. In this article we introduce a novel method for semi-supervised l...