In this paper we prove an asymptotically tight bound (asymptotic with respect to the number of polynomials for fixed degrees and number of variables) on the number of connected components of the realizations of all realizable sign conditions of a family of real polynomials. More precisely, we prove that the number of connected components of the realizations of all realizable sign conditions of ...

• Ω = ∫ E(R) |ω|, and ω is the global section of Ω 1 N(E)/Z corresponding to a choice of basis of the Z-line Cot0(N(E)) for the Néron model N(E) of E over Z, • cp is the number of connected components of N(E)Fp that are geometrically connected over Fp, or equivalently (by Lang’s theorem applied to N(E)0Fptorsors) have a rational point, so cp coincides with the number of Fp-points of the finite ...

We introduce a decomposition scheme for abstract dialectical frameworks (ADFs). The decomposition proceeds along the ADF’s strongly connected components. For several semantics, the decomposition-based version coincides with the original semantics. For others, the scheme defines new semantics. These new semantics allow us to deal with pertinent problems such as odd-length negative cycles in a mo...

In this paper we characterize the automorphisms (collineations) of the Segre product of partial linear spaces. In particular, we show that if all components of the product are strongly connected, then every collineation is determined by a set of isomorphisms between its components. The formalization follows the ideas presented in the Journal of Geometry paper [16] by Naumowicz and Prażmowski.

Let G be a tree and let H be a collection of subgraphs of G, each having at most d connected components. Let ν(H) denote the maximum number of members of H no two of which share a common vertex, and let τ(H) denote the minimum cardinality of a set of vertices of G that intersects all members of H. It is shown that τ(H) ≤ 2dν(H). A similar, more general result is proved replacing the assumption ...

Density analysis plays an important role in font design and recognition. This paper presents a method of density analysis for Chinese characters. A number of density metrics are adopted to describe the density degree of a character from both local and global perspectives, including center-to-center distance of connected components, gap between connected components, ratio of perimeter and area, ...

We prove an asymptotically tight bound (asymptotic with respect to the number of polynomials for fixed degrees and number of variables) on the number of semi-algebraically connected components of the realizations of all realizable sign conditions of a family of real polynomials. More precisely, we prove that the number of semi-algebraically connected components of the realizations of all realiz...

In this paper, a novel and efficient method for skew detection in document images is proposed. The proposed method is based on connected component blotching and linear regression. The proposed algorithm works well irrespective of the type of script even for a wide range of skew angle (with in ±90o).

In this paper, we determine some limit distributions of pattern statistics in rational stochastic models. We present a general approach to analyze these statistics in rational models having an arbitrary number of strongly connected components. We explicitly establish the limit distributions in most significant cases; they are characterized by a family of unimodal density functions defined by me...