This paper introduces an algorithm for determining data clusters called TILO/PRC (Topologically Intrinsic Lexicographic Ordering/Pinch Ratio Clustering). The theoretical foundation for this algorithm, developed in [14], uses ideas from topology (particularly knot theory) suggesting that it should be very flexible and robust with respect to noise. The TILO portion of the algorithm progressively ...

The object of the investigation are X-phemisms (euphemisms or/and dysphemisms), i. e. units affective semantics and polite communication. Euphemisms dysphemisms that make evaluative judgements stance taking possible treated dialectically, as variants a naming in/through its contextual ambivalence relativity (relationality). evidential base research builds on findings theoretical analysis empiri...

The complexity class CC is defined as the set of problems AC0 reducible to the comparator circuit value problem. Subramanian proved that several other problems are complete for CC, including the stable marriage problem, and finding the lexicographical first maximal matching in a bipartite graph. We introduce a two-sorted theory VCC for CC. We simplify Subramanian’s completeness proofs for the a...

In this paper, we present an automatic system for the morphosyntactic annotation and lexicographical evaluation of historical Portuguese corpora. Using rule-based orthographical normalization, we were able to apply a standard parser (PALAVRAS) to historical data (Colonia corpus) and to achieve accurate annotation for both POS and syntax. By aligning original and standardized word forms, our met...

We improve certain degree bounds for Gröbner bases of polynomial ideals in generic position. We work exclusively in deterministically verifiable and achievable generic positions of a combinatorial nature, namely either strongly stable position or quasi stable position. Furthermore, we exhibit new dimension(and depth-)dependent upper bounds for the Castelnuovo-Mumford regularity and the degrees ...

We present an efficient algorithm for the transformation of a Gröbner basis of a zero–dimensional ideal with respect to any given ordering into a Gröbner basis with respect to any other ordering. This algorithm is polynomial in the degree of the ideal. In particular the lexicographical Gröbner basis can be obtained by applying this algorithm after a total degree Gröbner basis computation: it is...

Given a set of n unit squares in the plane, the goal is to rank them in space in such a way that only few squares see each other vertically. We prove that ranking the squares according to the lexicographic order of their centers results in at most 3n-7 pairwise visibilities for n at least 4. We also show that this bound is best possible, by exhibiting a set of n squares with at least 3n-7 pairw...

We extend the discrete-time dynamic ow algorithms presented in the literature to solve the analogous continuous-time dynamic ow problems. These problems include nding maximum dynamic ows, quickest ows, universally maximum dynamic ows, lexicographically maximum dynamic ows, dynamic transshipments, and quickest transshipments in networks with capacities and transit times on the edges.

Abstract. Let G be a finite abelian group of exponent m ≥ 2. For subsets A,S ⊆ G, denote by ∂S(A) the number of edges from A to its complement G \ A in the directed Cayley graph, induced by S on G. We show that if S generates G, and A is non-empty, then ∂S(A) ≥ e m |A| ln |G| |A| . Here the coefficient e = 2.718 . . . is best possible and cannot be replaced with a number larger than e. For homo...

We prove that if 4 is an analytic partial order then either 4 can be extended to a ∆2 linear order similar to an antichain in 21 ordered lexicographically or a certain Borel partial order ≤0 embeds in 4 . Some corollaries for analytic equivalence relations are given, for instance, if E is a Σ1 1 [z] equivalence relation such that E0 does not embed in E then E is determined by intersections with...