Search results for " Geometry."
showing 10 items of 2189 documents
Regular Minimality and Thurstonian-type modeling
2009
Abstract A Thurstonian-type model for pairwise comparisons is any model in which the response (e.g., “they are the same” or “they are different”) to two stimuli being compared depends, deterministically or probabilistically, on the realizations of two randomly varying representations (perceptual images) of these stimuli. The two perceptual images in such a model may be stochastically interdependent but each has to be selectively dependent on its stimulus. It has been previously shown that all possible discrimination probability functions for same–different comparisons can be generated by Thurstonian-type models of the simplest variety, with independent percepts and deterministic decision ru…
Capabilities of Ultrametric Automata with One, Two, and Three States
2016
Ultrametric automata use p-adic numbers to describe the random branching of the process of computation. Previous research has shown that ultrametric automata can have a significant decrease in computing complexity. In this paper we consider the languages that can be recognized by one-way ultrametric automata with one, two, and three states. We also show an example of a promise problem that can be solved by ultrametric integral automaton with three states.
Generation of Valid Labeled Binary Trees
2003
International audience; Generating binary trees is a well-known problem. In this paper, we add some constraints to leaves of these trees. Such trees are used in the morphing of polygons, where a polygon P is represented by a binary tree T and each angle of P is a weight on a leaf of T. In the following, we give two algorithms to generate all binary trees, without repetitions, having the same weight distribution to their leaves and representing all parallel polygons to P.
Efficient computation of the branching structure of an algebraic curve
2012
An efficient algorithm for computing the branching structure of a compact Riemann surface defined via an algebraic curve is presented. Generators of the fundamental group of the base of the ramified covering punctured at the discriminant points of the curve are constructed via a minimal spanning tree of the discriminant points. This leads to paths of minimal length between the points, which is important for a later stage where these paths are used as integration contours to compute periods of the surface. The branching structure of the surface is obtained by analytically continuing the roots of the equation defining the algebraic curve along the constructed generators of the fundamental gro…
Combinatorial aspects of L-convex polyominoes
2007
We consider the class of L-convex polyominoes, i.e. those polyominoes in which any two cells can be connected with an ''L'' shaped path in one of its four cyclic orientations. The paper proves bijectively that the number f"n of L-convex polyominoes with perimeter 2(n+2) satisfies the linear recurrence relation f"n"+"2=4f"n"+"1-2f"n, by first establishing a recurrence of the same form for the cardinality of the ''2-compositions'' of a natural number n, a simple generalization of the ordinary compositions of n. Then, such 2-compositions are studied and bijectively related to certain words of a regular language over four letters which is in turn bijectively related to L-convex polyominoes. In …
On the Hierarchy Classes of Finite Ultrametric Automata
2015
This paper explores the language classes that arise with respect to the head count of a finite ultrametric automaton. First we prove that in the one-way setting there is a language that can be recognized by a one-head ultrametric finite automaton and cannot be recognized by any k-head non-deterministic finite automaton. Then we prove that in the two-way setting the class of languages recognized by ultrametric finite k-head automata is a proper subclass of the class of languages recognized by (k + 1)-head automata. Ultrametric finite automata are similar to probabilistic and quantum automata and have only just recently been introduced by Freivalds. We introduce ultrametric Turing machines an…
On t-covers in finite projective spaces
1979
A t-cover of the finite projective space PG(d,q) is a setS of t-dimensional subspaces such that any point of PG(d,q) is contained in at least one element ofS. In Theorem 1 a lower bound for the cardinality of a t-coverS in PG(d,q) is obtained and in Theorem 2 it is shown that this bound is best possible for all positive integers t,d and for any prime-power q.
Classification of n-dimensional subvarieties of G(1, 2n) that can be projected to G(1, n + 1)
2005
A structure theorem is given for n-dimensional smooth subvarieties of the Grassmannian G(1, N); with N >= n + 3, that can be isomorphically projected to G(1, n + 1). A complete classification in the cases N = 2n + 1 and N = 2n follows, as a corollary.
The branch set of a quasiregular mapping between metric manifolds
2016
Abstract In this note, we announce some new results on quantitative countable porosity of the branch set of a quasiregular mapping in very general metric spaces. As applications, we solve a recent conjecture of Fassler et al., an open problem of Heinonen–Rickman, and an open question of Heinonen–Semmes.
Complete, Exact and Efficient Implementation for Computing the Adjacency Graph of an Arrangement of Quadrics
2007
The original publication is available at www.springerlink.com ; ISBN 978-3-540-75519-7 ; ISSN 0302-9743 (Print) 1611-3349 (Online); International audience; We present a complete, exact and efficient implementation to compute the adjacency graph of an arrangement of quadrics, \ie surfaces of algebraic degree~2. This is a major step towards the computation of the full 3D arrangement. We enhanced an implementation for an exact parameterization of the intersection curves of two quadrics, such that we can compute the exact parameter value for intersection points and from that the adjacency graph of the arrangement. Our implementation is {\em complete} in the sense that it can handle all kinds of…