STATEMENT OF PROBLEM In complete mouth reconstructive dentistry, the occlusal vertical dimension may be increased to provide adequate restorative space or to improve esthetics. The effect of increasing the occlusal vertical dimension on the smile is not well understood. PURPOSE The purpose of this study was to evaluate the effect of increasing the occlusal vertical dimension on the dimensions...

We find the minimax rate of convergence in Hausdorff distance for estimating a manifold M of dimension d embedded in R given a noisy sample from the manifold. Under certain conditions, we show that the optimal rate of convergence is n−2/(2+d). Thus, the minimax rate depends only on the dimension of the manifold, not on the dimension of the space in which M is embedded.

Given a graph G, we say S ⊆ V (G) is resolving if for each pair of distinct u, v ∈ V (G) there is a vertex x in S where d(u, x) 6= d(v, x). The metric dimension of G is the minimum cardinality of all resolving sets. For w ∈ V (G), the distance from w to S, denoted d(w, S), is the minimum distance between w and the vertices of S. Given P = {P1, P2, . . . , Pk} an ordered partition of V (G) we sa...

Introduction The balance scale task has become a benchmark task in cognitive developmental psychology. Development on the balance scale task is characterized as a progression through a series of increasingly complex rules (Rule I, II, III, IV). Children using Rule IV understand the multiplicative relation between the two task features, weight and distance information of blocks placed at both si...

The objective of the present work is to evaluate the potential of the use of the image fractal dimension as textural feature in a content-based image retrieval system. In order to compare and classify the regions of an image, we have used two distances between two partitions of the image: (1) a classic distance computed with some features (contrast, energy, entropy, homogeneity, correlation) ex...

A set of n + k points (k > 0) in projective space of dimension n is said to be an (n + k)-arc if there is no hyperplane containing any n + 1 points of the set. It is well-known that for the projective space PG(n, q), this is equivalent to a maximum distance separable linear code with symbols in the finite field GF(q), of length n + k, dimension n + 1, and distance d = k that satisfies the Singl...

Cyclic codes are an interesting class of linear codes due to their efficient encoding and decoding algorithms as well as their theoretical importance. BCH codes form a subclass of cyclic codes and are very important in both theory and practice as they have good error-correcting capability and are widely used in communication systems, storage devices and consumer electronics. However, the dimens...

It has been developed a C++ program that generates random fuzzy relations of a given dimension and computes their T-transitive closure (that contains the initial relation) and the new T-transitivized relation (that is contained in the initial relation) for the t-norms minimum, product and Lukasiewicz. It has been computed several distances between both transitive closure and transitivized relat...

We illustrate the advantages of distance weighted discrimination for classification and feature extraction in a High Dimension Low Sample Size (HDLSS) situation. The HDLSS context is a gender classification problem of face images in which the dimension of the data is several orders of magnitude larger than the sample size. We compare distance weighted discrimination with Fisher’s linear discrim...

Cyclic orbit codes are constant dimension subspace codes that arise as the orbit of a cyclic subgroup of the general linear group acting on subspaces in the given ambient space. With the aid of the largest subfield over which the given subspace is a vector space, the cardinality of the orbit code can be determined, and estimates for its distance can be found. This subfield is closely related to...