Jose C. Ciria

Separation Theorems for Simplicity 26-Surfaces

The main goal of this paper is to prove a Digital Jordan-Brouwer Theorem and an Index Theorem for simplicity 26-surfaces. For this, we follow the approach to Digital Topology introduced in [2], and find a digital space such that the continuous analogue of each simplicity 26-surface is a combinatorial 2-manifold. Thus, the separation theorems quoted above turn out to be an immediate consequence of the general results obtained in [2] and [3] for arbitrary digital n-manifolds.

A maximum set of (26,6)-connected digital surfaces

In the class

Local characterization of a maximum set of digital (26,6)-surfaces

\mathcal{H}

A plate-based definition of discrete surfaces

of (26,6)–connected homogeneous digital spaces on R3 we find a digital space EU with the largest set of digital surfaces in that class. That is, if a digital objet S is a digital surface in any space

The history-based authentication pattern

E \epsilon \mathcal{H}

Universal Spaces for \((k, \overline{k})-\)Surfaces

then S is a digital surface in EU too.

Single-vortex dynamics in resistively shunted Josephson junction arrays

We introduce a new family S of surfaces in the discrete space Z^3 for the usual (26,6)-adjacency that strictly contains the family of simplicity 26-surfaces and other objects considered as surfaces in the literature. Actually, S characterizes the strongly 6-separating objects of a family S^U of digital surfaces defined by means of continuous analogues. The family S^U consists of all objects whose continuous analogue is a surface in some homogeneous (26,6)-connected digital space as defined in the approach to Digital Topology introduced in [R. Ayala, E. Dominguez, A.R. Frances, A. Quintero, Weak Lighting Functions and Strong 26-surfaces. Theoretical Computer Science 283 (2002) 29-66.]. Therefore, S is the largest possible set of surfaces in Z^3 in that setting.

A collection of patterns for prime generation

Highlights? A new class of discrete surfaces for each adjacency pair in the grid Z 3 . ? The definition mimics that of a combinatorial surface by using discrete plates. ? They form the largest set of surfaces for a framework based on continuous analogues. ? The strong and simplicity 26-surfaces as well as other Jordan objects are examples. ? The number of configurations around a (26,6)-surface voxel is estimated in 10,580. By the use of certain discrete plates in the role of polygonal faces we mimic the definition of a combinatorial surface to produce, for each adjacency pair ( k , k ? ) ? ( 6 , 6 ) , k , k ? ? { 6 , 18 , 26 } , a new family S k k ? of discrete surfaces, termed ( k , k ? ) -surfaces, in the grid Z 3 that strictly contains several well-known families of surfaces, such as the strong and simplicity surfaces, as well as other objects considered as surfaces in the literature. Moreover, the number of possible configurations in the 26-neighbourhood of a (26,6)-surface voxel is estimated to rise up to 10,580. In addition, we show that S k k ? is the largest set of discrete surfaces that can be defined within the framework for Digital Topology in (Ayala et al., 2002).

The task-oriented occurrence pattern

We propose a security pattern, namely the History-Based Authentication pattern, designed to strengthen the authentication process. It can be applied to entities endowed with communication, memory and processing capabilities. Our proposal consists of exploiting such capabilities to enable entities to record, be aware of and report on their own history. Authentication is based upon the capability of an entity to satisfactorily account for its history. Our proposal is test-bedded in a security and safety system, framed within the context of smart environments, designed for the protection of personnel and facilities and responsible for its self-protection and self-monitoring.

Generalized simple surface points

In the graph–theoretical approach to Digital Topology, the search for a definition of digital surfaces as subsets of voxels is still a work in progress since it was started in the early 1980’s. Despite the interest of the applications in which it is involved (ranging from visualization to image segmentation and graphics), there is not yet a well established general notion of digital surface that naturally extends to higher dimensions (see [5] for a proposal). The fact is that, after the first definition of surface, proposed by Morgenthaler [13] for \({\mathbb Z}^3\) with the usual adjacency pairs (26,6) and (6,26), each new contribution [10,4,9], either increasing the number of surfaces or extendeding the definition to other adjacencies, has still left out some objects considered as surfaces for practical purposes [12].