1,013 research outputs found
Simplification Techniques for Maps in Simplicial Topology
This paper offers an algorithmic solution to the problem of obtaining
"economical" formulae for some maps in Simplicial Topology, having, in
principle, a high computational cost in their evaluation. In particular, maps
of this kind are used for defining cohomology operations at the cochain level.
As an example, we obtain explicit combinatorial descriptions of Steenrod k-th
powers exclusively in terms of face operators
A Tool for Integer Homology Computation: Lambda-At Model
In this paper, we formalize the notion of lambda-AT-model (where is
a non-null integer) for a given chain complex, which allows the computation of
homological information in the integer domain avoiding using the Smith Normal
Form of the boundary matrices. We present an algorithm for computing such a
model, obtaining Betti numbers, the prime numbers p involved in the invariant
factors of the torsion subgroup of homology, the amount of invariant factors
that are a power of p and a set of representative cycles of generators of
homology mod p, for each p. Moreover, we establish the minimum valid lambda for
such a construction, what cuts down the computational costs related to the
torsion subgroup. The tools described here are useful to determine topological
information of nD structured objects such as simplicial, cubical or simploidal
complexes and are applicable to extract such an information from digital
pictures.Comment: Journal Image and Vision Computing, Volume 27 Issue 7, June, 200
Geometric Objects and Cohomology Operations
Cohomology operations (including the cohomology ring) of a geometric object
are finer algebraic invariants than the homology of it.
In the literature, there exist various algorithms for computing the homology
groups of simplicial complexes but concerning the algorithmic treatment of
cohomology operations, very little is known. In this paper, we establish a
version of the incremental algorithm for computing homology which saves
algebraic information, allowing us the computation of the cup product and the
effective evaluation of the primary and secondary cohomology operations on the
cohomology of a finite simplicial complex. We study the computational
complexity of these processes and a program in Mathematica for cohomology
computations is presented.Comment: International Conference Computer Algebra and Scientific Computing
CASC'02. Big Yalta, Crimea (Ucrania). Septiembre 200
Ammonia effects on proton conductivity properties of coordination polymers
Crystalline metal phosphonates are referred to as a type of structurally versatile coordination polymers [1]. Many of them contain guest molecules (H2O, heterocyclics, etc.), acidic sites and, furthermore, their structure can be also amenable for post‐synthesis modifications in order to enhance desired properties [2].
In the present work, we examine the relationships between crystal structure and proton conductivity for several metal phosphonates derive from multifunctional ligands, such as 5-(dihydroxyphosphoryl)isophthalic acid (PiPhtA) [3] and 2-hydroxyphosphonoacetic acid (H3HPAA). Crystalline divalent metal derivatives show a great structural diversity, from 1D to 3D open-frameworks, possessing hydrogen-bonded water molecules and acid groups. These solids present a proton conductivity range between 7.2·10-6 and 1.3·10−3 S·cm-1. Upon exposure to ammonia vapor, from an aqueous solution, solid state transformations are observed accompanied of enhance proton conductivities. The stability of these solids under different environment conditions (temperature and relative humidities) as well as the influence of the ammonia adsorption on the proton conduction properties of the resulting solids will be discussed.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech
Chain Homotopies for Object Topological Representations
This paper presents a set of tools to compute topological information of
simplicial complexes, tools that are applicable to extract topological
information from digital pictures. A simplicial complex is encoded in a
(non-unique) algebraic-topological format called AM-model. An AM-model for a
given object K is determined by a concrete chain homotopy and it provides, in
particular, integer (co)homology generators of K and representative (co)cycles
of these generators. An algorithm for computing an AM-model and the
cohomological invariant HB1 (derived from the rank of the cohomology ring) with
integer coefficients for a finite simplicial complex in any dimension is
designed here. A concept of generators which are "nicely" representative cycles
is also presented. Moreover, we extend the definition of AM-models to 3D binary
digital images and we design algorithms to update the AM-model information
after voxel set operations (union, intersection, difference and inverse)
Using membrane computing for obtaining homology groups of binary 2D digital images
Membrane Computing is a new paradigm inspired from cellular communication. Until now, P systems have been used in research areas like modeling chemical process, several ecosystems, etc. In this paper, we apply P systems to Computational Topology within the context of the Digital Image. We work with a variant of P systems called tissue-like P systems to calculate in a general maximally parallel manner the homology groups of 2D images. In fact, homology computation for binary pixel-based 2D digital images can be reduced to connected component labeling of white and black regions. Finally, we use a software called Tissue Simulator to show with some examples how these systems wor
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