Associating cell complexes to four dimensional digital objects

The goal of this paper is to construct an algebraic-topological representation of a 80–adjacent doxel-based 4–dimensional digital object. Such that representation consists on associating a cell complex homologically equivalent to the digital object. To determine the pieces of this cell complex, algorithms based on weighted complete graphs and integral operators are shown. We work with integer coefficients, in order to compute the integer homology of the digital object

Homological spanning forest framework for 2D image analysis

A 2D topology-based digital image processing framework is presented here. This framework consists of the computation of a flexible geometric graph-based structure, starting from a raster representation of a digital image I. This structure is called Homological Spanning Forest (HSF for short), and it is built on a cell complex associated to I. The HSF framework allows an efficient and accurate topological analysis of regions of interest (ROIs) by using a four-level architecture. By topological analysis, we mean not only the computation of Euler characteristic, genus or Betti numbers, but also advanced computational algebraic topological information derived from homological classification of cycles. An initial HSF representation can be modified to obtain a different one, in which ROIs are almost isolated and ready to be topologically analyzed. The HSF framework is susceptible of being parallelized and generalized to higher dimensions

Getting topological information for a 80-adjacency doxel-based 4D volume through a polytopal cell complex

Given an 80-adjacency doxel-based digital four-dimensional hypervolume V, we construct here an associated oriented 4–dimensional polytopal cell complex K(V), having the same integer homological information (that related to n-dimensional holes that object has) than V. This is the first step toward the construction of an algebraic-topological representation (AT-model) for V, which suitably codifies it mainly in terms of its homological information. This AT-model is especially suitable for global and local topological analysis of digital 4D images

A stochastic model of catalytic reaction networks in protocells

Protocells are supposed to have played a key role in the self-organizing processes leading to the emergence of life. Existing models either (i) describe protocell architecture and dynamics, given the existence of sets of collectively self-replicating molecules for granted, or (ii) describe the emergence of the aforementioned sets from an ensemble of random molecules in a simple experimental setting (e.g. a closed system or a steady-state flow reactor) that does not properly describe a protocell. In this paper we present a model that goes beyond these limitations by describing the dynamics of sets of replicating molecules within a lipid vesicle. We adopt the simplest possible protocell architecture, by considering a semi-permeable membrane that selects the molecular types that are allowed to enter or exit the protocell and by assuming that the reactions take place in the aqueous phase in the internal compartment. As a first approximation, we ignore the protocell growth and division dynamics. The behavior of catalytic reaction networks is then simulated by means of a stochastic model that accounts for the creation and the extinction of species and reactions. While this is not yet an exhaustive protocell model, it already provides clues regarding some processes that are relevant for understanding the conditions that can enable a population of protocells to undergo evolution and selection.Comment: 20 pages, 5 figure