An Alternative Archiving Technique for Evolutionary Polygonal Approximation

Proceedings of: Fifth International Conference on Future Computational Technologies and Applications (FUTURE COMPUTING 2013), Valencia, Spain, May 27 - June 1, 2013Archiving procedures are a key parameter for Multi-objective evolutionary algorithms, since they guarantee the algorithm convergence and the good spread of the obtained solutions in the final Pareto front. For many practical applications, the cost of the algorithm is clearly dominated by the computational cost of the underlying fitness functions, allowing complex processes to be incorporated into the archiving procedure. This work presents a study of the archiving technique for evolutionary polygonal approximation (the division of a given curve into a set of n segments represented by a linear model) based on the epsilon-glitch concept, highlighting the cost of the technique compared to the fitness computation, and proposing a novel alternative archiving procedure, which yields statistically significant better results compared to available approaches.This work was supported in part by Projects MINECO TEC2012-37832-C02-01, CICYT TEC2011-28626-C02-02, CAM CONTEXTS (S2009/TIC-1485)Publicad

Optimal polygonal L1 linearization and fast interpolation of nonlinear systems

The analysis of complex nonlinear systems is often carried out using simpler piecewise linear representations of them. A principled and practical technique is proposed to linearize and evaluate arbitrary continuous nonlinear functions using polygonal (continuous piecewise linear) models under the L1 norm. A thorough error analysis is developed to guide an optimal design of two kinds of polygonal approximations in the asymptotic case of a large budget of evaluation subintervals N. The method allows the user to obtain the level of linearization (N) for a target approximation error and vice versa. It is suitable for, but not limited to, an efficient implementation in modern Graphics Processing Units (GPUs), allowing real-time performance of computationally demanding applications. The quality and efficiency of the technique has been measured in detail on two nonlinear functions that are widely used in many areas of scientific computing and are expensive to evaluate

Multi-input distributed classifiers for synthetic genetic circuits

For practical construction of complex synthetic genetic networks able to perform elaborate functions it is important to have a pool of relatively simple "bio-bricks" with different functionality which can be compounded together. To complement engineering of very different existing synthetic genetic devices such as switches, oscillators or logical gates, we propose and develop here a design of synthetic multiple input distributed classifier with learning ability. Proposed classifier will be able to separate multi-input data, which are inseparable for single input classifiers. Additionally, the data classes could potentially occupy the area of any shape in the space of inputs. We study two approaches to classification, including hard and soft classification and confirm the schemes of genetic networks by analytical and numerical results

An Unstructured Mesh Convergent Reaction-Diffusion Master Equation for Reversible Reactions

The convergent reaction-diffusion master equation (CRDME) was recently developed to provide a lattice particle-based stochastic reaction-diffusion model that is a convergent approximation in the lattice spacing to an underlying spatially-continuous particle dynamics model. The CRDME was designed to be identical to the popular lattice reaction-diffusion master equation (RDME) model for systems with only linear reactions, while overcoming the RDME's loss of bimolecular reaction effects as the lattice spacing is taken to zero. In our original work we developed the CRDME to handle bimolecular association reactions on Cartesian grids. In this work we develop several extensions to the CRDME to facilitate the modeling of cellular processes within realistic biological domains. Foremost, we extend the CRDME to handle reversible bimolecular reactions on unstructured grids. Here we develop a generalized CRDME through discretization of the spatially continuous volume reactivity model, extending the CRDME to encompass a larger variety of particle-particle interactions. Finally, we conclude by examining several numerical examples to demonstrate the convergence and accuracy of the CRDME in approximating the volume reactivity model.Comment: 35 pages, 9 figures. Accepted, J. Comp. Phys. (2018

Thinning-free Polygonal Approximation of Thick Digital Curves Using Cellular Envelope

Since the inception of successful rasterization of curves and objects in the digital space, several algorithms have been proposed for approximating a given digital curve. All these algorithms, however, resort to thinning as preprocessing before approximating a digital curve with changing thickness. Described in this paper is a novel thinning-free algorithm for polygonal approximation of an arbitrarily thick digital curve, using the concept of "cellular envelope", which is newly introduced in this paper. The cellular envelope, defined as the smallest set of cells containing the given curve, and hence bounded by two tightest (inner and outer) isothetic polygons, is constructed using a combinatorial technique. This envelope, in turn, is analyzed to determine a polygonal approximation of the curve as a sequence of cells using certain attributes of digital straightness. Since a real-world curve=curve-shaped object with varying thickness, unexpected disconnectedness, noisy information, etc., is unsuitable for the existing algorithms on polygonal approximation, the curve is encapsulated by the cellular envelope to enable the polygonal approximation. Owing to the implicit Euclidean-free metrics and combinatorial properties prevailing in the cellular plane, implementation of the proposed algorithm involves primitive integer operations only, leading to fast execution of the algorithm. Experimental results that include output polygons for different values of the approximation parameter corresponding to several real-world digital curves, a couple of measures on the quality of approximation, comparative results related with two other well-referred algorithms, and CPU times, have been presented to demonstrate the elegance and efficacy of the proposed algorithm