The Computational Complexity of Tissue P Systems with Evolutional Symport/Antiport Rules

Tissue P systems with evolutional communication (symport/antiport) rules are computational models inspired by biochemical systems consisting of multiple individuals living and cooperating in a certain environment, where objects can be modified when moving from one region to another region. In this work, cell separation, inspired from membrane fission process, is introduced in the framework of tissue P systems with evolutional communication rules.The computational complexity of this kind of P systems is investigated. It is proved that only problems in class P can be efficiently solved by tissue P systems with cell separation with evolutional communication rules of length at most (��, 1), for each natural number �� ≥ 1. In the case where that length is upper bounded by (3, 2), a polynomial time solution to the SAT problem is provided, hence, assuming that P ̸= NP a new boundary between tractability and NP-hardness on the basis of the length of evolutional communication rules is provided. Finally, a new simulator for tissue P systems with evolutional communication rules is designed and is used to check the correctness of the solution to the SAT problem

Solving Subset Sum in Linear Time by Using Tissue P Systems with Cell Division

Tissue P systems with cell division is a computing model in the framework of Membrane Computing based on intercellular communication and cooperation between neurons. The ability of cell division allows us to obtain an exponential amount of cells in linear time and to design cellular solutions to NP-complete problems in polynomial time. In this paper we present a solution to the Subset Sum problem via a family of such devices. This is the first solution to a numerical NP-complete problem by using tissue P systems with cell division.Ministerio de Educación y Ciencia TIN2006-13425Junta de Andalucía TIC-58

Solving the Bin-Packing Problem by Means of Tissue P System with 2-Division

The ability of tissue P systems with 2-division for solving NP problems in polynomial time is well-known and many solutions can be found in the literature to several of such problems. Nonetheless, there are very few papers devoted to the Bin-packing problem. The reason may be the difficulties for dealing with different number of bins, capacity and number of objects by using exclusively division rules that produce two offsprings in each application. In this paper we present the design of a family of tissue P systems with 2 division which solves the Bin-packing problem in polynomial time by combining design techniques which can be useful for further research

Cell-like and Tissue-like Membrane Systems as Recognizer Devices

Most of the variants of membrane systems found in the literature are generally thought as generating devices. In this paper recognizer computational devices (cell–like and tissue–like) are presented in the framework of Membrane Computing, using the biological membranes arranged hierarchically, inspired from the structure of the cell, and using the biological membranes placed in the nodes of a graph, inspired from the cell inter–communication in tissues. In this context, polynomial complexity classes of recognizer membrane systems are introduced. The paper also addresses the P versus NP problem, and the (efficient) solvability of computationally hard problems, in the framework of these new complexity classes.Ministerio de Educación y Ciencia TIN2005-09345-C04-0

Kinetic and Dynamic Delaunay tetrahedralizations in three dimensions

We describe the implementation of algorithms to construct and maintain three-dimensional dynamic Delaunay triangulations with kinetic vertices using a three-simplex data structure. The code is capable of constructing the geometric dual, the Voronoi or Dirichlet tessellation. Initially, a given list of points is triangulated. Time evolution of the triangulation is not only governed by kinetic vertices but also by a changing number of vertices. We use three-dimensional simplex flip algorithms, a stochastic visibility walk algorithm for point location and in addition, we propose a new simple method of deleting vertices from an existing three-dimensional Delaunay triangulation while maintaining the Delaunay property. The dual Dirichlet tessellation can be used to solve differential equations on an irregular grid, to define partitions in cell tissue simulations, for collision detection etc.Comment: 29 pg (preprint), 12 figures, 1 table Title changed (mainly nomenclature), referee suggestions included, typos corrected, bibliography update

Non-Euclidean geometry in nature

I describe the manifestation of the non-Euclidean geometry in the behavior of collective observables of some complex physical systems. Specifically, I consider the formation of equilibrium shapes of plants and statistics of sparse random graphs. For these systems I discuss the following interlinked questions: (i) the optimal embedding of plants leaves in the three-dimensional space, (ii) the spectral statistics of sparse random matrix ensembles.Comment: 52 pages, 21 figures, last section is rewritten, a reference to chaotic Hamiltonian systems is adde

Minimal Cooperation in P Systems with Symport/Antiport: A Complexity Approach

Membrane systems with symport/antiport rules compute by just moving objects among membranes, and not by changing the objects themselves. In these systems the environment plays an active role because, not only it receives objects from the system, but it also sends objects into the system. Actually, in this framework it is commonly assumed that an arbitrarily large number of copies of some objects are initially available in the environment. This special feature has been widely exploited for the design of e cient solutions to computationally hard problems in the framework of tissue like P systems able to create an exponential workspace in polynomial time (e.g. via cell division or cell separation rules). This paper deals with cell-like P systems which use symport/antiport rules as communication rules, and the role played by the minimal cooperation is studied from a computational complexity point of view. Speci cally, the limitations on the e ciency of P systems with membrane separation whose symport/antiport rules involve at most two objects are established. In addition, a polynomial time solution to HAM-CYCLE problem, a well known NP-complete problem, by using a family of such kind of P systems with membrane division, is provided. Therefore, in the framework of cell-like P systems with minimal cooperation in communication rules, passing from membrane separation to membrane division amounts to passing from tractability to NP{hardness.Ministerio de Economía y Competitividad TIN2012-3743

Computational Complexity Theory in Membrane Computing: Seventeen Years After

In this work we revisit the basic concepts, definitions of computational complexity theory in membrane computing. The paper also discusses a novel methodology to tackle the P versus NP problem in the context of the aforementioned theory. The methodology is illustrated with a collection of frontiers of tractability for several classes of P systems.Ministerio de Economía, Industria y Competitividad TIN2017-89842-

Multivariate NIR studies of seed-water interaction in Scots Pine Seeds (Pinus sylvestris L.)

This thesis describes seed-water interaction using near infrared (NIR) spectroscopy, multivariate regression models and Scots pine seeds. The presented research covers classification of seed viability, prediction of seed moisture content, selection of NIR wavelengths and interpretation of seed-water interaction modelled and analysed by principal component analysis, ordinary least squares (OLS), partial least squares (PLS), bi-orthogonal least squares (BPLS) and genetic algorithms. The potential of using multivariate NIR calibration models for seed classification was demonstrated using filled viable and non-viable seeds that could be separated with an accuracy of 98-99%. It was also shown that multivariate NIR calibration models gave low errors (0.7% and 1.9%) in prediction of seed moisture content for bulk seed and single seeds, respectively, using either NIR reflectance or transmittance spectroscopy. Genetic algorithms selected three to eight wavelength bands in the NIR region and these narrow bands gave about the same prediction of seed moisture content (0.6% and 1.7%) as using the whole NIR interval in the PLS regression models. The selected regions were simulated as NIR filters in OLS regression resulting in predictions of the same quality (0.7 % and 2.1%). This finding opens possibilities to apply NIR sensors in fast and simple spectrometers for the determination of seed moisture content. Near infrared (NIR) radiation interacts with overtones of vibrating bonds in polar molecules. The resulting spectra contain chemical and physical information. This offers good possibilities to measure seed-water interactions, but also to interpret processes within seeds. It is shown that seed-water interaction involves both transitions and changes mainly in covalent bonds of O-H, C-H, C=O and N-H emanating from ongoing physiological processes like seed respiration and protein metabolism. I propose that BPLS analysis that has orthonormal loadings and orthogonal scores giving the same predictions as using conventional PLS regression, should be used as a standard to harmonise the interpretation of NIR spectra