On Hamiltonians with position-dependent mass from Kaluza-Klein compactifications

In a recent paper (J.R. Morris, Quant. Stud. Math. Found. 2 (2015) 359), an inhomogeneous compactification of the extra dimension of a five-dimensional Kaluza-Klein metric has been shown to generate a position-dependent mass (PDM) in the corresponding four-dimensional system. As an application of this dimensional reduction mechanism, a specific static dilatonic scalar field has been connected with a PDM Lagrangian describing a well-known nonlinear PDM oscillator. Here we present more instances of this construction that lead to PDM systems with radial symmetry, and the properties of their corresponding inhomogeneous extra dimensions are compared with the ones in the nonlinear oscillator model. Moreover, it is also shown how the compactification introduced in this type of models can alternatively be interpreted as a novel mechanism for the dynamical generation of curvature.Comment: 11 pages, 6 figures. New figures. Updated to match the published version in Physics Letters

Logic Negation with Spiking Neural P Systems

Nowadays, the success of neural networks as reasoning systems is doubtless. Nonetheless, one of the drawbacks of such reasoning systems is that they work as black-boxes and the acquired knowledge is not human readable. In this paper, we present a new step in order to close the gap between connectionist and logic based reasoning systems. We show that two of the most used inference rules for obtaining negative information in rule based reasoning systems, the so-called Closed World Assumption and Negation as Finite Failure can be characterized by means of spiking neural P systems, a formal model of the third generation of neural networks born in the framework of membrane computing.Comment: 25 pages, 1 figur

Other Buds in Membrane Computing

It is well-known the huge Mario’s contribution to the development of Membrane Computing. Many researchers may relate his name to the theory of complexity classes in P systems, the research of frontiers of the tractability or the application of Membrane Computing to model real-life situations as the Quorum Sensing System in Vibrio fischeri or the Bearded Vulture ecosystem. Beyond these research areas, in the last years Mario has presented many new research lines which can be considered as buds in the robust Membrane Computing tree. Many of them were the origin of new research branches, but some others are still waiting to be developed. This paper revisits some of these buds

A P-Lingua Programming Environment for Membrane Computing

A new programming language for membrane computing, PLingua, is developed in this paper. This language is not designed for a speci c simulator software. On the contrary, its purpose is to o er a general syntactic framework that could de ne a uni ed standard for membrane computing, covering a broad variety of models. At the present stage, P-Lingua can only handle P systems with active membranes, although the authors intend to extend it to other models in the near future. P-Lingua allows to write programs in a friendly way, as its syntax is very close to standard scienti c notation, and parameterized expressions can be used as shorthand for sets of rules. There is a built-in compiler that parses these human-style programs and generates XML documents that can be given as input to simulation tools, di erent plugins can be designed to produce speci c adequate outputs for existing simulators. Furthermore, we present in this paper an integrated development environment that plays the role of interface where P-lingua programs can be written and compiled. We also present a simulator for the class of recognizer P systems with active membranes, and we illustrate it by following the writing, compiling and simulating processes with a family of P systems solving the SAT problem.Ministerio de Educación y Ciencia TIN2006-13425Junta de Andalucía TIC-58

Performing Arithmetic Operations with Spiking Neural P Systems

We consider spiking neural P systems as devices which can be used to perform some basic arithmetic operations, namely addition, subtraction, comparison and multiplication by a fixed factor. The input to these systems are natural numbers expressed in binary form, encoded as appropriate sequences of spikes. A single system accepts as inputs numbers of any size. The present work may be considered as a ¯rst step towards the design of a CPU based on the working of spiking neural P systems.Ministerio de Educación y Ciencia TIN2006–13425Junta de Andalucía P08-TIC-0420

A Case Study in (Mem)Brane Computation: Generating Squares of Natural Numbers

The aim of this paper is to start an investigation and a comparison of the expressiveness of the two most relevant formalisms inspired by membranes interactions, namely, P systems and Brane Calculi. We compare the two formalisms with respect to their ability to act as generator devices. In particular, we show different ways of generating the set L = {n2 | n ≥ 1} in P systems and in Brane Calculi.Ministerio de Educación y Ciencia TIN2005-09345-C03-01Junta de Andalucía TIC-58

A Case Study in (Mem)Brane Computation: Generating {n2 | n 1}

The aim of this paper is to start an investigation and a comparison of the expressiveness of the two most relevant formalisms inspired by membranes interactions, namely, P systems and Brane Calculi. We compare the two formalisms w.r.t. their ability to act as language generators. In particular, we show different ways of generating the set L = {n2 | n 1} in P systems and in Brane Calculi.Ministerio de Educación y Ciencia TIC2002-04220-C03-0

A Characterization of PSPACE with Antimatter and Membrane Creation

The use of negative information provides a new tool for exploring the limits of P systems as computational devices. In this paper we prove that the combination of antimatter and annihilation rules (based on the annihilation of physical particles and antiparticles) and membrane creation (based on autopoiesis) provides a P system model able to solve PSPACE-complete problems. Namely, we provide a uniform family of P system in such P system model which solves the satis ability problem for quanti ed Boolean formulas (QSAT). In the second part of the paper, we prove that all the decision problems which can be solved with this P system model belong to the complexity class PSPACE, so this P system model characterises PSPACE.Ministerio de Economía y Competitividad TIN2012-3743

Some Notes on (Mem)Brane Computation

Membrane Computing and Brane Calculi are two recent computational paradigms in the framework of Natural Computing. They are based on the study of the structure and functioning of living cells as living organisms able to process and generate information. In this paper we give a short introduction to both areas and point out some open research lines.Ministerio de Educación y Ciencia TIN2005-09345-C04-01Junta de Andalucía TIC-58

An Application of Genetic Algorithms to Membrane Computing

The process of designing a P system in order to perform a task is a hard job. The researcher has often only an approximate idea of the design, but finding the exact description of the rules is a heavy hand-made work. In this paper we introduce PSystemEvolver, an evolutionary algorithm based on generative encoding, that could help to design a P system to perform a specific task. We illustrate the use of PSystemEvolver with a simple mathematical problem: the computation of squared numbers.Ministerio de Ciencia e Innovación TIN2008-04487-EMinisterio de Ciencia e Innovación TIN-2009-13192Junta de Andalucía P08-TIC-0420