Membrane computing: traces, neural inspired models, controls

Membrane Computing:Traces, Neural Inspired Models, ControlsAutor: Armand-Mihai IonescuDirectores: Dr. Victor Mitrana (URV)Dr. Takashi Yokomori (Universidad Waseda, Japón)Resumen Castellano:El presente trabajo está dedicado a una área muy activa del cálculo natural (que intenta descubrir la odalidad en la cual la naturaleza calcula, especialmente al nivel biológico), es decir el cálculo con membranas, y más preciso, a los modelos de membranas inspirados de la funcionalidad biológica de la neurona.La disertación contribuye al área de cálculo con membranas en tres direcciones principales. Primero, introducimos una nueva manera de definir el resultado de una computación siguiendo los rastros de un objeto especificado dentro de una estructura celular o de una estructura neuronal. A continuación, nos acercamos al ámbito de la biología del cerebro, con el objetivo de obtener varias maneras de controlar la computación por medio de procesos que inhiben/de-inhiben. Tercero, introducimos e investigamos en detallo - aunque en una fase preliminar porque muchos aspectos tienen que ser clarificados - una clase de sistemas inspirados de la manera en la cual las neuronas cooperan por medio de spikes, pulsos eléctricos de formas idénticas.English summary:The present work is dedicated to a very active branch of natural computing (which tries to discover the way nature computes, especially at a biological level), namely membrane computing, more precisely, to those models of membrane systems mainly inspired from the functioning of the neural cell.The present dissertation contributes to membrane computing in three main directions. First, we introduce a new way of defining the result of a computation by means of following the traces of a specified object within a cell structure or a neural structure. Then, we get closer to the biology of the brain, considering various ways to control the computation by means of inhibiting/de-inhibiting processes. Third, we introduce and investigate in a great - though preliminary, as many issues remain to be clarified - detail a class of P systems inspired from the way neurons cooperate by means of spikes, electrical pulses of identical shapes

Communication in membrana Systems with symbol Objects.

Esta tesis está dedicada a los sistemas de membranas con objetos-símbolo como marco teórico de los sistemas paralelos y distribuidos de procesamiento de multiconjuntos.Una computación de parada puede aceptar, generar o procesar un número, un vector o una palabra; por tanto el sistema define globalmente (a través de los resultados de todas sus computaciones) un conjunto de números, de vectores, de palabras (es decir, un lenguaje), o bien una función. En esta tesis estudiamos la capacidad de estos sistemas para resolver problemas particulares, así como su potencia computacional. Por ejemplo, las familias de lenguajes definidas por diversas clases de estos sistemas se comparan con las familias clásicas, esto es, lenguajes regulares, independientes del contexto, generados por sistemas 0L tabulados extendidos, generados por gramáticas matriciales sin chequeo de apariciones, recursivamente enumerables, etc. Se prestará especial atención a la comunicación de objetos entre regiones y a las distintas formas de cooperación entre ellos.Se pretende (Sección 3.4) realizar una formalización los sistemas de membranas y construir una herramienta tipo software para la variante que usa cooperación no distribuida, el navegador de configuraciones, es decir, un simulador, en el cual el usuario selecciona la siguiente configuración entre todas las posibles, estando permitido volver hacia atrás. Se considerarán diversos modelos distribuidos. En el modelo de evolución y comunicación (Capítulo 4) separamos las reglas tipo-reescritura y las reglas de transporte (llamadas symport y antiport). Los sistemas de bombeo de protones (proton pumping, Secciones 4.8, 4.9) constituyen una variante de los sistemas de evolución y comunicación con un modo restrictivo de cooperación. Un modelo especial de computación con membranas es el modelo puramente comunicativo, en el cual los objetos traspasan juntos una membrana. Estudiamos la potencia computacional de las sistemas de membranas con symport/antiport de 2 o 3 objetos (Capítulo 5) y la potencia computacional de las sistemas de membranas con alfabeto limitado (Capítulo 6).El determinismo (Secciones 4.7, 5.5, etc.) es una característica especial (restrictiva) de los sistemas computacionales. Se pondrá especial énfasis en analizar si esta restricción reduce o no la potencia computacional de los mismos. Los resultados obtenidos para sistemas de bombeo del protones están transferidos (Sección 7.3) a sistemas con catalizadores bistabiles. Unos ejemplos de aplicación concreta de los sistemas de membranas (Secciones 7.1, 7.2) son la resolución de problemas NP-completos en tiempo polinomial y la resolución de problemas de ordenación.This thesis deals with membrane systems with symbol objects as a theoretical framework of distributed parallel multiset processing systems.A halting computation can accept, generate or process a number, a vector or a word, so the system globally defines (by the results of all its computations) a set of numbers or a set of vectors or a set of words, (i.e., a language), or a function. The ability of these systems to solve particular problems is investigated, as well as their computational power, e.g., the language families defined by different classes of these systems are compared to the classical ones, i.e., regular, context-free, languages generated by extended tabled 0L systems, languages generated by matrix grammars without appearance checking, recursively enumerable languages, etc. Special attention is paid to communication of objects between the regions and to the ways of cooperation between the objects.An attempt to formalize the membrane systems is made (Section 3.4), and a software tool is constructed for the non-distributed cooperative variant, the configuration browser, i.e., a simulator, where the user chooses the next configuration among the possible ones and can go back. Different distributed models are considered. In the evolution-communication model (Chapter 4) rewriting-like rules are separated from transport rules. Proton pumping systems (Sections 4.8, 4.9) are a variant of the evolution-communication systems with a restricted way of cooperation. A special membrane computing model is a purely communicative one: the objects are moved together through a membrane. We study the computational power of membrane systems with symport/antiport of 2 or 3 objects (Chapter 5) and the computational power of membrane systems with a limited alphabet (Chapter 6).Determinism (Sections 4.7, 5.5, etc.) is a special property of computational systems; the question of whether this restriction reduces the computational power is addressed. The results on proton pumping systems can be carried over (Section 7.3) to the systems with bi-stable catalysts. Some particular examples of membrane systems applications are solving NP-complete problems in polynomial time, and solving the sorting problem

Large Scale Stochastic Dynamics

[no abstract available

Verifying polymer reaction networks using bisimulation

The Chemical Reaction Network model has been proposed as a programming language for molecular programming. Methods to implement arbitrary CRNs using DNA strand displacement circuits have been investigated, as have methods to prove the correctness of those or other implementations. However, the stochastic Chemical Reaction Network model is provably not deterministically Turing-universal, that is, it is impossible to create a stochastic CRN where a given output molecule is produced if and only if an arbitrary Turing machine accepts. A DNA stack machine that can simulate arbitrary Turing machines with minimal slowdown deterministically has been proposed, but it uses unbounded polymers that cannot be modeled as a Chemical Reaction Network. We propose an extended version of a Chemical Reaction Network that models unbounded linear polymers made from a finite number of monomers. This Polymer Reaction Network model covers the DNA stack machine, as well as copy-tolerant Turing machines and some examples from biochemistry. We adapt the bisimulation method of verifying DNA implementations of Chemical Reaction Networks to our model, and use it to prove the correctness of the DNA stack machine implementation. We define a subclass of single-locus Polymer Reaction Networks and show that any member of that class can be bisimulated by a network using only four primitives, suggesting a method of DNA implementation. Finally, we prove that deciding whether an implementation is a bisimulation is Π⁰₂-complete, and thus undecidable in the general case, although it is tractable in many special cases of interest. We hope that the ability to model and verify implementations of Polymer Reaction Networks will aid in the rational design of molecular systems

Verifying polymer reaction networks using bisimulation

The Chemical Reaction Network model has been proposed as a programming language for molecular programming. Methods to implement arbitrary CRNs using DNA strand displacement circuits have been investigated, as have methods to prove the correctness of those or other implementations. However, the stochastic Chemical Reaction Network model is provably not deterministically Turing-universal, that is, it is impossible to create a stochastic CRN where a given output molecule is produced if and only if an arbitrary Turing machine accepts. A DNA stack machine that can simulate arbitrary Turing machines with minimal slowdown deterministically has been proposed, but it uses unbounded polymers that cannot be modeled as a Chemical Reaction Network. We propose an extended version of a Chemical Reaction Network that models unbounded linear polymers made from a finite number of monomers. This Polymer Reaction Network model covers the DNA stack machine, as well as copy-tolerant Turing machines and some examples from biochemistry. We adapt the bisimulation method of verifying DNA implementations of Chemical Reaction Networks to our model, and use it to prove the correctness of the DNA stack machine implementation. We define a subclass of single-locus Polymer Reaction Networks and show that any member of that class can be bisimulated by a network using only four primitives, suggesting a method of DNA implementation. Finally, we prove that deciding whether an implementation is a bisimulation is Π⁰₂-complete, and thus undecidable in the general case, although it is tractable in many special cases of interest. We hope that the ability to model and verify implementations of Polymer Reaction Networks will aid in the rational design of molecular systems

Variational Methods for the Modelling of Inelastic Solids

This workshop brought together two communities working on the same topic from different perspectives. It strengthened the exchange of ideas between experts from both mathematics and mechanics working on a wide range of questions related to the understanding and the prediction of processes in solids. Common tools in the analysis include the development of models within the broad framework of continuum mechanics, calculus of variations, nonlinear partial differential equations, nonlinear functional analysis, Gamma convergence, dimension reduction, homogenization, discretization methods and numerical simulations. The applications of these theories include but are not limited to nonlinear models in plasticity, microscopic theories at different scales, the role of pattern forming processes, effective theories, and effects in singular structures like blisters or folding patterns in thin sheets, passage from atomistic or discrete models to continuum models, interaction of scales and passage from the consideration of one specific time step to the continuous evolution of the system, including the evolution of appropriate measures of the internal structure of the system