Membrane Computing was introduced as a computational paradigm in Natural Computing. The models introduced, called Membrane (or P) Systems, provide a coherent platform to describe and study living cells as computational systems. Membrane Systems have been investigated for their computational aspects and employed to model problems in other fields, like: Computer Science, Linguistics, Biology, Economy, Computer Graphics, Robotics, etc. Their inherent parallelism, heterogeneity and intrinsic versatilityallow them to model a broad range of processes and phenomena, being also an efficient means to solve and analyze problems in a novel way.

Membrane Computing has been used to model biological systems, becoming with time a thorough modeling paradigm comparable, in its modeling and predicting capabilities, to more established models in this area. This book is the result of the need to collect, in an organic way, different facets of this paradigm.

The chapters of this book, together with the web pages accompanying them, present different applications of Membrane Systems to Biology. Deterministic, non-deterministic and stochastic systems paired with different algorithms and methodologies show the full potential of this framework.

The book is addressed to researchers interested in applications of discrete biological models and the interplay between Membrane Systems and other approaches to analyze complex systems."

Membrane Computing was introduced as a computational paradigm in Natural Computing. The models introduced, called Membrane (or P) Systems, provide a coherent platform to describe and study living cells as computational systems. Membrane Systems have been investigated for their computational aspects and employed to model problems in other fields, like: Computer Science, Linguistics, Biology, Economy, Computer Graphics, Robotics, etc. Their inherent parallelism, heterogeneity and intrinsic versatility allow them to model a broad range of processes and phenomena, being also an efficient means to solve and analyze problems in a novel way. Membrane Computing has been used to model biological systems, becoming with time a thorough modeling paradigm comparable, in its modeling and predicting capabilities, to more established models in this area. This book is the result of the need to collect, in an organic way, different facets of this paradigm. The chapters of this book, together with the web pages accompanying them, present different applications of Membrane Systems to Biology. Deterministic, non-deterministic and stochastic systems paired with different algorithms and methodologies show the full potential of this framework. The book is addressed to researchers interested in applications of discrete biological models and the interplay between Membrane Systems and other approaches to analyze complex systems.

This volume contains a selection of papers presented at the 9th Workshop on Membrane Computing, WMC9, which took place in Edinburgh, UK, during July 28-31,2008. The ?rst three workshopson membrane computing were or- nized in Curtea de Arge, s, Romania - they took place in August 2000 (with the proceedings published in Lecture Notes in Computer Science, volume 2235), in August 2001 (with a selection of papers published as a special issue of Fun- menta Informaticae, volume 49, numbers 1-3, 2002), and in August 2002 (with the proceedings published in Lecture Notes in Computer Science, volume 2597). The next ?ve workshops were organized in Tarragona, Spain, in July 2003, in Milan, Italy, in June 2004, in Vienna, Austria, in July 2005, in Leiden, The Netherlands, in July 2006, and in Thessaloniki, Greece, in June 2007, with the proceedings published as volumes 2933, 3365, 3850, 4361, and 4860 of Lecture Notes in Computer Science."

Membrane systems are a new class of distributed and parallel model of computation inspired by the subdivision of living cells into compartments delimited by membranes. Their hierarchical internal structure, their locality of interactions, their inherent parallelism and also their capacity to create new compartments, represent the distinguishing hallmarks of membrane systems. Membrane computing, the study of membrane systems, is a fascinating and fast growing area of research. The main streams of current investigations in Membrane Computing concern theoretical computer science and the modelling of complex systems. In this monograph Pierluigi Frisco considers the former trend: he presents an in-depth study of the formal language and computational complexity aspects of the most widely investigated models of membrane systems. This study gives a comprehensive understanding of the computational power of the models considered, shows different proof techniques used for such study, and introduces links highlighting the similarities and differences between the their computational power. These models cover a broad range of features, giving a grasp of the enormous flexibility of the framework offered by membrane systems. Aimed at graduates and researchers in the field, who can use it as a reference text, and to people with an initial interest in Membrane Computing, who can use it as a clear and up to date starting point for Membrane Computing.

Two new goodness-of-_t tests are developed for the three-parameter Weibull distribution with known shape parameter. These procedures eliminate the need for estimating the unknown location and scale parameters prior to initiating the tests and are easily adapted for censored data. This is accomplished by employing the Anderson-Darling A2 s and Cram_er-von Mises W2 S statistics based on the normalized spacings of the sample data. Critical values of A2 s and W2 s are obtained for common signi_cance levels by large Monte Carlo simulations for shapes of 0.5(0.5)4.0 and sample sizes of 5(5)40 with up to 40% censoring (type II) from the left and/or right. An extensive Monte Carlo power study is also conducted to compare the two tests with each other and with their prominent competitors. The competitors include another spacings test, Z_, and the modi_ed Kolmogorov-Smirnov (KS), Cram_er- von Mises (W2) and Anderson-Darling (A2) EDF tests. The power results indicate that no one test is superior in all situations. When the alternatives considered are tested against a skewed Weibull null distribution, A2 s and W2 s achieve considerably higher power than the other EDF tests, but do not perform as well as Z_. On the other hand, when the null distribution is symmetric, Z_ loses all of its power, while A2 s and W2 s yield power comparable to the other EDF tests. Results also show A2 s generally outperforms W2 s, and for these reasons, A2 s is the preferred test for the three-parameter Weibull with known shape.

Jack Brown is once again asked to go on a mission, this time to locate a person of extreme importance. This person is Jacks friend and mentor who was investigating rumors of terrorists building a massive army. Jack soon realizes the rumors to be true and the army had infiltrated to the highest levels of government of almost every major civilized country. There is a high possibility that Jacks own country may not be able to stop the take over by the Crimson Brigade.

A First Book of Morphy illustrates basic principles of chess with more than 60 brilliant and instructive games played by the first American chess champion, Paul Morphy.