An R Library for Compositional Data Analysis in Archaeometry

Compositional data naturally arises from the scientific analysis of the chemical composition of archaeological material such as ceramic and glass artefacts. Data of this type can be explored using a variety of techniques, from standard multivariate methods such as principal components analysis and cluster analysis, to methods based upon the use of log-ratios. The general aim is to identify groups of chemically similar artefacts that could potentially be used to answer questions of provenance. This paper will demonstrate work in progress on the development of a documented library of methods, implemented using the statistical package R, for the analysis of compositional data. R is an open source package that makes available very powerful statistical facilities at no cost. We aim to show how, with the aid of statistical software such as R, traditional exploratory multivariate analysis can easily be used alongside, or in combination with, specialist techniques of compositional data analysis. The library has been developed from a core of basic R functionality, together with purpose-written routines arising from our own research (for example that reported at CoDaWork'03). In addition, we have included other appropriate publicly available techniques and libraries that have been implemented in R by other authors. Available functions range from standard multivariate techniques through to various approaches to log-ratio analysis and zero replacement. We also discuss and demonstrate a small selection of relatively new techniques that have hitherto been little-used in archaeometric applications involving compositional data. The application of the library to the analysis of data arising in archaeometry will be demonstrated; results from different analyses will be compared; and the utility of the various methods discussed

Compositional data analysis in archaeometry

We shall call an n × p data matrix fully-compositional if the rows sum to a constant, and sub-compositional if the variables are a subset of a fully-compositional data set1. Such data occur widely in archaeometry, where it is common to determine the chemical composition of ceramic, glass, metal or other artefacts using techniques such as neutron activation analysis (NAA), inductively coupled plasma spectroscopy (ICPS), X-ray fluorescence analysis (XRF) etc. Interest often centres on whether there are distinct chemical groups within the data and whether, for example, these can be associated with different origins or manufacturing technologies

Estudi dels carotenoides en espècies marrons de bacteris verds del sofre: diversitat, eco-fisiologia i regulació

El present treball es centra en l'estudi a diferents nivells dels carotenoides de les espècies marrons de Bacteris Verds del Sofre (GSB, de l'anglès Green Sulfur Bacteria). L'objectiu global ha estat el d'esbrinar quina és la funció d'aquests pigments dins l'aparell fotosintètic d'aquests microorganismes i aprofundir en el coneixement de la seva estructura i interaccions amb els altres pigments de l'aparell fotosintètic. En primer lloc es va dissenyar un nou mètode de cromatografia líquida d'alta resolució (HPLC) per analitzar de manera més ràpida i precisa els carotenoides de diferents soques de GSB (Capítol 3). Aquest mètode es basa en una purificació prèvia dels extractes pigmentaris amb columnes d'alúmina per eliminar les bacterioclorofil·les (BCls). Això va permetre analitzar amb una elevada resolució i en tan sols 45 min de carrera cromatogràfica els diferents carotenoides i els seus precursors, així com les configuracions trans i cis dels seus isòmers. El segon mètode utilitzat va consistir en una modificació del mètode de Borrego i Garcia-Gil (1994) i va permetre la separació precisa de tot tipus de pigments, procedents tant de cultius purs com de mostres de caràcter complex. Un exemple concret foren uns paleosediments de la zona lacustre de Banyoles. En aquests sediments (0,7-1,5 milions d'anys d'antiguitat) es van detectar, entre d'altres pigments, carotenoides específics de les espècies marrons de GSB, la qual cosa va permetre confirmar la presència d'aquests bacteris a la zona lacustre de Banyoles ja des del Pleistocè inferior. En aquest primer capítol també es van analitzar els carotenoides de Chlorobium (Chl.) phaeobacteroides CL1401 mitjançant cromatografia líquida acoblada a espectrometria de masses (LC-MS/MS), amb l'objectiu de confirmar la seva identificació i el seu pes molecular. A més, també es va avaluar l'efecte de la temperatura, la llum i diferents agents oxidants i reductors en la composició quantitativa i qualitativa dels carotenoides i les BCls d'aquesta espècie. Això va permetre confirmar el caràcter fotosensible de les BCls i que els isòmers trans/cis dels diferents carotenoides no són artefactes produïts durant la manipulació de les mostres, sinó que són constitutius de l'aparell fotosintètic d'aquests microorganismes. El Capítol 4 inclou els experiments de fisiologia duts a terme amb algunes espècies de GSB, a partir dels quals es va intentar esbrinar la dinàmica de síntesi dels diferents pigments de l'aparell fotosintètic (BCl antena, BCl a i carotenoides) durant el creixement d'aquestes espècies. Aquestes investigacions van permetre monitoritzar també els canvis en el nombre de centres de reacció (CR) durant el procés d'adaptació lumínica. La determinació experimental del nombre de CR es va realitzar a partir de la quantificació de la BCl663, l'acceptor primari en la cadena de transport d'electrons dels GSB. L'estimació del nombre de CR/clorosoma es va realitzar tant a partir de dades estequiomètriques i biomètriques presents a la bibliografia, com a partir de les dades experimentals obtingudes en el present treball. El bon ajust obtingut entre les diferents estimacions va donar solidesa al valor estequiomètric calculat, que fou, com a promig, d'uns 70 CR per clorosoma. En aquest capítol de fisiologia també es van estudiar les variacions en les relacions trans/cis pels principals carotenoides de les espècies marrons de GSB. Aquestes es van determinar a partir de cultius purs de laboratori i de poblacions naturals de GSB. Pel que fa als valors trobats en cultius de laboratori no es van observar diferències destacades entre el valor calculat a alta intensitat de llum i el calculat a baixa intensitat, essent en ambdós casos proper a 2. En els clorosomes aïllats de diferents soques marrons aquest quocient prengué un valor similar tant pels isòmers de l'isorenieratè (Isr) com pels del -isorenieratè (-Isr). En poblacions naturals de Chl. phaeobacteroides aquesta relació va ser també de 2 isòmers trans per cada isòmer cis, mantenint-se constant tant en fondària com al llarg del temps. Finalment, en el Capítol 5 es presenta un marcador molecular que permet la identificació específica d'espècies marrons de GSB. Malgrat que inicialment aquest marcador fou dissenyat a partir d'un gen implicat en la síntesi de carotenoides (crtY, el qual codifica per a una licopè ciclasa) la seqüència final a partir de la qual s'han aconseguit els encebadors selectius està relacionada amb la família de proteïnes de les Policètid-ceto-sintases (PKT). Tot i així, l'eina dissenyada pot ser de gran utilitat per a la discriminació d'espècies marrons de GSB respecte les verdes en poblacions mixtes com les que es troben en ambients naturals i obre la porta a futurs experiments d'ecologia microbiana utilitzant tècniques com la PCR en temps real, que permetria la monitorització selectiva de les poblacions d'espècies marrons de GSB en ecosistemes naturals.

Modelling, control and supervision for a class of hybrid systems

The aim of this thesis is to narrow the gap between two different control techniques: the continuous control and the discrete event control techniques DES. This gap can be reduced by the study of Hybrid systems, and by interpreting as Hybrid systems the majority of large-scale systems. In particular, when looking deeply into a process, it is often possible to identify interaction between discrete and continuous signals. Hybrid systems are systems that have both continuous, and discrete signals. Continuous signals are generally supposed continuous and differentiable in time, since discrete signals are neither continuous nor differentiable in time due to their abrupt changes in time. Continuous signals often represent the measure of natural physical magnitudes such as temperature, pressure etc. The discrete signals are normally artificial signals, operated by human artefacts as current, voltage, light etc. Typical processes modelled as Hybrid systems are production systems, chemical process, or continuos production when time and continuous measures interacts with the transport, and stock inventory system. Complex systems as manufacturing lines are hybrid in a global sense. They can be decomposed into several subsystems, and their links. Another motivation for the study of Hybrid systems is the tools developed by other research domains. These tools benefit from the use of temporal logic for the analysis of several properties of Hybrid systems model, and use it to design systems and controllers, which satisfies physical or imposed restrictions. This thesis is focused in particular types of systems with discrete and continuous signals in interaction. That can be modelled hard non-linealities, such as hysteresis, jumps in the state, limit cycles, etc. and their possible non-deterministic future behaviour expressed by an interpretable model description. The Hybrid systems treated in this work are systems with several discrete states, always less than thirty states (it can arrive to NP hard problem), and continuous dynamics evolving with expression: with Ki ¡ Rn constant vectors or matrices for X components vector. In several states the continuous evolution can be several of them Ki = 0. In this formulation, the mathematics can express Time invariant linear system. By the use of this expression for a local part, the combination of several local linear models is possible to represent non-linear systems. And with the interaction with discrete events of the system the model can compose non-linear Hybrid systems. Especially multistage processes with high continuous dynamics are well represented by the proposed methodology. Sate vectors with more than two components, as third order models or higher is well approximated by the proposed approximation. Flexible belt transmission, chemical reactions with initial start-up and mobile robots with important friction are several physical systems, which profits from the benefits of proposed methodology (accuracy). The motivation of this thesis is to obtain a solution that can control and drive the Hybrid systems from the origin or starting point to the goal. How to obtain this solution, and which is the best solution in terms of one cost function subject to the physical restrictions and control actions is analysed. Hybrid systems that have several possible states, different ways to drive the system to the goal and different continuous control signals are problems that motivate this research. The requirements of the system on which we work is: a model that can represent the behaviour of the non-linear systems, and that possibilities the prediction of possible future behaviour for the model, in order to apply an supervisor which decides the optimal and secure action to drive the system toward the goal. Specific problems can be determined by the use of this kind of hybrid models are: - The unity of order. - Control the system along a reachable path. - Control the system in a safe path. - Optimise the cost function. - Modularity of control The proposed model solves the specified problems in the switching models problem, the initial condition calculus and the unity of the order models. Continuous and discrete phenomena are represented in Linear hybrid models, defined with defined eighth-tuple parameters to model different types of hybrid phenomena. Applying a transformation over the state vector : for LTI system we obtain from a two-dimensional SS a single parameter, alpha, which still maintains the dynamical information. Combining this parameter with the system output, a complete description of the system is obtained in a form of a graph in polar representation. Using Tagaki-Sugeno type III is a fuzzy model which include linear time invariant LTI models for each local model, the fuzzyfication of different LTI local model gives as a result a non-linear time invariant model. In our case the output and the alpha measure govern the membership function. Hybrid systems control is a huge task, the processes need to be guided from the Starting point to the desired End point, passing a through of different specific states and points in the trajectory. The system can be structured in different levels of abstraction and the control in three layers for the Hybrid systems from planning the process to produce the actions, these are the planning, the process and control layer. In this case the algorithms will be applied to robotics ¡V a domain where improvements are well accepted ¡V it is expected to find a simple repetitive processes for which the extra effort in complexity can be compensated by some cost reductions. It may be also interesting to implement some control optimisation to processes such as fuel injection, DC-DC converters etc. In order to apply the RW theory of discrete event systems on a Hybrid system, we must abstract the continuous signals and to project the events generated for these signals, to obtain new sets of observable and controllable events. Ramadge & Wonham¡¦s theory along with the TCT software give a Controllable Sublanguage of the legal language generated for a Discrete Event System (DES). Continuous abstraction transforms predicates over continuous variables into controllable or uncontrollable events, and modifies the set of uncontrollable, controllable observable and unobservable events. Continuous signals produce into the system virtual events, when this crosses the bound limits. If this event is deterministic, they can be projected. It is necessary to determine the controllability of this event, in order to assign this to the corresponding set, , controllable, uncontrollable, observable and unobservable set of events. Find optimal trajectories in order to minimise some cost function is the goal of the modelling procedure. Mathematical model for the system allows the user to apply mathematical techniques over this expression. These possibilities are, to minimise a specific cost function, to obtain optimal controllers and to approximate a specific trajectory. The combination of the Dynamic Programming with Bellman Principle of optimality, give us the procedure to solve the minimum time trajectory for Hybrid systems. The problem is greater when there exists interaction between adjacent states. In Hybrid systems the problem is to determine the partial set points to be applied at the local models. Optimal controller can be implemented in each local model in order to assure the minimisation of the local costs. The solution of this problem needs to give us the trajectory to follow the system. Trajectory marked by a set of set points to force the system to passing over them. Several ways are possible to drive the system from the Starting point Xi to the End point Xf. Different ways are interesting in: dynamic sense, minimum states, approximation at set points, etc. These ways need to be safe and viable and RchW. And only one of them must to be applied, normally the best, which minimises the proposed cost function. A Reachable Way, this means the controllable way and safe, will be evaluated in order to obtain which one minimises the cost function. Contribution of this work is a complete framework to work with the majority Hybrid systems, the procedures to model, control and supervise are defined and explained and its use is demonstrated. Also explained is the procedure to model the systems to be analysed for automatic verification. Great improvements were obtained by using this methodology in comparison to using other piecewise linear approximations. It is demonstrated in particular cases this methodology can provide best approximation. The most important contribution of this work, is the Alpha approximation for non-linear systems with high dynamics While this kind of process is not typical, but in this case the Alpha approximation is the best linear approximation to use, and give a compact representation.