Some last thoughts on compositional data analysis

One of the disadvantages of old age is that there is more past than future: this,however, may be turned into an advantage if the wealth of experience and, hopefully,wisdom gained in the past can be reflected upon and throw some light on possiblefuture trends. To an extent, then, this talk is necessarily personal, certainly nostalgic,but also self critical and inquisitive about our understanding of the discipline ofstatistics. A number of almost philosophical themes will run through the talk: searchfor appropriate modelling in relation to the real problem envisaged, emphasis onsensible balances between simplicity and complexity, the relative roles of theory andpractice, the nature of communication of inferential ideas to the statistical layman, theinter-related roles of teaching, consultation and research. A list of keywords might be:identification of sample space and its mathematical structure, choices betweentransform and stay, the role of parametric modelling, the role of a sample spacemetric, the underused hypothesis lattice, the nature of compositional change,particularly in relation to the modelling of processes. While the main theme will berelevance to compositional data analysis we shall point to substantial implications forgeneral multivariate analysis arising from experience of the development ofcompositional data analysis…

Some last thoughts on compositional data analysis

One of the disadvantages of old age is that there is more past than future: this, however, may be turned into an advantage if the wealth of experience and, hopefully, wisdom gained in the past can be reflected upon and throw some light on possible future trends. To an extent, then, this talk is necessarily personal, certainly nostalgic, but also self critical and inquisitive about our understanding of the discipline of statistics. A number of almost philosophical themes will run through the talk: search for appropriate modelling in relation to the real problem envisaged, emphasis on sensible balances between simplicity and complexity, the relative roles of theory and practice, the nature of communication of inferential ideas to the statistical layman, the inter-related roles of teaching, consultation and research. A list of keywords might be: identification of sample space and its mathematical structure, choices between transform and stay, the role of parametric modelling, the role of a sample space metric, the underused hypothesis lattice, the nature of compositional change, particularly in relation to the modelling of processes. While the main theme will be relevance to compositional data analysis we shall point to substantial implications for general multivariate analysis arising from experience of the development of compositional data analysis…

Compositional hypotheses of subcompositional stability and specific perturbation change and their testing

In standard multivariate statistical analysis common hypotheses of interest concern changes in mean vectors and subvectors. In compositional data analysis it is now well established that compositional change is most readily described in terms of the simplicial operation of perturbation and that subcompositions replace the marginal concept of subvectors. To motivate the statistical developments of this paper we present two challenging compositional problems from food production processes. Against this background the relevance of perturbations and subcompositions can be clearly seen. Moreover we can identify a number of hypotheses of interest involving the specification of particular perturbations or differences between perturbations and also hypotheses of subcompositional stability. We identify the two problems as being the counterpart of the analysis of paired comparison or split plot experiments and of separate sample comparative experiments in the jargon of standard multivariate analysis. We then develop appropriate estimation and testing procedures for a complete lattice of relevant compositional hypotheses

The chemical variability at the surface of Mars: implications for exogenic processes

The chemical composition of sediments and rocks, as well as their distribution at the Martian surface, represent a long term archive of processes, which have formed the planetary surface. A survey of chemical compositions by means of Compositional Data Analysis represents a valuable tool to extract direct evidence for weathering processes and allows to quantify weathering and sedimentation rates. clr-biplot techniques are applied for visualization of chemical relationships across the surface (“chemical maps”). The variability among individual suites of data is further analyzed by means of clr-PCA, in order to extract chemical alteration vectors between fresh rocks and their crusts and for an assessment of different source reservoirs accessible to soil formation. Both techniques are applied to elucidate the influence of remote weathering by combined analysis of several soil forming branches. Vector analysis in the Simplex provides the opportunity to study atmosphere surface interactions, including the role and composition of volcanic gases

A compositional approach to stable isotope data analysis

Isotopic data are currently becoming an important source of information regarding sources, evolution and mixing processes of water in hydrogeologic systems. However, it is not clear how to treat with statistics the geochemical data and the isotopic data together. We propose to introduce the isotopic information as new parts, and apply compositional data analysis with the resulting increased composition. Results are equivalent to downscale the classical isotopic delta variables, because they are already relative (as needed in the compositional framework) and isotopic variations are almost always very small. This methodology is illustrated and tested with the study of the Llobregat River Basin (Barcelona, NE Spain), where it is shown that, though very small, isotopic variations comp lement geochemical principal components, and help in the better identification of pollution sources

Compositional evolution with mass transfer in closed systems

Evolution of compositions in time, space, temperature or other covariates is frequent in practice. For instance, the radioactive decomposition of a sample changes its composition with time. Some of the involved isotopes decompose into other isotopes of the sample, thus producing a transfer of mass from some components to other ones, but preserving the total mass present in the system. This evolution is traditionally modelled as a system of ordinary di erential equations of the mass of each component. However, this kind of evolution can be decomposed into a compositional change, expressed in terms of simplicial derivatives, and a mass evolution (constant in this example). A rst result is that the simplicial system of di erential equations is non-linear, despite of some subcompositions behaving linearly. The goal is to study the characteristics of such simplicial systems of di erential equa- tions such as linearity and stability. This is performed extracting the compositional dif ferential equations from the mass equations. Then, simplicial derivatives are expressed in coordinates of the simplex, thus reducing the problem to the standard theory of systems of di erential equations, including stability. The characterisation of stability of these non-linear systems relays on the linearisation of the system of di erential equations at the stationary point, if any. The eigenvelues of the linearised matrix and the associated behaviour of the orbits are the main tools. For a three component system, these orbits can be plotted both in coordinates of the simplex or in a ternary diagram. A characterisation of processes with transfer of mass in closed systems in terms of stability is thus concluded. Two examples are presented for illustration, one of them is a radioactive decay

Granularity and disaggregation in compositional modelling with applications to ecological systems

In the past decade, compositional modelling (CM) has established itself as the predominant knowledge-based approach to construct mathematical (simulation) models automatically. Although it is mainly applied to physical systems, there is a growing interest in applying CM to other domains, such as ecological and socio-economic systems. Inspired by this observation, this paper presents a method for extending the conventional CM techniques to suit systems that are fundamentally presented by interacting populations of individuals instead of physical components or processes. The work supports building model repositories for such systems, especially in addressing the most critical outstanding issues of granularity and disaggregation in ecological systems modelling.

On Compositional Modelling

Many solutions to AI problems require the task to be represented in one of a multitude of rigorous mathematical formalisms. The construction of such mathematical models forms a difficult problem which is often left to the user of the problem solver. This void between problem solvers and the problems is studied by the eclectic field of automated modelling. Within this field, compositional modelling, a knowledge-based methodology for system modelling, has established itself as a leading approach. In general, a compositional modeller organises knowledge in a structure of composable fragments that relate to particular system components or processes. Its embedded inference mechanism chooses the appropriate fragments with respect to a given problem, instantiates and assembles them into a consistent system model. Many different types of compositional modeller exist, however, with significant differences in their knowledge representation and approach to inference. This paper examines compositional modelling. It presents a general framework for building and analysing compositional modellers. Based on this framework, a number of influential compositional modellers are examined and compared. The paper also identifies the strengths and weaknesses of compositional modelling and discusses some typical applications.

Compositional modulation and surface stability in InGaP films: Understanding and controlling surface properties

We investigate the formation of compositional modulation and atomic ordering in InGaP films. Such bulk properties - as well as surface morphologies - present a strong dependence on growth parameters, mainly the V/III ratio. Our results indicate the importance of surface diffusion and, particularly, surface reconstruction for these processes. Most importantly from the application point of view, we show that the compositional modulation is not necessarily coupled to the surface instabilities, so that smooth InGaP films with periodic compositional variation could be obtained. This opens a new route for the generation of templates for quantum dot positioning and three-dimensional arrays of nanostructures. © 2007 American Institute of Physics.

Sedimentary processes on the NW Iberian Continental Shelf since the Little Ice Age

The OMEX core CD110 W90, retrieved from the Douro Mud Patch (DMP) off the River Douro in the north of Portugal, records the period since the beginning of Little Ice Age (LIA). The core chronology is based upon the data attributes for Pb-210, Cs-137 and a C-14 dating from a level near the core base. Geochemical, granulometric, microfaunal (benthic foraminifera) and compositional data suggest the occurrence of precipitation changes which may have been, at least partially, influenced by the North Atlantic Oscillation (NAO), that contributes to the regulation of the ocean-atmosphere dynamics in the North Atlantic. Southwesterly Atlantic storm track is associated with the negative phases of the NAO, when the Azores High is anomalously weak, higher oceanographic hydrodynamism, downwelling events and increased rainfall generally occurs. Prevalence of these characteristics during the LIA left a record that corresponds to phases of major floods. During these phases the DMP received a higher contribution of relatively coarse-grained terrigenous sediments, enriched in quartz particles, which diluted the contribution of other minerals, as indicated by reduced concentrations of several lithogenic chemical elements such as: Al, As, Ba, Ce, Co, Cu, Fe, K, La, Li, Mg, Mn, Mo, Na, Ni, P, Rb, Sc, Sn, Th, V and Y. The presence of biogenic carbonate particles also underwent dilution, as revealed by the smaller abundance of foraminifera and correlative lower concentrations of Ca and Sr. During this period, the DMP also received an increased contribution of organic matter, indicated by higher values of lignin remains and a benthic foraminifera high productivity index, or BFHP, which gave rise to early diagenetic changes with pyrite formation. Since the beginning of the 20th century this contribution diminished, probably due to several drier periods and the impact of human activities in the river basins, e.g. construction of dams, or, on the littoral areas, construction of hard-engineering structures and sand extraction activities. During the first half of the 20th century mainly positive phases of the NAO prevailed, caused by the above normal strengthening of the subtropical high pressure centre of the Azores and the deepening of the low pressure centre in Iceland. These phases may have contributed to the reduction in the supply of both terrigenous sediments and organic matter from shallow water to the DMP. During the positive phases of the NAO, sedimentation became finer. The development of mining and industrial activities during the 20th century is marked, in this core, by higher concentrations of Pb. Furthermore, the erosion of heaps resulting from wolfram exploitation leaves its signature as a peak of W concentrations recorded in the sediments of the DMP deposited between the 1960s and the 1990s. Wolfram exploitation was an important activity in the middle part of the 20th century, particularly during the period of the Second World War. (C) 2012 Elsevier Ltd. All rights reserved.

Compositional signatures of the Cenozoic sedimentary succesions of the Malaguide Complex (Betic Cordillera, Spain)

The studied Cenozoic sedimentary successions consist of deposits from continental/shallow-water to deep-marine environments of the Malaguide Complex (Betic Cordillera) outcropping in the Sierra Espuña area (SE Spain). The aim of this study is to characterize the composition, source area(s) provenance and weathering processes of these sedimentary successions from the pre-orogenic (Paleocene-Early Oligocene) to the syn-orogenic (Late Oligocene-Early Miocene) stage using petrological and geochemical methodologies. The studied sandstones are mainly quartzolithic with abundant metamorphic and sedimentary lithic fragments. In particular, the composition of samples from the pre-orogenic cycle is mainly carbonate with important siliciclastic components that occur within the medium to fine grained arenites. The composition of samples from the syn-orogenic cycle is characterized by a sharp change from carbonate to siliciclastic terms. Thus, the composition of the overall sandstone samples is very heterogeneous and suggests a source area mainly characterized by the Malaguide basement and lower units of the Internal Betic Zone, that partially compose the Mesomediterranean Microplate. The geochemical proxies suggest a provenance mainly from felsic source area with a minor supply from mafic rocks in some samples of the syn-orogenic stage. Furthermore, palaeoweathering indices indicate low to moderate weathering conditions for the sources. The Cenozoic sedimentary successions of the Malaguide Complex played an important role in the geodynamic evolution of the Betic Cordillera that represents the key tectonic element of the western domains of the Mesomediterranean Microplate.

Compositional semantics of dataflow networks with query-driven communication of exact values

We develop and study the concept of dataflow process networks as used for exampleby Kahn to suit exact computation over data types related to real numbers, such as continuous functions and geometrical solids. Furthermore, we consider communicating these exact objectsamong processes using protocols of a query-answer nature as introduced in our earlier work. This enables processes to provide valid approximations with certain accuracy and focusing on certainlocality as demanded by the receiving processes through queries. We define domain-theoretical denotational semantics of our networks in two ways: (1) directly, i. e. by viewing the whole network as a composite process and applying the process semantics introduced in our earlier work; and (2) compositionally, i. e. by a fixed-point construction similarto that used by Kahn from the denotational semantics of individual processes in the network. The direct semantics closely corresponds to the operational semantics of the network (i. e. it iscorrect) but very difficult to study for concrete networks. The compositional semantics enablescompositional analysis of concrete networks, assuming it is correct. We prove that the compositional semantics is a safe approximation of the direct semantics. Wealso provide a method that can be used in many cases to establish that the two semantics fully coincide, i. e. safety is not achieved through inactivity or meaningless answers. The results are extended to cover recursively-defined infinite networks as well as nested finitenetworks. A robust prototype implementation of our model is available.

Model Construction and Research using System Compositional Approach on Natural Hierarchical Neural Networks. Development of Computer Toolbox

System compositional approach to model construction and research of informational processes, which take place in biological hierarchical neural networks, is being discussed. A computer toolbox has been successfully developed for solution of tasks from this scientific sphere. A series of computational experiments investigating the work of this toolbox on olfactory bulb model has been carried out. The well-known psychophysical phenomena have been reproduced in experiments.

Exploring the joint compositional variability of major components and trace elements in the Tellus soil geochemistry survey (Northern Ireland)

The complexity of modern geochemical data sets is increasing in several aspects (number of available samples, number of elements measured, number of matrices analysed, geological-environmental variability covered, etc), hence it is becoming increasingly necessary to apply statistical methods to elucidate their structure. This paper presents an exploratory analysis of one such complex data set, the Tellus geochemical soil survey of Northern Ireland (NI). This exploratory analysis is based on one of the most fundamental exploratory tools, principal component analysis (PCA) and its graphical representation as a biplot, albeit in several variations: the set of elements included (only major oxides vs. all observed elements), the prior transformation applied to the data (none, a standardization or a logratio transformation) and the way the covariance matrix between components is estimated (classical estimation vs. robust estimation). Results show that a log-ratio PCA (robust or classical) of all available elements is the most powerful exploratory setting, providing the following insights: the first two processes controlling the whole geochemical variation in NI soils are peat coverage and a contrast between “mafic” and “felsic” background lithologies; peat covered areas are detected as outliers by a robust analysis, and can be then filtered out if required for further modelling; and peat coverage intensity can be quantified with the %Br in the subcomposition (Br, Rb, Ni).

Eruptive and depositional processes of widely dispersed volcanic ash: Insights from the Brown Tuffs (Aeolian Islands)

This is a multidisciplinary study of the Brown Tuffs (BT) ash deposits of the Aeolian Islands in northern Sicily and representing the most voluminous and widely distributed tephra deposit in this region. A large dataset of major and minor elements of the BT glass has defined a range from K-series basaltic-andesites and trachy-andesites through to tephri-phonolites and trachytes that is consistent with the Vulcano magmatic system. Combined with stratigraphic information and new radiocarbon ages, four stratigraphic macro-units are defined: the Lower (80-56 ky; LBT), Intermediate (56-27 ky; IBT), Intermediate-upper (26-24 ky; IBT-upper) and Upper BT (24-6 ky; UBT). Glass compositional data provide constraints on proximal-distal correlations of the BT with deep-sea tephra layers in the Tyrrhenian and Adriatic Seas and new insights on the definition of the dispersal area of the BT eruptions. Sedimentological evidence of massive to stratified deposits and shear-related structures, coupled with grain-size and componentry analyses, have allowed to interpret the BT as the result of laterally-spreading, concentrated ash-rich PDCs, with a high potential of erosion of the substratum. Shear-structures similar to those observed in the field in the BT deposits have been reproduced by small-medium scale laboratory experiments carried out on ash granular flows, which have also allowed to describe the behaviour of ash-rich PDcs and their mobility depending on variations of slope-ratio, grain size and flow channelization. The resulting integrated dataset provides a contribution to the knowledge of the BT eruptions and insights on long-term hazard assessment in the study area. The eruptive dynamics of the BT may have a role in characterizing the whole magmatic system of the La Fossa Caldera on Vulcano, in the light of the geochemical link highlighted between the UBT macrounit and the early products of the La Fossa cone.