Application of compositional data analysis to geochemical data of marine sediments

In an earlier investigation (Burger et al., 2000) five sediment cores near the RodriguesTriple Junction in the Indian Ocean were studied applying classical statistical methods(fuzzy c-means clustering, linear mixing model, principal component analysis) for theextraction of endmembers and evaluating the spatial and temporal variation ofgeochemical signals. Three main factors of sedimentation were expected by the marinegeologists: a volcano-genetic, a hydro-hydrothermal and an ultra-basic factor. Thedisplay of fuzzy membership values and/or factor scores versus depth providedconsistent results for two factors only; the ultra-basic component could not beidentified. The reason for this may be that only traditional statistical methods wereapplied, i.e. the untransformed components were used and the cosine-theta coefficient assimilarity measure.During the last decade considerable progress in compositional data analysis was madeand many case studies were published using new tools for exploratory analysis of thesedata. Therefore it makes sense to check if the application of suitable data transformations,reduction of the D-part simplex to two or three factors and visualinterpretation of the factor scores would lead to a revision of earlier results and toanswers to open questions . In this paper we follow the lines of a paper of R. Tolosana-Delgado et al. (2005) starting with a problem-oriented interpretation of the biplotscattergram, extracting compositional factors, ilr-transformation of the components andvisualization of the factor scores in a spatial context: The compositional factors will beplotted versus depth (time) of the core samples in order to facilitate the identification ofthe expected sources of the sedimentary process.Kew words: compositional data analysis, biplot, deep sea sediments

Using problem-based learning for introducing producer theory and market structure in intermediate microeconomics

This paper shows how instructors can use the problem‐based learning method to introduce producer theory and market structure in intermediate microeconomics courses. The paper proposes a framework where different decision problems are presented to students, who are asked to imagine that they are the managers of a firm who need to solve a problem in a particular business setting. In this setting, the instructors’ role isto provide both guidance to facilitate student learning and content knowledge on a just‐in‐time basis

Robust Factor Analysis for Compositional Data

Factor analysis as frequent technique for multivariate data inspection is widely used also for compositional data analysis. The usual way is to use a centered logratio (clr)transformation to obtain the random vector y of dimension D. The factor model istheny = Λf + e (1)with the factors f of dimension k & D, the error term e, and the loadings matrix Λ.Using the usual model assumptions (see, e.g., Basilevsky, 1994), the factor analysismodel (1) can be written asCov(y) = ΛΛT + ψ (2)where ψ = Cov(e) has a diagonal form. The diagonal elements of ψ as well as theloadings matrix Λ are estimated from an estimation of Cov(y).Given observed clr transformed data Y as realizations of the random vectory. Outliers or deviations from the idealized model assumptions of factor analysiscan severely effect the parameter estimation. As a way out, robust estimation ofthe covariance matrix of Y will lead to robust estimates of Λ and ψ in (2), seePison et al. (2003). Well known robust covariance estimators with good statisticalproperties, like the MCD or the S-estimators (see, e.g. Maronna et al., 2006), relyon a full-rank data matrix Y which is not the case for clr transformed data (see,e.g., Aitchison, 1986).The isometric logratio (ilr) transformation (Egozcue et al., 2003) solves thissingularity problem. The data matrix Y is transformed to a matrix Z by usingan orthonormal basis of lower dimension. Using the ilr transformed data, a robustcovariance matrix C(Z) can be estimated. The result can be back-transformed tothe clr space byC(Y ) = V C(Z)V Twhere the matrix V with orthonormal columns comes from the relation betweenthe clr and the ilr transformation. Now the parameters in the model (2) can beestimated (Basilevsky, 1994) and the results have a direct interpretation since thelinks to the original variables are still preserved.The above procedure will be applied to data from geochemistry. Our specialinterest is on comparing the results with those of Reimann et al. (2002) for the Kolaproject data

Alternative ways to estimate change points in multinomial sequences. An application to an authorship attribution problem

The statistical analysis of literary style is the part of stylometry that compares measurable characteristicsin a text that are rarely controlled by the author, with those in other texts. When thegoal is to settle authorship questions, these characteristics should relate to the author’s style andnot to the genre, epoch or editor, and they should be such that their variation between authors islarger than the variation within comparable texts from the same author.For an overview of the literature on stylometry and some of the techniques involved, see for exampleMosteller and Wallace (1964, 82), Herdan (1964), Morton (1978), Holmes (1985), Oakes (1998) orLebart, Salem and Berry (1998).Tirant lo Blanc, a chivalry book, is the main work in catalan literature and it was hailed to be“the best book of its kind in the world” by Cervantes in Don Quixote. Considered by writterslike Vargas Llosa or Damaso Alonso to be the first modern novel in Europe, it has been translatedseveral times into Spanish, Italian and French, with modern English translations by Rosenthal(1996) and La Fontaine (1993). The main body of this book was written between 1460 and 1465,but it was not printed until 1490.There is an intense and long lasting debate around its authorship sprouting from its first edition,where its introduction states that the whole book is the work of Martorell (1413?-1468), while atthe end it is stated that the last one fourth of the book is by Galba (?-1490), after the death ofMartorell. Some of the authors that support the theory of single authorship are Riquer (1990),Chiner (1993) and Badia (1993), while some of those supporting the double authorship are Riquer(1947), Coromines (1956) and Ferrando (1995). For an overview of this debate, see Riquer (1990).Neither of the two candidate authors left any text comparable to the one under study, and thereforediscriminant analysis can not be used to help classify chapters by author. By using sample textsencompassing about ten percent of the book, and looking at word length and at the use of 44conjunctions, prepositions and articles, Ginebra and Cabos (1998) detect heterogeneities that mightindicate the existence of two authors. By analyzing the diversity of the vocabulary, Riba andGinebra (2000) estimates that stylistic boundary to be near chapter 383.Following the lead of the extensive literature, this paper looks into word length, the use of the mostfrequent words and into the use of vowels in each chapter of the book. Given that the featuresselected are categorical, that leads to three contingency tables of ordered rows and therefore tothree sequences of multinomial observations.Section 2 explores these sequences graphically, observing a clear shift in their distribution. Section 3describes the problem of the estimation of a suden change-point in those sequences, in the followingsections we propose various ways to estimate change-points in multinomial sequences; the methodin section 4 involves fitting models for polytomous data, the one in Section 5 fits gamma modelsonto the sequence of Chi-square distances between each row profiles and the average profile, theone in Section 6 fits models onto the sequence of values taken by the first component of thecorrespondence analysis as well as onto sequences of other summary measures like the averageword length. In Section 7 we fit models onto the marginal binomial sequences to identify thefeatures that distinguish the chapters before and after that boundary. Most methods rely heavilyon the use of generalized linear models

A survey addressing the fundamental matrix estimation problem

Epipolar geometry is a key point in computer vision and the fundamental matrix estimation is the only way to compute it. This article surveys several methods of fundamental matrix estimation which have been classified into linear methods, iterative methods and robust methods. All of these methods have been programmed and their accuracy analysed using real images. A summary, accompanied with experimental results, is given

Bernstein's problem on weighted polynomial approximation

We formulate a necessary and sufficient condition for polynomials to be dense in a space of continuous functions on the real line, with respect to Bernstein's weighted uniform norm. Equivalently, for a positive finite measure [lletra "mu" minúscula de l'alfabet grec] on the real line we give a criterion for density of polynomials in Lp[lletra "mu" minúscula de l'alfabet grec entre parèntesis].

New delay-dependent stability criteria for uncertain neutral systems with mixed time-varying delays and nonlinear perturbations

The problem of stability analysis for a class of neutral systems with mixed time-varying neutral, discrete and distributed delays and nonlinear parameter perturbations is addressed. By introducing a novel Lyapunov-Krasovskii functional and combining the descriptor model transformation, the Leibniz-Newton formula, some free-weighting matrices, and a suitable change of variables, new sufficient conditions are established for the stability of the considered system, which are neutral-delay-dependent, discrete-delay-range dependent, and distributeddelay-dependent. The conditions are presented in terms of linear matrix inequalities (LMIs) and can be efficiently solved using convex programming techniques. Two numerical examples are given to illustrate the efficiency of the proposed method

Application of discriminant function analysis and change-point problem in dating volcanic ashes

The application of Discriminant function analysis (DFA) is not a new idea in the studyof tephrochrology. In this paper, DFA is applied to compositional datasets of twodifferent types of tephras from Mountain Ruapehu in New Zealand and MountainRainier in USA. The canonical variables from the analysis are further investigated witha statistical methodology of change-point problems in order to gain a betterunderstanding of the change in compositional pattern over time. Finally, a special caseof segmented regression has been proposed to model both the time of change and thechange in pattern. This model can be used to estimate the age for the unknown tephrasusing Bayesian statistical calibration

A simulation-based algorithm for solving the resource-assignment problem in satellite telecommunication networks

This paper proposes an heuristic for the scheduling of capacity requests and the periodic assignment of radio resources in geostationary (GEO) satellite networks with star topology, using the Demand Assigned Multiple Access (DAMA) protocol in the link layer, and Multi-Frequency Time Division Multiple Access (MF-TDMA) and Adaptive Coding and Modulation (ACM) in the physical layer.

Algorithm creation and optimization for the crew pairing problem

Algoritmo que optimiza y crea pairings para tripulaciones de líneas aéreas mediante la posterior programación en Java.

Intramolecular basis set superposition error effects on the planarity of benzene and other aromatic molecules: A solution to the problem

Recently, the surprising result that ab initio calculations on benzene and other planar arenes at correlated MP2, MP3, configuration interaction with singles and doubles (CISD), and coupled cluster with singles and doubles levels of theory using standard Pople’s basis sets yield nonplanar minima has been reported. The planar optimized structures turn out to be transition states presenting one or more large imaginary frequencies, whereas single-determinant-based methods lead to the expected planar minima and no imaginary frequencies. It has been suggested that such anomalous behavior can be originated by two-electron basis set incompleteness error. In this work, we show that the reported pitfalls can be interpreted in terms of intramolecular basis set superposition error (BSSE) effects, mostly between the C–H moieties constituting the arenes. We have carried out counterpoise-corrected optimizations and frequency calculations at the Hartree–Fock, B3LYP, MP2, and CISD levels of theory with several basis sets for a number of arenes. In all cases, correcting for intramolecular BSSE fixes the anomalous behavior of the correlated methods, whereas no significant differences are observed in the single-determinant case. Consequently, all systems studied are planar at all levels of theory. The effect of different intramolecular fragment definitions and the particular case of charged species, namely, cyclopentadienyl and indenyl anions, respectively, are also discussed

ILS-ESP An efficient, simple, and parameter-free algorithm for solving the permutation flow-shop problem

From a managerial point of view, the more effcient, simple, and parameter-free (ESP) an algorithm is, the more likely it will be used in practice for solving real-life problems. Following this principle, an ESP algorithm for solving the Permutation Flowshop Sequencing Problem (PFSP) is proposed in this article. Using an Iterated Local Search (ILS) framework, the so-called ILS-ESP algorithm is able to compete in performance with other well-known ILS-based approaches, which are considered among the most effcient algorithms for the PFSP. However, while other similar approaches still employ several parameters that can affect their performance if not properly chosen, our algorithm does not require any particular fine-tuning process since it uses basic "common sense" rules for the local search, perturbation, and acceptance criterion stages of the ILS metaheuristic. Our approach defines a new operator for the ILS perturbation process, a new acceptance criterion based on extremely simple and transparent rules, and a biased randomization process of the initial solution to randomly generate different alternative initial solutions of similar quality -which is attained by applying a biased randomization to a classical PFSP heuristic. This diversification of the initial solution aims at avoiding poorly designed starting points and, thus, allows the methodology to take advantage of current trends in parallel and distributed computing. A set of extensive tests, based on literature benchmarks, has been carried out in order to validate our algorithm and compare it against other approaches. These tests show that our parameter-free algorithm is able to compete with state-of-the-art metaheuristics for the PFSP. Also, the experiments show that, when using parallel computing, it is possible to improve the top ILS-based metaheuristic by just incorporating to it our biased randomization process with a high-quality pseudo-random number generator.

A polynomial algorithm for special case of the one-machine scheduling problem with time-lags

The standard one-machine scheduling problem consists in schedulinga set of jobs in one machine which can handle only one job at atime, minimizing the maximum lateness. Each job is available forprocessing at its release date, requires a known processing timeand after finishing the processing, it is delivery after a certaintime. There also can exists precedence constraints between pairsof jobs, requiring that the first jobs must be completed beforethe second job can start. An extension of this problem consistsin assigning a time interval between the processing of the jobsassociated with the precedence constrains, known by finish-starttime-lags. In presence of this constraints, the problem is NP-hardeven if preemption is allowed. In this work, we consider a specialcase of the one-machine preemption scheduling problem with time-lags, where the time-lags have a chain form, and propose apolynomial algorithm to solve it. The algorithm consist in apolynomial number of calls of the preemption version of the LongestTail Heuristic. One of the applicability of the method is to obtainlower bounds for NP-hard one-machine and job-shop schedulingproblems. We present some computational results of thisapplication, followed by some conclusions.

A mathematical excursion: From the three-door problem to a Cantor-type perfect set

We start with a generalization of the well-known three-door problem:the n-door problem. The solution of this new problem leads us toa beautiful representation system for real numbers in (0,1] as alternated series, known in the literature as Pierce expansions. A closer look to Pierce expansions will take us to some metrical properties of sets defined through the Pierce expansions of its elements. Finally, these metrical properties will enable us to present 'strange' sets, similar to the classical Cantor set.

Locating emergency services with priority rules: The priority queuing covering location problem

One of the assumptions of the Capacitated Facility Location Problem (CFLP) is thatdemand is known and fixed. Most often, this is not the case when managers take somestrategic decisions such as locating facilities and assigning demand points to thosefacilities. In this paper we consider demand as stochastic and we model each of thefacilities as an independent queue. Stochastic models of manufacturing systems anddeterministic location models are put together in order to obtain a formula for thebacklogging probability at a potential facility location.Several solution techniques have been proposed to solve the CFLP. One of the mostrecently proposed heuristics, a Reactive Greedy Adaptive Search Procedure, isimplemented in order to solve the model formulated. We present some computationalexperiments in order to evaluate the heuristics performance and to illustrate the use ofthis new formulation for the CFLP. The paper finishes with a simple simulationexercise.