Extensions of discrete triangular distributions and boundary bias in kernel estimation for discrete functions

Asymmetric discrete triangular distributions are introduced in order to extend the symmetric ones serving for discrete associated kernels in the nonparametric estimation for discrete functions. The extension from one to two orders around the mode provides a large family of discrete distributions having a finite support. Establishing a bridge between Dirac and discrete uniform distributions, some different shapes are also obtained and their properties are investigated. In particular, the mean and variance are pointed out. Applications to discrete kernel estimators are given with a solution to a boundary bias problem. (C) 2010 Elsevier B.V. All rights reserved.

A review of peer support in the context of cancer

Peer support interventions for people with cancer, their families, and friends have been widely used throughout the world. The present study reviewed the research literature on psychosocial oncology over the past decade to assess the prevalence and contribution of articles on peer support. Using CD-Rom databases, 25 articles were retrieved for review. In each article, patients or their family members were the target group for supportive interventions, which were primarily for the delivery of peer support and included either a qualitative or quantitative evaluation of the program. A definitional taxonomy for peer support interventions, which identified eight discrete settings, was derived from three key dimensions: style of supervision, interpersonal context, and mode of delivery. The studies suggested that peer support programs help by providing emotional and informational support from the perspective of shared personal experience. However, a paucity of research-particularly randomized controlled trials-was noted. The reasons may include inherent difficulties in isolating for study what is essentially a naturalistically occurring interpersonal dynamic from the complex social and community contexts from which it emanates. The authors discuss the gap between practice and theory in this area and recommend a broader and more inclusive view of supportive care for people with cancer. (C) 2003 by The Haworth Press, Inc. All rights reserved.

A communication support for real-time distributed computer controlled systems

In this paper, we analyse the ability of P-NET [1] fieldbus to cope with the timing requirements of a Distributed Computer Control System (DCCS), where messages associated to discrete events should be made available within a maximum bound time. The main objective of this work is to analyse how the network access and queueing delays, imposed by P-NET’s virtual token Medium Access Control (MAC) mechanism, affect the realtime behaviour of the supported DCCS.

Compositional analysis of bivariate discrete probabilities

A joint distribution of two discrete random variables with finite support can be displayed as a two way table of probabilities adding to one. Assume that this table hasn rows and m columns and all probabilities are non-null. This kind of table can beseen as an element in the simplex of n · m parts. In this context, the marginals areidentified as compositional amalgams, conditionals (rows or columns) as subcompositions. Also, simplicial perturbation appears as Bayes theorem. However, the Euclideanelements of the Aitchison geometry of the simplex can also be translated into the tableof probabilities: subspaces, orthogonal projections, distances.Two important questions are addressed: a) given a table of probabilities, which isthe nearest independent table to the initial one? b) which is the largest orthogonalprojection of a row onto a column? or, equivalently, which is the information in arow explained by a column, thus explaining the interaction? To answer these questionsthree orthogonal decompositions are presented: (1) by columns and a row-wise geometric marginal, (2) by rows and a columnwise geometric marginal, (3) by independenttwo-way tables and fully dependent tables representing row-column interaction. Animportant result is that the nearest independent table is the product of the two (rowand column)-wise geometric marginal tables. A corollary is that, in an independenttable, the geometric marginals conform with the traditional (arithmetic) marginals.These decompositions can be compared with standard log-linear models.Key words: balance, compositional data, simplex, Aitchison geometry, composition,orthonormal basis, arithmetic and geometric marginals, amalgam, dependence measure,contingency table

Improving Transportation and Warehousing Efficiency with Simulation-Based Decision Support Systems

Transportation and warehousing are large and growing sectors in the society, and their efficiency is of high importance. Transportation also has a large share of global carbondioxide emissions, which are one the leading causes of anthropogenic climate warming. Various countries have agreed to decrease their carbon emissions according to the Kyoto protocol. Transportation is the only sector where emissions have steadily increased since the 1990s, which highlights the importance of transportation efficiency. The efficiency of transportation and warehousing can be improved with the help of simulations, but models alone are not sufficient. This research concentrates on the use of simulations in decision support systems. Three main simulation approaches are used in logistics: discrete-event simulation, systems dynamics, and agent-based modeling. However, individual simulation approaches have weaknesses of their own. Hybridization (combining two or more approaches) can improve the quality of the models, as it allows using a different method to overcome the weakness of one method. It is important to choose the correct approach (or a combination of approaches) when modeling transportation and warehousing issues. If an inappropriate method is chosen (this can occur if the modeler is proficient in only one approach or the model specification is not conducted thoroughly), the simulation model will have an inaccurate structure, which in turn will lead to misleading results. This issue can further escalate, as the decision-maker may assume that the presented simulation model gives the most useful results available, even though the whole model can be based on a poorly chosen structure. In this research it is argued that simulation- based decision support systems need to take various issues into account to make a functioning decision support system. The actual simulation model can be constructed using any (or multiple) approach, it can be combined with different optimization modules, and there needs to be a proper interface between the model and the user. These issues are presented in a framework, which simulation modelers can use when creating decision support systems. In order for decision-makers to fully benefit from the simulations, the user interface needs to clearly separate the model and the user, but at the same time, the user needs to be able to run the appropriate runs in order to analyze the problems correctly. This study recommends that simulation modelers should start to transfer their tacit knowledge to explicit knowledge. This would greatly benefit the whole simulation community and improve the quality of simulation-based decision support systems as well. More studies should also be conducted by using hybrid models and integrating simulations with Graphical Information Systems.

Improving strategic decision-making with simulation based decision support systems

Combating climate change is one of the key tasks of humanity in the 21st century. One of the leading causes is carbon dioxide emissions due to usage of fossil fuels. Renewable energy sources should be used instead of relying on oil, gas, and coal. In Finland a significant amount of energy is produced using wood. The usage of wood chips is expected to increase in the future significantly, over 60 %. The aim of this research is to improve understanding over the costs of wood chip supply chains. This is conducted by utilizing simulation as the main research method. The simulation model utilizes both agent-based modelling and discrete event simulation to imitate the wood chip supply chain. This thesis concentrates on the usage of simulation based decision support systems in strategic decision-making. The simulation model is part of a decision support system, which connects the simulation model to databases but also provides a graphical user interface for the decisionmaker. The main analysis conducted with the decision support system concentrates on comparing a traditional supply chain to a supply chain utilizing specialized containers. According to the analysis, the container supply chain is able to have smaller costs than the traditional supply chain. Also, a container supply chain can be more easily scaled up due to faster emptying operations. Initially the container operations would only supply part of the fuel needs of a power plant and it would complement the current supply chain. The model can be expanded to include intermodal supply chains as due to increased demand in the future there is not enough wood chips located close to current and future power plants.

Notes on PCA, Regularization, Sparsity and Support Vector Machines

We derive a new representation for a function as a linear combination of local correlation kernels at optimal sparse locations and discuss its relation to PCA, regularization, sparsity principles and Support Vector Machines. We first review previous results for the approximation of a function from discrete data (Girosi, 1998) in the context of Vapnik"s feature space and dual representation (Vapnik, 1995). We apply them to show 1) that a standard regularization functional with a stabilizer defined in terms of the correlation function induces a regression function in the span of the feature space of classical Principal Components and 2) that there exist a dual representations of the regression function in terms of a regularization network with a kernel equal to a generalized correlation function. We then describe the main observation of the paper: the dual representation in terms of the correlation function can be sparsified using the Support Vector Machines (Vapnik, 1982) technique and this operation is equivalent to sparsify a large dictionary of basis functions adapted to the task, using a variation of Basis Pursuit De-Noising (Chen, Donoho and Saunders, 1995; see also related work by Donahue and Geiger, 1994; Olshausen and Field, 1995; Lewicki and Sejnowski, 1998). In addition to extending the close relations between regularization, Support Vector Machines and sparsity, our work also illuminates and formalizes the LFA concept of Penev and Atick (1996). We discuss the relation between our results, which are about regression, and the different problem of pattern classification.

Compositional analysis of bivariate discrete probabilities

A joint distribution of two discrete random variables with finite support can be displayed as a two way table of probabilities adding to one. Assume that this table has n rows and m columns and all probabilities are non-null. This kind of table can be seen as an element in the simplex of n · m parts. In this context, the marginals are identified as compositional amalgams, conditionals (rows or columns) as subcompositions. Also, simplicial perturbation appears as Bayes theorem. However, the Euclidean elements of the Aitchison geometry of the simplex can also be translated into the table of probabilities: subspaces, orthogonal projections, distances. Two important questions are addressed: a) given a table of probabilities, which is the nearest independent table to the initial one? b) which is the largest orthogonal projection of a row onto a column? or, equivalently, which is the information in a row explained by a column, thus explaining the interaction? To answer these questions three orthogonal decompositions are presented: (1) by columns and a row-wise geometric marginal, (2) by rows and a columnwise geometric marginal, (3) by independent two-way tables and fully dependent tables representing row-column interaction. An important result is that the nearest independent table is the product of the two (row and column)-wise geometric marginal tables. A corollary is that, in an independent table, the geometric marginals conform with the traditional (arithmetic) marginals. These decompositions can be compared with standard log-linear models. Key words: balance, compositional data, simplex, Aitchison geometry, composition, orthonormal basis, arithmetic and geometric marginals, amalgam, dependence measure, contingency table

Discrete Dynamical Systems

Exercises and solutions for a third or fourth year maths course. Diagrams for the questions are all together in the support.zip file, as .eps files

Model catalyst studies of the strong metal-support interaction: Surface structure identified by STM on Pd nanoparticles on TiO2(110)

Model catalysts of Pd nanoparticles and films on TiO2 (I 10) were fabricated by metal vapour deposition (MVD). Molecular beam measurements show that the particles are active for CO adsorption, with a global sticking probability of 0.25, but that they are deactivated by annealing above 600 K, an effect indicative of SMSI. The Pd nanoparticles are single crystals oriented with their (I 11) plane parallel to the surface plane of the titania. Analysis of the surface by atomic resolution STM shows that new structures have formed at the surface of the Pd nanoparticles and films after annealing above 800 K. There are only two structures, a zigzag arrangement and a much more complex "pinwheel" structure. The former has a unit cell containing 7 atoms, and the latter is a bigger unit cell containing 25 atoms. These new structures are due to an overlayer of titania that has appeared on the surface of the Pd nanoparticles after annealing, and it is proposed that the surface layer that causes the SMSI effect is a mixed alloy of Pd and Ti, with only two discrete ratios of atoms: Pd/Ti of 1: 1 (pinwheel) and 1:2 (zigzag). We propose that it is these structures that cause the SMSI effect. (c) 2005 Elsevier Inc. All rights reserved.

Bayesian analysis of correlated evolution of discrete characters by reversible-jump Markov chain Monte Carlo

We describe a Bayesian method for investigating correlated evolution of discrete binary traits on phylogenetic trees. The method fits a continuous-time Markov model to a pair of traits, seeking the best fitting models that describe their joint evolution on a phylogeny. We employ the methodology of reversible-jump ( RJ) Markov chain Monte Carlo to search among the large number of possible models, some of which conform to independent evolution of the two traits, others to correlated evolution. The RJ Markov chain visits these models in proportion to their posterior probabilities, thereby directly estimating the support for the hypothesis of correlated evolution. In addition, the RJ Markov chain simultaneously estimates the posterior distributions of the rate parameters of the model of trait evolution. These posterior distributions can be used to test among alternative evolutionary scenarios to explain the observed data. All results are integrated over a sample of phylogenetic trees to account for phylogenetic uncertainty. We implement the method in a program called RJ Discrete and illustrate it by analyzing the question of whether mating system and advertisement of estrus by females have coevolved in the Old World monkeys and great apes.

SUPPORT OF MAXIMIZING MEASURES FOR TYPICAL C(0) DYNAMICS ON COMPACT MANIFOLDS

Given a compact manifold X, a continuous function g : X -> IR, and a map T : X -> X, we study properties of the T-invariant Borel probability measures that maximize the integral of g. We show that if X is a n-dimensional connected Riemaniann manifold, with n >= 2, then the set of homeomorphisms for which there is a maximizing measure supported on a periodic orbit is meager. We also show that, if X is the circle, then the ""topological size"" of the set of endomorphisms for which there are g maximizing measures with support on a periodic orbit depends on properties of the function g. In particular, if g is C(1), it has interior points.

On computational aspects of discrete Sobolev inner products on the unit circle

In this paper, we show how to compute in O(n2) steps the Fourier coefficients associated with the Gelfand-Levitan approach for discrete Sobolev orthogonal polynomials on the unit circle when the support of the discrete component involving derivatives is located outside the closed unit disk. As a consequence, we deduce the outer relative asymptotics of these polynomials in terms of those associated with the original orthogonality measure. Moreover, we show how to recover the discrete part of our Sobolev inner product. © 2013 Elsevier Inc. All rights reserved.

Patients' preferences for a prostate cancer consultation, a discrete choice experiment

Four basic medical decision making models are commonly discussed in the literature in reference to physician-patient interactions. All fall short in their attempt to capture the nuances of physician-patient interactions, and none satisfactorily address patients' preferences for communication and other attributes of care. Prostate cancer consultations are one setting where preferences matter and are likely to vary among patients. Fortunately, discrete choice experiments are capable of casting light on patients' preferences for communication and other attributes of value that make up a consultation before the consultation occurs, which is crucial if patients are to derive the most utility from the process of reaching a decision as well as the decision itself. The results of my dissertation provide strong support to the notion that patients, at least in the hypothetical setting of a DCE, have identifiable preferences for the attributes of a prostate cancer consultation and that those preferences are capable of being elicited before a consultation takes place. Further, patients' willingness-to-pay for the non-cost attributes of the consultation is surprisingly robust to a variety of individual level variables of interest. ^

(Table S2) Cell concentrations of individual and combined Alexandrium spp. and phylogenetic groups as obtained by qPCR assay and Utermöhl counts, as well as particulate PSP toxin concentrations from discrete water depths

Molecular methods provide promising tools for routine detection and quantification of toxic microalgae in plankton samples. To this end, novel TaqMan minor groove binding probes and primers targeting the small (SSU) or large (LSU) ribosomal subunit (rRNA) were developed for two species of the marine dinoflagellate genus Alexandrium (A. minutum, A. tamutum) and for three groups/ribotypes of the A. tamarense species complex: Group I/North American (NA), Group II/Mediterranean (ME) and Group III/Western European (WE). Primers and probes for real-time quantitative PCR (qPCR) were species-specific and highly efficient when tested in qPCR assays for cross-validation with pure DNA from cultured Alexandrium strains. Suitability of the qPCR assays as molecular tools for the detection and estimation of relative cell abundances of Alexandrium species and groups was evaluated from samples of natural plankton assemblages along the Scottish east coast. The results were compared with inverted microscope cell counts (Utermöhl technique) of Alexandrium spp. and associated paralytic shellfish poisoning (PSP) toxin concentrations. The qPCR assays indicated that A. tamarense (Group I) and A. tamutum were the most abundant Alexandrium taxa and both were highly positively correlated with PSP toxin content of plankton samples. Cells of A. tamarense (Group III) were present at nearly all stations but in low abundance. Alexandrium minutum and A. tamarense (Group II) cells were not detected in any of the samples, thereby arguing for their absence from the specific North Sea region, at least at the time of the survey. The sympatric occurrence of A. tamarense Group I and Group III gives further support to the hypothesis that the groups/ribotypes of the A. tamarense species complex are cryptic species rather than variants belonging to the same species.