On optimal completions of incomplete pairwise comparison matrices

An important variant of a key problem for multi-attribute decision making is considered. We study the extension of the pairwise comparison matrix to the case when only partial information is available: for some pairs no comparison is given. It is natural to define the inconsistency of a partially filled matrix as the inconsistency of its best, completely filled completion. We study here the uniqueness problem of the best completion for two weighting methods, the Eigen-vector Method and the Logarithmic Least Squares Method. In both settings we obtain the same simple graph theoretic characterization of the uniqueness. The optimal completion will be unique if and only if the graph associated with the partially defined matrix is connected. Some numerical experiences are discussed at the end of the paper.

Solving the Least Squares Method problem in the AHP for 3 X 3 and 4 X 4 matrices

The Analytic Hierarchy Process (AHP) is one of the most popular methods used in Multi-Attribute Decision Making. The Eigenvector Method (EM) and some distance minimizing methods such as the Least Squares Method (LSM) are of the possible tools for computing the priorities of the alternatives. A method for generating all the solutions of the LSM problem for 3 × 3 and 4 × 4 matrices is discussed in the paper. Our algorithms are based on the theory of resultants.

Solution of the Least Squares Method problem of pairwise comparison matrices

The aim of the paper is to present a new global optimization method for determining all the optima of the Least Squares Method (LSM) problem of pairwise comparison matrices. Such matrices are used, e.g., in the Analytic Hierarchy Process (AHP). Unlike some other distance minimizing methods, LSM is usually hard to solve because of the corresponding nonlinear and non-convex objective function. It is found that the optimization problem can be reduced to solve a system of polynomial equations. Homotopy method is applied which is an efficient technique for solving nonlinear systems. The paper ends by two numerical example having multiple global and local minima.

On Saaty's and Koczkodaj's inconsistencies of pairwise comparison matrices

The aim of the paper is to obtain some theoretical and numerical properties of Saaty’s and Koczkodaj’s inconsistencies of pairwise comparison matrices (PRM). In the case of 3 × 3 PRM, a differentiable one-to-one correspondence is given between Saaty’s inconsistency ratio and Koczkodaj’s inconsistency index based on the elements of PRM. In order to make a comparison of Saaty’s and Koczkodaj’s inconsistencies for 4 × 4 pairwise comparison matrices, the average value of the maximal eigenvalues of randomly generated n × n PRM is formulated, the elements aij (i < j) of which were randomly chosen from the ratio scale ... ... with equal probability 1/(2M − 1) and a ji is defined as 1/a ij . By statistical analysis, the empirical distributions of the maximal eigenvalues of the PRM depending on the dimension number are obtained. As the dimension number increases, the shape of distributions gets similar to that of the normal ones. Finally, the inconsistency of asymmetry is dealt with, showing a different type of inconsistency.

On pairwise comparison matrices that can be made consistent by the modification of a few elements

Pairwise comparison matrices are often used in Multi-attribute Decision Making forweighting the attributes or for the evaluation of the alternatives with respect to a criteria. Matrices provided by the decision makers are rarely consistent and it is important to index the degree of inconsistency. In the paper, the minimal number of matrix elements by the modification of which the pairwise comparison matrix can be made consistent is examined. From practical point of view, the modification of 1, 2, or, for larger matrices, 3 elements seems to be relevant. These cases are characterized by using the graph representation of the matrices. Empirical examples illustrate that pairwise comparison matrices that can be made consistent by the modification of a few elements are present in the applications.

Incomplete pairwise comparison matrices and weighting methods

A special class of preferences, given by a directed acyclic graph, is considered. They are represented by incomplete pairwise comparison matrices as only partial information is available: for some pairs no comparison is given in the graph. A weighting method satisfies the property linear order preservation if it always results in a ranking such that an alternative directly preferred to another does not have a lower rank. We study whether two procedures, the Eigenvector Method and the Logarithmic Least Squares Method meet this axiom. Both weighting methods break linear order preservation, moreover, the ranking according to the Eigenvector Method depends on the incomplete pairwise comparison representation chosen.

Eddy covariance and meteorological tower in a long-hydroperiod Everglades marsh during the height of the wet season, 2008 (at SRS-2), Shark River Slough

This material is based upon work supported by the National Science Foundation through the Florida Coastal Everglades Long-Term Ecological Research program under Cooperative Agreements #DBI-0620409 and #DEB-9910514. This image is made available for non-commercial or educational use only.

Eddy covariance tower in long-hydroperiod Everglades marsh in mid-dry season, 2009 (at SRS-2), Shark River Slough

This material is based upon work supported by the National Science Foundation through the Florida Coastal Everglades Long-Term Ecological Research program under Cooperative Agreements #DBI-0620409 and #DEB-9910514. This image is made available for non-commercial or educational use only.

The development of direct ultra-fast PCR for forensic genotyping using short channel microfluidic systems with enhanced sieving matrices

There are situations in which it is very important to quickly and positively identify an individual. Examples include suspects detained in the neighborhood of a bombing or terrorist incident, individuals detained attempting to enter or leave the country, and victims of mass disasters. Systems utilized for these purposes must be fast, portable, and easy to maintain. The goal of this project was to develop an ultra fast, direct PCR method for forensic genotyping of oral swabs. The procedure developed eliminates the need for cellular digestion and extraction of the sample by performing those steps in the PCR tube itself. Then, special high-speed polymerases are added which are capable of amplifying a newly developed 7 loci multiplex in under 16 minutes. Following the amplification, a postage stamp sized microfluidic device equipped with specially designed entangled polymer separation matrix, yields a complete genotype in 80 seconds. The entire process is rapid and reliable, reducing the time from sample to genotype from 1-2 days to under 20 minutes. Operation requires minimal equipment and can be easily performed with a small high-speed thermal-cycler, reagents, and a microfluidic device with a laptop. The system was optimized and validated using a number of test parameters and a small test population. The overall precision was better than 0.17 bp and provided a power of discrimination greater than 1 in 106. The small footprint, and ease of use will permit this system to be an effective tool to quickly screen and identify individuals detained at ports of entry, police stations and remote locations. The system is robust, portable and demonstrates to the forensic community a simple solution to the problem of rapid determination of genetic identity.

Elemental analysis of biological matrices by laser ablation high resolution inductively coupled plasma mass spectrometry (LA-HR-ICP-MS) and high resolution inductively coupled plasma mass spectrometry (HR -ICP -MS)

The need for elemental analysis of biological matrices such as bone, teeth, and plant matter for sourcing purposes has emerged within the forensic and geochemical laboratories. Trace elemental analyses for the comparison of materials such as glass by inductively coupled plasma mass spectrometry (ICP-MS) and laser ablation ICP-MS has been shown to offer a high degree of discrimination between different manufacturing sources. Unit resolution ICP-MS instruments may suffer from some polyatomic interferences including 40Ar16O+, 40Ar 16O1H+, and 40Ca 16O+ that affect iron measurement at trace levels. Iron is an important element in the analysis of glass and also of interest for the analysis of several biological matrices. A comparison of the analytical performance of two different ICP-MS systems for iron analysis in glass for determining the method detection limits (MDLs), accuracy, and precision of the measurement is presented. Acid digestion and laser ablation methods are also compared. Iron polyatomic interferences were reduced or resolved by using dynamic reaction cell and high resolution ICP-MS. MDLs as low as 0.03 μg g-1 and 0.14 μg g-1 for laser ablation and solution based analyses respectively were achieved. The use of helium as a carrier gas demonstrated improvement in the detection limits of both iron isotopes (56Fe and 57Fe) in medium resolution for the HR-ICP-MS and with a dynamic reaction cell (DRC) coupled to a quadrupole ICP-MS system. ^ The development and application of robust analytical methods for the quantification of trace elements in biological matrices has lead to a better understanding of the potential utility of these measurements in forensic chemical analyses. Standard reference materials (SRMs) were used in the development of an analytical method using HR-ICP-MS and LA-HR-ICP-MS that was subsequently applied on the analysis of real samples. Bone, teeth and ashed marijuana samples were analyzed with the developed method. ^ Elemental analysis of bone samples from 12 different individuals provided discrimination between individuals, when femur and humerus bones were considered separately. Discrimination of 14 teeth samples based on elemental composition was achieved with the exception of one case where samples from the same individual were not associated with each other. The discrimination of 49 different ashed plant (cannabis) samples was achieved using the developed method. ^

Modeling Light Use Efficiency in a Subtropical Mangrove Forest Equipped with CO2 Eddy Covariance °C

Despite the importance of mangrove ecosystems in the global carbon budget, the relationships between environmental drivers and carbon dynamics in these forests remain poorly understood. This limited understanding is partly a result of the challenges associated with in situ flux studies. Tower-based CO2 eddy covariance (EC) systems are installed in only a few mangrove forests worldwide, and the longest EC record from the Florida Everglades contains less than 9 years of observations. A primary goal of the present study was to develop a methodology to estimate canopy-scale photosynthetic light use efficiency in this forest. These tower-based observations represent a basis for associating CO2 fluxes with canopy light use properties, and thus provide the means for utilizing satellite-based reflectance data for larger scale investigations. We present a model for mangrove canopy light use efficiency utilizing the enhanced green vegetation index (EVI) derived from the Moderate Resolution Imaging Spectroradiometer (MODIS) that is capable of predicting changes in mangrove forest CO2 fluxes caused by a hurricane disturbance and changes in regional environmental conditions, including temperature and salinity. Model parameters are solved for in a Bayesian framework. The model structure requires estimates of ecosystem respiration (RE), and we present the first ever tower-based estimates of mangrove forest RE derived from nighttime CO2 fluxes. Our investigation is also the first to show the effects of salinity on mangrove forest CO2 uptake, which declines 5% per each 10 parts per thousand (ppt) increase in salinity. Light use efficiency in this forest declines with increasing daily photosynthetic active radiation, which is an important departure from the assumption of constant light use efficiency typically applied in satellite-driven models. The model developed here provides a framework for estimating CO2 uptake by these forests from reflectance data and information about environmental conditions.

Environmental analysis of polar herbicides in complex organic-rich matrices by high performance liquid chromatography atmospheric pressure ionization mass spectrometry (HPLC-API-MS)

A comprehensive forensic investigation of sensitive ecosystems in the Everglades Area is presented. Assessing the background levels of contamination in these ecosystems represents a vital resource to build up forensic evidence required to enforce future environmental crimes within the studied areas. This investigation presents the development and validation of a fractionation and isolation method for two families of herbicides commonly applied in the vicinity of the study area, including phenoxy acids like 2,4-D, MCPA, and silvex; as well as the most common triazine-based herbicides like atrazine, prometyne, simazine and related metabolites like DIA and DEA. Accelerated solvent extraction (ASE) and solid phase extraction (SPE) were used to isolate the analytes from abiotic matrices containing large amounts of organic material. Atmospheric-pressure ionization (API) with electrospray ionization in negative mode (ESP-), and Chemical Ionization in the positive mode (APCI+) were used to perform the characterization of the herbicides of interest.

Environmental stability affects phenotypic evolution in a globally distributed marine picoplankton

Marine phytoplankton can evolve rapidly when confronted with aspects of climate change because of their large population sizes and fast generation times. Despite this, the importance of environment fluctuations, a key feature of climate change, has received little attention-selection experiments with marine phytoplankton are usually carried out in stable environments and use single or few representatives of a species, genus or functional group. Here we investigate whether and by how much environmental fluctuations contribute to changes in ecologically important phytoplankton traits such as C:N ratios and cell size, and test the variability of changes in these traits within the globally distributed species Ostreococcus. We have evolved 16 physiologically distinct lineages of Ostreococcus at stable high CO2 (1031±87?µatm CO2, SH) and fluctuating high CO2 (1012±244?µatm CO2, FH) for 400 generations. We find that although both fluctuation and high CO2 drive evolution, FH-evolved lineages are smaller, have reduced C:N ratios and respond more strongly to further increases in CO2 than do SH-evolved lineages. This indicates that environmental fluctuations are an important factor to consider when predicting how the characteristics of future phytoplankton populations will have an impact on biogeochemical cycles and higher trophic levels in marine food webs.

Optimización de la factorización de matrices no negativas en Bioinformática

En los últimos años se ha incrementado el interés de la comunidad científica en la Factorización de matrices no negativas (Non-negative Matrix Factorization, NMF). Este método permite transformar un conjunto de datos de grandes dimensiones en una pequeña colección de elementos que poseen semántica propia en el contexto del análisis. En el caso de Bioinformática, NMF suele emplearse como base de algunos métodos de agrupamiento de datos, que emplean un modelo estadístico para determinar el número de clases más favorable. Este modelo requiere de una gran cantidad de ejecuciones de NMF con distintos parámetros de entrada, lo que representa una enorme carga de trabajo a nivel computacional. La mayoría de las implementaciones de NMF han ido quedando obsoletas ante el constante crecimiento de los datos que la comunidad científica busca analizar, bien sea porque los tiempos de cómputo llegan a alargarse hasta convertirse en inviables, o porque el tamaño de esos datos desborda los recursos del sistema. Por ello, esta tesis doctoral se centra en la optimización y paralelización de la factorización NMF, pero no solo a nivel teórico, sino con el objetivo de proporcionarle a la comunidad científica una nueva herramienta para el análisis de datos de origen biológico. NMF expone un alto grado de paralelismo a nivel de datos, de granularidad variable; mientras que los métodos de agrupamiento mencionados anteriormente presentan un paralelismo a nivel de cómputo, ya que las diversas instancias de NMF que se ejecutan son independientes. Por tanto, desde un punto de vista global, se plantea un modelo de optimización por capas donde se emplean diferentes tecnologías de alto rendimiento...