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Matrix Methods (matrix + methods)
Selected AbstractsMatrix Models as a Tool for Understanding Invasive Plant and Native Plant InteractionsCONSERVATION BIOLOGY, Issue 3 2005DIANE M. THOMSON competencia; invasión biológica; plantas invasoras; modelo matricial; perturbación Abstract:,Demographic matrix models are an increasingly standard way to evaluate the effects of different impacts and management approaches on species of concern. Although invasive species are now considered among the greatest threats to biodiversity, matrix methods have been little used to explore and integrate the potentially complicated effects of invasions on native species. I developed stage-structured models to assess the impacts of invasive grasses on population growth and persistence of a federally listed (U.S.A.) endemic plant, the Antioch Dunes evening primrose (Oenothera deltoides subsp. howellii [Munz] W. Klein). I used these models to evaluate two frequently made assumptions: (1) when rare plant populations decline in invaded habitats, invasive species are the cause and (2) invasive plants suppress rare plants primarily through direct resource competition. I compared two control and two removal matrices based on previous experimental work that showed variable effects of invasive grasses on different life-history stages of O. deltoides. Matrix analysis showed that these effects translated into substantial changes in population growth rates and persistence, with control matrices predicting a mean stochastic population growth rate (,) of 0.86 and removal matrices predicting growth rates from 0.92 to 0.93. Yet even the most optimistic invasive removal scenarios predicted rapid decline and a probability of extinction near one in the next 100 years. Competitive suppression of seedlings had much smaller effects on growth rates than did lowered germination, which probably resulted from thatch accumulation and reduced soil disturbance. These results indicate that although invasive grasses have important effects on the population growth of this rare plant, invasion impacts are not solely responsible for observed declines and are likely to be interacting with other factors such as habitat degradation. Further, changes in the disturbance regime may be as important a mechanism creating these impacts as direct resource competition. My results highlight the value of demographic modeling approaches in creating an integrated assessment of the threats posed by invasive species and the need for more mechanistic studies of invasive plant interactions with native plants. Resumen:,Los modelos demográficos matriciales son una forma cada vez más utilizada para evaluar los efectos de diferentes impactos y métodos de gestión sobre las especies en cuestión. Aunque actualmente se considera a las plantas invasoras entre las mayores amenazas a la biodiversidad, los modelos matriciales han sido poco utilizados para explorar e integrar los efectos potencialmente complicados de las invasiones sobre las especies nativas. Desarrollé modelos estructurados por etapas para evaluar los impactos de pastos invasores sobre el crecimiento poblacional y la persistencia de una especie de planta endémica, enlistada federalmente (E.U.A.), Oenothera deltoides ssp. howellii [Munz] W. Klein. Utilicé estos modelos para evaluar dos suposiciones frecuentes: (1) cuando las poblaciones de plantas raras declinan en hábitats invadidos, las especies invasoras son la causa y (2) las plantas invasoras suprimen a las plantas raras principalmente mediante la competencia directa por recursos. Comparé dos matrices de control y dos de remoción con base en trabajo experimental previo que mostró efectos variables de los pastos invasores sobre las diferentes etapas de la historia de vida de O. deltoides. El análisis de la matriz mostró que estos efectos se tradujeron en cambios sustanciales en las tasas de crecimiento y persistencia de la población, las matrices de control predijeron una tasa media de crecimiento poblacional estocástica (,) de 0.86 y las matrices de remoción predijeron tasas de crecimiento de 0.92-0.93. Aun los escenarios más optimistas de remoción de invasores predijeron una rápida declinación y una probabilidad de extinción en 100 años cerca de uno. La supresión competitiva de plántulas tuvo mucho menor efecto sobre las tasas de crecimiento que la disminución en la germinación, que probablemente resultó de la acumulación de paja y reducción en la perturbación del suelo. Estos resultados indican que, aunque los pastos invasores tienen efectos importantes sobre el crecimiento poblacional de esta planta rara, los impactos de la invasión no son los únicos responsables de las declinaciones observadas y probablemente están interactuando con otros factores como la degradación del hábitat. Más aun, los cambios en el régimen de perturbación pueden ser un mecanismo tan importante en la creación de estos impactos como la competencia directa por recursos. Mis resultados resaltan el valor del enfoque de los modelos demográficos para la evaluación integral de las amenazas de especies invasoras y la necesidad de estudios más mecanicistas de las interacciones de plantas invasoras con plantas nativas. [source] Evaluating low level sequence identitiesFEBS JOURNAL, Issue 2 2001AROM homologous?, Are Aspergillus QUTA A review published several years ago [Hawkins, A.R. & Lamb, H.K. (1995) Eur. J. Biochem. 232, 7,18] proposed that genetic, biochemical and physiological data can override sequence comparison in the determination of homology in instances where structural information is unavailable. Their lead example was the hypothesis that the transcriptional activator protein for quinate catabolism in Aspergillus nidulans, QUTA, is derived from the pentafunctional AROM protein by a gene duplication followed by cleavage [Hawkins, A.R., Lamb, H.K., Moore, J.D. & Roberts, C.F. (1993) Gene136, 49,54]. We tested this hypothesis by a sensitive combination of position-specific log-odds scoring matrix methods. The position-specific log-odds scoring matrices were derived from a large number of 3-dehydroquinate synthase and 5- enolpyruvylshikimate-3-phosphate synthase domains that were proposed to be the domains from the AROM protein that gave rise to the transcriptional activator protein for quinate metabolism. We show that the degree and pattern of similarity between these position-specific log-odds scoring matrices and the transcriptional activator protein for quinate catabolism in A. nidulans is that expected for random sequences of the same composition. This level of similarity provides no support for the suggested gene duplication and cleavage. The lack of any trace of evidence for homology following a comprehensive sequence analysis indicates that the homology hypothesis is without foundation, underlining the necessity to accept only similarity of sequence and/or structure as evidence of evolutionary relatedness. Further, QUTA is homologous throughout its entire length to an extended family of fungal transcriptional regulatory proteins, rendering the hypothesized QUTA,AROM homology even more problematic. [source] Remarks on the updated Hessian matrix methodsINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 6 2003Josep Maria Bofill Abstract Optimizing a function with respect to a set of variables using the quasi-Newton,Raphson method implies updating the Hessian matrix at each iteration. The Broyden,Fletcher,Goldfarb,Shanno update formula is used for minimization and the Murtagh,Sargent,Powell update formula for optimization of first-order saddle points. Two new formulae are proposed to update the Hessian matrix. One of these formulae is derived using exponential weights and should be used to locate first-order saddle points. The second formula is a modification of the TS,Broyden,Fletcher,Goldfarb,Shanno update and could used for both minimum and first-order saddle point optimizations. These two update Hessian matrix formulae present a performance that is the same and in many cases better that the Broyden,Fletcher,Goldfarb,Shanno and Murtagh,Sargent,Powell formulae. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 94: 324,332, 2003 [source] Structured matrix methods for CAGD: an application to computing the resultant of polynomials in the Bernstein basisNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 8 2005Dario A. Bini Abstract We devise a fast fraction-free algorithm for the computation of the triangular factorization of Bernstein,Bezoutian matrices with entries over an integral domain. Our approach uses the Bareiss fraction-free variant of Gaussian elimination, suitably modified to take into account the structural properties of Bernstein,Bezoutian matrices. The algorithm can be used to solve problems in algebraic geometry that arise in computer aided geometric design and computer graphics. In particular, an example of the application of this algorithm to the numerical computation of the intersection points of two planar rational Bézier curves is presented. Copyright © 2005 John Wiley & Sons, Ltd. [source] Determination of pseudophakic accommodation with translation lenses using Purkinje image analysisOPHTHALMIC AND PHYSIOLOGICAL OPTICS, Issue 2 2005Achim Langenbucher Abstract Purpose:, To determine pseudophakic accommodation of an accommodating posterior chamber intraocular lens (translation lens) using Purkinje image analysis and linear matrix methods in the paraxial space. Methods:, A 2 × 2 system matrix was defined for each Purkinje image I to IV using refraction, translation and mirror matrices. Image size (m) and axial image position (z) was determined as an example for an off-axis object (a 0.2 m off-axis object located 0.5 m in front of the cornea.). First, our method was applied to the phakic relaxed (emmetropic) and accommodated (6.96 D) Le Grand eye. Secondly, for demonstration of the applicability of the calculation scheme to the pseudophakic eye, we provide a clinical example where we determine the accommodation amplitude of the translation lens (1 CU, HumanOptics, Erlangen, Germany) from photographed Purkinje images in the relaxed and accommodated state. From the biometric data: axial length 23.7 mm, corneal power 43.5, corneal thickness 550 microns, implanted intraocular lens (IOL) with a refractive power of 20.5 D (shape equi-biconvex, refractive index 1.46), and refractive indices of the cornea, aqueous and vitreous from the Le Grand model eye, we calculated the refractive state and the sizes of Purkinje images I and III initiated from two off-axis light sources. Results:, For the Le Grand model eye, Purkinje image II (z/m = 3.5850 mm/0.0064) is slightly smaller than and directly in front of image I (z/m = 3.8698 mm/0.0077). Purkinje image III (z/m = 10.6097 mm/0.0151) is nearly double the size of image I and during accommodation it moves from the vitreous into the crystalline lens. Purkinje IV (z/m = 4.3244 mm/,0.0059) is inverted, three quarters the size of image I, lies in the crystalline lens and moves slightly towards the retina. For the pseudophakic eye, pseudophakic accommodation of 1.10 D was calculated from the proportion of distances between both Purkinje images I and III in the relaxed (3.04) and accommodated (2.75) state, which is in contrast to the total subjective accommodation of 2.875 D evaluated with an accommodometer. Conclusions:, We present a straightforward mathematical strategy for calculation of the Purkinje images I,IV. Results of our model calculation resemble the values provided by Le Grand. In addition, this approach yields a simple en bloc scheme for determination of pseudophakic accommodation in pseudophakic eyes with accommodative lenses (translation lenses) using Purkinje image photography. [source] Origin of Fueguian-Patagonians: An approach to population history and structure using R matrix and matrix permutation methodsAMERICAN JOURNAL OF HUMAN BIOLOGY, Issue 3 2002Rolando González José A complicated history of isolation between Fueguian and Patagonian groups (originated by the appearance of the Straits of Magellan) as much as differences in population structure and life strategies constitute important factors in the clustering pattern of those groups. The aim of this work was to test several hypotheses about population structure and history of Fueguian-Patagonians to propose a model that incorporates predictions for future studies. R matrix methods and matrix permutation analyses were performed upon a data matrix of craniofacial measurements of 441 skulls divided into nine samples pertaining to six Patagonian and three Fueguian populations. Association of biological distances with three matrices representing several settlement patterns was tested using matrix permutation tests. Results of R matrix study show that the minimum genetic distance obtained confirms separation between Fueguians and Patagonians. Moreover, an analysis of residual variances from the expected regression line confirms admixture between Andean and Pampean populations and Araucanian groups, consistent with ethnohistorical observations. A model representing a long history of isolation between Fueguian and Patagonians, rather than a model emphasizing differences in life-strategies, presented the best correlation with the biological distance matrix. Because similar results were already obtained in archaeological, molecular, and morphological studies, a model for the settlement of Tierra del Fuego is proposed. It is summarized by four main hypotheses that can be tested independently by different disciplines in the future. Am. J. Hum. Biol. 14:308,320, 2002. © 2002 Wiley-Liss, Inc. [source] | |||||||||||||