Generalization of Ehrlich-Kjurkchiev Method for Multiple Roots of Algebraic Equations

In this paper a new method which is a generalization of the Ehrlich-Kjurkchiev method is developed. The method allows to find simultaneously all roots of the algebraic equation in the case when the roots are supposed to be multiple with known multiplicities. The offered generalization does not demand calculation of derivatives of order higher than first simultaneously keeping quaternary rate of convergence which makes this method suitable for application from practical point of view.

Simultaneous effects of ferulic and vanillic acids on peroxidase and phenylalanine ammonia-lyase in soybean (Glycine max) roots

Simultaneous effects of ferulic (FA) and vanillic (VA) acids on peroxidase (POD, EC 1.11.1.7) and phenylalanine ammonia-lyase (PAL, EC 4.3.1.5) activities on soybean (Glycine max (L.) MERR.) root growth were analyzed. Three-day-old seedlings were cultivated in nutrient solution containing FA or VA (0.5 mM; 1.0 mM or equimolar mixtures) for 48 h. Acting alone, both compounds (at 0.5 or 1.0 mM) decreased root length (RL), fresh weight (FW), dry weight (DW) and increased soluble POD and cell wall (CW)-bound POD activities. At 1.0 mM, FA increased (but VA decreased) the PAL activity. Acting simultaneously, the effects of the allelochemical interaction were lower than the sum of the effects of each compound tested separately, suggesting antagonism.

Simultaneous X-ray imaging of plant root growth and water uptake in thin-slab systems

Direct and simultaneous observation of root growth and plant water uptake is difficult because soils are opaque. X-ray imaging techniques such as projection radiography or Computer Tomography (CT) offer a partial alternative to such limitations. Nevertheless, there is a trade-off between resolution, large field-of-view and 3-dimensionality: With the current state of the technology, it is possible to have any two. In this study, we used X-ray transmission through thin-slab systems to monitor transient saturation fields that develop around roots as plants grow. Although restricted to 2-dimensions, this approach offers a large field-of-view together with high spatial and dynamic resolutions. To illustrate the potential of this technology, we grew peas in 1 cm thick containers filled with soil and imaged them at regular intervals. The dynamics of both the root growth and the water content field that developed around the roots could be conveniently monitored. Compared to other techniques such as X-ray CT, our system is relatively inexpensive and easy to implement. It can potentially be applied to study many agronomic problems, such as issues related to the impact of soil constraints (physical, chemical or biological) on root development.

Contrasts in the basins of attraction of structurally identical iterative root finding methods

A numerical comparison is performed between three methods of third order with the same structure, namely BSC, Halley’s and Euler–Chebyshev’s methods. As the behavior of an iterative method applied to a nonlinear equation can be highly sensitive to the starting points, the numerical comparison is carried out, allowing for complex starting points and for complex roots, on the basins of attraction in the complex plane. Several examples of algebraic and transcendental equations are presented.

The simultaneous conjugacy problem in groups of piecewise linear functions

Guba and Sapir asked, in their joint paper [8], if the simultaneous conjugacy problem was solvable in Diagram Groups or, at least, for Thompson's group F. We give an elementary proof for the solution of the latter question. This relies purely on the description of F as the group of piecewise linear orientation-preserving homeomorphisms of the unit. The techniques we develop allow us also to solve the ordinary conjugacy problem as well, and we can compute roots and centralizers. Moreover, these techniques can be generalized to solve the same questions in larger groups of piecewise-linear homeomorphisms.

Combination of fluorescent reporters for simultaneous monitoring of root colonization and antifungal gene expression by a biocontrol pseudomonad on cereals with flow cytometry.

Some root-associated pseudomonads sustain plant growth by suppressing root diseases caused by pathogenic fungi. We investigated to which extent select cereal cultivars influence expression of relevant biocontrol traits (i.e., root colonization efficacy and antifungal activity) in Pseudomonas fluorescens CHA0. In this representative plant-beneficial bacterium, the antifungal metabolites 2,4-diacetylphloroglucinol (DAPG), pyrrolnitrin (PRN), pyoluteorin (PLT), and hydrogen cyanide (HCN) are required for biocontrol. To monitor host plant effects on the expression of biosynthetic genes for these compounds on roots, we developed fluorescent dual-color reporters suited for flow cytometric analysis using fluorescence-activated cell sorting (FACS). In the dual-label strains, the constitutively expressed red fluorescent protein mCherry served as a cell tag and marker for root colonization, whereas reporter fusions based on the green fluorescent protein allowed simultaneous recording of antifungal gene expression within the same cell. FACS analysis revealed that expression of DAPG and PRN biosynthetic genes was promoted in a cereal rhizosphere, whereas expression of PLT and HCN biosynthetic genes was markedly less sustained. When analyzing the response of the bacterial reporters on roots of a selection of wheat, spelt, and triticale cultivars, we were able to detect subtle species- and cultivar-dependent differences in colonization and DAPG and HCN gene expression levels. The expression of these biocontrol traits was particularly favored on roots of one spelt cultivar, suggesting that a careful choice of pseudomonad-cereal combinations might be beneficial to biocontrol. Our approach may be useful for selective single-cell level analysis of plant effects in other bacteria-root interactions.

Genetic parameters and simultaneous selection for root yield, adaptability and stability of cassava genotypes

The objective of this work was to estimate genetic parameters and to evaluate simultaneous selection for root yield and for adaptability and stability of cassava genotypes. The effects of genotypes were assumed as fixed and random, and the mixed model methodology (REML/Blup) was used to estimate genetic parameters and the harmonic mean of the relative performance of genotypic values (HMRPGV), for simultaneous selection purposes. Ten genotypes were analyzed in a complete randomized block design, with four replicates. The experiment was carried out in the municipalities of Altamira, Santarém, and Santa Luzia do Pará in the state of Pará, Brazil, in the growing seasons of 2009/2010, 2010/2011, and 2011/2012. Roots were harvested 12 months after planting, in all tested locations. Root yield had low coefficients of genotypic variation (4.25%) and broad-sense heritability of individual plots (0.0424), which resulted in low genetic gain. Due to the low genotypic correlation (0.15), genotype classification as to root yield varied according to the environment. Genotypes CPATU 060, CPATU 229, and CPATU 404 stood out as to their yield, adaptability, and stability.

The Roots of Neurofibromas in Neurofibromatosis 1 — A Question of Multipotency, Differentiation and Hiding

Neurofibromatosis type 1 (NF1) is an autosomal dominant cancer predisposition syndrome that affects about 1 in 3500 individuals worldwide. NF1 is caused by mutations in the NF1 gene that encodes the tumor suppressor protein neurofibromin, an inactivator of the Ras oncogene. The hallmarks of NF1 include pigmentary lesions of the skin, Lisch nodules of the iris and cutaneous neurofibromas. Cutaneous neurofibromas are benign tumors composed of all the cell types of normal peripheral nerve. The traditional view of neurofibroma development has been that cutaneous neurofibromas arise from the disruption of the small nerve tributaries of the skin and subsequent proliferation of the resident cells. The second hit mutation in the NF1 gene has been considered as a prerequisite for neurofibroma development. The second hit is detectable in a subpopulation of primary Schwann cells cultured from neurofibromas. This thesis challenges the traditional concept of neurofibroma development. The results show that cutaneous neurofibromas are intimately associated with hair follicular structures and contain multipotent precursor cells (NFPs), suggesting that neurofibromas may arise from the multipotent cells which reside in hair follicles. Furthermore, this study presents that neurofibroma-derived Schwann cells that harbor bi-allelic inactivation in the NF1 gene express HLA class II genes and may act as nonprofessional antigen presenting cells. The CD4- and FoxP3-positive cells detected in cutaneous neurofibromas suggest that these cells may represent regulatory T cells (Tregs) which interact with HLA II –positive cells and aid the tumor cells in hiding from the immune system and are thus mediators of immune tolerance. This thesis also investigated neurofibroma development in the oral cavity and the use of different biomarkers to characterize cellular differentiation in neurofibromas. The results revealed that oral neurofibromas are not rare, but they usually appear as solitary lesions contrary to multiple cutaneous neurofibromas and present high heterogeneity within and between tumors. The use of class III beta-tubulin as a marker for neuronal differentiation led to an unexpected finding showing that multiple cell types express class III beta-tubulin during mitosis. The increased understanding of the multipotency of tumor cells, cellular differentiation and ability to hide from immune system will aid in the development of future treatments. Specifically, targeting Tregs in NF1 patients could provide a novel therapeutic approach to interfere with the development of neurofibromas.

Simultaneous extraction of order parameters and orientational distribution fuctions from 31[superscript]P NMR spectra of magnetically partially oriented phospholipid bilayers

Order parameter profiles extracted from the NMR spectra of model membranes are a valuable source of information about their structure and molecular motions. To al1alyze powder spectra the de-Pake-ing (numerical deconvolution) ~echnique can be used, but it assumes a random (spherical) dist.ribution of orientations in the sample. Multilamellar vesicles are known to deform and orient in the strong magnetic fields of NMR magnets, producing non-spherical orientation distributions. A recently developed technique for simultaneously extracting the anisotropies of the system as well as the orientation distributions is applied to the analysis of partially magnetically oriented 31p NMR spectra of phospholipids. A mixture of synthetic lipids, POPE and POPG, is analyzed to measure distortion of multilamellar vesicles in a magnetic field. In the analysis three models describing the shape of the distorted vesicles are examined. Ellipsoids of rotation with a semiaxis ratio of about 1.14 are found to provide a good approximation of the shape of the distorted vesicles. This is in reasonable agreement with published experimental work. All three models yield clearly non-spherical orientational distributions, as well as a precise measure of the anisotropy of the chemical shift. Noise in the experimental data prevented the analysis from concluding which of the three models is the best approximation. A discretization scheme for finding stability in the algorithm is outlined

Square Root Finding In Graphs

Abstract: Root and root finding are concepts familiar to most branches of mathematics. In graph theory, H is a square root of G and G is the square of H if two vertices x,y have an edge in G if and only if x,y are of distance at most two in H. Graph square is a basic operation with a number of results about its properties in the literature. We study the characterization and recognition problems of graph powers. There are algorithmic and computational approaches to answer the decision problem of whether a given graph is a certain power of any graph. There are polynomial time algorithms to solve this problem for square of graphs with girth at least six while the NP-completeness is proven for square of graphs with girth at most four. The girth-parameterized problem of root fining has been open in the case of square of graphs with girth five. We settle the conjecture that recognition of square of graphs with girth 5 is NP-complete. This result is providing the complete dichotomy theorem for square root finding problem.

Exudation of alcohol and aldehyde sugars from roots of defoliated Lolium perenne L. grown under sterile conditions

Root exudates were collected over a 27 day period from defoliated and non-defoliated Lolium perenne L. plants grown under sterile conditions in microlysimeters. Eleven individual sugars, including both aldehyde and alcohol sugars, were identified and quantified with a gas chromatograph-mass spectrometer (GC-MS). There was no change in the number of sugars present between 7 and 27 days, but the exudation of alcohol sugars decreased rapidly at about day 12. Xylose and glucose were present in the largest amounts. Defoliation initially increased the total amount of sugars in the exudates, but continuous defoliation reduced total sugar exudation by 16% and induced changes in the exudation patterns of individual sugars. Defoliation enhanced exudation of erythritol, threitol, and xylitol, reduced exudation of glucose and arabitol, but had little effect on the amounts of other sugars exuded. The more complex 6 C, 5 OH aldehyde sugars, especially glucose, showed changes earlier and to a greater extent (17 days), than the 5 C, 4 OH (xylose and ribose) and 6 C 4 OH (fucose) aldehyde groups. These findings confirm the general finding that repeated defoliation reduces the quantity of total sugars exuded, but the pattern of release of individual sugars is complex and variable.

Genetic parameters and simultaneous selection for root yield, adaptability and stability of cassava genotypes

O objetivo deste trabalho foi estimar parâmetros genéticos e avaliar a seleção simultânea quanto à produtividade de raízes e à adaptabilidade e estabilidade de genótipos de mandioca. Os efeitos dos genótipos foram considerados como fixos e aleatórios, e a metodologia de modelos mistos (REML/Blup) foi utilizada para estimar os parâmetros genéticos e a média harmônica do desempenho relativo dos valores genotípicos (MHPRVG), para seleção simultânea. Dez genótipos foram avaliados em delineamento de blocos ao acaso, com quatro repetições. O experimento foi realizado nos municípios de Altamira, Santarém e Santa Luzia do Pará, PA, nos anos agrícolas de 2009/2010, 2010/2011 e 2011/2012. As raízes foram colhidas 12 meses após o plantio, em todos os locais testados. A produtividade de raízes apresentou baixo coeficiente de variação genotípica (4,25%) e herdabilidade de parcelas individuais no sentido amplo (0,0424), o que resultou em baixo ganho genético. Em razão da baixa correlação genotípica (0,15), a classificação dos genótipos quanto à produtividade de raízes variou de acordo com o ambiente. Os genótipos CPATU 060, CPATU 229 e CPATU 404 destacaram-se quanto à produtividade, adaptabilidade e estabilidade.

Incorporating Latent Variables into Discrete Choice Models - A Simultaneous Estimation Approach Using SEM Software

Integrated choice and latent variable (ICLV) models represent a promising new class of models which merge classic choice models with the structural equation approach (SEM) for latent variables. Despite their conceptual appeal, applications of ICLV models in marketing remain rare. We extend previous ICLV applications by first estimating a multinomial choice model and, second, by estimating hierarchical relations between latent variables. An empirical study on travel mode choice clearly demonstrates the value of ICLV models to enhance the understanding of choice processes. In addition to the usually studied directly observable variables such as travel time, we show how abstract motivations such as power and hedonism as well as attitudes such as a desire for flexibility impact on travel mode choice. Furthermore, we show that it is possible to estimate such a complex ICLV model with the widely available structural equation modeling package Mplus. This finding is likely to encourage more widespread application of this appealing model class in the marketing field.

Biologically inspired visual landmark processing for simultaneous localization and mapping

This paper illustrates a method for finding useful visual landmarks for performing simultaneous localization and mapping (SLAM). The method is based loosely on biological principles, using layers of filtering and pooling to create learned templates that correspond to different views of the environment. Rather than using a set of landmarks and reporting range and bearing to the landmark, this system maps views to poses. The challenge is to produce a system that produces the same view for small changes in robot pose, but provides different views for larger changes in pose. The method has been developed to interface with the RatSLAM system, a biologically inspired method of SLAM. The paper describes the method of learning and recalling visual landmarks in detail, and shows the performance of the visual system in real robot tests.

Web-based Simultaneous Equation Solver

* This work has been supported by NIMP, University of Plovdiv under contract No MU-1.