Taylor Spectrum and Characteristic Functions of Commuting 2-Contractions

2000 Mathematics Subject Classification: 47A10, 47A13.

Generalized Derivations and Norm Equality in Normed Ideals

2000 Mathematics Subject Classification: 47A10, 47A12, 47A30, 47B10, 47B20, 47B37, 47B47, 47D50.

Transferability of Regional Permafrost Disturbance Susceptibility Modelling Using Generalized Linear and Generalized Additive Models

To effectively assess and mitigate risk of permafrost disturbance, disturbance-p rone areas can be predicted through the application of susceptibility models. In this study we developed regional susceptibility models for permafrost disturbances using a field disturbance inventory to test the transferability of the model to a broader region in the Canadian High Arctic. Resulting maps of susceptibility were then used to explore the effect of terrain variables on the occurrence of disturbances within this region. To account for a large range of landscape charac- teristics, the model was calibrated using two locations: Sabine Peninsula, Melville Island, NU, and Fosheim Pen- insula, Ellesmere Island, NU. Spatial patterns of disturbance were predicted with a generalized linear model (GLM) and generalized additive model (GAM), each calibrated using disturbed and randomized undisturbed lo- cations from both locations and GIS-derived terrain predictor variables including slope, potential incoming solar radiation, wetness index, topographic position index, elevation, and distance to water. Each model was validated for the Sabine and Fosheim Peninsulas using independent data sets while the transferability of the model to an independent site was assessed at Cape Bounty, Melville Island, NU. The regional GLM and GAM validated well for both calibration sites (Sabine and Fosheim) with the area under the receiver operating curves (AUROC) N 0.79. Both models were applied directly to Cape Bounty without calibration and validated equally with AUROC's of 0.76; however, each model predicted disturbed and undisturbed samples differently. Addition- ally, the sensitivity of the transferred model was assessed using data sets with different sample sizes. Results in- dicated that models based on larger sample sizes transferred more consistently and captured the variability within the terrain attributes in the respective study areas. Terrain attributes associated with the initiation of dis- turbances were similar regardless of the location. Disturbances commonly occurred on slopes between 4 and 15°, below Holocene marine limit, and in areas with low potential incoming solar radiation

Elucidating the interactions between the adhesive and transcriptioanl functions of beta-catenin in normal and cancerous cells

Wnt signalling is involved in a wide range of physiological and pathological processes. The presence of an extracellular Wnt stimulus induces cytoplasmic stabilisation and nuclear translocation of beta-catenin, a protein that also plays an essential role in cadherin-mediated adhesion. Two main hypotheses have been proposed concerning the balance between beta-catenin's adhesive and transcriptional functions: either beta-catenin's fate is determined by competition between its binding partners, or Wnt induces folding of beta-catenin into a conformation allocated preferentially to transcription. The experimental data supporting each hypotheses remain inconclusive. In this paper we present a new mathematical model of the Wnt pathway that incorporates beta-catenin's dual function. We use this model to carry out a series of in silico experiments and compare the behaviour of systems governed by each hypothesis. Our analytical results and model simulations provide further insight into the current understanding of Wnt signalling and, in particular, reveal differences in the response of the two modes of interaction between adhesion and signalling in certain in silico settings. We also exploit our model to investigate the impact of the mutations most commonly observed in human colorectal cancer. Simulations show that the amount of functional APC required to maintain a normal phenotype increases with increasing strength of the Wnt signal, a result which illustrates that the environment can substantially influence both tumour initiation and phenotype.

Unpolarized transverse momentum dependent parton distribution and fragmentation functions at next-to-next-to-leading order

The transverse momentum dependent parton distribution/fragmentation functions (TMDs) are essential in the factorization of a number of processes like Drell-Yan scattering, vector boson production, semi-inclusive deep inelastic scattering, etc. We provide a comprehensive study of unpolarized TMDs at next-to-next-to-leading order, which includes an explicit calculation of these TMDs and an extraction of their matching coefficients onto their integrated analogues, for all flavor combinations. The obtained matching coefficients are important for any kind of phenomenology involving TMDs. In the present study each individual TMD is calculated without any reference to a specific process. We recover the known results for parton distribution functions and provide new results for the fragmentation functions. The results for the gluon transverse momentum dependent fragmentation functions are presented for the first time at one and two loops. We also discuss the structure of singularities of TMD operators and TMD matrix elements, crossing relations between TMD parton distribution functions and TMD fragmentation functions, and renormalization group equations. In addition, we consider the behavior of the matching coefficients at threshold and make a conjecture on their structure to all orders in perturbation theory.

Transcription-Coupled DNA Supercoiling in Escherichia Coli: Mechanisms and Biological Functions

Transcription by RNA polymerase can induce the formation of hypernegatively supercoiled DNA both in vivo and in vitro. This phenomenon has been explained by a “twin-supercoiled-domain” model of transcription where a positively supercoiled domain is generated ahead of the RNA polymerase and a negatively supercoiled domain behind it. In E. coli cells, transcription-induced topological change of chromosomal DNA is expected to actively remodel chromosomal structure and greatly influence DNA transactions such as transcription, DNA replication, and recombination. In this study, an IPTG-inducible, two-plasmid system was established to study transcription-coupled DNA supercoiling (TCDS) in E. coli topA strains. By performing topology assays, biological studies, and RT-PCR experiments, TCDS in E. coli topA strains was found to be dependent on promoter strength. Expression of a membrane-insertion protein was not needed for strong promoters, although co-transcriptional synthesis of a polypeptide may be required. More importantly, it was demonstrated that the expression of a membrane-insertion tet gene was not sufficient for the production of hypernegatively supercoiled DNA. These phenomenon can be explained by the “twin-supercoiled-domain” model of transcription where the friction force applied to E. coli RNA polymerase plays a critical role in the generation of hypernegatively supercoiled DNA. Additionally, in order to explore whether TCDS is able to greatly influence a coupled DNA transaction, such as activating a divergently-coupled promoter, an in vivo system was set up to study TCDS and its effects on the supercoiling-sensitive leu-500 promoter. The leu-500 mutation is a single A-to-G point mutation in the -10 region of the promoter controlling the leu operon, and the AT to GC mutation is expected to increase the energy barrier for the formation of a functional transcription open complex. Using luciferase assays and RT-PCR experiments, it was demonstrated that transient TCDS, “confined” within promoter regions, is responsible for activation of the coupled transcription initiation of the leu-500 promoter. Taken together, these results demonstrate that transcription is a major chromosomal remodeling force in E. coli cells.

Insight into the fractional calculus via a spreadsheet

Many students of calculus are not aware that the calculus they have learned is a special case (integer order) of fractional calculus. Fractional calculus is the study of arbitrary order derivatives and integrals and their applications. The article begins by stating a naive question from a student in a paper by Larson (1974) and establishes, for polynomials and exponential functions, that they can be deformed into their derivative using the μ-th order fractional derivatives for 0<μ<1. Through the power of Excel we illustrate the continuous deformations dynamically through conditional formatting. Some applications are discussed and a connection made to mathematics education.

Predição do consumo de pasto de capim-elefante (Pennisetum purpureum, Schumack) por vacas mestiças Holandês x Zebu em lactação

Foram desenvolvidas equações de predição de consumo de pasto de capim-elefante (Pennisetum purpureum, Schumack) por vacas mestiças Holandês x Zebu em lactação, utilizando-se procedimentos de stepwise em regressões múltiplas, aplicados a um banco de dados de experimentos conduzidos ao longo de três anos na Empresa Brasileira de Pesquisa Agropecuária (EMBRAPA) Gado de Leite (Coronel Pacheco, MG). As variáveis independentes disponíveis foram relacionadas a características inerentes às vacas (dias em lactação; teores de proteína, gordura e extrato seco total e produções destes componentes no leite; produção de leite in natura ou corrigida para 4% de gordura; ordem de lactação; peso vivo atual; peso vivo ao parto e grau de sangue Holandês x Zebu); ao manejo (dias de pastejo; disponibilidade de forragem e período de descanso da pastagem); ao ambiente (estação do ano e precipitação pluviométrica) e à alimentação (digestibilidade in vitro e parâmetros da composição química do pasto de capim-elefante e da cana-de-açúcar - Saccharum officinarum (L.) corrigida com 1% de uréia; consumos de suplemento volumoso (cana corrigida com uréia) e concentrado; concentrações fecais de proteína bruta e de fibras em detergente neutro e ácido). Efeitos linear e quadrático e transformações logarítmicas foram adicionalmente incluídos no banco de dados. Foram obtidas equações de predição de consumo de pasto de capim-elefante (expresso em kg/vaca/dia ou % do peso vivo) com coeficientes de determinação de 65,2 a 67,0%. As principais variáveis independentes incluídas nas equações foram o consumo do suplemento volumoso usado na estação seca do ano (cana corrigida com uréia); a digestibilidade in vitro do pasto de capim-elefante; a precipitação pluviométrica; a produção de leite corrigida para 4% de gordura; o peso vivo atual ou, em alternativa a este, o valor da pesagem realizada após o parto da vaca; além do consumo de suplemento concentrado, que evidenciou um efeito de substituição àquele do pasto de capim-elefante.

Uma proposta alternativa para o ensino progressões relacionadas a funções

Generally, arithmetic and geometric progressions are taught separately from ane and exponential functions, only by the use of memorized formulas and without any concern of showing students how these contents are related. This paper aims at presenting a way of teaching such contents in an integrated way, starting with the definition of ane and exponential functions relating them to situations from the daily life of the students. Then, characteristics and graphics of those functions are presented and, subsequently, arithmetic and geometric progression are shown as a restriction of the ane and exponential functions. Thus, the study of the progressions is introduced based on the functions mentioned above using situations from students daily lives as examples

Laboratory verification of predicted permanent deformation in asphalt materials following climate change.

In the past a change in temperature of 5°C most often occurred over intervals of thousands of years. According to estimates by the IPCC, in the XXI century is expected an increase in average temperatures in Europe between 1.8 and 4.0°C in the best case caused by emissions of carbon dioxide and other GHG from human activities. As well as on the environment and economic context, global warming will have effects even on road safety. Several studies have already shown how increasing temperature may cause a worsening of some types of road surface damages, especially rutting, a permanent deformation of the road structures consisting in the formation of a longitudinal depression in the wheelpath, mostly due to the rheological behavior of bitumen. This deformation evolves during the hot season because of the heating capacity of the asphalt layers, in fact, the road surface temperature is up to 24°C higher than air. In this thesis, through the use of Wheeltrack test, it was studied the behavior of some types of asphalt concrete mixtures subjected to fatigue testing at different temperatures. The objectives of this study are: to determine the strain variation of different bituminous mixture subjected to fatigue testing at different temperature conditions; to investigate the effect of aggregates, bitumen and mixtures’ characteristics on rutting. Samples were made in the laboratory mostly using an already prepared mixtures, the others preparing the asphalt concrete from the grading curve and bitumen content. The same procedure was performed for each specimen: preparation, compaction using the roller compactor, cooling and heating before the test. The tests were carried out at 40 - 50 - 60°C in order to obtain the evolution of deformation with temperature variation, except some mixtures for which the tests were carried out only at 50°C. In the elaboration of the results were considered testing parameters, component properties and the characteristics of the mixture. Among the testing parameters, temperature was varied for each sample. The mixtures responded to this variation with a different behavior (linear logarithmic and exponential) not directly correlated with the asphalt characteristics; the others parameters as load, passage frequency and test condition were kept constant. According to the results obtained, the main contribution to deformation is due to the type of binder used, it was found that the modified bitumen have a better response than the same mixtures containing traditional bitumen; to the porosity which affects negatively the behavior of the samples and to the homogeneity ceteris paribus. The granulometric composition did not seem to have interfered with the results. Overall has emerged at working temperature, a decisive importance of bitumen composition, than the other characteristics of the mixture, that tends to disappear with heating in favor of increased dependence of rutting resistance from the granulometric composition of the sample considered. In particular it is essential, rather than the mechanical characteristics of the binder, its chemical properties given by the polymeric modification. To confirm some considered results, the maximum bulk density and the air voids content were determined. Tests have been conducted in the laboratories of the Civil Engineering Department at NTNU in Trondheim according to European Standards.

Introduction to the Maple Power Tool Intpakx

The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006

Analytical optimization of spread and change of exponential decay of generalized Wannier functions in one dimension

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Exact Search Directions for Optimization of Linear and Nonlinear Models Based on Generalized Orthonormal Functions

A novel technique for selecting the poles of orthonormal basis functions (OBF) in Volterra models of any order is presented. It is well-known that the usual large number of parameters required to describe the Volterra kernels can be significantly reduced by representing each kernel using an appropriate basis of orthonormal functions. Such a representation results in the so-called OBF Volterra model, which has a Wiener structure consisting of a linear dynamic generated by the orthonormal basis followed by a nonlinear static mapping given by the Volterra polynomial series. Aiming at optimizing the poles that fully parameterize the orthonormal bases, the exact gradients of the outputs of the orthonormal filters with respect to their poles are computed analytically by using a back-propagation-through-time technique. The expressions relative to the Kautz basis and to generalized orthonormal bases of functions (GOBF) are addressed; the ones related to the Laguerre basis follow straightforwardly as a particular case. The main innovation here is that the dynamic nature of the OBF filters is fully considered in the gradient computations. These gradients provide exact search directions for optimizing the poles of a given orthonormal basis. Such search directions can, in turn, be used as part of an optimization procedure to locate the minimum of a cost-function that takes into account the error of estimation of the system output. The Levenberg-Marquardt algorithm is adopted here as the optimization procedure. Unlike previous related work, the proposed approach relies solely on input-output data measured from the system to be modeled, i.e., no information about the Volterra kernels is required. Examples are presented to illustrate the application of this approach to the modeling of dynamic systems, including a real magnetic levitation system with nonlinear oscillatory behavior.

Heaviside generalized functions and shock waves for a Burger kind equation

The purpose of the work is to study the existence and nonexistence of shock wave solutions for the Burger equations. The study is developed in the context of Colombeau's theory of generalized functions (GFs). This study uses the equality in the strict sense and the weak equality of GFs. The shock wave solutions are given in terms of GFs that have the Heaviside function, in x and ( x, t) variables, as macroscopic aspect. This means that solutions are sought in the form of sequences of regularizations to the Heaviside function, in R-n and R-n x R, in the distributional limit sense.