Curvature measures for generalized linear models

First addressed by Beale (1960), the use of curvature measures of nonlinearity in nonlinear regression has been elucidated most comprehensively by Bates and Watts (1980). They used differential geometric results that exploit features of the Euclidean space imposed by the Normality assumption. The partitioning of these measures into intrinsic effects (due to the model) and parameter effects (due to the form or parameterization of the model) allows a proper assessment of model departures from linearity. Indeed, the term \u27linear\u27 has become synonymous with a lack of both of these effects, since the commonly designated \u27linear model\u27 with Normal disturbance does not contain either effect. These curvature measures are used to unravel the effects of model reformulation on convergence of fitting procedures, and on the appropriateness of confidence regions based on the linearization assumption. For model criticism using residual analysis, the presence of intrinsic curvature in a nonlinear regression model can distort the visual assessment procedures borrowed from linear modelling, since the fundamental basis of these procedures can be undermined when the model is nonlinear. When the disturbances are non-Normal, the consequent geometry is no longer Euclidean, necessitating a different approach, as outlined by Amari (1982a). The required approach generalizes the Euclidean inner product to a metric, and the ordinary derivative to an α-connection. The concept of these α-connections is fundamental to a proper understanding of the role of differential geometry to the investigation of estimator behaviour in the case of non-Normal errors. These connections provide the general method for comparing nearby points in the parameter space, for general classes of error distributions. In these cases, such a comparison is complicated by the difficulty of the existence of different bases for the neighbouring tangent spaces derived from the likelihood. The exception or special case is the linear model with Normal errors, where no such difficulty arises. Casting the generalization as being from Normal to non-Normal errors, the extension can be considered to cause an \u27unbundling\u27 of the statistical properties of estimators, which in the case of Normal errors can be enjoyed simultaneously by the same estimator. In the general non-Normal case, such behaviour can no longer be guaranteed, implying that all properties may need to be considered separately, since, in the general case, specific properties of the estimator are associated with particular values of α. This thesis outlines the fundamentals of the generalization of curvature measures to models of exponential type, in particular curved exponential families for which generalized linear models are an important subclass. This approach is used to generate insights into the properties of generalized linear models, with particular reference to the canonical link function as the non-Normal generalization of a linear model with Normal errors. Indeed, the underlying \u27theme\u27 of this study is the investigation of the generalization of \u27linearity\u27 for the Normal error linear model to the non-Normal error nonlinear model. The potential simultaneity of estimator properties for the Normal distribution does not carry over to the generalization from the Normal to the non-Normal, since now each property has to be investigated separately, for each particular value of a. As shown in Chapter 2, this individual treatment involves the statistical interpretation of each α-connection to demonstrate how key values of a are associated with estimator properties such as unbiasedness, stability of variance, lack of skewness, \u27normal\u27 likelihood and sufficiency. In terms of data analysis, all of these investigations need to be performed on the regression coefficients rather than on the fitted value (expectation parameter) scale. This requires the use of curved exponential families involving an imbedding of the regression coefficients in the original expectation space. One of the properties of Normal error linear models is estimator sufficiency, which for generalized linear models implies a canonical link function. The associated α-connection is the exponential or Efron connection. This connection could be considered as the springboard for the generalization of Normal error linear models to non-Normal error nonlinear models, since for generalized linear models it mimics the special case of Normal errors, by the conditions under which it vanishes. The investigation of this connection and its special relationship with generalized linear models has generated in Chapter 2 a test of adequacy for canonical link functions, based on the skewness of the regression coefficients. The generalization of curvature follows a similar path to the a-connections, being a function of them in terms of the expectation parameters. In line with the decomposition demonstrated by Bates and Watts (1980) for Normal errors, generalized a-curvature decomposes into intrinsic and parameter-effects curvature; now, each particular α-curvature is associated with individual properties of the model, depending on the value of α. The other main change from the curvature measures of Bates and Watts is that, in the general case, a contribution to curvature is made from the error distribution as well as from the model and its parameterization. A major new result in Chapter 3 has been the proof of the invariance of intrinsic α-curvature in the general case, using a coordinate based system. A consequence of examining the generalization has been to define in Chapter 3 a class of models, generalized nonlinear models, having a non-Normal error distribution and a general nonlinear response function. The relationship of this class with classes of known models such as generalized linear models again raises the question of what is meant by \u27nonlinearity\u27 in general. Several related derivations such as the invariance of parameter-effects curvature in generalized linear models, and results involving exponential curvature, generalized linear models and generalized nonlinear models verify expected behaviour and highlight the generalizations that are possible. The generalized curvature measures are shown in Chapter 4 to be related to quantities of statistical interest such as the bias and covariance of estimators for curved exponential families, mirroring the known situation for nonlinear regression. For generalized linear models, alternative link functions to the canonical can be chosen on the basis of properties such as variance stabilization, \u27normal\u27 likelihood and lack of skewness. As expected, these links have been shown in Chapter 4 to be associated with specific α-connections. A table is presented of those link functions that produce the required properties on the expected value scale for each error distribution in a generalized linear model. The special relationship between curvature measures, nonlinear regression and generalized linear models is further demonstrated in Chapter 5 by the use of a new method for nonlinear regression based on a second order approximant to the nonlinear function by means of a special generalized linear model. As expected, such an approximation follows the true function more closely than linearization; this is demonstrated empirically from calculations of leverage, parameter estimates and corresponding interval estimation. All these effects are predicted from considerations based on curvature measures, both intrinsic and parameter effects. The effect of replication on curvature is known empirically and theoretically in the case of nonlinear regression. In Chapter 5 it is shown that replication has two implications for the effects of curvature in a generalized nonlinear model. Firstly, the central limit theorem produces convergence to the Normal distribution, so that the error contribution to general α-curvature becomes zero asymptotically. The effect of replication on the model contribution is less clear, since the general limiting case is nonlinear regression if only the error component of a-curvature is considered. Locally, the generalized nonlinear model will be well approximated by a linear model. Secondly, under some conditions, a generalized nonlinear model will converge locally to a generalized linear model with canonical link. However, when the error component and the model component are considered, the overall effect of intense replication will be to produce locally a linear model with Normal errors

Excited State TBA for the ϕ2,1\phi_{2,1} perturbed M3,5M_{3,5} model

We examine some excited state energies in the non-unitary integrable quantum field theory obtained from the perturbation of the minimal conformal field theory model $M_{3,5}$ by its operator $\phi_{2,1}$. Using the correspondence of this IQFT to the scaling limit of the dilute $A_2$ lattice model (in a particular regime) we derive the functional equations for the QFT commuting transfer matrices. These functional equations can be transformed to a closed set of TBA-like integral equations which determine the excited state energies in the finite-size system. In particular, we explicitly construct these equations for the ground state and two lowest excited states. Numerical results for the associated energy gaps are compared with those obtained by the truncated conformal space approach (TCSA).Comment: LaTeX, 32 pages, 6 figure

Group work: horses for courses in first year biology

There are a number of student learning outcomes that are perhaps best achieved in a group approach and others where a group approach is a virtual guarantee that only a portion of the cohort will meaningfully engage in the learning task. We have taken the straight forward approach of ensuring that learning areas with a social interaction component such as ‘working in teams’, ‘team structure and function’, ‘hazard assessment’ and ‘peer review’ are delivered using group work in a way that allows a direct experience and deep learning of the processes. Other learning areas that focus on individual motor and organizational skills such as microscope usage or microbial plating are taught and assessed with students acting as individuals. Specific recognition that socially oriented tasks should be taught in a group environment suggests the obvious ideal that the group task be designed to make the most of the group environment. In this paper I examine two such group tasks that were run in first year biology at the University of Newcastle in 2006. The first of these ‘The Great Diversity Challenge’ was designed to engage students in a deep learning experience regarding their own approach to working in teams along with the basic theory of team structure and function and a team approach to hazard assessment. The second engaged students in the publication and peer review processes and provided personal experience in giving and receiving criticism professionally. Student attitudes to the effectiveness of the approach were assessed using an online survey tool in Blackboard that included both scale and written responses

A Leitura Deleite e suas contribuições para a Cultura do Livro

A Literatura se caracteriza como uma das mais completas experiências do ser humano e uma preciosa fonte de conhecimento. A leitura de textos literários favorece o contato com estético e o lúdico, estimula a imaginação e a fantasia, além de favorecer o contato com novos conhecimentos e a formação de um estreito vínculo entre ficção e realidade. Partindo da perspectiva de necessidade de uma maior aproximação entre o professor e a leitura literária, o presente artigo realiza uma reflexão sobre as contribuições da Leitura Deleite para a formação do professor leitor. Ademais, apresenta uma breve revisão de pesquisas capazes de serem relacionadas ao tema, buscando estabelecer os caminhos que os pesquisadores têm traçado para uma melhor compreensão do papel da leitura na formação docente. Entendida como um momento destinado ao prazer e fruição da leitura, com a capacidade de proporcionar a ampliação de saberes e o contato com diversos textos, o trabalho conclui sobre a importância da prática da atividade de Leitura Deleite na vida cotidiana do professor e aponta a necessidade de uma reaproximação desse profissional com a leitura literária, o que pode viabilizar um contato mais intenso entre criança e Literatura em um movimento no sentido de formá-las e torná-las leitores proficientes

Increased activity of cell surface peptidases in HeLa cells undergoing UV-induced apoptosis is not mediated by caspase 3

We have previously shown that in HeLa cells treated with a variety of agents there is an increase in cell surface peptidase (CSP) activity in those cells undergoing apoptosis. The increase in CSP activity observed in UVB-irradiated cells undergoing apoptosis was unaffected when the cultures were treated with the aminopeptidase inhibitor bestatin, and matrix metalloprotease inhibitor BB3103, but greatly enhanced when treated with the caspase 3 inhibitor-DEVD, and reduced in the presence of the poly(ADP-ribose) polymerase (PARP) inhibitor-3-aminobenzamide (3AB). Neither 3AB nor DEVD had an effect on the gross morphology of the apoptotic cells observed under electron microscopy, nor did they have an effect on phosphatidylserine eversion on the cell membrane, or that of PARP cleavage. All the agents except for DEVD had no effect on the level of caspase 3 activity in the cells. The results suggest that other caspases may cleave PARP in these cells. Both 3AB and DEVD treatment reduced the level of actin cleavage seen in the apoptotic cells. The increase in CSP activity observed in cells undergoing UVB-induced apoptosis appears to involve PARP but not caspase 3

Complete Nondiagonal Reflection Matrices of RSOS/SOS and Hard Hexagon Models

In this paper we compute the most general nondiagonal reflection matrices of the RSOS/SOS models and hard hexagon model using the boundary Yang-Baxter equations. We find new one-parameter family of reflection matrices for the RSOS model in addition to the previous result without any parameter. We also find three classes of reflection matrices for the SOS model, which has one or two parameters. For the hard hexagon model which can be mapped to RSOS(5) model by folding four RSOS heights into two, the solutions can be obtained similarly with a main difference in the boundary unitarity conditions. Due to this, the reflection matrices can have two free parameters. We show that these extra terms can be identified with the `decorated' solutions. We also generalize the hard hexagon model by `folding' the RSOS heights of the general RSOS(p) model and show that they satisfy the integrability conditions such as the Yang- Baxter and boundary Yang-Baxter equations. These models can be solved using the results for the RSOS models.Comment: 18pages,Late

A crise venezuelana e seus impactos no ámbito brasileiro: políticas linguísticas de integração de refugiados no Estado de Paraíba

The present article aims to present the welcoming language policies for Venezuelan refugees in Paraiba, throughout a highlight of the issue in the national context. The methodology used is qualitative, using documents and bibliography to support this proposal, which is justified by the relevance of the theme for the understanding of current Brazilian society, in the way it reinvents itself and receives people in refugee situations. Through historical and political contextualization, I will present the main factors contributing to the Venezuelan migratory crisis in the period before the Covid-19, approaching the specific issues that correspond to the Brazilian case, with the creation of the National Program for Interiorization. Next, I will present some aspects of the reception promoted by the state of Paraiba, with special attention to the actions of the project Teaching Portuguese as a Welcoming Language for Venezuelan Refugees and Asylum Seekers in Paraiba.O presente artigo tem o objetivo de pontuar as políticas de acolhimento linguístico de refugiados venezuelanos no estado da Paraíba, a partir de um levantamento da questão no âmbito nacional. A metodologia utilizada é a qualitativa, com o recurso a documentos e bibliografia que fundamentam a presente proposta, a qual justifica-se pela relevância do tema para a compreensão da sociedade brasileira atual, na forma como se reinventa e recebe pessoas em situação de refúgio. Através de contextualização histórica e política, apresentarei os principais fatores que contribuem para a crise migratória venezuelana no período anterior à Covid-19, passando para questões específicas que correspondem ao caso brasileiro, com a criação do Programa Nacional de Interiorização. A seguir, exporei alguns aspectos da acolhida promovida pelo estado da Paraíba, com especial atenção às ações do projeto Ensino do Português como Língua de Acolhimento para Refugiados e Solicitantes de Refúgio Venezuelanos na Paraíba

Rectificación de la inexactitud registral como garantía de la seguridad jurídica del asiento inscrito, oficina registral de Huacho, 2021

La presente investigación tuvo como objetivo precisar que la rectificación de la inexactitud registral constituye la garantía de la seguridad jurídica del asiento inscrito en la oficina registral de Huacho en el año 2021. Se desarrolló en el marco del diseño metodológico de la investigación de tipo básico, de nivel relacional de diseño no experimental y de medición transversal con enfoque mixto. Para el recojo de información se hizo uso del cuestionario que se aplicó a la población de estudio conformada por 75 personas. Los resultados expresados en la tabla 26 se aprecia un coeficiente de correlación directa de 0,345 Rho de Spearman y una significancia (bilateral) de 0,001 que es < a 0,05, por lo que se rechaza la hipótesis nula y se acepta la hipótesis alterna o hipótesis del investigador; es decir, hay una baja correlación directa entre la rectificación de la inexactitud y la garantía de la seguridad jurídica del asiento inscrito. De acuerdo con los resultados obtenidos se concluye entonces que, no es irregular que se produzca errores en los asientos registrales; sin embargo, en tanto se rectifique la inexactitud registral, se garantiza plenamente la seguridad jurídica del asiento inscrito en la oficina registral que la norma procesal registral lo prevé

Tales from the coalface: From tragedy to triumph in a blended learning approach to the teaching of 1st year biology

In 2004 we made a significant move to blended course delivery in 1st year Biology at the University of Newcastle. Innovations included electronic delivery of course notes, laboratory instructions and other support material including interactive templates, instructional and background videos, step by step guides for data analysis and some online laboratories. Students also submitted reports electronically and used email along with peer review to provide guided feedback to each other. Online discussion boards were used to interact with students and to assist students outside of class time. We also used some automatically marked online assessment. Feedback on the implementation of a blended learning approach in Semester 1 during and after the completion of the semester showed that, although grades were strong, student and staff satisfaction levels were the lowest on record. Key issues identified were workload, quality and quantity of feedback and collusion. In the light of this feedback changes were made to the delivery in Semester 2 to reduce workload, improve feedback and minimise collusion. At the conclusion of Semester 2 overall course grades and the results of student surveys showed that grades and satisfaction were the highest on record. All this with a 40% reduction in part time teaching costs for Semester 2. We believe that our experience shows that the blended learning environment can produce an improved quality learning environment at reduced cost, although only when that environment is matched with skilled and motivated teaching staff