The Gudermannian Growth Model: Theory, Application and Statistical Analysis

Abstract: Processes producing sigmoid curves are common in many areas such as biology, agrarian sciences, demography and engineering. Several mathematical functions have been proposed for modeling sigmoid curves. Some models such as the logistic, Gompertz, Richards and Weibull are widely used. This work introduces the Gudermannian function as an option for modeling sigmoid growth curves. The original function was transformed and the resulting equation was called the "Gudermannian growth model." This model was applied to four sets of experimental growth data to illustrate its practical application. The results were compared with those obtained by the logistic and Gompertz models. Since all these models are nonlinear in the parameters, the statistical properties of the least squares estimators were evaluated using measures of nonlinearity. For each experimental data set, the Akaike's corrected information criterion was utilized to discriminate among the models. In general, the Gudermannian model fitted better to the experimental data than the logistic and Gompertz models. The results showed that the Gudermannian model can be a good alternative to the classical sigmoid models.

¿Psicoanálisis y desarrollo? Aportes desde una perspectiva no lineal / Psychoanalysis and Development? Contributions from a non-Linear Perspective

Resumen El presente artículo problematiza la relación entre psicoanálisis freudiano y la perspectiva del desarrollo lineal, determinista y teleológica. A pesar de las impregnaciones evolucionistas del contexto histórico en que Freud gesta sus ideas, se encuentran conceptos que muestran una fuerte ruptura con la idea de un despliegue guiado por el ritmo de etapas prefijadas por edades. Así se postula la a-temporalidad de los procesos inconscientes y la Nachträglichkeit a la luz de las perspectivas no lineales emergentes desde las ciencias de la complejidad. Finalmente, se reflexiona sobre una psique que, en su carácter abierto y complejo, contempla lo aleatorio, lo impredecible y el azar en su devenir, y se transforma mediante trabajo elaborativo simbólico del yo. Así, sólo la historización, nunca lineal, contempla lo nuevo como posibilidad de (re)constituir la historia pasada.

Abstract This article problematizes the relationship between Freudian psychoanalysis and the linear, deterministic, and teleological perspective on development. Despite the evolutionist impregnations of the historical context in which Freud conceives his ideas, there are concepts that show a sharp break with the idea of an unfolding guided by a rhythm of stages prefixed by ages. Thus, the a-temporality of the unconscious processes and the Nachträglichkeit is postulated considering the non-linear perspectives that emerge from the sciences of complexity. Finally, we reflect on a psyche that, in its open and complex character, contemplates the fortuitous, the unpredictable and chance in its becoming, and is transformed through the elaborative symbolic work on the self. Like this, only the historicization, which is never linear, contemplates what is new as a possibility to (re)construct the past history.

Chanter model: nonlinear modeling of the fruit growth of cocoa / Modelo Chanter: modelagem não linear do crescimento de frutos do cacaueiro

ABSTRACT: The growth of plants and animals can be described through a growth curve. This curve is given by the equation of a nonlinear model, such as the Logistic model and the Gompertz model. The objective of this study was to adjust the Chanter model, as well as Logistic and Gompertz, using a set of cocoa (clone Sial-105) fruit whose length and diameter measurements were evaluated from 30 to 180 days after pollination, every 15 days. The Chanter model is a hybrid between the Logistic model and Gompertz model whose parameters can be interpreted similarly. A comparison of the quality of fit between the models was made using the following statistical measures: the Akaike's information criterion (AIC), the Akaike's weights criterion, Bayesian information criterion (BIC), residual standard deviation (RSD),the adjusted coefficient of determination (R²aj) and the measures of non-linearity Box's bias and curvature of Bates and Watts. It was verified that the Chanter model is the most suitable one among the studied models for modeling the cocoa data.

RESUMO: O crescimento de plantas e animais pode ser descrito por meio de uma curva. Essa curva é dada pela equação de um modelo não linear, como o modelo Logístico e o modelo Gompertz. O objetivo deste trabalho foi ajustar o modelo Chanter, assim como o Logístico e Gompertz, utilizando um conjunto de dados do fruto do cacaueiro do clone SIAL - 105, cujas medidas de comprimento e diâmetro foram avaliadas de 30 até 180 dias após a polinização, a cada 15 dias. O modelo Chanter é um híbrido entre o modelo Logístico e o modelo Gompertz cujos parâmetros podem ser interpretados similarmente. A avaliação da qualidade do ajuste entre os modelos foi feita utilizando as seguintes medidas estatísticas: o critério de informação de Akaike (AIC), o critério Peso de Akaike, o critério de informação de Bayes (BIC), o desvio padrão residual (DPR), o coeficiente de determinação ajustado (R²aj) e as medidas de não linearidade, vício de Box e curvatura de Bates e Watts. Verificou-se que o modelo Chanter dentre os modelos estudados neste trabalho é o mais adequado para o ajuste aos dados do fruto do cacaueiro.

Dose-response meta-analysis: application and practice using the R software / 한국역학회지

The objective of this study was to describe the general approaches of dose-response meta-analysis (DRMA) available for the quantitative synthesis of data using the R software. We conducted a DRMA using two types of data, the difference of means in continuous data and the odds ratio in binary data. The package commands of the R software were “doseresmeta” for the overall effect sizes that were separated into a linear model, quadratic model, and restricted cubic split model for better understanding. The effect sizes according to the dose and a test for linearity were demonstrated and interpreted by analyzing one-stage and two-stage DRMA. The authors examined several flexible models of exposure to pool study-specific trends and made a graphical presentation of the dose-response trend. This study focused on practical methods of DRMA rather than theoretical concepts for researchers who did not major in statistics. The authors hope that this study will help many researchers use the R software to perform DRMAs more easily, and that related research will be pursued.

Dose-response meta-analysis: application and practice using the R software / 한국역학회지

The objective of this study was to describe the general approaches of dose-response meta-analysis (DRMA) available for the quantitative synthesis of data using the R software. We conducted a DRMA using two types of data, the difference of means in continuous data and the odds ratio in binary data. The package commands of the R software were “doseresmeta” for the overall effect sizes that were separated into a linear model, quadratic model, and restricted cubic split model for better understanding. The effect sizes according to the dose and a test for linearity were demonstrated and interpreted by analyzing one-stage and two-stage DRMA. The authors examined several flexible models of exposure to pool study-specific trends and made a graphical presentation of the dose-response trend. This study focused on practical methods of DRMA rather than theoretical concepts for researchers who did not major in statistics. The authors hope that this study will help many researchers use the R software to perform DRMAs more easily, and that related research will be pursued.

Interações não lineares na arborização dendrítica de modelos de motoneurônios / Nonlinear interactions in the dendritic tree of motoneuron models

Este trabalho tem como objetivo verificar as diferenças funcionais entre sinapses proximais e distais e investigar as interações não line­ares de ativações sinápticas em modelos de motoneurônios em con­dições passivas. Os modelos utilizados, implementados em C++, são uma versão expandida dos desenvolvidos por Vieira e Kohn (2005), com uma arborização dendrítica mais detalhada: 5 ramos dendríti­cos equivalentes com 17 ou 19 compartimentos dendríticos cada um. Testes verificaram as diferenças funcionais de sinapses que ocorrem próximas ao soma e ao longo do dendrito além de avaliarem o grau de não linearidade de resposta da arborização dendrítica para dife­rentes ativações sinápticas em diferentes sítios. As diferenças funcio­nais entre as sinapses proximais e distais foram avaliadas pela injeção de senoides puras em diferentes compartimentos dendríticos. Os re­sultados mostraram atenuações mais intensas nas altas frequências e frequência de corte mais baixas em compartimentos dendríticos mais distantes do soma. As interações não lineares foram avaliadas apli­cando entradas sinápticas senoidais com frequências primas entre si, em dois ou mais ramos dendríticos equivalentes simultaneamente e em compartimentos dendríticos diferentes. O espectro de frequên­cia da corrente efetiva foi analisado, comparando a amplitude do pico das distorções harmônicas e por intermodulação com o pico da frequência fundamental de menor amplitude: quanto menores estas diferenças maior o grau de não linearidade entre as ativações sinápti­cas em compartimentos dendríticos distintos. Os resultados sugerem expressivo grau de não linearidade entre as entradas sinápticas nos dendritos. Notou­-se que, em todas as situações, quando se variou a condutância sináptica, maior foi o grau de não linearidade em relação aos casos em que se variou a corrente sináptica, bem como entradas sinápticas mais próximas eletrotonicamente apresentaram maior grau de não linearidade em...

The aim of this work was to verify the functional differences between proximal and distal synapses and to investigate the nonlinear interactions of synaptic activation in models of motoneurons in passive conditions. The models, implemented in C++, are an expanded version of that developed by Vieira and Kohn (2005), with a more detailed dendritic arborization: five equivalent dendrites with 17 or 19 dendritic compartments each one. Tests verified the functional differences of synapses that occur close to the soma and along the dendrite in addition to evaluating the degree of nonlinearity response from dendritic arborization for different synaptic activation at different sites. The functional differences between the proximal and distal synapses were evaluated by injection of pure sinusoids in different dendritic compartments. The results showed severe attenuation at high frequencies and a lower cut-off frequency in more distant dendritic compartments of the soma. The nonlinear interactions were evaluated by applying sinusoidal synaptic input at prime frequencies with each other in two or more dendritic branches simultaneously and at different dendritic compartments. The frequency spectrum of the effective current was analyzed by comparing the peak amplitude of harmonics and spurious rays with the peak amplitude of the fundamental frequency of smaller amplitude: the smaller these differences are, the greater the degree of nonlinearity between the synaptic activation of distinct dendritic compartments. The results suggest a high degree of nonlinearity between the dendrites. In all situations was noted that when the synaptic conductance was varied, the nonlinearities was greater in relation to the cases in which the synaptic current was varied, and nonlinear summation is expected for synapses located electrotonically close together in relation for electrotonically separated inputs, suggesting a dependence on membrane potential.

Evolución, teoraa de las extinciones, complejidad / Evolution, Theory of Extinctions, Complexity

Este texto discute la posibilidad del desarrollo de una teoría de las extinciones, una teoría inexistente hasta la fecha, y que vendría a ser la contraparte o el complemento de la teoría de la evolución. El problema central es el de la exploración de una teoría general de la complejidad, una tarea que permanece abierta e inconclusa hasta el momento. La paleontología y la biología evolutiva pueden verse como las dos caras de una moneda cuyo rasgo distintivo no es el gradualismo, sino los equilibrios puntuados y el catastrofismo. El tema de las extinciones se concentra aquí en la importancia y el papel de las extinciones masivas. A partir del diálogo entre biología y paleontología, evolución y extinciones, varias reflexiones se extrapolan al plano social, cultural y filosófico. El marco amplio es el de las ciencias de la complejidad.

This paper discusses the possibility of reaching a theory of extinctions, a theory nonexistent so far that can be taken as complementary to the theory of evolution. The core problem is here the exploration of the general theory of complexity, a task that remains open and without a definite conclusion until now. Paleontology and biology can be grasped as the two faces of one and the same token whose most salient feature is punctuated equilibria and catastrophism, and not gradualism any longer. Extinctions are viewed here particularly as massive extinctions. After the dialogue between paleontology and biology, evolution and extinctions, a number of reflections are extrapolated to the social, cultural and philosophical framework. The general context hence is the one provided by the sciences of complexity.

On characteristic properties of TCM dose-effect relationship / 中华中医药杂志

The relationship of dose and effect in TCM formulae was an important subject in the TCM modernization research.Some characteristic properties of TCM dose-effect relationship were proposed in this paper: the dose-effect relationship of TCM had a specifi c regulation from the whole-view idea in traditional medical theories besides common properties,nonlinear character from the compatibility of medicine properties,and multi-effects varied with the different compatibility from the alternation of doses.The subjects of dose-effect relationship included single medicine,drug pair and formulae.The study on the dose-effect relationship of TCM might be helpful to the explanation of conception,connotation,ideas and methods of TCM,provide scientifi c supports and instructions for the TCM clinical practices,and provide research bases for the TCM innovation.

The Relation of Clinical Scale and Non-Linearity of EEG in Early Parkinson's Disease

BACKGROUND: Many recent studies based on non-linearity have been performed to quantify the complex behavior of the brain in order to understand the pathophysiology of Parkinson's disease (PD). METHODS: We calculated the Fractal dimension (FD) and Lyapunov exponent (L1), the non-linear biologic signals, by digital EEG using 'CHASIM' program, non-linear times series signal simulator and then compared the UPDRS score with the degree of atrophy in the substantia nigra upon brain MRI and EEG data respectively. All subjects (N=20) showed definite hemiparkinsonism. RESULTS: Upon EEG analysis, a strong positive correlation was noted between FD of the left hemispheric electrodes (FP1,F3,T3,T5) and the UPDRS scores in left-sided symptomatic patients. Additionally, positive correlations were noted between the ipsilateral MRI index ratio in the right and left-sided symptomatic patients and respective UPDRS scores. CONCLUSIONS: These results suggested that thalamocortical drive is reduced in the contralateral hemisphere to parkinsonian symptoms and thalamocortical or corticothalamic glutaminergic projection in the ipsilateral hemisphere is increased in the early stage of Parkinson's disease. Additionally, hemiparkinsonim may primarilly cause anatomic and functional changes in the contralateral hemisphere and a compensatory effect in the ipsilateral hemisphere at the same time. We suggest that disease duration may be a compensating factor and of which require further investigation. We hope that our results will aid the understanding of the specific patterns of dysfunction and treatment effects by non-linear EEG measures and anatomic changes of the substantia nigra through continuous follow up of the patients. (J Korean Neurol Assoc 19(3):232~238, 2001)

Study of non-linearity relation of MTS cytotoxicity assay / 中国药理学通报

AIM We found in experiment that the relation of cell number-OD in MTS cytotoxicity assay is non-linearity. In this paper we probe into the relations of cell number-OD and drug dose-inhibition rate. METHODS Cells HL-60 and Raji were used in this experiment. Assay on the relation of cell number-OD: Cells of different concentrations were seeded into 96 well plates. OD was read at 490 nm after incubating with MTS for 1～5 hour. The regression curves were estimated from the data with the software SPSS 11.0. Cytotoxicity assay: Cells were seeded into 96 well plate and incubated with drug of different doses for 72 hours. OD was read at 490 nm after incubating with MTS for 3 hour. The regression curves were estimated from the data with the software SPSS 11.0. RESULTS The cubic curves fit well the relations of cell number-OD of the 2 strains of cells at 5 time points and the coefficient R2 of these cubic curves is 0.997～1.000, greater than the R2 0.938～0.993 of linear model. For the relations of dose-inhibition rate, the cubic curves also have best fitness and their R2 is 0.998～1.000 greater than the R2 0.948～0.987 of linear model of logarithm dose-probit. CONCLUSION For the relations of cell number-OD in MTS cytotoxicity assay, the fitness of cubic curves are better than the linear model. A more accurate IC 50 would be obtained by the cubic curve equation than by probit regression that is in common use.