Differential calculus and integration of generalized functions over membranes

In this paper we continue the development of the differential calculus started in Aragona et al. (Monatsh. Math. 144: 13-29, 2005). Guided by the so-called sharp topology and the interpretation of Colombeau generalized functions as point functions on generalized point sets, we introduce the notion of membranes and extend the definition of integrals, given in Aragona et al. (Monatsh. Math. 144: 13-29, 2005), to integrals defined on membranes. We use this to prove a generalized version of the Cauchy formula and to obtain the Goursat Theorem for generalized holomorphic functions. A number of results from classical differential and integral calculus, like the inverse and implicit function theorems and Green's theorem, are transferred to the generalized setting. Further, we indicate that solution formulas for transport and wave equations with generalized initial data can be obtained as well.

Reliable estimation of dense optical flow fields with large displacements

[EN] In this paper we show that a classic optical flow technique by Nagel and Enkelmann can be regarded as an early anisotropic diffusion method with a diffusion tensor. We introduce three improvements into the model formulation that avoid inconsistencies caused by centering the brightness term and the smoothness term in different images use a linear scale-space focusing strategy from coarse to fine scales for avoiding convergence to physically irrelevant local minima, and create an energy functional that is invariant under linear brightness changes.  Applying a gradient descent method to the resulting energy functional leads to a system of diffusion-reaction equations. We prove that this system has a unique solution under realistic assumptions on the initial data, and we present an efficient linear implicit numerical scheme in detail. Our method creates flow fields with 100% density over the entire image domain, it is robust under a large range of parameter variations, and it can recover displacement fields that are far beyond the typical one-pixel limits which are characteristic for many differential methods for determining optical flow. We show that it performs better than the classic optical flow methods with 100%  density that are evaluated by Barron et al. (1994). Our software is available from the Internet.

Radar based improvements and diagnosis of the convective capabilities of the cosmo-2 model

In the last few years the resolution of numerical weather prediction (nwp) became higher and higher with the progresses of technology and knowledge. As a consequence, a great number of initial data became fundamental for a correct initialization of the models. The potential of radar observations has long been recognized for improving the initial conditions of high-resolution nwp models, while operational application becomes more frequent. The fact that many nwp centres have recently taken into operations convection-permitting forecast models, many of which assimilate radar data, emphasizes the need for an approach to providing quality information which is needed in order to avoid that radar errors degrade the model's initial conditions and, therefore, its forecasts. Environmental risks can can be related with various causes: meteorological, seismical, hydrological/hydraulic. Flash floods have horizontal dimension of 1-20 Km and can be inserted in mesoscale gamma subscale, this scale can be modeled only with nwp model with the highest resolution as the COSMO-2 model. One of the problems of modeling extreme convective events is related with the atmospheric initial conditions, in fact the scale dimension for the assimilation of atmospheric condition in an high resolution model is about 10 Km, a value too high for a correct representation of convection initial conditions. Assimilation of radar data with his resolution of about of Km every 5 or 10 minutes can be a solution for this problem. In this contribution a pragmatic and empirical approach to deriving a radar data quality description is proposed to be used in radar data assimilation and more specifically for the latent heat nudging (lhn) scheme. Later the the nvective capabilities of the cosmo-2 model are investigated through some case studies. Finally, this work shows some preliminary experiments of coupling of a high resolution meteorological model with an Hydrological one.

Changes in coral reef communities across a natural gradient in seawater pH

Ocean acidification threatens the survival of coral reef ecosystems worldwide. The negative effects of ocean acidification observed in many laboratory experiments have been seen in studies of naturally low-pH reefs, with little evidence to date for adaptation. Recently, we reported initial data suggesting that low-pH coral communities of the Palau Rock Islands appear healthy despite the extreme conditions in which they live. Here, we build on that observation with a comprehensive statistical analysis of benthic communities across Palau's natural acidification gradient. Our analysis revealed a shift in coral community composition but no impact of acidification on coral richness, coralline algae abundance, macroalgae cover, coral calcification, or skeletal density. However, coral bioerosion increased 11-fold as pH decreased from the barrier reefs to the Rock Island bays. Indeed, a comparison of the naturally low-pH coral reef systems studied so far revealed increased bioerosion to be the only consistent feature among them, as responses varied across other indices of ecosystem health. Our results imply that whereas community responses may vary, escalation of coral reef bioerosion and acceleration of a shift from net accreting to net eroding reef structures will likely be a global signature of ocean acidification.

Pleistocene and upper Pliocene sapropels in the Tyrrhenian Sea, Mediterranean Sea

A most significant finding of the ODP Leg 107 drilling campaign was the recovery of at least 56 distinct sapropel intervals in upper Pliocene to Pleistocene sediments of six sites drilled in the Tyrrhenian Sea. Except for 3 repots of disturbed organic-rich sediments - recovered in Core 201 of the Swedish Deep-Sea Expedition, in Core 2R-1,107 cm of Site 373 (Leg 13 DSDP) and at Site 373, Core 1-2,O-5 cm of DSDP Leg 42A - sapropels had previously only been described from the eastern Mediterranean and the Black Sea. Scientific deep-sea drilling in the Tyrrhenian Sea during DSDP Legs 13 and 42A apparently missed most of these deposits due to spot coring and rotary drilling techniques; high sedimentation rates may have precluded recovery by conventional gravity coring devices. The recovery of multiple layers of sapropels and sapropelic sediments in the Tyrrhenian Sea demonstrates that oceanographic conditions conducive to sapropel formation were not confined to the Black Sea and eastern Mediterranean, but occurred sporadically and possibly simultaneously in the entire Mediterranean during the Pliocene and Pleistocene. In the light of this finding, previous models of sapropel genesis may need reconsideration. In this paper, we present some initial data on the Tyrrhenian sapropels and suggest some implications of their massive occurrence in the western Mediterranean realm. We end by outlining possible causes for deposition of sapropels in an attempt to revive the interest in sapropels and their paleoceanographic significance.

Hydrochemical Atlas of the Arctic Ocean

Introduction: Chemical composition of water determines its physical properties and character of processes proceeding in it: freezing temperature, volume of evaporation, density, color, transparency, filtration capacity, etc. Presence of chemical elements in water solution confers waters special physical properties exerting significant influence on their circulation, creates necessary conditions for development and inhabitance of flora and fauna, and imparts to the ocean waters some chemical features that radically differ them from the land waters (Alekin & Liakhin, 1984). Hydrochemical information helps to determine elements of water circulation, convection depth, makes it easier to distinguish water masses and gives additional knowledge of climatic variability of ocean conditions. Hydrochemical information is a necessary part of biological research. Water chemical composition can be the governing characteristics determining possibility and limits of use of marine objects, both stationary and moving in sea water. Subject of investigation of hydrochemistry is study of dynamics of chemical composition, i.e. processes of its formation and hydrochemical conditions of water bodies (Alekin & Liakhin 1984). The hydrochemical processes in the Arctic Ocean are the least known. Some information on these processes can be obtained in odd publications. A generalizing study of hydrochemical conditions in the Arctic Ocean based on expeditions conducted in the years 1948-1975 has been carried out by Rusanov et al. (1979). The "Atlas of the World Ocean: the Arctic Ocean" contains a special section "Hydrochemistry" (Gorshkov, 1980). Typical vertical profiles, transects and maps for different depths - 0, 100, 300, 500, 1000, 2000, 3000 m are given in this section for the following parameters: dissolved oxygen, phosphate, silicate, pH and alkaline-chlorine coefficient. The maps were constructed using the data of expeditions conducted in the years 1948-1975. The illustrations reflect main features of distribution of the hydrochemical elements for multi-year period and represent a static image of hydrochemical conditions. Distribution of the hydrochemical elements on the ocean surface is given for two seasons - winter and summer, for the other depths are given mean annual fields. Aim of the present Atlas is description of hydrochemical conditions in the Arctic Ocean on the basis of a greater body of hydrochemical information for the years 1948-2000 and using the up-to-date methods of analysis and electronic forms of presentation of hydrochemical information. The most wide-spread characteristics determined in water samples were used as hydrochemical indices. They are: dissolved oxygen, phosphate, silicate, pH, total alkalinity, nitrite and nitrate. An important characteristics of water salt composition - "salinity" has been considered in the Oceanographic Atlas of the Arctic Ocean (1997, 1998). Presentation of the hydrochemical characteristics in this Hydrochemical Atlas is wider if compared with that of the former Atlas (Gorshkov, 1980). Maps of climatic distribution of the hydrochemical elements were constructed for all the standard depths, and seasonal variability of the hydrochemical parameters is given not only for the surface, but also for the underlying standard depths up to 400 m and including. Statistical characteristics of the hydrochemical elements are given for the first time. Detailed accuracy estimates of initial data and map construction are also given in the Atlas. Calculated values of mean-root deviations, maximum and minimum values of the parameters demonstrate limits of their variability for the analyzed period of observations. Therefore, not only investigations of chemical statics are summarized in the Atlas, but also some elements of chemical dynamics are demonstrated. Digital arrays of the hydrochemical elements obtained in nodes of a regular grid are the new form of characteristics presentation in the Atlas. It should be mentioned that the same grid and the same boxes were used in the Atlas, as those that had been used by creation of the US-Russian climatic Oceanographic Atlas. It allows to combine hydrochemical and oceanographic information of these Atlases. The first block of the digital arrays contains climatic characteristics calculated using direct observational data. These climatic characteristics were not calculated in the regions without observations, and the information arrays for these regions have gaps. The other block of climatic information in a gridded form was obtained with the help of objective analysis of observational data. Procedure of the objective analysis allowed us to obtain climatic estimates of the hydrochemical characteristics for the whole water area of the Arctic Ocean including the regions not covered by observations. Data of the objective analysis can be widely used, in particular, in hydrobiological investigations and in modeling of hydrochemical conditions of the Arctic Ocean. Array of initial measurements is a separate block. It includes all the available materials of hydrochemical observations in the form, as they were presented in different sources. While keeping in mind that this array contains some amount of perverted information, the authors of the Atlas assumed it necessary to store this information in its primary form. Methods of data quality control can be developed in future in the process of hydrochemical information accumulation. It can be supposed that attitude can vary in future to the data that were rejected according to the procedure accepted in the Atlas. The hydrochemical Atlas of the Arctic Ocean is the first specialized and electronic generalization of hydrochemical observations in the Arctic Ocean and finishes the program of joint efforts of Russian and US specialists in preparation of a number of atlases for the Arctic. The published Oceanographic Atlas (1997, 1998), Atlas of Arctic Meteorology and Climate (2000), Ice Atlas of the Arctic Ocean prepared for publication and Hydrochemical Atlas of the Arctic Ocean represent a united series of fundamental generalizations of empirical knowledge of Arctic Ocean nature at climatic level. The Hydrochemical Atlas of the Arctic Ocean was elaborated in the result of joint efforts of the SRC of the RF AARI and IARC. Dr. Ye. Nikiforov was scientific supervisor of the Atlas, Dr. R. Colony was manager on behalf of the USA and Dr. L. Timokhov - on behalf of Russia.

Asymptotic stability of a mathematical model of cell population

We consider a simplified system of a growing colony of cells described as a free boundary problem. The system consists of two hyperbolic equations of first order coupled to an ODE to describe the behavior of the boundary. The system for cell populations includes non-local terms of integral type in the coefficients. By introducing a comparison with solutions of an ODE's system, we show that there exists a unique homogeneous steady state which is globally asymptotically stable for a range of parameters under the assumption of radially symmetric initial data.

On a competitive system under chemotactic effects with non-local terms

In this paper, we study a system of partial differential equations describing the evolution of a population under chemotactic effects with non-local reaction terms. We consider an external application of chemoattractant in the system and study the cases of one and two populations in competition. By introducing global competitive/cooperative factors in terms of the total mass of the populations, weobtain, forarangeofparameters, thatanysolutionwithpositive and bounded initial data converges to a spatially homogeneous state with positive components. The proofs rely on the maximum principle for spatially homogeneous sub- and super-solutions.

Application of Independent Components Analysis with the JADE algorithm and NIR hyperspectral imaging for revealing food adulteration

In recent years, Independent Components Analysis (ICA) has proven itself to be a powerful signal-processing technique for solving the Blind-Source Separation (BSS) problems in different scientific domains. In the present work, an application of ICA for processing NIR hyperspectral images to detect traces of peanut in wheat flour is presented. Processing was performed without a priori knowledge of the chemical composition of the two food materials. The aim was to extract the source signals of the different chemical components from the initial data set and to use them in order to determine the distribution of peanut traces in the hyperspectral images. To determine the optimal number of independent component to be extracted, the Random ICA by blocks method was used. This method is based on the repeated calculation of several models using an increasing number of independent components after randomly segmenting the matrix data into two blocks and then calculating the correlations between the signals extracted from the two blocks. The extracted ICA signals were interpreted and their ability to classify peanut and wheat flour was studied. Finally, all the extracted ICs were used to construct a single synthetic signal that could be used directly with the hyperspectral images to enhance the contrast between the peanut and the wheat flours in a real multi-use industrial environment. Furthermore, feature extraction methods (connected components labelling algorithm followed by flood fill method to extract object contours) were applied in order to target the spatial location of the presence of peanut traces. A good visualization of the distributions of peanut traces was thus obtained

Predicción de tráfico de contenedores a corto plazo mediante técnicas de minería de datos : redes neuronales artificiales y redes bayesianas

El correcto pronóstico en el ámbito de la logística de transportes es de vital importancia para una adecuada planificación de medios y recursos, así como de su optimización. Hasta la fecha los estudios sobre planificación portuaria se basan principalmente en modelos empíricos; que se han utilizado para planificar nuevas terminales y desarrollar planes directores cuando no se dispone de datos iniciales, analíticos; más relacionados con la teoría de colas y tiempos de espera con formulaciones matemáticas complejas y necesitando simplificaciones de las mismas para hacer manejable y práctico el modelo o de simulación; que requieren de una inversión significativa como para poder obtener resultados aceptables invirtiendo en programas y desarrollos complejos. La Minería de Datos (MD) es un área moderna interdisciplinaria que engloba a aquellas técnicas que operan de forma automática (requieren de la mínima intervención humana) y, además, son eficientes para trabajar con las grandes cantidades de información disponible en las bases de datos de numerosos problemas prácticos. La aplicación práctica de estas disciplinas se extiende a numerosos ámbitos comerciales y de investigación en problemas de predicción, clasificación o diagnosis. Entre las diferentes técnicas disponibles en minería de datos las redes neuronales artificiales (RNA) y las redes probabilísticas o redes bayesianas (RB) permiten modelizar de forma conjunta toda la información relevante para un problema dado. En el presente trabajo se han analizado dos aplicaciones de estos casos al ámbito portuario y en concreto a contenedores. En la Tesis Doctoral se desarrollan las RNA como herramienta para obtener previsiones de tráfico y de recursos a futuro de diferentes puertos, a partir de variables de explotación, obteniéndose valores continuos. Para el caso de las redes bayesianas (RB), se realiza un trabajo similar que para el caso de las RNA, obteniéndose valores discretos (un intervalo). El principal resultado que se obtiene es la posibilidad de utilizar tanto las RNA como las RB para la estimación a futuro de parámetros físicos, así como la relación entre los mismos en una terminal para una correcta asignación de los medios a utilizar y por tanto aumentar la eficiencia productiva de la terminal. Como paso final se realiza un estudio de complementariedad de ambos modelos a corto plazo, donde se puede comprobar la buena aceptación de los resultados obtenidos. Por tanto, se puede concluir que estos métodos de predicción pueden ser de gran ayuda a la planificación portuaria. The correct assets’ forecast in the field of transportation logistics is a matter of vital importance for a suitable planning and optimization of the necessary means and resources. Up to this date, ports planning studies were basically using empirical models to deal with new terminals planning or master plans development when no initial data are available; analytical models, more connected to the queuing theory and the waiting times, and very complicated mathematical formulations requiring significant simplifications to acquire a practical and easy to handle model; or simulation models, that require a significant investment in computer codes and complex developments to produce acceptable results. The Data Mining (DM) is a modern interdisciplinary field that include those techniques that operate automatically (almost no human intervention is required) and are highly efficient when dealing with practical problems characterized by huge data bases containing significant amount of information. These disciplines’ practical application extends to many commercial or research fields, dealing with forecast, classification or diagnosis problems. Among the different techniques of the Data Mining, the Artificial Neuronal Networks (ANN) and the probabilistic – or Bayesian – networks (BN) allow the joint modeling of all the relevant information for a given problem. This PhD work analyses their application to two practical cases in the ports field, concretely to container terminals. This PhD work details how the ANN have been developed as a tool to produce traffic and resources forecasts for several ports, based on exploitation variables to obtain continuous values. For the Bayesian networks case (BN), a similar development has been carried out, obtaining discreet values (an interval). The main finding is the possibility to use ANN and BN to estimate future needs of the port’s or terminal’s physical parameters, as well as the relationship between them within a specific terminal, that allow a correct assignment of the necessary means and, thus, to increase the terminal’s productive efficiency. The final step is a short term complementarily study of both models, carried out in order to verify the obtained results. It can thus be stated that these prediction methods can be a very useful tool in ports’ planning.

El Problema de Lambert en el Contexto de Optimización de Trayectorias Espaciales

Esta tesis se basa en el estudio de la trayectoria que pasa por dos puntos en el problema de los dos cuerpos, inicialmente desarrollado por Lambert, del que toma su nombre. En el pasado, el Problema de Lambert se ha utilizado para la determinación de órbitas a partir de observaciones astronómicas de los cuerpos celestes. Actualmente, se utiliza continuamente en determinación de órbitas, misiones planetaria e interplanetarias, encuentro espacial e interceptación, o incluso en corrección de orbitas. Dada su gran importancia, se decide investigar especialmente sobre su solución y las aplicaciones en las misiones espaciales actuales. El campo de investigación abierto, es muy amplio, así que, es necesario determinar unos objetivos específicos realistas, en el contexto de ejecución de una Tesis, pero que sirvan para mostrar con suficiente claridad el potencial de los resultados aportados en este trabajo, e incluso poder extenderlos a otros campos de aplicación. Como resultado de este análisis, el objetivo principal de la Tesis se enfoca en el desarrollo de algoritmos para resolver el Problema de Lambert, que puedan ser aplicados de forma muy eficiente en las misiones reales donde aparece. En todos los desarrollos, se ha considerado especialmente la eficiencia del cálculo computacional necesario en comparación con los métodos existentes en la actualidad, destacando la forma de evitar la pérdida de precisión inherente a este tipo de algoritmos y la posibilidad de aplicar cualquier método iterativo que implique el uso de derivadas de cualquier orden. En busca de estos objetivos, se desarrollan varias soluciones para resolver el Problema de Lambert, todas ellas basadas en la resolución de ecuaciones transcendentes, con las cuales, se alcanzan las siguientes aportaciones principales de este trabajo: • Una forma genérica completamente diferente de obtener las diversas ecuaciones para resolver el Problema de Lambert, mediante desarrollo analítico, desde cero, a partir de las ecuaciones elementales conocidas de las cónicas (geométricas y temporal), proporcionando en todas ellas fórmulas para el cálculo de derivadas de cualquier orden. • Proporcionar una visión unificada de las ecuaciones más relevantes existentes, mostrando la equivalencia con variantes de las ecuaciones aquí desarrolladas. • Deducción de una nueva variante de ecuación, el mayor logro de esta Tesis, que destaca en eficiencia sobre todas las demás (tanto en coste como en precisión). • Estudio de la sensibilidad de la solución ante variación de los datos iniciales, y como aplicar los resultados a casos reales de optimización de trayectorias. • También, a partir de los resultados, es posible deducir muchas propiedades utilizadas en la literatura para simplificar el problema, en particular la propiedad de invariancia, que conduce al Problema Transformado Simplificado. ABSTRACT This thesis is based on the study of the two-body, two-point boundary-value problem, initially developed by Lambert, from who it takes its name. Since the past, Lambert's Problem has been used for orbit determination from astronomical observations of celestial bodies. Currently, it is continuously used in orbit determinations, for planetary and interplanetary missions, space rendezvous, and interception, or even in orbit corrections. Given its great importance, it is decided to investigate their solution and applications in the current space missions. The open research field is very wide, it is necessary to determine specific and realistic objectives in the execution context of a Thesis, but that these serve to show clearly enough the potential of the results provided in this work, and even to extended them to other areas of application. As a result of this analysis, the main aim of the thesis focuses on the development of algorithms to solve the Lambert’s Problem which can be applied very efficiently in real missions where it appears. In all these developments, it has been specially considered the efficiency of the required computational calculation compared to currently existing methods, highlighting how to avoid the loss of precision inherent in such algorithms and the possibility to apply any iterative method involving the use of derivatives of any order. Looking to meet these objectives, a number of solutions to solve the Lambert’s Problem are developed, all based on the resolution of transcendental equations, with which the following main contributions of this work are reached: • A completely different generic way to get the various equations to solve the Lambert’s Problem by analytical development, from scratch, from the known elementary conic equations (geometrics and temporal), by providing, in all cases, the calculation of derivatives of any order. • Provide a unified view of most existing relevant equations, showing the equivalence with variants of the equations developed here. • Deduction of a new variant of equation, the goal of this Thesis, which emphasizes efficiency (both computational cost and accuracy) over all other. • Estudio de la sensibilidad de la solución ante la variación de las condiciones iniciales, mostrando cómo aprovechar los resultados a casos reales de optimización de trayectorias. • Study of the sensitivity of the solution to the variation of the initial data, and how to use the results to real cases of trajectories’ optimization. • Additionally, from results, it is possible to deduce many properties used in literature to simplify the problem, in particular the invariance property, which leads to a simplified transformed problem.

Application of a SPH depth-integrated model to landslide run-out analysis

Hazard and risk assessment of landslides with potentially long run-out is becoming more and more important. Numerical tools exploiting different constitutive models, initial data and numerical solution techniques are important for making the expert’s assessment more objective, even though they cannot substitute for the expert’s understanding of the site-specific conditions and the involved processes. This paper presents a depth-integrated model accounting for pore water pressure dissipation and applications both to real events and problems for which analytical solutions exist. The main ingredients are: (i) The mathematical model, which includes pore pressure dissipation as an additional equation. This makes possible to model flowslide problems with a high mobility at the beginning, the landslide mass coming to rest once pore water pressures dissipate. (ii) The rheological models describing basal friction: Bingham, frictional, Voellmy and cohesive-frictional viscous models. (iii) We have implemented simple erosion laws, providing a comparison between the approaches of Egashira, Hungr and Blanc. (iv) We propose a Lagrangian SPH model to discretize the equations, including pore water pressure information associated to the moving SPH nodes

Classical solutions for a logarithmic fractional diffusion equation

We prove global existence and uniqueness of strong solutions to the logarithmic porous medium type equation with fractional diffusion ?tu + (?)1/2 log(1 + u) = 0, posed for x ? R, with nonnegative initial data in some function space of LlogL type. The solutions are shown to become bounded and C? smooth in (x, t) for all positive times. We also reformulate this equation as a transport equation with nonlocal velocity and critical viscosity, a topic of current relevance. Interesting functional inequalities are involved.

Well posedness of an integrodifferential kinetic model of Fokker-Planck type for angiogenesis.

Tumor induced angiogenesis processes including the effect of stochastic motion and branching of blood vessels can be described coupling a (nonlocal in time) integrodifferential kinetic equation of Fokker–Planck type with a diffusion equation for the tumor induced ingiogenic factor. The chemotactic force field depends on the flux of blood vessels through the angiogenic factor. We develop an existence and uniqueness theory for this system under natural assumptions on the initial data. The proof combines the construction of fundamental solutions for associated linearized problems with comparison principles, sharp estimates of the velocity integrals and compactness results for this type of kinetic and parabolic operators

Contribuições ao processo de inserção das PMES no mercado de capitais brasileiro

O crescimento de uma empresa pode ser apoiado com recursos de terceiros provenientes do mercado de crédito ou do mercado de capitais. Credores ou potenciais investidores disponibilizam recursos a partir de um processo de avaliação de indicadores de performance. Para as PMEs que consideram o crescimento, conhecer como os indicadores relevantes se comportam ao longo de um ciclo de crescimento é uma questão estratégica. Fatores como tamanho, lucratividade, oportunidades de crescimento, composição de ativos das empresas, risco inerente aos resultados, têm sido vinculados a determinantes de uma estrutura de capital. Assim sendo, este trabalho busca verificar quais indicadores podem nortear o desempenho empresarial de PMEs ao longo de um ciclo de crescimento. Como contribuição original, este trabalho apresenta um painel com indicadores em diferentes estágios de crescimento que resultam na geração de valor para os proprietários e potenciais investidores do mercado de capitais. A amostra inicial é composta por 1.610 empresas para o período de 2010 a 2014. Entretanto, considerando a disponibilidade de informações, a amostra final é composta por 28 empresas de porte médio/grande, 387 empresas grandes e 138 empresas listadas na BM&FBOVESPA, totalizando 553 empresas. A metodologia adotada envolve a classificação de porte de empresa do BNDES como critério para definir ciclo de crescimento, e testes de estatística descritiva, análise fatorial, análise de correlação, regressão múltipla linear e montagem de painel. Como resultado, verificou-se que as variáveis tamanho, composição de ativos e lucratividade são fatores que explicam o endividamento de curto prazo para o estágio médias/grandes empresas. Ainda, que esses fatores explicam o endividamento de longo prazo para os estágios grandes e empresas listadas na BM&FBOVESPA. Tais resultados estão de acordo com estudos prévios, mas as variáveis relacionadas a volatilidade e crescimento não foram significantes nos modelos para os estágios de empresas. O painel montado a partir das variáveis de composição de ativos e lucratividade indicou que endividamento de curto prazo, endividamento de longo prazo, receita líquida, retorno sobre o patrimônio líquido e lucros antes de juros, impostos, depreciação e amortização (EBITDA) sinalizam empresas, em cada estágio de ciclo de crescimento do estudo, que buscam o crescimento com rentabilidade acima da média e atendem a critérios valorizados pelo investidor do mercado de capitais. Estes indicadores podem sinalizar o desempenho empresarial de PMEs ao longo de um ciclo de crescimento