The interaction of postural and voluntary strategies for stability in Parkinson's disease

de Lima-Pardini AC, Papegaaij S, Cohen RG, Teixeira LA, Smith BA, Horak FB. The interaction of postural and voluntary strategies for stability in Parkinson's disease. J Neurophysiol 108: 1244-1252, 2012. First published June 6, 2012; doi:10.1152/jn.00118.2012.-This study assessed the effects of stability constraints of a voluntary task on postural responses to an external perturbation in subjects with Parkinson's disease (PD) and healthy elderly participants. Eleven PD subjects and twelve control subjects were perturbed with backward surface translations while standing and performing two versions of a voluntary task: holding a tray with a cylinder placed with the flat side down [low constraint (LC)] or with the rolling, round side down [high constraint (HC)]. Participants performed alternating blocks of LC and HC trials. PD participants accomplished the voluntary task as well as control subjects, showing slower tray velocity in the HC condition compared with the LC condition. However, the latency of postural responses was longer in the HC condition only for control subjects. Control subjects presented different patterns of hip-shoulder coordination as a function of task constraint, whereas PD subjects had a relatively invariant pattern. Initiating the experiment with the HC task led to 1) decreased postural stability in PD subjects only and 2) reduced peak hip flexion in control subjects only. These results suggest that PD impairs the capacity to adapt postural responses to constraints imposed by a voluntary task.

The coronal heating problem

The heating of the solar corona has been investigated during four of decades and several mechanisms able to produce heating have been proposed. It has until now not been possible to produce quantitative estimates that would establish any of these heating mechanism as the most important in the solar corona. In order to investigate which heating mechanism is the most important, a more detailed approach is needed. In this thesis, the heating problem is approached ”ab initio”, using well observed facts and including realistic physics in a 3D magneto-hydrodynamic simulation of a small part of the solar atmosphere. The ”engine” of the heating mechanism is the solar photospheric velocity field, that braids the magnetic field into a configuration where energy has to be dissipated. The initial magnetic field is taken from an observation of a typical magnetic active region scaled down to fit inside the computational domain. The driving velocity field is generated by an algorithm that reproduces the statistical and geometrical fingerprints of solar granulation. Using a standard model atmosphere as the thermal initial condition, the simulation goes through a short startup phase, where the initial thermal stratification is quickly forgotten, after which the simulation stabilizes in statistical equilibrium. In this state, the magnetic field is able to dissipate the same amount of energy as is estimated to be lost through radiation, which is the main energy loss mechanism in the solar corona. The simulation produces heating that is intermittent on the smallest resolved scales and hot loops similar to those observed through narrow band filters in the ultra violet. Other observed characteristics of the heating are reproduced, as well as a coronal temperature of roughly one million K. Because of the ab initio approach, the amount of heating produced in these simulations represents a lower limit to coronal heating and the conclusion is that such heating of the corona is unavoidable.

Towards the construction of a validated numerical system to study the mesoscale dynamics of the North East Atlantic (2003-2006)

Máster en Oceanografía

Ensemble forecasting in the Mediterranean sea

A new methodology is being devised for ensemble ocean forecasting using distributions of the surface wind field derived from a Bayesian Hierarchical Model (BHM). The ocean members are forced with samples from the posterior distribution of the wind during the assimilation of satellite and in-situ ocean data. The initial condition perturbations are then consistent with the best available knowledge of the ocean state at the beginning of the forecast and amplify the ocean response to uncertainty only in the forcing. The ECMWF Ensemble Prediction System (EPS) surface winds are also used to generate a reference ocean ensemble to evaluate the performance of the BHM method that proves to be eective in concentrating the forecast uncertainty at the ocean meso-scale. An height month experiment of weekly BHM ensemble forecasts was performed in the framework of the operational Mediterranean Forecasting System. The statistical properties of the ensemble are compared with model errors throughout the seasonal cycle proving the existence of a strong relationship between forecast uncertainties due to atmospheric forcing and the seasonal cycle.

Modelli non lineari statici e dinamici su dati microeconomici: analisi delle condizioni finanziarie delle famiglie italiane

The thesis studies the economic and financial conditions of Italian households, by using microeconomic data of the Survey on Household Income and Wealth (SHIW) over the period 1998-2006. It develops along two lines of enquiry. First it studies the determinants of households holdings of assets and liabilities and estimates their correlation degree. After a review of the literature, it estimates two non-linear multivariate models on the interactions between assets and liabilities with repeated cross-sections. Second, it analyses households financial difficulties. It defines a quantitative measure of financial distress and tests, by means of non-linear dynamic probit models, whether the probability of experiencing financial difficulties is persistent over time. Chapter 1 provides a critical review of the theoretical and empirical literature on the estimation of assets and liabilities holdings, on their interactions and on households net wealth. The review stresses the fact that a large part of the literature explain households debt holdings as a function, among others, of net wealth, an assumption that runs into possible endogeneity problems. Chapter 2 defines two non-linear multivariate models to study the interactions between assets and liabilities held by Italian households. Estimation refers to a pooling of cross-sections of SHIW. The first model is a bivariate tobit that estimates factors affecting assets and liabilities and their degree of correlation with results coherent with theoretical expectations. To tackle the presence of non normality and heteroskedasticity in the error term, generating non consistent tobit estimators, semi-parametric estimates are provided that confirm the results of the tobit model. The second model is a quadrivariate probit on three different assets (safe, risky and real) and total liabilities; the results show the expected patterns of interdependence suggested by theoretical considerations. Chapter 3 reviews the methodologies for estimating non-linear dynamic panel data models, drawing attention to the problems to be dealt with to obtain consistent estimators. Specific attention is given to the initial condition problem raised by the inclusion of the lagged dependent variable in the set of explanatory variables. The advantage of using dynamic panel data models lies in the fact that they allow to simultaneously account for true state dependence, via the lagged variable, and unobserved heterogeneity via individual effects specification. Chapter 4 applies the models reviewed in Chapter 3 to analyse financial difficulties of Italian households, by using information on net wealth as provided in the panel component of the SHIW. The aim is to test whether households persistently experience financial difficulties over time. A thorough discussion is provided of the alternative approaches proposed by the literature (subjective/qualitative indicators versus quantitative indexes) to identify households in financial distress. Households in financial difficulties are identified as those holding amounts of net wealth lower than the value corresponding to the first quartile of net wealth distribution. Estimation is conducted via four different methods: the pooled probit model, the random effects probit model with exogenous initial conditions, the Heckman model and the recently developed Wooldridge model. Results obtained from all estimators accept the null hypothesis of true state dependence and show that, according with the literature, less sophisticated models, namely the pooled and exogenous models, over-estimate such persistence.

Modeling and simulation of a synthetic genetic circuit that implements a multicelled behavior in a growing microcolony of E. coli

Synthetic Biology is a relatively new discipline, born at the beginning of the New Millennium, that brings the typical engineering approach (abstraction, modularity and standardization) to biotechnology. These principles aim to tame the extreme complexity of the various components and aid the construction of artificial biological systems with specific functions, usually by means of synthetic genetic circuits implemented in bacteria or simple eukaryotes like yeast. The cell becomes a programmable machine and its low-level programming language is made of strings of DNA. This work was performed in collaboration with researchers of the Department of Electrical Engineering of the University of Washington in Seattle and also with a student of the Corso di Laurea Magistrale in Ingegneria Biomedica at the University of Bologna: Marilisa Cortesi. During the collaboration I contributed to a Synthetic Biology project already started in the Klavins Laboratory. In particular, I modeled and subsequently simulated a synthetic genetic circuit that was ideated for the implementation of a multicelled behavior in a growing bacterial microcolony. In the first chapter the foundations of molecular biology are introduced: structure of the nucleic acids, transcription, translation and methods to regulate gene expression. An introduction to Synthetic Biology completes the section. In the second chapter is described the synthetic genetic circuit that was conceived to make spontaneously emerge, from an isogenic microcolony of bacteria, two different groups of cells, termed leaders and followers. The circuit exploits the intrinsic stochasticity of gene expression and intercellular communication via small molecules to break the symmetry in the phenotype of the microcolony. The four modules of the circuit (coin flipper, sender, receiver and follower) and their interactions are then illustrated. In the third chapter is derived the mathematical representation of the various components of the circuit and the several simplifying assumptions are made explicit. Transcription and translation are modeled as a single step and gene expression is function of the intracellular concentration of the various transcription factors that act on the different promoters of the circuit. A list of the various parameters and a justification for their value closes the chapter. In the fourth chapter are described the main characteristics of the gro simulation environment, developed by the Self Organizing Systems Laboratory of the University of Washington. Then, a sensitivity analysis performed to pinpoint the desirable characteristics of the various genetic components is detailed. The sensitivity analysis makes use of a cost function that is based on the fraction of cells in each one of the different possible states at the end of the simulation and the wanted outcome. Thanks to a particular kind of scatter plot, the parameters are ranked. Starting from an initial condition in which all the parameters assume their nominal value, the ranking suggest which parameter to tune in order to reach the goal. Obtaining a microcolony in which almost all the cells are in the follower state and only a few in the leader state seems to be the most difficult task. A small number of leader cells struggle to produce enough signal to turn the rest of the microcolony in the follower state. It is possible to obtain a microcolony in which the majority of cells are followers by increasing as much as possible the production of signal. Reaching the goal of a microcolony that is split in half between leaders and followers is comparatively easy. The best strategy seems to be increasing slightly the production of the enzyme. To end up with a majority of leaders, instead, it is advisable to increase the basal expression of the coin flipper module. At the end of the chapter, a possible future application of the leader election circuit, the spontaneous formation of spatial patterns in a microcolony, is modeled with the finite state machine formalism. The gro simulations provide insights into the genetic components that are needed to implement the behavior. In particular, since both the examples of pattern formation rely on a local version of Leader Election, a short-range communication system is essential. Moreover, new synthetic components that allow to reliably downregulate the growth rate in specific cells without side effects need to be developed. In the appendix are listed the gro code utilized to simulate the model of the circuit, a script in the Python programming language that was used to split the simulations on a Linux cluster and the Matlab code developed to analyze the data.

The Feynman-Kac formula and applications to PDEs

The thesis presents a probabilistic approach to the theory of semigroups of operators, with particular attention to the Markov and Feller semigroups. The first goal of this work is the proof of the fundamental Feynman-Kac formula, which gives the solution of certain parabolic Cauchy problems, in terms of the expected value of the initial condition computed at the associated stochastic diffusion processes. The second target is the characterization of the principal eigenvalue of the generator of a semigroup with Markov transition probability function and of second order elliptic operators with real coefficients not necessarily self-adjoint. The thesis is divided into three chapters. In the first chapter we study the Brownian motion and some of its main properties, the stochastic processes, the stochastic integral and the Itô formula in order to finally arrive, in the last section, at the proof of the Feynman-Kac formula. The second chapter is devoted to the probabilistic approach to the semigroups theory and it is here that we introduce Markov and Feller semigroups. Special emphasis is given to the Feller semigroup associated with the Brownian motion. The third and last chapter is divided into two sections. In the first one we present the abstract characterization of the principal eigenvalue of the infinitesimal generator of a semigroup of operators acting on continuous functions over a compact metric space. In the second section this approach is used to study the principal eigenvalue of elliptic partial differential operators with real coefficients. At the end, in the appendix, we gather some of the technical results used in the thesis in more details. Appendix A is devoted to the Sion minimax theorem, while in appendix B we prove the Chernoff product formula for not necessarily self-adjoint operators.

Evaluation of Year-round Forage Management Systems for Spring- and Fall-Calving Beef Cows (A Progress Report)

A year-round grazing system for spring- and fall-calving cows was developed to compare animal production and performance, hay production and feeding, winter forage composition changes, and summer pasture yield and nutrient composition to that from a conventional, or minimal land system. Systems compared forage from smooth bromegrass-orchardgrass-birdsfoot trefoil pastures for both systems in the summer and corn crop residues and stockpiled grass-legume pastures for the year-round system to drylot hay feeding during winter for the minimal land system. The year-round grazing system utilized 1.67 acres of smooth bromegrassorchardgrass- birdsfoot trefoil (SB-O-T) pasture per cow in the summer, compared with 3.33 acres of (SB-O-T) pasture per cow in the control (minimal land) system. In addition to SB-O-T pastures, the year-round grazing system utilized 2.5 acres of tall fescue-red clover (TFRC) and 2.5 acres of smooth bromegrass-red clover (SBRC) per cow for grazing in both mid-summer and winter for fall- and spring-calving cows, respectively. First-cutting hay was harvested from the TF-RC and SB-RC pastures, and regrowth was grazed for approximately 45 days in the summer. These pastures were then fertilized with 40 lbs N/acre and stockpiled for winter grazing. Also utilized during the winter for spring-calving cows in the year-round grazing system were corn crop residue (CCR) pastures at an allowance of 2.5 acres per cow. In the minimal land system, hay was harvested from three-fourths of the area in SB-O-T pastures and stored for feeding in a drylot through the winter. Summer grazing was managed with rotational stocking for both systems, and winter grazing of stockpiled forages and corn crop residues by year-round system cows was managed by strip-stocking. Hay was fed to maintain a body condition score of 5 on a 9 point scale for spring-calving cows in both systems. Hay was supplemented as needed to maintain a body condition score of 3 for fall-calving cows nursing calves through the winter. Although initial condition scores for cows in both systems were different at the initiation of grazing for both winter and summer, there were no significant differences (P > .05) in overall condition score changes throughout both grazing seasons. In year 1, fall-calving cows in the year-round grazing system lost more (P < .05) body weight during winter than spring-calving cows in either system. In year 2, there were no differences seen in weight changes over winter for any group of cows. Average daily gains of fall calves in the yearround system were 1.9 lbs/day compared with weight gains of 2.5 lbs/day for spring calves from both systems. Yearly growing animal production from pastures for both years did not differ between systems when weight gains of stockers that grazed summer pastures in the year-round grazing system were added to weight gains of suckling calves. Carcass characteristics for all calves finished in the feedlot for both systems were similar. There were no significant differences in hay production between systems for year 1; however, amounts of hay needed to maintain cows were 923, 1373, 4732 lbs dry matter/cow for year-round fall-calving, year-round spring-calving, and minimal land spring-calving cows, respectively. In year 2, hay production per acre in the minimal land system was greater (P < .05) than for the year-round system, but the amounts of hay required per cow were 0, 0, and 4720 lbs dry matter/cow for yearround fall-calving, year-round spring-calving, and minimal land spring-calving cows, respectively.

Evolution of dominance under frequency-dependent intraspecific competition

A population-genetic analysis is performed of a two-locus two-allele model, in which the primary locus has a major effect on a quantitative trait that is under frequency-dependent disruptive selection caused by intraspecific competition for a continuum of resources. The modifier locus determines the degree of dominance at the trait level. We establish the conditions when a modifier allele can invade and when it becomes fixed if sufficiently frequent. In general, these are not equivalent because an unstable internal equilibrium may exist and the condition for successful invasion of the modifier is more restrictive than that for eventual fixation from already high frequency. However, successful invasion implies global fixation, i.e., fixation from any initial condition. Modifiers of large effect can become fixed, and also invade, in a wider parameter range than modifiers of small effect. We also study modifiers with a direct, frequency-independent deleterious fitness effect. We show that they can invade if they induce a sufficiently high level of dominance and if disruptive selection on the ecological trait is strong enough. For deleterious modifiers, successful invasion no longer implies global fixation because they can become stuck at an intermediate frequency due to a stable internal equilibrium. Although the conditions for invasion and for fixation if sufficiently frequent are independent of the linkage relation between the two loci, the rate of spread depends strongly on it. The present study provides further support to the view that evolution of dominance may be an efficient mechanism to remove unfit heterozygotes that are maintained by balancing selection. It also demonstrates that an invasion analysis of mutants of very small effect is insufficient to obtain a full understanding of the evolutionary dynamics under frequency-dependent selection.

Los manuscritos de El yo y el ello : Una relectura del Icc

Indagamos, a partir de los manuscritos inéditos de Das Ich und das Es, los puntos eminentes instaurados por la lectura de sus tres versiones: borrador, copia en limpio y texto publicado, en el momento en que surge una disimetría entre lo reprimido-icc y un Icc no-todo reprimido. Estos documentos revelan una transcripción 'casi' directa de las formulaciones freudianas en un estado naciente que llevan la marca de pensamientos urgidos por lo real del psicoanálisis, cuando todavía no está presente el tiempo de hacerse comprender en el contexto de su obra. Y es, justamente, en esta condición de inicial que el texto manuscrito ofrece una novedosa redefinición del Icc. Tal como señala en la Introducción las cuestiones que interroga en El yo y el ello retoman los pensamientos iniciados en su escrito de 1920 pero sin seguir la elaboración teórica que llama 'especulación analítica', aunque a último momento incluya sus conclusiones. Esta relectura interroga el encuentro de la pulsión de muerte con la segunda tópica, es decir, con ese material Icc que permanece no-reconocido. Y, a partir de 1924, establece de que manera el supuesto de la pulsión de muerte ilumina la discontinuidad existente ente icc e Icc [ello]. El cruce entre la hipótesis especulativa y un masoquismo erógeno primario produce un giro y da entrada a la cura misma como satisfacción sustitutiva. En síntesis, la lectura de los textos de El yo y el ello contando, por primera vez, con las tres versiones y sus dos anexos, introducen, con la disimilitud icc e Icc, un cambio de pregunta; anticipan la hendidura o Spaltung del sujeto, con ese objeto [el yo-cuerpo] que Freud no termina de construir; y anuncian que el Icc es lo que se funda de la huella de lo no-reconocido, que clama por ese mismo campo heterogéneo que obligaba en 1920 a tomar en consideración un más allá del principio de placer que divide el espacio euclidiano dejando asomar también su carácter disímil, asimétrico. Así, en ciertos momentos privilegiados de un análisis, vía trabajo del sueño, se produce la activación de los restos de lo visto y de lo oído, es decir, de un saber hecho de sedimentos, de los excedentes traumáticos del tesoro de palabras, para cada cual, de su lengua materna, cuando dicha lengua se separa del lenguaje produciendo un Icc no-todo reprimido que bordea el agujero de lo no-reconocido, es decir, de su punto de fracaso mismo: la imposibilidad con que el sexo se inscribe en el inconsciente

Los manuscritos de El yo y el ello : Una relectura del Icc

Indagamos, a partir de los manuscritos inéditos de Das Ich und das Es, los puntos eminentes instaurados por la lectura de sus tres versiones: borrador, copia en limpio y texto publicado, en el momento en que surge una disimetría entre lo reprimido-icc y un Icc no-todo reprimido. Estos documentos revelan una transcripción 'casi' directa de las formulaciones freudianas en un estado naciente que llevan la marca de pensamientos urgidos por lo real del psicoanálisis, cuando todavía no está presente el tiempo de hacerse comprender en el contexto de su obra. Y es, justamente, en esta condición de inicial que el texto manuscrito ofrece una novedosa redefinición del Icc. Tal como señala en la Introducción las cuestiones que interroga en El yo y el ello retoman los pensamientos iniciados en su escrito de 1920 pero sin seguir la elaboración teórica que llama 'especulación analítica', aunque a último momento incluya sus conclusiones. Esta relectura interroga el encuentro de la pulsión de muerte con la segunda tópica, es decir, con ese material Icc que permanece no-reconocido. Y, a partir de 1924, establece de que manera el supuesto de la pulsión de muerte ilumina la discontinuidad existente ente icc e Icc [ello]. El cruce entre la hipótesis especulativa y un masoquismo erógeno primario produce un giro y da entrada a la cura misma como satisfacción sustitutiva. En síntesis, la lectura de los textos de El yo y el ello contando, por primera vez, con las tres versiones y sus dos anexos, introducen, con la disimilitud icc e Icc, un cambio de pregunta; anticipan la hendidura o Spaltung del sujeto, con ese objeto [el yo-cuerpo] que Freud no termina de construir; y anuncian que el Icc es lo que se funda de la huella de lo no-reconocido, que clama por ese mismo campo heterogéneo que obligaba en 1920 a tomar en consideración un más allá del principio de placer que divide el espacio euclidiano dejando asomar también su carácter disímil, asimétrico. Así, en ciertos momentos privilegiados de un análisis, vía trabajo del sueño, se produce la activación de los restos de lo visto y de lo oído, es decir, de un saber hecho de sedimentos, de los excedentes traumáticos del tesoro de palabras, para cada cual, de su lengua materna, cuando dicha lengua se separa del lenguaje produciendo un Icc no-todo reprimido que bordea el agujero de lo no-reconocido, es decir, de su punto de fracaso mismo: la imposibilidad con que el sexo se inscribe en el inconsciente

Los manuscritos de El yo y el ello : Una relectura del Icc

Indagamos, a partir de los manuscritos inéditos de Das Ich und das Es, los puntos eminentes instaurados por la lectura de sus tres versiones: borrador, copia en limpio y texto publicado, en el momento en que surge una disimetría entre lo reprimido-icc y un Icc no-todo reprimido. Estos documentos revelan una transcripción 'casi' directa de las formulaciones freudianas en un estado naciente que llevan la marca de pensamientos urgidos por lo real del psicoanálisis, cuando todavía no está presente el tiempo de hacerse comprender en el contexto de su obra. Y es, justamente, en esta condición de inicial que el texto manuscrito ofrece una novedosa redefinición del Icc. Tal como señala en la Introducción las cuestiones que interroga en El yo y el ello retoman los pensamientos iniciados en su escrito de 1920 pero sin seguir la elaboración teórica que llama 'especulación analítica', aunque a último momento incluya sus conclusiones. Esta relectura interroga el encuentro de la pulsión de muerte con la segunda tópica, es decir, con ese material Icc que permanece no-reconocido. Y, a partir de 1924, establece de que manera el supuesto de la pulsión de muerte ilumina la discontinuidad existente ente icc e Icc [ello]. El cruce entre la hipótesis especulativa y un masoquismo erógeno primario produce un giro y da entrada a la cura misma como satisfacción sustitutiva. En síntesis, la lectura de los textos de El yo y el ello contando, por primera vez, con las tres versiones y sus dos anexos, introducen, con la disimilitud icc e Icc, un cambio de pregunta; anticipan la hendidura o Spaltung del sujeto, con ese objeto [el yo-cuerpo] que Freud no termina de construir; y anuncian que el Icc es lo que se funda de la huella de lo no-reconocido, que clama por ese mismo campo heterogéneo que obligaba en 1920 a tomar en consideración un más allá del principio de placer que divide el espacio euclidiano dejando asomar también su carácter disímil, asimétrico. Así, en ciertos momentos privilegiados de un análisis, vía trabajo del sueño, se produce la activación de los restos de lo visto y de lo oído, es decir, de un saber hecho de sedimentos, de los excedentes traumáticos del tesoro de palabras, para cada cual, de su lengua materna, cuando dicha lengua se separa del lenguaje produciendo un Icc no-todo reprimido que bordea el agujero de lo no-reconocido, es decir, de su punto de fracaso mismo: la imposibilidad con que el sexo se inscribe en el inconsciente

B-LOG: A branch and bound methodology for the parallel execution of logic programs

We propose a computational methodology -"B-LOG"-, which offers the potential for an effective implementation of Logic Programming in a parallel computer. We also propose a weighting scheme to guide the search process through the graph and we apply the concepts of parallel "branch and bound" algorithms in order to perform a "best-first" search using an information theoretic bound. The concept of "session" is used to speed up the search process in a succession of similar queries. Within a session, we strongly modify the bounds in a local database, while bounds kept in a global database are weakly modified to provide a better initial condition for other sessions. We also propose an implementation scheme based on a database machine using "semantic paging", and the "B-LOG processor" based on a scoreboard driven controller.

Inverse kinematics of a humanoid robot with non-spherical hip: a hybrid algorithm approach

This paper describes an approach to solve the inverse kinematics problem of humanoid robots whose construction shows a small but non negligible offset at the hip which prevents any purely analytical solution to be developed. Knowing that a purely numerical solution is not feasible due to variable efficiency problems, the proposed one first neglects the offset presence in order to obtain an approximate “solution” by means of an analytical algorithm based on screw theory, and then uses it as the initial condition of a numerical refining procedure based on the Levenberg‐Marquardt algorithm. In this way, few iterations are needed for any specified attitude, making it possible to implement the algorithm for real‐time applications. As a way to show the algorithm’s implementation, one case of study is considered throughout the paper, represented by the SILO2 humanoid robot.

Solution of optimal continuous low-thrust transfer using Lie transforms

This paper addresses the problem of optimal constant continuous low-thrust transfer in the context of the restricted two-body problem (R2BP). Using the Pontryagin’s principle, the problem is formulated as a two point boundary value problem (TPBVP) for a Hamiltonian system. Lie transforms obtained through the Deprit method allow us to obtain the canonical mapping of the phase flow as a series in terms of the order of magnitude of the thrust applied. The reachable set of states starting from a given initial condition using optimal control policy is obtained analytically. In addition, a particular optimal transfer can be computed as the solution of a non-linear algebraic equation. Se investiga el uso de series y transformadas de Lie en problemas de optimización de trayectorias de satélites impulsados por motores de bajo empuje