Extended kalman filter for estimation of parameters in nonlinear state-space models of biochemical networks.

It is system dynamics that determines the function of cells, tissues and organisms. To develop mathematical models and estimate their parameters are an essential issue for studying dynamic behaviors of biological systems which include metabolic networks, genetic regulatory networks and signal transduction pathways, under perturbation of external stimuli. In general, biological dynamic systems are partially observed. Therefore, a natural way to model dynamic biological systems is to employ nonlinear state-space equations. Although statistical methods for parameter estimation of linear models in biological dynamic systems have been developed intensively in the recent years, the estimation of both states and parameters of nonlinear dynamic systems remains a challenging task. In this report, we apply extended Kalman Filter (EKF) to the estimation of both states and parameters of nonlinear state-space models. To evaluate the performance of the EKF for parameter estimation, we apply the EKF to a simulation dataset and two real datasets: JAK-STAT signal transduction pathway and Ras/Raf/MEK/ERK signaling transduction pathways datasets. The preliminary results show that EKF can accurately estimate the parameters and predict states in nonlinear state-space equations for modeling dynamic biochemical networks.

Signalling ballet in space and time.

Although we have amassed extensive catalogues of signalling network components, our understanding of the spatiotemporal control of emergent network structures has lagged behind. Dynamic behaviour is starting to be explored throughout the genome, but analysis of spatial behaviours is still confined to individual proteins. The challenge is to reveal how cells integrate temporal and spatial information to determine specific biological functions. Key findings are the discovery of molecular signalling machines such as Ras nanoclusters, spatial activity gradients and flexible network circuitries that involve transcriptional feedback. They reveal design principles of spatiotemporal organization that are crucial for network function and cell fate decisions.

Sulforaphane improves cognitive function administered following traumatic brain injury.

Recent studies have shown that sulforaphane, a naturally occurring compound that is found in cruciferous vegetables, offers cellular protection in several models of brain injury. When administered following traumatic brain injury (TBI), sulforaphane has been demonstrated to attenuate blood-brain barrier permeability and reduce cerebral edema. These beneficial effects of sulforaphane have been shown to involve induction of a group of cytoprotective, Nrf2-driven genes, whose protein products include free radical scavenging and detoxifying enzymes. However, the influence of sulforaphane on post-injury cognitive deficits has not been examined. In this study, we examined if sulforaphane, when administered following cortical impact injury, can improve the performance of rats tested in hippocampal- and prefrontal cortex-dependent tasks. Our results indicate that sulforaphane treatment improves performance in the Morris water maze task (as indicated by decreased latencies during learning and platform localization during a probe trial) and reduces working memory dysfunction (tested using the delayed match-to-place task). These behavioral improvements were only observed when the treatment was initiated 1h, but not 6h, post-injury. These studies support the use of sulforaphane in the treatment of TBI, and extend the previously observed protective effects to include enhanced cognition.

The Beach in Anglophone Literatures and Cultures: Reading Littoral Space

From early colonial encounters to the ecological disasters of the twenty-first century, the performativity of contact has been a crucial element in the political significance of the beach. Conceptualising the beach as a creative trope and as a socio-cultural site, as well as an aesthetically productive topography, this collection examines its multiplicity of meanings and functions as a natural environment engendering both desire and fear in the human imagination from the Victorian period to the present. The contributors examine literature, film, and art, in addition to moments of encounter and environmental crisis, to highlight the beach as a social space inspiring particular codes of behaviour and specific discourses, as a geographical frontier between land and water, as an historical site of contact and conflict, and as a vacationscape promising regeneration and withdrawal from everyday life. The diversity of the beach is reflected in the geographical range, with essays on locales and texts from Britain, Ireland, the Caribbean, South Africa, the United States, Polynesia, and New Zealand. Focusing on the changed function of the beach as a result of processes of industrialisation and the rise of a modern leisure and health culture, this interdisciplinary volume theorises the beach as a demarcater of the precarious boundary between land and the sea, as well as between nature and culture.

Keep at bay! - Abnormal personal space regulation as marker of paranoia in schizophrenia.

BACKGROUND During threat, interpersonal distance is deliberately increased. Personal space regulation is related to amygdala function and altered in schizophrenia, but it remains unknown whether it is particularly associated with paranoid threat. METHODS We compared performance in two tests on personal space between 64 patients with schizophrenia spectrum disorders and 24 matched controls. Patients were stratified in those with paranoid threat, neutral affect or paranoid experience of power. In the stop-distance paradigm, participants indicated the minimum tolerable interpersonal distance. In the fixed-distance paradigm, they indicated the level of comfort at fixed interpersonal distances. RESULTS Paranoid threat increased interpersonal distance two-fold in the stop-distance paradigm, and reduced comfort ratings in the fixed-distance paradigm. In contrast, patients experiencing paranoid power had high comfort ratings at any distance. Patients with neutral affect did not differ from controls in the stop-distance paradigm. Differences between groups remained when controlling for gender and positive symptom severity. Among schizophrenia patients, the stop-distance paradigm detected paranoid threat with 93% sensitivity and 83% specificity. CONCLUSIONS Personal space regulation is not generally altered in schizophrenia. However, state paranoid experience has distinct contributions to personal space regulation. Subjects experiencing current paranoid threat share increased safety-seeking behavior.

Composition Space Analysis in the Development of Copper Molybdate Hybrids Decorated by a Bifunctional Pyrazolyl/1,2,4-Triazole Ligand

A bitopic ligand, 4-(3,5-dimethylpyrazol-4-yl)-1,2,4-triazole (Hpz-tr) (1), containing two different heterocyclic moieties was employed for the design of copper(II)–molybdate solids under hydrothermal conditions. In the multicomponent CuII/Hpz-tr/MoVI system, a diverse set of coordination hybrids, [Cu(Hpz-tr)2SO4]·3H2O (2), [Cu(Hpz-tr)Mo3O10] (3), [Cu4(OH)4(Hpz-tr)4Mo8O26]·6H2O (4), [Cu(Hpz-tr)2Mo4O13] (5), and [Mo2O6(Hpz-tr)]·H2O (6), was prepared and characterized. A systematic investigation of these systems in the form of a ternary crystallization diagram approach was utilized to show the influence of the molar ratios of starting reagents, the metal (CuII and MoVI) sources, the temperature, etc., on the reaction products outcome. Complexes 2–4 dominate throughout a wide crystallization range of the composition triangle, while the other two compounds 5 and 6 crystallize as minor phases in a narrow concentration range. In the crystal structures of 2–6, the organic ligand behaves as a short [N–N]-triazole linker between metal centers Cu···Cu in 2–4, Cu···Mo in 5, and Mo···Mo in 6, while the pyrazolyl function remains uncoordinated. This is the reason for the exceptional formation of low-dimensional coordination motifs: 1D for 2, 4, and 6 and 2D for 3 and 5. In all cases, the pyrazolyl group is involved in H bonding (H-donor/H-acceptor) and is responsible for π–π stacking, thus connecting the chain and layer structures in more complicated H-bonding architectures. These compounds possess moderate thermal stability up to 250–300 °C. The magnetic measurements were performed for 2–4, revealing in all three cases antiferromagnetic exchange interactions between neighboring CuII centers and long-range order with a net moment below Tc of 13 K for compound 4.

Space requirement of a prefabricated bar on two interforaminal implants: a prospective clinical study

OBJECTIVES This clinical study measured the dimensional changes of existing lower complete dentures due to the integration of a prefabricated implant bar. Additionally, the impact of this dimensional change on patient satisfaction and oral function was analyzed. METHODS Twenty edentulous patients (10 men/10 women; aged 65.9 ± 11.8 years) received two interforaminal implants. Subsequent to surgery, a chair side adapted, prefabricated bar (SFI Bar(®), C+M, Biel, Switzerland) was inserted, and the matrix was polymerized into the existing lower denture. The change of the denture's lingual dimension was recorded by means of a bicolored, silicone denture duplicate that was sectioned in the oro-vestibular direction in the regions of the symphysis (S) and the implants (I-left, I-right). On the sections, the dimensional increase was measured using a light microscope. Six months after bar insertion, patients answered a standardized questionnaire. RESULTS All dentures exhibited increased lingual volume, more extensively at S than at I (P = 0.001). At S, the median diagonal size of the denture was doubled (+4.33 mm), and at I, the median increase was 50% (I-left/-right = +2.66/+2.62 mm). The original denture size influenced the volume increase (P = 0.024): smaller dentures led to a larger increase. The amount of denture increase did not have negative impact on either self-perceived oral function or patient satisfaction. Approximately, 95% of the patients were satisfied with the treatment results. CONCLUSIONS The lingual size of a lower denture was enlarged by the integration of a prefabricated bar without any negative side effects. Thus, this attachment system is suitable to convert an existing full denture into an implant-supported overdenture.

Carbon-Based Ocean Productivity and Phytoplankton Physiology from Space

Ocean biogeochemical and ecosystem processes are linked by net primary production (NPP) in the ocean's surface layer, where inorganic carbon is fixed by photosynthetic processes. Determinations of NPP are necessarily a function of phytoplankton biomass and its physiological status, but the estimation of these two terms from space has remained an elusive target. Here we present new satellite ocean color observations of phytoplankton carbon (C) and chlorophyll (Chl) biomass and show that derived Chl:C ratios closely follow anticipated physiological dependencies on light, nutrients, and temperature. With this new information, global estimates of phytoplankton growth rates (mu) and carbon-based NPP are made for the first time. Compared to an earlier chlorophyll-based approach, our carbon-based values are considerably higher in tropical oceans, show greater seasonality at middle and high latitudes, and illustrate important differences in the formation and demise of regional algal blooms. This fusion of emerging concepts from the phycological and remote sensing disciplines has the potential to fundamentally change how we model and observe carbon cycling in the global oceans.

NONLINEAR TIME SERIES/SYSTEM ANALYSIS (STATE-SPACE, DYNAMICS, INTERVENTION, RESILIENCE, KALMAN)

A discussion of nonlinear dynamics, demonstrated by the familiar automobile, is followed by the development of a systematic method of analysis of a possibly nonlinear time series using difference equations in the general state-space format. This format allows recursive state-dependent parameter estimation after each observation thereby revealing the dynamics inherent in the system in combination with random external perturbations.^ The one-step ahead prediction errors at each time period, transformed to have constant variance, and the estimated parametric sequences provide the information to (1) formally test whether time series observations y(,t) are some linear function of random errors (ELEM)(,s), for some t and s, or whether the series would more appropriately be described by a nonlinear model such as bilinear, exponential, threshold, etc., (2) formally test whether a statistically significant change has occurred in structure/level either historically or as it occurs, (3) forecast nonlinear system with a new and innovative (but very old numerical) technique utilizing rational functions to extrapolate individual parameters as smooth functions of time which are then combined to obtain the forecast of y and (4) suggest a measure of resilience, i.e. how much perturbation a structure/level can tolerate, whether internal or external to the system, and remain statistically unchanged. Although similar to one-step control, this provides a less rigid way to think about changes affecting social systems.^ Applications consisting of the analysis of some familiar and some simulated series demonstrate the procedure. Empirical results suggest that this state-space or modified augmented Kalman filter may provide interesting ways to identify particular kinds of nonlinearities as they occur in structural change via the state trajectory.^ A computational flow-chart detailing computations and software input and output is provided in the body of the text. IBM Advanced BASIC program listings to accomplish most of the analysis are provided in the appendix. ^

Novel Gravity Distortion Evaluation on Large Antenna Array for Deep Space Communication

This paper presents a simple gravity evaluation model for large reflector antennas and the experimental example for a case study of one uplink array of 4x35-m antennas at X and Ka band. This model can be used to evaluate the gain reduction as a function of the maximum gravity distortion, and also to specify this at system designer level. The case study consists of one array of 35-m antennas for deep space missions. Main issues due to the gravity effect have been explored with Monte Carlo based simulation analysis.

Preference intensity in MCDM when an additive utility function represents DM preferences

We propose a new method for ranking alternatives in multicriteria decision-making problems when there is imprecision concerning the alternative performances, component utility functions and weights. We assume decision maker?s preferences are represented by an additive multiattribute utility function, in which weights can be modeled by independent normal variables, fuzzy numbers, value intervals or by an ordinal relation. The approaches are based on dominance measures or exploring the weight space in order to describe which ratings would make each alternative the preferred one. On the one hand, the approaches based on dominance measures compute the minimum utility difference among pairs of alternatives. Then, they compute a measure by which to rank the alternatives. On the other hand, the approaches based on exploring the weight space compute confidence factors describing the reliability of the analysis. These methods are compared using Monte Carlo simulation.

Bare-tether cathodic contact through thermoionic emission by low work-function materials

A new material, C12A7 : electride, which might present a work function as low as 0.6 eV and moderately high temperature stability, was recently proposed as coating for floating bare tethers. Arising from heating under space operation, current is emitted by thermionic emission along a thus coated cathodic segment. A preliminary study on the space-charge-limited (SCL) double layer in front of the cathodic segment is presented using Langmuir’s SCL electron current between cylindrical electrodes and orbital-motion-limited ion-collection sheath. A detailed calculation of current and bias profiles along the entire tether length is carried out with ohmic effects and the transition from SCL to full Richardson-Dushman emission included. Analysis shows that in the simplest drag mode, under typical orbital and tether conditions, thermionic emission leads to a short cathodic section and may eliminate the need for an active cathodic device and its corresponding gas feed requirements and power subsystem, which results in a truly “propellant-less” tether system for such basic applications as de-orbiting low earth orbit satellites.

Analysis of Magnetic Nozzles For Space Plasma Thrusters = Análisis de Toberas Magnéticas para Motores Espaciales de Plasma

Esta tesis presenta un análisis teórico del funcionamiento de toberas magnéticas para la propulsión espacial por plasmas. El estudio está basado en un modelo tridimensional y bi-fluido de la expansión supersónica de un plasma caliente en un campo magnético divergente. El modelo básico es ampliado progresivamente con la inclusión de términos convectivos dominantes de electrones, el campo magnético inducido por el plasma, poblaciones electrónicas múltiples a distintas temperaturas, y la capacidad de integrar el flujo en la región de expansión lejana. La respuesta hiperbólica del plasma es integrada con alta precisión y eficiencia haciendo uso del método de las líneas características. Se realiza una caracterización paramétrica de la expansión 2D del plasma en términos del grado de magnetización de iones, la geometría del campo magnético, y el perfil inicial del plasma. Se investigan los mecanismos de aceleración, mostrando que el campo ambipolar convierte la energía interna de electrones en energía dirigida de iones. Las corrientes diamagnéticas de Hall, que pueden hallarse distribuidas en el volumen del plasma o localizadas en una delgada capa de corriente en el borde del chorro, son esenciales para la operación de la tobera, ya que la fuerza magnética repulsiva sobre ellas es la encargada de confinar radialmente y acelerar axialmente el plasma. El empuje magnético es la reacción a esta fuerza sobre el motor. La respuesta del plasma muestra la separación gradual hacia adentro de los tubos de iones respecto de los magnéticos, lo cual produce la formación de corrientes eléctricas longitudinales y pone el plasma en rotación. La ganancia de empuje obtenida y las pérdidas radiales de la pluma de plasma se evalúan en función de los parámetros de diseño. Se analiza en detalle la separación magnética del plasma aguas abajo respecto a las líneas magnéticas (cerradas sobre sí mismas), necesaria para la aplicación de la tobera magnética a fines propulsivos. Se demuestra que tres teorías existentes sobre separación, que se fundamentan en la resistividad del plasma, la inercia de electrones, y el campo magnético que induce el plasma, son inadecuadas para la tobera magnética propulsiva, ya que producen separación hacia afuera en lugar de hacia adentro, aumentando la divergencia de la pluma. En su lugar, se muestra que la separación del plasma tiene lugar gracias a la inercia de iones y la desmagnetización gradual del plasma que tiene lugar aguas abajo, que permiten la separación ilimitada del flujo de iones respecto a las líneas de campo en condiciones muy generales. Se evalúa la cantidad de plasma que permanece unida al campo magnético y retorna hacia el motor a lo largo de las líneas cerradas de campo, mostrando que es marginal. Se muestra cómo el campo magnético inducido por el plasma incrementa la divergencia de la tobera magnética y por ende de la pluma de plasma en el caso propulsivo, contrariamente a las predicciones existentes. Se muestra también cómo el inducido favorece la desmagnetización del núcleo del chorro, acelerando la separación magnética. La hipótesis de ambipolaridad de corriente local, común a varios modelos de tobera magnética existentes, es discutida críticamente, mostrando que es inadecuada para el estudio de la separación de plasma. Una inconsistencia grave en la derivación matemática de uno de los modelos más aceptados es señalada y comentada. Incluyendo una especie adicional de electrones supratérmicos en el modelo, se estudia la formación y geometría de dobles capas eléctricas en el interior del plasma. Cuando dicha capa se forma, su curvatura aumenta cuanto más periféricamente se inyecten los electrones supratérmicos, cuanto menor sea el campo magnético, y cuanto más divergente sea la tobera magnética. El plasma con dos temperaturas electrónicas posee un mayor ratio de empuje magnético frente a total. A pesar de ello, no se encuentra ninguna ventaja propulsiva de las dobles capas, reforzando las críticas existentes frente a las propuestas de estas formaciones como un mecanismo de empuje. Por último, se presenta una formulación general de modelos autosemejantes de la expansión 2D de una pluma no magnetizada en el vacío. El error asociado a la hipótesis de autosemejanza es calculado, mostrando que es pequeño para plumas hipersónicas. Tres modelos de la literatura son particularizados a partir de la formulación general y comparados. Abstract This Thesis presents a theoretical analysis of the operation of magnetic nozzles for plasma space propulsion. The study is based on a two-dimensional, two-fluid model of the supersonic expansion of a hot plasma in a divergent magnetic field. The basic model is extended progressively to include the dominant electron convective terms, the plasma-induced magnetic field, multi-temperature electron populations, and the capability to integrate the plasma flow in the far expansion region. The hyperbolic plasma response is integrated accurately and efficiently with the method of the characteristic lines. The 2D plasma expansion is characterized parametrically in terms of the ion magnetization strength, the magnetic field geometry, and the initial plasma profile. Acceleration mechanisms are investigated, showing that the ambipolar electric field converts the internal electron energy into directed ion energy. The diamagnetic electron Hall current, which can be distributed in the plasma volume or localized in a thin current sheet at the jet edge, is shown to be central for the operation of the magnetic nozzle. The repelling magnetic force on this current is responsible for the radial confinement and axial acceleration of the plasma, and magnetic thrust is the reaction to this force on the magnetic coils of the thruster. The plasma response exhibits a gradual inward separation of the ion streamtubes from the magnetic streamtubes, which focuses the jet about the nozzle axis, gives rise to the formation of longitudinal currents and sets the plasma into rotation. The obtained thrust gain in the magnetic nozzle and radial plasma losses are evaluated as a function of the design parameters. The downstream plasma detachment from the closed magnetic field lines, required for the propulsive application of the magnetic nozzle, is investigated in detail. Three prevailing detachment theories for magnetic nozzles, relying on plasma resistivity, electron inertia, and the plasma-induced magnetic field, are shown to be inadequate for the propulsive magnetic nozzle, as these mechanisms detach the plume outward, increasing its divergence, rather than focusing it as desired. Instead, plasma detachment is shown to occur essentially due to ion inertia and the gradual demagnetization that takes place downstream, which enable the unbounded inward ion separation from the magnetic lines beyond the turning point of the outermost plasma streamline under rather general conditions. The plasma fraction that remains attached to the field and turns around along the magnetic field back to the thruster is evaluated and shown to be marginal. The plasmainduced magnetic field is shown to increase the divergence of the nozzle and the resulting plasma plume in the propulsive case, and to enhance the demagnetization of the central part of the plasma jet, contrary to existing predictions. The increased demagnetization favors the earlier ion inward separation from the magnetic field. The local current ambipolarity assumption, common to many existing magnetic nozzle models, is critically discussed, showing that it is unsuitable for the study of plasma detachment. A grave mathematical inconsistency in a well-accepted model, related to the acceptance of this assumption, is found out and commented on. The formation and 2D shape of electric double layers in the plasma expansion is studied with the inclusion of an additional suprathermal electron population in the model. When a double layer forms, its curvature is shown to increase the more peripherally suprathermal electrons are injected, the lower the magnetic field strength, and the more divergent the magnetic nozzle is. The twoelectron- temperature plasma is seen to have a greater magnetic-to-total thrust ratio. Notwithstanding, no propulsive advantage of the double layer is found, supporting and reinforcing previous critiques to their proposal as a thrust mechanism. Finally, a general framework of self-similar models of a 2D unmagnetized plasma plume expansion into vacuum is presented and discussed. The error associated with the self-similarity assumption is calculated and shown to be small for hypersonic plasma plumes. Three models of the literature are recovered as particularizations from the general framework and compared.

A unified framework for linear function approximation of value functions in stochastic control

This paper contributes with a unified formulation that merges previ- ous analysis on the prediction of the performance ( value function ) of certain sequence of actions ( policy ) when an agent operates a Markov decision process with large state-space. When the states are represented by features and the value function is linearly approxi- mated, our analysis reveals a new relationship between two common cost functions used to obtain the optimal approximation. In addition, this analysis allows us to propose an efficient adaptive algorithm that provides an unbiased linear estimate. The performance of the pro- posed algorithm is illustrated by simulation, showing competitive results when compared with the state-of-the-art solutions.

Bare-tape scaling laws for de-orbit missions in a space debris environment

El entorno espacial actual hay un gran numero de micro-meteoritos y basura espacial generada por el hombre, lo cual plantea un riesgo para la seguridad de las operaciones en el espacio. La situación se agrava continuamente a causa de las colisiones de basura espacial en órbita, y los nuevos lanzamientos de satélites. Una parte significativa de esta basura son satélites muertos, y fragmentos de satélites resultantes de explosiones y colisiones de objetos en órbita. La mitigación de este problema se ha convertido en un tema de preocupación prioritario para todas las instituciones que participan en operaciones espaciales. Entre las soluciones existentes, las amarras electrodinámicas (EDT) proporcionan un eficiente dispositivo para el rápido de-orbitado de los satélites en órbita terrestre baja (LEO), al final de su vida útil. El campo de investigación de las amarras electrodinámicas (EDT) ha sido muy fructífero desde los años 70. Gracias a estudios teóricos, y a misiones para la demostración del funcionamiento de las amarras en órbita, esta tecnología se ha desarrollado muy rápidamente en las últimas décadas. Durante este período de investigación, se han identificado y superado múltiples problemas técnicos de diversa índole. Gran parte del funcionamiento básico del sistema EDT depende de su capacidad de supervivencia ante los micro-meteoritos y la basura espacial. Una amarra puede ser cortada completamente por una partícula cuando ésta tiene un diámetro mínimo. En caso de corte debido al impacto de partículas, una amarra en sí misma, podría ser un riesgo para otros satélites en funcionamiento. Por desgracia, tras varias demostraciones en órbita, no se ha podido concluir que este problema sea importante para el funcionamiento del sistema. En esta tesis, se presenta un análisis teórico de la capacidad de supervivencia de las amarras en el espacio. Este estudio demuestra las ventajas de las amarras de sección rectangular (cinta), en cuanto a la probabilidad de supervivencia durante la misión, frente a las amarras convencionales (cables de sección circular). Debido a su particular geometría (longitud mucho mayor que la sección transversal), una amarra puede tener un riesgo relativamente alto de ser cortado por un único impacto con una partícula de pequeñas dimensiones. Un cálculo analítico de la tasa de impactos fatales para una amarra cilindrica y de tipo cinta de igual longitud y masa, considerando el flujo de partículas de basura espacial del modelo ORDEM2000 de la NASA, muestra mayor probabilidad de supervivencia para las cintas. Dicho análisis ha sido comparado con un cálculo numérico empleando los modelos de flujo el ORDEM2000 y el MASTER2005 de ESA. Además se muestra que, para igual tiempo en órbita, una cinta tiene una probabilidad de supervivencia un orden y medio de magnitud mayor que una amarra cilindrica con igual masa y longitud. Por otra parte, de-orbitar una cinta desde una cierta altitud, es mucho más rápido, debido a su mayor perímetro que le permite capturar más corriente. Este es un factor adicional que incrementa la probabilidad de supervivencia de la cinta, al estar menos tiempo expuesta a los posibles impactos de basura espacial. Por este motivo, se puede afirmar finalmente y en sentido práctico, que la capacidad de supervivencia de la cinta es bastante alta, en comparación con la de la amarra cilindrica. El segundo objetivo de este trabajo, consiste en la elaboración de un modelo analítico, mejorando la aproximación del flujo de ORDEM2000 y MASTER2009, que permite calcular con precisión, la tasa de impacto fatal al año para una cinta en un rango de altitudes e inclinaciones, en lugar de unas condiciones particulares. Se obtiene el numero de corte por un cierto tiempo en función de la geometría de la cinta y propiedades de la órbita. Para las mismas condiciones, el modelo analítico, se compara con los resultados obtenidos del análisis numérico. Este modelo escalable ha sido esencial para la optimización del diseño de la amarra para las misiones de de-orbitado de los satélites, variando la masa del satélite y la altitud inicial de la órbita. El modelo de supervivencia se ha utilizado para construir una función objetivo con el fin de optimizar el diseño de amarras. La función objectivo es el producto del cociente entre la masa de la amarra y la del satélite y el numero de corte por un cierto tiempo. Combinando el modelo de supervivencia con una ecuación dinámica de la amarra donde aparece la fuerza de Lorentz, se elimina el tiempo y se escribe la función objetivo como función de la geometría de la cinta y las propietades de la órbita. Este modelo de optimización, condujo al desarrollo de un software, que esta en proceso de registro por parte de la UPM. La etapa final de este estudio, consiste en la estimación del número de impactos fatales, en una cinta, utilizando por primera vez una ecuación de límite balístico experimental. Esta ecuación ha sido desarollada para cintas, y permite representar los efectos tanto de la velocidad de impacto como el ángulo de impacto. Los resultados obtenidos demuestran que la cinta es altamente resistente a los impactos de basura espacial, y para una cinta con una sección transversal definida, el número de impactos críticos debidos a partículas no rastreables es significativamente menor. ABSTRACT The current space environment, consisting of man-made debris and tiny meteoroids, poses a risk to safe operations in space, and the situation is continuously deteriorating due to in-orbit debris collisions and to new satellite launches. Among these debris a significant portion is due to dead satellites and fragments of satellites resulted from explosions and in-orbit collisions. Mitigation of space debris has become an issue of first concern for all the institutions involved in space operations. Bare electrodynamic tethers (EDT) can provide an efficient mechanism for rapid de-orbiting of defunct satellites from low Earth orbit (LEO) at end of life. The research on EDT has been a fruitful field since the 70’s. Thanks to both theoretical studies and in orbit demonstration missions, this technology has been developed very fast in the following decades. During this period, several technical issues were identified and overcome. The core functionality of EDT system greatly depends on their survivability to the micrometeoroids and orbital debris, and a tether can become itself a kind of debris for other operating satellites in case of cutoff due to particle impact; however, this very issue is still inconclusive and conflicting after having a number of space demonstrations. A tether can be completely cut by debris having some minimal diameter. This thesis presents a theoretical analysis of the survivability of tethers in space. The study demonstrates the advantages of tape tethers over conventional round wires particularly on the survivability during the mission. Because of its particular geometry (length very much larger than cross-sectional dimensions), a tether may have a relatively high risk of being severed by the single impact of small debris. As a first approach to the problem, survival probability has been compared for a round and a tape tether of equal mass and length. The rates of fatal impact of orbital debris on round and tape tether, evaluated with an analytical approximation to debris flux modeled by NASA’s ORDEM2000, shows much higher survival probability for tapes. A comparative numerical analysis using debris flux model ORDEM2000 and ESA’s MASTER2005 shows good agreement with the analytical result. It also shows that, for a given time in orbit, a tape has a probability of survival of about one and a half orders of magnitude higher than a round tether of equal mass and length. Because de-orbiting from a given altitude is much faster for the tape due to its larger perimeter, its probability of survival in a practical sense is quite high. As the next step, an analytical model derived in this work allows to calculate accurately the fatal impact rate per year for a tape tether. The model uses power laws for debris-size ranges, in both ORDEM2000 and MASTER2009 debris flux models, to calculate tape tether survivability at different LEO altitudes. The analytical model, which depends on tape dimensions (width, thickness) and orbital parameters (inclinations, altitudes) is then compared with fully numerical results for different orbit inclinations, altitudes and tape width for both ORDEM2000 and MASTER2009 flux data. This scalable model not only estimates the fatal impact count but has proved essential in optimizing tether design for satellite de-orbit missions varying satellite mass and initial orbital altitude and inclination. Within the frame of this dissertation, a simple analysis has been finally presented, showing the scalable property of tape tether, thanks to the survivability model developed, that allows analyze and compare de-orbit performance for a large range of satellite mass and orbit properties. The work explicitly shows the product of tether-to-satellite mass-ratio and fatal impact count as a function of tether geometry and orbital parameters. Combining the tether dynamic equation involving Lorentz drag with space debris impact survivability model, eliminates time from the expression. Hence the product, is independent of tether de-orbit history and just depends on mission constraints and tether length, width and thickness. This optimization model finally led to the development of a friendly software tool named BETsMA, currently in process of registration by UPM. For the final step, an estimation of fatal impact rate on a tape tether has been done, using for the first time an experimental ballistic limit equation that was derived for tapes and accounts for the effects of both the impact velocity and impact angle. It is shown that tape tethers are highly resistant to space debris impacts and considering a tape tether with a defined cross section, the number of critical events due to impact with non-trackable debris is always significantly low.