Software for Designing Custom Orbital-Craniofacial Implant Plans

Purpose: Custom cranio-orbital implants have been shown to achieve better performance than their hand-shaped counterparts by restoring skull anatomy more accurately and by reducing surgery time. Designing a custom implant involves reconstructing a model of the patient's skull using their computed tomography (CT) scan. The healthy side of the skull model, contralateral to the damaged region, can then be used to design an implant plan. Designing implants for areas of thin bone, such as the orbits, is challenging due to poor CT resolution of bone structures. This makes preoperative design time-intensive since thin bone structures in CT data must be manually segmented. The objective of this thesis was to research methods to accurately and efficiently design cranio-orbital implant plans, with a focus on the orbits, and to develop software that integrates these methods. Methods: The software consists of modules that use image and surface restoration approaches to enhance both the quality of CT data and the reconstructed model. It enables users to input CT data, and use tools to output a skull model with restored anatomy. The skull model can then be used to design the implant plan. The software was designed using 3D Slicer, an open-source medical visualization platform. It was tested on CT data from thirteen patients. Results: The average time it took to create a skull model with restored anatomy using our software was 0.33 hours ± 0.04 STD. In comparison, the design time of the manual segmentation method took between 3 and 6 hours. To assess the structural accuracy of the reconstructed models, CT data from the thirteen patients was used to compare the models created using our software with those using the manual method. When registering the skull models together, the difference between each set of skulls was found to be 0.4 mm ± 0.16 STD. Conclusions: We have developed a software to design custom cranio-orbital implant plans, with a focus on thin bone structures. The method described decreases design time, and is of similar accuracy to the manual method.

Efficient algorithms for beacon routing in polygons

In a paper by Biro et al. [7], a novel twist on guarding in art galleries is introduced. A beacon is a fixed point with an attraction pull that can move points within the polygon. Points move greedily to monotonically decrease their Euclidean distance to the beacon by moving straight towards the beacon or sliding on the edges of the polygon. The beacon attracts a point if the point eventually reaches the beacon. Unlike most variations of the art gallery problem, the beacon attraction has the intriguing property of being asymmetric, leading to separate definitions of attraction region and inverse attraction region. The attraction region of a beacon is the set of points that it attracts. For a given point in the polygon, the inverse attraction region is the set of beacon locations that can attract the point. We first study the characteristics of beacon attraction. We consider the quality of a "successful" beacon attraction and provide an upper bound of $\sqrt{2}$ on the ratio between the length of the beacon trajectory and the length of the geodesic distance in a simple polygon. In addition, we provide an example of a polygon with holes in which this ratio is unbounded. Next we consider the problem of computing the shortest beacon watchtower in a polygonal terrain and present an $O(n \log n)$ time algorithm to solve this problem. In doing this, we introduce $O(n \log n)$ time algorithms to compute the beacon kernel and the inverse beacon kernel in a monotone polygon. We also prove that $\Omega(n \log n)$ time is a lower bound for computing the beacon kernel of a monotone polygon. Finally, we study the inverse attraction region of a point in a simple polygon. We present algorithms to efficiently compute the inverse attraction region of a point for simple, monotone, and terrain polygons with respective time complexities $O(n^2)$, $O(n \log n)$ and $O(n)$. We show that the inverse attraction region of a point in a simple polygon has linear complexity and the problem of computing the inverse attraction region has a lower bound of $\Omega(n \log n)$ in monotone polygons and consequently in simple polygons.

Autonomous formation flying: unified control and collision avoidance methods for close manoeuvring spacecraft

The idea of spacecraft formations, flying in tight configurations with maximum baselines of a few hundred meters in low-Earth orbits, has generated widespread interest over the last several years. Nevertheless, controlling the movement of spacecraft in formation poses difficulties, such as in-orbit high-computing demand and collision avoidance capabilities, which escalate as the number of units in the formation is increased and complicated nonlinear effects are imposed to the dynamics, together with uncertainty which may arise from the lack of knowledge of system parameters. These requirements have led to the need of reliable linear and nonlinear controllers in terms of relative and absolute dynamics. The objective of this thesis is, therefore, to introduce new control methods to allow spacecraft in formation, with circular/elliptical reference orbits, to efficiently execute safe autonomous manoeuvres. These controllers distinguish from the bulk of literature in that they merge guidance laws never applied before to spacecraft formation flying and collision avoidance capacities into a single control strategy. For this purpose, three control schemes are presented: linear optimal regulation, linear optimal estimation and adaptive nonlinear control. In general terms, the proposed control approaches command the dynamical performance of one or several followers with respect to a leader to asymptotically track a time-varying nominal trajectory (TVNT), while the threat of collision between the followers is reduced by repelling accelerations obtained from the collision avoidance scheme during the periods of closest proximity. Linear optimal regulation is achieved through a Riccati-based tracking controller. Within this control strategy, the controller provides guidance and tracking toward a desired TVNT, optimizing fuel consumption by Riccati procedure using a non-infinite cost function defined in terms of the desired TVNT, while repelling accelerations generated from the CAS will ensure evasive actions between the elements of the formation. The relative dynamics model, suitable for circular and eccentric low-Earth reference orbits, is based on the Tschauner and Hempel equations, and includes a control input and a nonlinear term corresponding to the CAS repelling accelerations. Linear optimal estimation is built on the forward-in-time separation principle. This controller encompasses two stages: regulation and estimation. The first stage requires the design of a full state feedback controller using the state vector reconstructed by means of the estimator. The second stage requires the design of an additional dynamical system, the estimator, to obtain the states which cannot be measured in order to approximately reconstruct the full state vector. Then, the separation principle states that an observer built for a known input can also be used to estimate the state of the system and to generate the control input. This allows the design of the observer and the feedback independently, by exploiting the advantages of linear quadratic regulator theory, in order to estimate the states of a dynamical system with model and sensor uncertainty. The relative dynamics is described with the linear system used in the previous controller, with a control input and nonlinearities entering via the repelling accelerations from the CAS during collision avoidance events. Moreover, sensor uncertainty is added to the control process by considering carrier-phase differential GPS (CDGPS) velocity measurement error. An adaptive control law capable of delivering superior closed-loop performance when compared to the certainty-equivalence (CE) adaptive controllers is finally presented. A novel noncertainty-equivalence controller based on the Immersion and Invariance paradigm for close-manoeuvring spacecraft formation flying in both circular and elliptical low-Earth reference orbits is introduced. The proposed control scheme achieves stabilization by immersing the plant dynamics into a target dynamical system (or manifold) that captures the desired dynamical behaviour. They key feature of this methodology is the addition of a new term to the classical certainty-equivalence control approach that, in conjunction with the parameter update law, is designed to achieve adaptive stabilization. This parameter has the ultimate task of shaping the manifold into which the adaptive system is immersed. The performance of the controller is proven stable via a Lyapunov-based analysis and Barbalat’s lemma. In order to evaluate the design of the controllers, test cases based on the physical and orbital features of the Prototype Research Instruments and Space Mission Technology Advancement (PRISMA) are implemented, extending the number of elements in the formation into scenarios with reconfigurations and on-orbit position switching in elliptical low-Earth reference orbits. An extensive analysis and comparison of the performance of the controllers in terms of total Δv and fuel consumption, with and without the effects of the CAS, is presented. These results show that the three proposed controllers allow the followers to asymptotically track the desired nominal trajectory and, additionally, those simulations including CAS show an effective decrease of collision risk during the performance of the manoeuvre.

El exceso de confianza y el statu quo dentro de la estructuración de capital: una perspectiva de las finanzas corporativas del comportamiento

El presente artículo, presenta un análisis de las decisiones de estructuración de capital de la compañía Merck Sharp & Dome S.A.S, desde la perspectiva de las finanzas comportamentales, comparando los métodos utilizados actualmente por la compañía seleccionada con la teoría tradicional de las finanzas, para así poder evaluar el desempeño teórico y real. Incorporar elementos comportamentales dentro del estudio permite profundizar más sobre de las decisiones corporativas en un contexto más cercano a los avances investigativos de las finanzas del comportamiento, lo cual lleva a que el análisis de este artículo se enfoque en la identificación y entendimiento de los sesgos de exceso de confianza y statu quo, pero sobre todo su implicación en las decisiones de financiación. Según la teoría tradicional el proceso de estructuración de capital se guía por los costos, pero este estudio de caso permitió observar que en la práctica esta relación de costo-decisión está en un segundo lugar, después de la relación riesgo-decisión a la hora del proceso de estructuración de capital.

Towards automation of constellation management with analytical models for collision avoidance

The growing interest for constellation of small, less expensive satellites is bringing space junk and traffic management to the attention of space community. At the same time, the continuous quest for more efficient propulsion systems put the spotlight on electric (low thrust) propulsion as an appealing solution for collision avoidance. Starting with an overview of the current techniques for conjunction assessment and avoidance, we then highlight the possible problems when a low thrust propulsion is used. The need for accurate propagation model shows up from the conducted simulations. Thus, aiming at propagation models with low computational burden, we study the available models from the literature and propose an analytical alternative to improve propagation accuracy. The model is then tested in the particular case of a tangential maneuver. Results show that the proposed solution significantly improve on state of the art methods and is a good candidate to be used in collision avoidance operations. For instance to propagate satellite uncertainty or optimizing avoidance maneuver when conjunction occurs within few (3-4) orbits from measurements time.

Back-in-time void finder: dynamical detection of cosmic voids for precision cosmology

Cosmic voids are vast and underdense regions emerging between the elements of the cosmic web and dominating the large-scale structure of the Universe. Void number counts and density profiles have been demonstrated to provide powerful cosmological probes. Indeed, thanks to their low-density nature and they very large sizes, voids represent natural laboratories to test alternative dark energy scenarios, modifications of gravity and the presence of massive neutrinos. Despite the increasing use of cosmic voids in Cosmology, a commonly accepted definition for these objects has not yet been reached. For this reason, different void finding algorithms have been proposed during the years. Voids finder algorithms based on density or geometrical criteria are affected by intrinsic uncertainties. In recent years, new solutions have been explored to face these issues. The most interesting is based on the idea of identify void positions through the dynamics of the mass tracers, without performing any direct reconstruction of the density field. The goal of this Thesis is to provide a performing void finder algorithm based on dynamical criteria. The Back-in-time void finder (BitVF) we present use tracers as test particles and their orbits are reconstructed from their actual clustered configuration to an homogeneous and isotropic distribution, expected for the Universe early epoch. Once the displacement field is reconstructed, the density field is computed as its divergence. Consequently, void centres are identified as local minima of the field. In this Thesis work we applied the developed void finding algorithm to simulations. From the resulting void samples we computed different void statistics, comparing the results to those obtained with VIDE, the most popular void finder. BitVF proved to be able to produce a more reliable void samples than the VIDE ones. The BitVF algorithm will be a fundamental tool for precision cosmology, especially with upcoming galaxy-survey.

Dynamics of galaxies in the cluster environment: a resonant origin for the ISP?

The internal dynamics of elliptical galaxies in clusters depends on many factors, including the environment in which the galaxy is located. In addition to the strong encounters with the other galaxies, we can also consider the gravitational interaction with the ubiquitous Cluster Tidal Field (CTF). As recognized in many studies, one possible way in which CTF affects the dynamics of galaxies inside the cluster is related to the fact that they may start oscillating as “rigid bodies” around their equilibrium positions in the field, with the periods of these oscillations curiously similar to those of stellar orbits in the outer parts of galaxies. Resonances between the two motions are hence expected and this phenomenon could significantly contribute to the formation of the Intracluster Stellar Population (ISP), whose presence is abundantly confirmed by observations. In this thesis work, we propose to study the motion of an elliptical galaxy, modelled as a rigid body, in the CTF, especially when its center of mass traces a quasi-circular orbit in the cluster gravitational potential. This case extends and generalizes the previous models and findings, proceeding towards a much more realistic description of galaxy motion. In addition to this, the presence of a further oscillation, namely that of the entire galaxy along its orbit, will possibly increase the probability of having resonances and, consequently, the rate of ISP production nearly to observed values. Thus, after reviewing the dynamics of a rigid body in a generic force field, we will assess some physically relevant studies and report their main results, discussing their implications with respect to our problem. We will conclude our discussion focusing on the more realistic scenario of an elliptical galaxy whose center of mass moves on a quasi-circular orbit in a spherically symmetric potential. The derivation of the fundamental equations of motion will serve as the basis for future modelling and discussions.

Ephemeris generation of the Galilean moons by using VLBI observations in support to stellar occultations

Stellar occultations are the most accurate Earth-based astronomy technique to obtain the lateral position of celestial bodies, in the case of natural satellites, their accuracy also depends on the central body to which the satellite orbits. The main goal of this thesis work is to analyze if and how very long baseline interferometry (VLBI) measurements of a body like Jupiter can be used in support to stellar occultations of its natural satellites by reducing the planetary uncertainty at the time of the occultation. In particular, we analyzed the events of the stellar occultations of Callisto (15.01.2024) and Io (02.04.2021). The stellar occultation of Callisto has been predicted and simulated using the stellar occultation reduction analysis (SORA) toolkit while the stellar occultation of Io has been already studied by Morgado et al. We then simulated the VLBI data of Jupiter according to the current JUNO trajectories. The required observation were then used as input of an estimation to which then we performed a covariance analysis on the estimated parameters to retrieve the formal errors (1 − σ uncertainties) at each epoch of the propagation. The results show that the addition of the VLBI slightly improves the uncertainty of Callisto even when Jupiter knowledge is worse while for Io we observed that the VLBI data is especially crucial in the scenario of an a priori uncertainty in Jupiter state of about 10km. Here we can have improvements of the estimated initial states of Io of about 70m, 230m and 900m to the radial, along-track and cross-track directions respectively. Moreover, we have also obtained the propagated errors of the two moons in terms of right ascension and declination which both show uncertainties in the mas level at the occultation time. Finally, we simulated Io and Europa together and we observed that at the time of the stellar occultation of Europa the along-track component of Io is constrained, confirming the coupling between the two inner moons.