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In this study, we introduce MGA-Net, a novel mask-guided attention neural network, which extends the U-net model for precision neonatal brain imaging. MGA-Net is designed to extract the brain from other structures and reconstruct high-quality brain images. The network employs a common encoder and two decoders: one for brain mask extraction and the other for brain region reconstruction. A key feature of MGA-Net is its high-level mask-guided attention module, which leverages features from the brain mask decoder to enhance image reconstruction. To enable the same encoder and decoder to process both MRI and ultrasound (US) images, MGA-Net integrates sinusoidal positional encoding. This encoding assigns distinct positional values to MRI and US images, allowing the model to effectively learn from both modalities. Consequently, features learned from a single modality can aid in learning a modality with less available data, such as US. We extensively validated the proposed MGA-Net on diverse datasets from varied clinical settings and neonatal age groups. The metrics used for assessment included the DICE similarity coefficient, recall, and accuracy for image segmentation; structural similarity for image reconstruction; and root mean squared error for total brain volume estimation from 3D ultrasound images. Our results demonstrate that MGA-Net significantly outperforms traditional methods, offering superior performance in brain extraction and segmentation while achieving high precision in image reconstruction and volumetric analysis. Thus, MGA-Net represents a robust and effective preprocessing tool for MRI and 3D ultrasound images, marking a significant advance in neuroimaging that enhances both research and clinical diagnostics in the neonatal period and beyond.

This paper presents a multiobjective Home Care Scheduling Problem (from now on multiobjective HCSP) related to a home care company for elderly and dependent people located in the North of Spain. In particular, a biobjective problem is considered, with the following two conflicting objectives: the welfare of users and the cost of schedules. To tackle the problem, a custom metaheuristic algorithm based on the Multi-Directional Local Search (MDLS) was designed, obtaining good approximations of the Pareto frontier in efficient computational times. This biobjective algorithm can be divided into three steps: initializing the set of non dominated solutions, generating solutions composed by different routes and obtaining non dominated solutions. The performance of the biobjective algorithm was analyzed by implementing two other well known methods in the literature: the exact method AUGMECON2, which is just an improved version of the Epsilon Constraint approach, and an NSGA-II-based algorithm. Finally, an extensive computational study was developed to compare the three methods over a set of instances from the literature, where the biobjective algorithm exhibited a superior behaviour. Furthermore, the algorithm was also applied to real instances providing solutions to the company with a good trade-off between the two objectives.

We construct, for any $H\in \mathbb{R}$, infinitely many free boundary annuli in geodesic balls of $\mathbb{S}^3$ with constant mean curvature $H$ and a discrete, non-rotational, symmetry group. Some of these free boundary CMC annuli are actually embedded if $H\geq 1/\sqrt{3}$. We also construct embedded, non-rotational, free boundary CMC annuli in geodesic balls of $\mathbb{H}^3$, for all values $H>1$ of the mean curvature $H$., Comment: 42 pages, 7 figures

For a convex body $C$ in $\mathbb{R}^d$ and a division of $C$ into convex subsets $C_1,\ldots,C_n$, we can consider $max\{F(C_1),\ldots, F(C_n)\}$ (respectively, $min\{F(C_1),\ldots, F(C_n)\}$), where $F$ represents one of these classical geometric magnitudes: the diameter, the minimal width, or the inradius. In this work we study the divisions of $C$ minimizing (respectively, maximizing) the previous value, as well as other related questions., Comment: 23 pages, 18 figures

MELAGE, a pioneering Python-based neuroimaging software, emerges as a versatile tool for the visualization, processing, and analysis of medical images. Initially conceived to address the unique challenges of processing 3D ultrasound and MRI brain images during the neonatal period, MELAGE exhibits remarkable adaptability, extending its utility to the domain of adult human brain imaging. At its core, MELAGE features a semi-automatic brain extraction tool empowered by a deep learning module, ensuring precise and efficient brain structure extraction from MRI and 3D Ultrasound data. Moreover, MELAGE offers a comprehensive suite of features, encompassing dynamic 3D visualization, accurate measurements, and interactive image segmentation. This transformative software holds immense promise for researchers and clinicians, offering streamlined image analysis, seamless integration with deep learning algorithms, and broad applicability in the realm of medical imaging.

Autonomous robots have real-world applications in diverse fields, such as mobile manipulation and environmental exploration, and many such tasks benefit from a hands-off approach in terms of human user involvement over a long task horizon. However, the level of autonomy achievable by a deployment is limited in part by the problem definition or task specification required by the system. Task specifications often require technical, low-level information that is unintuitive to describe and may result in generic solutions, burdening the user technically both before and after task completion. In this thesis, we aim to advance task specification abstraction toward the goal of increasing robot autonomy in real-world scenarios. We do so by tackling problems that address several different angles of this goal. First, we develop a way for the automatic discovery of optimal transition points between subtasks in the context of constrained mobile manipulation, removing the need for the human to hand-specify these in the task specification. We further propose a way to automatically describe constraints on robot motion by using demonstrated data as opposed to manually-defined constraints. Then, within the context of environmental exploration, we propose a flexible task specification framework, requiring just a set of quantiles of interest from the user that allows the robot to directly suggest locations in the environment for the user to study. We next systematically study the effect of including a robot team in the task specification and show that multirobot teams have the ability to improve performance under certain specification conditions, including enabling inter-robot communication. Finally, we propose methods for a communication protocol that autonomously selects useful but limited information to share with the other robots., Comment: PhD dissertation. 160 pages

Fine-tuning generic but smooth spherically-symmetric initial data for general relativity to the threshold of dynamical black hole formation creates arbitrarily large curvatures, mediated by a universal self-similar solution that acts as an intermediate attractor. For vacuum gravitational waves, however, these critical phenomena have been elusive. We present, for the first time, excellent agreement among three independent numerical simulations of this collapse. Surprisingly, we find no universality, and observe approximate self-similarity for some families of initial data but not for others., Comment: 6 pages, 3 figures

We are motivated by quantile estimation of algae concentration in lakes and how decentralized multirobot teams can effectively tackle this problem. We find that multirobot teams improve performance in this task over single robots, and communication-enabled teams further over communication-deprived teams; however, real robots are resource-constrained, and communication networks cannot support arbitrary message loads, making naive, constant information-sharing but also complex modeling and decision-making infeasible. With this in mind, we propose online, locally computable metrics for determining the utility of transmitting a given message to the other team members and a decision-theoretic approach that chooses to transmit only the most useful messages, using a decentralized and independent framework for maintaining beliefs of other teammates. We validate our approach in simulation on a real-world aquatic dataset, and we show that restricting communication via a utility estimation method based on the expected impact of a message on future teammate behavior results in a 42% decrease in network load while simultaneously decreasing quantile estimation error by 1.84%., Comment: 7 pages, 1 table, 7 figures

Quantiles of a natural phenomena can provide scientists with an important understanding of different spreads of concentrations. When there are several available robots, it may be advantageous to pool resources in a collaborative way to improve performance. A multirobot team can be difficult to practically bring together and coordinate. To this end, we present a study across several axes of the impact of using multiple robots to estimate quantiles of a distribution of interest using an informative path planning formulation. We measure quantile estimation accuracy with increasing team size to understand what benefits result from a multirobot approach in a drone exploration task of analyzing the algae concentration in lakes. We additionally perform an analysis on several parameters, including the spread of robot initial positions, the planning budget, and inter-robot communication, and find that while using more robots generally results in lower estimation error, this benefit is achieved under certain conditions. We present our findings in the context of real field robotic applications and discuss the implications of the results and interesting directions for future work., Comment: 7 pages, 2 tables, 7 figures

For any $n\in \mathbb{N}$, $n\geq 2$, we construct a real analytic, one-parameter family of compact embedded CMC annuli with free boundary in the unit ball $\mathbb{B}^3$ of $\mathbb{R}^3$ with a prismatic symmetry group of order $4n$. These examples give a negative answer to the uniqueness problem by Nitsche and Wente of whether any annular solution to the partitioning problem in the ball should be rotational., Comment: 22 pages, 1 figure

We prove that any uniformly elliptic Weingarten (topological) sphere in S2xR must be congruent to the canonical example associated to the Weingarten equation. The result is obtained by proving that rotational uniformly elliptic Weingarten surfaces in S2xR have bounded second fundamental form together with a Hopf type result by J. A. G\'alvez and P. Mira.

We construct a family of compact free boundary minimal annuli immersed in the unit ball $\mathbb{B}^3$ of $\mathbb{R}^3$, the first such examples other than the critical catenoid. This solves a problem formulated by Nitsche in 1985. These annuli are symmetric with respect to two orthogonal planes and a finite group of rotations around an axis, and are foliated by spherical curvature lines. We show that the only free boundary minimal annulus embedded in $\mathbb{B}^3$ foliated by spherical curvature lines is the critical catenoid; in particular, the minimal annuli that we construct are not embedded. On the other hand, we also construct families of non-rotational compact embedded capillary minimal annuli in $\mathbb{B}^3$. Their existence solves in the negative a problem proposed by Wente in 1995., Comment: 39 pages, 11 figures. We added a uniqueness section, we explained in more detail several arguments, and introduced new figures. The existence theorems of version 1 remain unchanged

As a first application of the new adaptive mesh functionality of the the pseudospectral numerical relativity code bamps, we evolve twist-free, axisymmetric gravitational waves close to the threshold of collapse. We consider six different one-parameter families of Brill wave initial data; two centered and four off-centered families. Of these the latter have not been treated before. Within each family we tune the parameter towards the threshold of black hole formation. The results for centered data agree with earlier work. Our key results are first, that close to the threshold of collapse the global peak in the curvature appears on the symmetry axis but away from the origin, indicating that in the limit they will collapse around disjoint centers. This is confirmed in three of the six families by explicitly finding apparent horizons around these large curvature peaks. Second, we find evidence neither for strict discrete-self-similarity nor for universal power-law scaling of curvature quantities. Finally, as in Ledvinka & Khirnov's recent study, we find approximately universal strong curvature features. These features appear multiple times within individual spacetimes close to the threshold and are furthermore present within all six families., Comment: 11 pages, 7 figures

Missing values are common in many real-life datasets. However, most of the current machine learning methods can not handle missing values. This means that they should be imputed beforehand. Gaussian Processes (GPs) are non-parametric models with accurate uncertainty estimates that combined with sparse approximations and stochastic variational inference scale to large data sets. Sparse GPs can be used to compute a predictive distribution for missing data. Here, we present a hierarchical composition of sparse GPs that is used to predict missing values at each dimension using all the variables from the other dimensions. We call the approach missing GP (MGP). MGP can be trained simultaneously to impute all observed missing values. Specifically, it outputs a predictive distribution for each missing value that is then used in the imputation of other missing values. We evaluate MGP in one private clinical data set and four UCI datasets with a different percentage of missing values. We compare the performance of MGP with other state-of-the-art methods for imputing missing values, including variants based on sparse GPs and deep GPs. The results obtained show a significantly better performance of MGP.

We show by phase space analysis that there are exactly 17 possible qualitative behaviors for a rotational surface in $\mathbb{R}^3$ that satisfies an arbitrary elliptic Weingarten equation $W(\kappa_1,\kappa_2)=0$, and study the singularities of such examples. As global applications of this classification, we prove a sharp halfspace theorem for general elliptic Weingarten equations of finite order, and a classification of peaked elliptic Weingarten spheres with at most two singularities. In the case that $W$ is not elliptic, we give a negative answer to a question by Yau regarding the uniqueness of rotational ellipsoids., Comment: 28 pages, 13 figures

Scientists interested in studying natural phenomena often take physical specimens from locations in the environment for later analysis. These analysis locations are typically specified by expert heuristics. Instead, we propose to choose locations for scientific analysis by using a robot to perform an informative path planning survey. The survey results in a list of locations that correspond to the quantile values of the phenomenon of interest. We develop a robot planner using novel objective functions to improve the estimates of the quantile values over time and an approach to find locations which correspond to the quantile values. We test our approach in four different environments using previously collected aquatic data and validate it in a field trial. Our proposed approach to estimate quantiles has a 10.2% mean reduction in median error when compared to a baseline approach which attempts to maximize spatial coverage. Additionally, when localizing these values in the environment, we see a 15.7% mean reduction in median error when using cross-entropy with our loss function compared to a baseline., Comment: 8 pages, 9 figures

Motivated by studies of critical phenomena in the gravitational collapse of vacuum gravitational waves we compare, at the linear level, two common approaches to constructing gravitational-wave initial data. Specifically, we construct analytical, linear Brill wave initial data and compare these with Teukolsky waves in an attempt to understand the different numerical behavior observed in dynamical (nonlinear) evolutions of these two different sets of data. In general, the Brill waves indeed feature higher multipole moments than the quadrupolar Teukolsky waves, which might have provided an explanation for the differences observed in the dynamical evolution of the two types of waves. However, we also find that, for a common choice of the Brill-wave seed function, all higher-order moments vanish identically, rendering the (linear) Brill initial data surprisingly similar to the Teukolsky data for a similarly common choice of its seed function., Comment: 10 pages, 4 figures

Constrained robot motion planning is a widely used technique to solve complex robot tasks. We consider the problem of learning representations of constraints from demonstrations with a deep neural network, which we call Equality Constraint Manifold Neural Network (ECoMaNN). The key idea is to learn a level-set function of the constraint suitable for integration into a constrained sampling-based motion planner. Learning proceeds by aligning subspaces in the network with subspaces of the data. We combine both learned constraints and analytically described constraints into the planner and use a projection-based strategy to find valid points. We evaluate ECoMaNN on its representation capabilities of constraint manifolds, the impact of its individual loss terms, and the motions produced when incorporated into a planner.

In spherical symmetry compelling numerical evidence suggests that in general relativity solutions near the threshold of black hole formation exhibit critical behavior. One aspect of this is that threshold solutions themselves are self-similar and are, in a certain sense, unique. To an extent yet to be fully understood, the same phenomena persist beyond spherical symmetry. It is therefore desirable to construct models that exhibit such symmetry at the threshold of blow-up. Starting with deformations of the wave equation, we discuss models which have discretely self-similar threshold solutions. We study threshold solutions in the past light cone of the blow-up point. In spherical symmetry there is a sense in which a unique critical solution exists. Spherical numerical evolutions are also presented for more general models, and exhibit similar behavior. Away from spherical symmetry threshold solutions attain more freedom. Different topologies of blow-up are possible, and even locally the critical solution needs reinterpretation as a parameterized family., Comment: 18 pages, 9 figures

Motion planning with constraints is an important part of many real-world robotic systems. In this work, we study manifold learning methods to learn such constraints from data. We explore two methods for learning implicit constraint manifolds from data: Variational Autoencoders (VAE), and a new method, Equality Constraint Manifold Neural Network (ECoMaNN). With the aim of incorporating learned constraints into a sampling-based motion planning framework, we evaluate the approaches on their ability to learn representations of constraints from various datasets and on the quality of paths produced during planning., Comment: Accepted for presentation at the Robotics: Science and Systems (RSS) 2020 Workshop for Learning (in) Task and Motion Planning. Paper length is 4 pages (i.e. 3 pages of technical content and 1 page of the references)

We address the problem of planning robot motions in constrained configuration spaces where the constraints change throughout the motion. The problem is formulated as a fixed sequence of intersecting manifolds, which the robot needs to traverse in order to solve the task. We specify a class of sequential motion planning problems that fulfill a particular property of the change in the free configuration space when transitioning between manifolds. For this problem class, we develop the algorithm Planning on Sequenced Manifolds (PSM*) which searches for optimal intersection points between manifolds by using RRT* in an inner loop with a novel steering strategy. We provide a theoretical analysis regarding PSM*s probabilistic completeness and asymptotic optimality. Further, we evaluate its planning performance on multi-robot object transportation tasks. Video: https://youtu.be/Q8kbILTRxfU Code: https://github.com/etpr/sequential-manifold-planning

We prove that any complete, uniformly elliptic Weingarten surface in Euclidean $3$-space whose Gauss map image omits an open hemisphere is a cylinder or a plane. This generalizes a classical theorem by Hoffman, Osserman and Schoen for constant mean curvature surfaces. In particular, this proves that planes are the only complete, uniformly elliptic Weingarten multigraphs. We also show that this result holds for a large class of non-uniformly elliptic Weingarten equations. In particular, this solves in the affirmative the Bernstein problem for entire graphs for that class of elliptic equations. To obtain these results, we prove that planes are the only complete multigraphs with quasiconformal Gauss map and bounded second fundamental form., Comment: 29 pages, 10 figures