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When developing a clinical prediction model, the sample size of the development dataset is a key consideration. Small sample sizes lead to greater concerns of overfitting, instability, poor performance and lack of fairness. Previous research has outlined minimum sample size calculations to minimise overfitting and precisely estimate the overall risk. However even when meeting these criteria, the uncertainty (instability) in individual-level risk estimates may be considerable. In this article we propose how to examine and calculate the sample size required for developing a model with acceptably precise individual-level risk estimates to inform decisions and improve fairness. We outline a five-step process to be used before data collection or when an existing dataset is available. It requires researchers to specify the overall risk in the target population, the (anticipated) distribution of key predictors in the model, and an assumed 'core model' either specified directly (i.e., a logistic regression equation is provided) or based on specified C-statistic and relative effects of (standardised) predictors. We produce closed-form solutions that decompose the variance of an individual's risk estimate into Fisher's unit information matrix, predictor values and total sample size; this allows researchers to quickly calculate and examine individual-level uncertainty interval widths and classification instability for specified sample sizes. Such information can be presented to key stakeholders (e.g., health professionals, patients, funders) using prediction and classification instability plots to help identify the (target) sample size required to improve trust, reliability and fairness in individual predictions. Our proposal is implemented in software module pmstabilityss. We provide real examples and emphasise the importance of clinical context including any risk thresholds for decision making., Comment: 36 pages, 6 figures, 1 table

When evaluating the performance of a model for individualised risk prediction, the sample size needs to be large enough to precisely estimate the performance measures of interest. Current sample size guidance is based on precisely estimating calibration, discrimination, and net benefit, which should be the first stage of calculating the minimum required sample size. However, when a clinically important threshold is used for classification, other performance measures can also be used. We extend the previously published guidance to precisely estimate threshold-based performance measures. We have developed closed-form solutions to estimate the sample size required to target sufficiently precise estimates of accuracy, specificity, sensitivity, PPV, NPV, and F1-score in an external evaluation study of a prediction model with a binary outcome. This approach requires the user to pre-specify the target standard error and the expected value for each performance measure. We describe how the sample size formulae were derived and demonstrate their use in an example. Extension to time-to-event outcomes is also considered. In our examples, the minimum sample size required was lower than that required to precisely estimate the calibration slope, and we expect this would most often be the case. Our formulae, along with corresponding Python code and updated R and Stata commands (pmvalsampsize), enable researchers to calculate the minimum sample size needed to precisely estimate threshold-based performance measures in an external evaluation study. These criteria should be used alongside previously published criteria to precisely estimate the calibration, discrimination, and net-benefit., Comment: 27 pages, 1 figure

We use lattice-Boltzmann molecular dynamics (LBMD) simulations to study the compression of a confined polymer immersed in a fluid and pushed by a large spherical colloid with a diameter comparable to the channel width. We examined the chain's deformation with both purely repulsive and weakly attractive Lennard-Jones (LJ) potentials applied between the monomers. The sphere's velocity was varied over 3 orders of magnitude. The chain is in a non-dense state at low pushing velocities for both repulsive and attractive monomer interactions. When the velocity of the spherical colloid exceeds a threshold $v^*$, the back end of the chain transitions to a high density state with low mean square monomer displacement (MSD) values. The front end, however, remains in a non-dense state with high MSD indicating a pseudo two-state coexistence. This crossover is also revealed through volume per monomer and MSD as a function of the sphere's velocity. We also studied polymer dynamics by investigating folding events at different times., Comment: 17 pages, 11 figures

The current standard model of cosmology successfully describes a variety of measurements, but the nature of its main ingredients, dark matter and dark energy, remains unknown. Euclid is a medium-class mission in the Cosmic Vision 2015-2025 programme of the European Space Agency (ESA) that will provide high-resolution optical imaging, as well as near-infrared imaging and spectroscopy, over about 14,000 deg^2 of extragalactic sky. In addition to accurate weak lensing and clustering measurements that probe structure formation over half of the age of the Universe, its primary probes for cosmology, these exquisite data will enable a wide range of science. This paper provides a high-level overview of the mission, summarising the survey characteristics, the various data-processing steps, and data products. We also highlight the main science objectives and expected performance., Comment: Accepted for publication in the A&A special issue`Euclid on Sky'

This paper presents the specification, design, and development of the Visible Camera (VIS) on the ESA Euclid mission. VIS is a large optical-band imager with a field of view of 0.54 deg^2 sampled at 0.1" with an array of 609 Megapixels and spatial resolution of 0.18". It will be used to survey approximately 14,000 deg^2 of extragalactic sky to measure the distortion of galaxies in the redshift range z=0.1-1.5 resulting from weak gravitational lensing, one of the two principal cosmology probes of Euclid. With photometric redshifts, the distribution of dark matter can be mapped in three dimensions, and, from how this has changed with look-back time, the nature of dark energy and theories of gravity can be constrained. The entire VIS focal plane will be transmitted to provide the largest images of the Universe from space to date, reaching m_AB>24.5 with S/N >10 in a single broad I_E~(r+i+z) band over a six year survey. The particularly challenging aspects of the instrument are the control and calibration of observational biases, which lead to stringent performance requirements and calibration regimes. With its combination of spatial resolution, calibration knowledge, depth, and area covering most of the extra-Galactic sky, VIS will also provide a legacy data set for many other fields. This paper discusses the rationale behind the VIS concept and describes the instrument design and development before reporting the pre-launch performance derived from ground calibrations and brief results from the in-orbit commissioning. VIS should reach fainter than m_AB=25 with S/N>10 for galaxies of full-width half-maximum of 0.3" in a 1.3" diameter aperture over the Wide Survey, and m_AB>26.4 for a Deep Survey that will cover more than 50 deg^2. The paper also describes how VIS works with the other Euclid components of survey, telescope, and science data processing to extract the cosmological information., Comment: Paper submitted as part of the A&A special issue `Euclid on Sky', which contains Euclid key reference papers and first results from the Euclid Early Release Observations

Placement of electromagnetic signal emitting devices, such as light sources, has important usage in for signal coverage tasks. Automatic placement of these devices is challenging because of the complex interaction of the signal and environment due to reflection, refraction and scattering. In this work, we iteratively improve the placement of these devices by interleaving device placement and sensing actions, correcting errors in the model of the signal propagation. To this end, we propose a novel factor-graph based belief model which combines the measurements taken by the robot and an analytical light propagation model. This model allows accurately modelling the uncertainty of the light propagation with respect to the obstacles, which greatly improves the informative path planning routine. Additionally, we propose a method for determining when to re-plan the emitter placements to balance a trade-off between information about a specific configuration and frequent updating of the configuration. This method incorporates the uncertainty from belief model to adaptively determine when re-configuration is needed. We find that our system has a 9.8% median error reduction compared to a baseline system in simulations in the most difficult environment. We also run on-robot tests and determine that our system performs favorably compared to the baseline., Comment: Submitted to RA-L

We study the relation between measured high-$x_B$, high-$Q^2$, Helium-3 to Tritium, $(e,e')$ inclusive-scattering cross-section ratios and the relative abundance of high-momentum neutron-proton ($np$) and proton-proton ($pp$) short-range correlated (SRC) nucleon pairs in three-body ($A=3$) nuclei. Analysis of this data using a simple pair-counting cross-section model suggested a much smaller $np/pp$ ratio than previously measured in heavier nuclei, questioning our understanding of $A=3$ nuclei and, by extension, all other nuclei. Here we examine this finding using spectral-function-based cross-section calculations, with both an \textit{ab initio} $A=3$ spectral function and effective Generalized Contact Formalism (GCF) spectral functions using different nucleon-nucleon interaction models. The \textit{ab initio} calculation agrees with the data, showing good understanding of the structure of $A=3$ nuclei. An 8\% uncertainty on the simple pair-counting model, as implied by the difference between it and the \textit{ab initio} calculation, gives a factor of 5 uncertainty in the extracted $np/pp$ ratio. Thus we see no evidence for the claimed ``unexpected structure in the high-momentum wavefunction for hydrogen-3 and helium-3''., Comment: 6 pages, 4 figures

We extend the QCD Parton Model analysis using a factorized nuclear structure model incorporating individual nucleons and pairs of correlated nucleons. Our analysis of high-energy data from lepton Deep-Inelastic Scattering, Drell-Yan and W/Z production simultaneously extracts the universal effective distribution of quarks and gluons inside correlated nucleon pairs, and their nucleus-specific fractions. Such successful extraction of these universal distributions marks a significant advance in our understanding of nuclear structure properties connecting nucleon- and parton-level quantities., Comment: 7 pages, 2 figures, 1 table

In recent decades, computer experiments have led to an accurate and fundamental understanding of atomic and molecular mechanisms in fluids, such as different kinds of relaxation processes toward steady physical states. In this paper, we investigate how exactly the configuration of initial states in a molecular-dynamics simulation can affect the rates of decay toward equilibrium for the widely-known Langevin canonical ensemble. For this purpose, we derive an original expression relating the system relaxation time {\tau}_{sys} and the radial distribution function g(r) in the near-zero and high-density limit. We found that for an initial state which is slightly marginally inhomogeneous in the number density of atoms, the system relaxation time {\tau}_{sys} is much longer than that for the homogeneous case and an increasing function of the Langevin coupling constant, {\gamma}. We also found during structural equilibration, g(r) at large distances approaches 1 from above for the inhomogeneous case and from below for the macroscopically homogeneous one.

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

Introducing nanorods into a polymeric matrix can enhance the physical and mechanical properties of the resulting material. In this paper, we focus on understanding the dispersion and orientation patterns of nanorods in an unentangled polymer melt, particularly as a function of nanorod concentration, using Molecular Dynamics (MD) simulations. The system is comprised of flexible polymer chains and multi-thread nanorods that are equilibrated in the NPT ensemble. All interactions are purely repulsive except for those between polymers and rods. Results with attractive versus repulsive polymer-rod interactions are compared and contrasted. The concentration of rods has a direct impact on the phase behaviour of the system. At lower concentrations rods phase separate into nematic clusters, while at higher concentrations more isotropic and less structured rod configurations are observed. A detailed examination of the conformation of the polymer chains near the rod surface shows extension of the chains along the director of the rods (especially within clusters). The dispersion and orientation of the nanorods is a result of the competition between depletion entropic forces responsible for the formation of rod clusters, the enthalpic effects that improve mixing of rods and polymer, and entropic losses of polymers interpenetrating rod clusters., Comment: 16 pages, 15 figures

When robots are deployed in the field for environmental monitoring they typically execute pre-programmed motions, such as lawnmower paths, instead of adaptive methods, such as informative path planning. One reason for this is that adaptive methods are dependent on parameter choices that are both critical to set correctly and difficult for the non-specialist to choose. Here, we show how to automatically configure a planner for informative path planning by training a reinforcement learning agent to select planner parameters at each iteration of informative path planning. We demonstrate our method with 37 instances of 3 distinct environments, and compare it against pure (end-to-end) reinforcement learning techniques, as well as approaches that do not use a learned model to change the planner parameters. Our method shows a 9.53% mean improvement in the cumulative reward across diverse environments when compared to end-to-end learning based methods; we also demonstrate via a field experiment how it can be readily used to facilitate high performance deployment of an information gathering robot., Comment: 8 pages, Submitted to IROS 2023

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

In active source seeking, a robot takes repeated measurements in order to locate a signal source in a cluttered and unknown environment. A key component of an active source seeking robot planner is a model that can produce estimates of the signal at unknown locations with uncertainty quantification. This model allows the robot to plan for future measurements in the environment. Traditionally, this model has been in the form of a Gaussian process, which has difficulty scaling and cannot represent obstacles. %In this work, We propose a global and local factor graph model for active source seeking, which allows the model to scale to a large number of measurements and represent unknown obstacles in the environment. We combine this model with extensions to a highly scalable planner to form a system for large-scale active source seeking. We demonstrate that our approach outperforms baseline methods in both simulated and real robot experiments., Comment: 6 pages, Submitted to ICRA 2023 - Contains Appendix

We report the first measurement of $x_B$-scaling in $(e,e'p)$ cross-section ratios off nuclei relative to deuterium at large missing-momentum of $350 \leq p_{miss} \leq 600$ MeV/c. The observed scaling extends over a kinematic range of $0.7 \leq x_B \leq 1.8$, which is significantly wider than $1.4 \leq x_B \leq 1.8$ previously observed for inclusive $(e,e')$ cross-section ratios. The $x_B$-integrated cross-section ratios become constant (i.e., scale) beginning at $p_{miss}\approx k_F$, the nuclear Fermi momentum. Comparing with theoretical calculations we find good agreement with Generalized Contact Formalism calculations for high missing-momentum ($> 375$ MeV/c), suggesting the observed scaling results from interacting with nucleons in short-range correlated (SRC) pairs. For low missing-momenta, mean-field calculations show good agreement with the data for $p_{miss}\le k_F$, and suggest that contributions to the measured cross-section ratios from scattering off single, un-correlated, nucleons are non-negligible up to $p_{miss}\approx 350$ MeV/c. Therefore, SRCs become dominant in nuclei at $p_{miss}\approx 350$ MeV/c, well above the nuclear Fermi Surface of $k_F \approx 250$ MeV/c., Comment: 7 pages, 4 figures and supplementary materials

This paper reports on the state of the art in underground SLAM by discussing different SLAM strategies and results across six teams that participated in the three-year-long SubT competition. In particular, the paper has four main goals. First, we review the algorithms, architectures, and systems adopted by the teams; particular emphasis is put on lidar-centric SLAM solutions (the go-to approach for virtually all teams in the competition), heterogeneous multi-robot operation (including both aerial and ground robots), and real-world underground operation (from the presence of obscurants to the need to handle tight computational constraints). We do not shy away from discussing the dirty details behind the different SubT SLAM systems, which are often omitted from technical papers. Second, we discuss the maturity of the field by highlighting what is possible with the current SLAM systems and what we believe is within reach with some good systems engineering. Third, we outline what we believe are fundamental open problems, that are likely to require further research to break through. Finally, we provide a list of open-source SLAM implementations and datasets that have been produced during the SubT challenge and related efforts, and constitute a useful resource for researchers and practitioners., Comment: 21 pages including references. This survey paper is submitted to IEEE Transactions on Robotics for pre-approval

Search and rescue with a team of heterogeneous mobile robots in unknown and large-scale underground environments requires high-precision localization and mapping. This crucial requirement is faced with many challenges in complex and perceptually-degraded subterranean environments, as the onboard perception system is required to operate in off-nominal conditions (poor visibility due to darkness and dust, rugged and muddy terrain, and the presence of self-similar and ambiguous scenes). In a disaster response scenario and in the absence of prior information about the environment, robots must rely on noisy sensor data and perform Simultaneous Localization and Mapping (SLAM) to build a 3D map of the environment and localize themselves and potential survivors. To that end, this paper reports on a multi-robot SLAM system developed by team CoSTAR in the context of the DARPA Subterranean Challenge. We extend our previous work, LAMP, by incorporating a single-robot front-end interface that is adaptable to different odometry sources and lidar configurations, a scalable multi-robot front-end to support inter- and intra-robot loop closure detection for large scale environments and multi-robot teams, and a robust back-end equipped with an outlier-resilient pose graph optimization based on Graduated Non-Convexity. We provide a detailed ablation study on the multi-robot front-end and back-end, and assess the overall system performance in challenging real-world datasets collected across mines, power plants, and caves in the United States. We also release our multi-robot back-end datasets (and the corresponding ground truth), which can serve as challenging benchmarks for large-scale underground SLAM.

Multi-robot SLAM systems in GPS-denied environments require loop closures to maintain a drift-free centralized map. With an increasing number of robots and size of the environment, checking and computing the transformation for all the loop closure candidates becomes computationally infeasible. In this work, we describe a loop closure module that is able to prioritize which loop closures to compute based on the underlying pose graph, the proximity to known beacons, and the characteristics of the point clouds. We validate this system in the context of the DARPA Subterranean Challenge and on numerous challenging underground datasets and demonstrate the ability of this system to generate and maintain a map with low error. We find that our proposed techniques are able to select effective loop closures which results in 51% mean reduction in median error when compared to an odometric solution and 75% mean reduction in median error when compared to a baseline version of this system with no prioritization. We also find our proposed system is able to find a lower error in the mission time of one hour when compared to a system that processes every possible loop closure in four and a half hours. The code and dataset for this work can be found https://github.com/NeBula-Autonomy/LAMP, Comment: 8 pages, Accepted to RA-L/IROS 2022

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

We investigate the configuration space $\mathcal{S}_{G,b,\ell}$ associated with the movement of a robotic arm of length $\ell$ on a grid over an underlying graph $G$, anchored at a vertex $b \in G$. We study an associated PIP (poset with inconsistent pairs) $\text{IP}_{G,b,\ell}$ consisting of indexed paths on $G$. This PIP acts as a combinatorial model for the robotic arm, and we use $\text{IP}_{G,b,\ell}$ to show that the space $\mathcal{S}_{G,b,\ell}$ is a CAT(0) cubical complex, generalizing work of Ardila, Bastidas, Ceballos, and Guo. This establishes that geodesics exist within the configuration space, and yields explicit algorithms for moving the robotic arm between different configurations in an optimal fashion. We also give a tight bound on the diameter of the robotic arm transition graph (the maximal number of moves necessary to change from one configuration to another) and compute this diameter for a large family of underlying graphs $G$.

We investigate improving Monte Carlo Tree Search based solvers for Partially Observable Markov Decision Processes (POMDPs), when applied to adaptive sampling problems. We propose improvements in rollout allocation, the action exploration algorithm, and plan commitment. The first allocates a different number of rollouts depending on how many actions the agent has taken in an episode. We find that rollouts are more valuable after some initial information is gained about the environment. Thus, a linear increase in the number of rollouts, i.e. allocating a fixed number at each step, is not appropriate for adaptive sampling tasks. The second alters which actions the agent chooses to explore when building the planning tree. We find that by using knowledge of the number of rollouts allocated, the agent can more effectively choose actions to explore. The third improvement is in determining how many actions the agent should take from one plan. Typically, an agent will plan to take the first action from the planning tree and then call the planner again from the new state. Using statistical techniques, we show that it is possible to greatly reduce the number of rollouts by increasing the number of actions taken from a single planning tree without affecting the agent's final reward. Finally, we demonstrate experimentally, on simulated and real aquatic data from an underwater robot, that these improvements can be combined, leading to better adaptive sampling. The code for this work is available at https://github.com/uscresl/AdaptiveSamplingPOMCP, Comment: Accepted at ICRA 2021 6 pages + 1 page Appendix. The first two authors had an equal contribution

To accurately reproduce measurements from the real world, simulators need to have an adequate model of the physical system and require the parameters of the model be identified. We address the latter problem of estimating parameters through a Bayesian inference approach that approximates a posterior distribution over simulation parameters given real sensor measurements. By extending the commonly used Gaussian likelihood model for trajectories via the multiple-shooting formulation, our chosen particle-based inference algorithm Stein Variational Gradient Descent is able to identify highly nonlinear, underactuated systems. We leverage GPU code generation and differentiable simulation to evaluate the likelihood and its gradient for many particles in parallel. Our algorithm infers non-parametric distributions over simulation parameters more accurately than comparable baselines and handles constraints over parameters efficiently through gradient-based optimization. We evaluate estimation performance on several physical experiments. On an underactuated mechanism where a 7-DOF robot arm excites an object with an unknown mass configuration, we demonstrate how our inference technique can identify symmetries between the parameters and provide highly accurate predictions. Project website: https://uscresl.github.io/prob-diff-sim, Comment: Extended version. To appear at ICRA 2022