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Physical therapy (PT) plays a crucial role in muscle injury recovery, but people struggle to adhere to and perform PT exercises correctly from home. To support challenges faced with in-home PT, augmented reality (AR) holds promise in enhancing patient's engagement and accuracy through immersive interactive visualizations. However, effectively leveraging AR requires a better understanding of patient needs during injury recovery. Through interviews with six individuals undergoing physical therapy, this paper introduces user-centered design considerations integrating AR and body motion data to enhance in-home PT for injury recovery. Our findings identify key challenges and propose design variables for future body-based visualizations of body motion data for PT.

A submanifold of the standard symplectic space determines a partially defined, multi-valued symplectic map, the outer symplectic billiard correspondence. Two points are in this correspondence if the midpoint of the segment connecting them is on the submanifold, and this segment is symplectically orthogonal to the tangent space of the submanifold at its midpoint. This is a far-reaching generalization of the outer billiard map in the plane; the particular cases, when the submanifold is a closed convex hypersurface or a Lagrangian submanifold, were considered earlier. Using a variational approach, we establish the existence of odd-periodic orbits of the outer symplectic billiard correspondence. On the other hand, we give examples of curves in 4-space which do not admit 4-periodic orbits at all. If the submanifold satisfies 49 pages, certain conditions (which are always satisfied if its dimension is at least half of the ambient dimension) we prove the existence of two $n$-reflection orbits connecting two transverse affine Lagrangian subspaces for every $n\geq1$. In addition, for every immersed closed submanifold, the number of single outer symplectic billiard ``shots" from one affine Lagrangian subspace to another is no less than the number of critical points of a smooth function on this submanifold. We study, in detail, the behavior of this correspondence when the submanifold is a curve or a Lagrangian submanifold. For Lagrangian submanifolds in 4-dimensional space we present a criterion for the outer symplectic billiard correspondence to be an actual map. We show, in every dimension, that if a Lagrangian submanifold has a cubic generating function, then the outer symplectic billiard correspondence is completely integrable in the Liouville sense., Comment: 49 pages, 4 figures

In the rapidly evolving field of information visualization, rigorous evaluation is essential for validating new techniques, understanding user interactions, and demonstrating the effectiveness and usability of visualizations. Faithful evaluations provide valuable insights into how users interact with and perceive the system, enabling designers to identify potential weaknesses and make informed decisions about design choices and improvements. However, an emerging trend of multiple evaluations within a single research raises critical questions about the sustainability, feasibility, and methodological rigor of such an approach. New researchers and students, influenced by this trend, may believe -- multiple evaluations are necessary for a study, regardless of the contribution types. However, the number of evaluations in a study should depend on its contributions and merits, not on the trend of including multiple evaluations to strengthen a paper. So, how many evaluations are enough? This is a situational question and cannot be formulaically determined. Our objective is to summarize current trends and patterns to assess the distribution of evaluation methods over different paper contribution types. In this paper, we identify this trend through a non-exhaustive literature survey of evaluation patterns in 214 papers in the two most recent years' VIS issues in IEEE TVCG from 2023 and 2024. We then discuss various evaluation strategy patterns in the information visualization field to guide practical choices and how this paper will open avenues for further discussion.

Shape is commonly used to distinguish between categories in multi-class scatterplots. However, existing guidelines for choosing effective shape palettes rely largely on intuition and do not consider how these needs may change as the number of categories increases. Although shapes can be a finite number compared to colors, they can not be represented by a numerical space, making it difficult to propose a general guideline for shape choices or shed light on the design heuristics of designer-crafted shape palettes. This paper presents a series of four experiments evaluating the efficiency of 39 shapes across three tasks -- relative mean judgment tasks, expert choices, and data correlation estimation. Given how complex and tangled results are, rather than relying on conventional features for modeling, we built a model and introduced a corresponding design tool that offers recommendations for shape encodings. The perceptual effectiveness of shapes significantly varies across specific pairs, and certain shapes may enhance perceptual efficiency and accuracy. However, how performance varies does not map well to classical features of shape such as angles, fill, or convex hull. We developed a model based on pairwise relations between shapes measured in our experiments and the number of shapes required to intelligently recommend shape palettes for a given design. This tool provides designers with agency over shape selection while incorporating empirical elements of perceptual performance captured in our study. Our model advances the understanding of shape perception in visualization contexts and provides practical design guidelines for advanced shape usage in visualization design that optimize perceptual efficiency.

Individuals with Intellectual and Developmental Disabilities (IDD) have unique needs and challenges when working with data. While visualization aims to make data more accessible to a broad audience, our understanding of how to design cognitively accessible visualizations remains limited. In this study, we engaged 20 participants with IDD as co-designers to explore how they approach and visualize data. Our preliminary investigation paired four participants as data pen-pals in a six-week online asynchronous participatory design workshop. In response to the observed conceptual, technological, and emotional struggles with data, we subsequently organized a two-day in-person co-design workshop with 16 participants to further understand relevant visualization authoring and sensemaking strategies. Reflecting on how participants engaged with and represented data, we propose two strategies for cognitively accessible data visualizations: transforming numbers into narratives and blending data design with everyday aesthetics. Our findings emphasize the importance of involving individuals with IDD in the design process, demonstrating their capacity for data analysis and expression, and underscoring the need for a narrative and tangible approach to accessible data visualization.

This paper introduces the sigma flow model for the prediction of structured labelings of data observed on Riemannian manifolds, including Euclidean image domains as special case. The approach combines the Laplace-Beltrami framework for image denoising and enhancement, introduced by Sochen, Kimmel and Malladi about 25 years ago, and the assignment flow approach introduced and studied by the authors. The sigma flow arises as Riemannian gradient flow of generalized harmonic energies and thus is governed by a nonlinear geometric PDE which determines a harmonic map from a closed Riemannian domain manifold to a statistical manifold, equipped with the Fisher-Rao metric from information geometry. A specific ingredient of the sigma flow is the mutual dependency of the Riemannian metric of the domain manifold on the evolving state. This makes the approach amenable to machine learning in a specific way, by realizing this dependency through a mapping with compact time-variant parametrization that can be learned from data. Proof of concept experiments demonstrate the expressivity of the sigma flow model and prediction performance. Structural similarities to transformer network architectures and networks generated by the geometric integration of sigma flows are pointed out, which highlights the connection to deep learning and, conversely, may stimulate the use of geometric design principles for structured prediction in other areas of scientific machine learning., Comment: 51 pages

In the late stages of accretion leading up to the formation of planetesimals, particles grew to pebbles the size of 1-mm to tens of cm. That is the same size range that dominates the present-day comet mass loss. Meteoroids that size cause visible meteors on Earth. Here, we hypothesize that the size distribution and the physical and chemical properties of young meteoroid streams still contain information about the conditions in the solar nebula during these late stages of accretion. From observations of 47 young meteor showers, we find that freshly ejected meteoroids from long-period comets tend to have low bulk density and are distributed with equal surface area per log-mass interval (magnitude distribution index chi ~ 1.85), suggesting gentle accretion conditions. Jupiter-family comets, on the other hand, mostly produce meteoroids twice as dense and distributed with a steeper chi ~ 2.15 or even chi ~ 2.5, which implies that those pebbles grew from particles fragmenting in a collisional cascade or by catastrophic collisions, respectively. Both comet populations contain an admixture of compact materials that are sometimes sodium-poor, but Jupiter-family comets show a higher percentage (~8% on average) than long-period comet showers (~4%), and a wider range. While there are exceptions in both groups, the implication is that most long-period comets formed under gentle particle growth conditions, possibly near the 30 AU edge of the Trans Neptunian Disk, while most Jupiter family comets formed closer to the Sun where pebbles reached or passed the fragmentation barrier. This is possible if the Scattered Disk represents all objects scattered by Neptune during its migration, while the present-day outer Oort cloud formed only during and after the Sun had moved away from sibling stars., Comment: 82 pages, 14 figures, 3 tables

We demonstrate that standard delay systems with a linear instantaneous and a delayed nonlinear term show weak chaos, asymptotically subdiffusive behavior, and weak ergodicity breaking if the nonlinearity is chosen from a specific class of functions. In the limit of large constant delay times, anomalous behavior may not be observable due to exponentially large crossover times. A periodic modulation of the delay causes a strong reduction of the effective dimension of the chaotic phases, leads to hitherto unknown types of solutions, and the occurrence of anomalous diffusion already at short times. The observed anomalous behavior is caused by non-hyperbolic fixed points in function space., Comment: 7 pages, 5 figures

We present several competitive ratios for the online busy time scheduling problem with flexible jobs. The busy time scheduling problem is a fundamental scheduling problem motivated by energy efficiency with the goal of minimizing the total time that machines with multiple processors are enabled. In the busy time scheduling problem, an unbounded number of machines is given, where each machine has $g$ processors. No more than $g$ jobs can be scheduled simultaneously on each machine. A machine consumes energy whenever at least one job is scheduled at any time on the machine. Scheduling a single job at some time $t$ consumes the same amount of energy as scheduling $g$ jobs at time $t$. In the online setting, jobs are revealed when they are released. We consider the cases where $g$ is unbounded and bounded. In this paper, we revisit the bounds of the unbounded general setting from the literature and tighten it significantly. We also consider agreeable jobs. For the bounded setting, we show a tightened upper bound. Furthermore, we show the first constant competitive ratio in the bounded setting that does not require lookahead.

Quantum technology is predicted to have a significant impact on society once it matures. This study (n = 637 adults representative of the Dutch population) examined the effect of different frames on engagement - specifically, information seeking, internal efficacy, general interest and perceived knowledge - with quantum technology. The different frames were: enigmatic, explaining quantum physics, benefit, risk and balanced. Results indicated that framing quantum as enigmatic does not affect engagement, while explaining quantum physics positively influences general interest. Furthermore, emphasising a benefit of quantum technology increases participants' internal efficacy, whereas highlighting both a benefit and a risk of quantum technology decreases perceived knowledge. Based on these findings, we offer practical advice for science communicators in the field and suggest further research., Comment: 19 pages

People with Parkinson's Disease (PD) can slow the progression of their symptoms with physical therapy. However, clinicians lack insight into patients' motor function during daily life, preventing them from tailoring treatment protocols to patient needs. This paper introduces PD-Insighter, a system for comprehensive analysis of a person's daily movements for clinical review and decision-making. PD-Insighter provides an overview dashboard for discovering motor patterns and identifying critical deficits during activities of daily living and an immersive replay for closely studying the patient's body movements with environmental context. Developed using an iterative design study methodology in consultation with clinicians, we found that PD-Insighter's ability to aggregate and display data with respect to time, actions, and local environment enabled clinicians to assess a person's overall functioning during daily life outside the clinic. PD-Insighter's design offers future guidance for generalized multiperspective body motion analytics, which may significantly improve clinical decision-making and slow the functional decline of PD and other medical conditions., Comment: 18 pages, 11 figures, Proceedings of the CHI Conference on Human Factors in Computing Systems (CHI '24), May 11--16, 2024, Honolulu, HI, USA

Existing guidelines for categorical color selection are heuristic, often grounded in intuition rather than empirical studies of readers' abilities. While design conventions recommend palettes maximize hue differences, more recent exploratory findings indicate other factors, such as lightness, may play a role in effective categorical palette design. We conducted a crowdsourced experiment on mean value judgments in multi-class scatterplots using five color palette families--single-hue sequential, multi-hue sequential, perceptually-uniform multi-hue sequential, diverging, and multi-hue categorical--that differ in how they manipulate hue and lightness. Participants estimated relative mean positions in scatterplots containing 2 to 10 categories using 20 colormaps. Our results confirm heuristic guidance that hue-based categorical palettes are most effective. However, they also provide additional evidence that scalable categorical encoding relies on more than hue variance., Comment: Accepted for publication in EuroVis 2024 Short Paper

Assessing the similarity of matrices is valuable for analyzing the extent to which data sets exhibit common features in tasks such as data clustering, dimensionality reduction, pattern recognition, group comparison, and graph analysis. Methods proposed for comparing vectors, such as cosine similarity, can be readily generalized to matrices. However, this approach usually neglects the inherent two-dimensional structure of matrices. Here, we propose singular angle similarity (SAS), a measure for evaluating the structural similarity between two arbitrary, real matrices of the same shape based on singular value decomposition. After introducing the measure, we compare SAS with standard measures for matrix comparison and show that only SAS captures the two-dimensional structure of matrices. Further, we characterize the behavior of SAS in the presence of noise and as a function of matrix dimensionality. Finally, we apply SAS to two use cases: square non-symmetric matrices of probabilistic network connectivity, and non-square matrices representing neural brain activity. For synthetic data of network connectivity, SAS matches intuitive expectations and allows for a robust assessment of similarities and differences. For experimental data of brain activity, SAS captures differences in the structure of high-dimensional responses to different stimuli. We conclude that SAS is a suitable measure for quantifying the shared structure of matrices with arbitrary shape., Comment: 12 pages, 6 figures

Intensive care unit (ICU) patients exhibit erratic blood glucose (BG) fluctuations, including hypoglycemic and hyperglycemic episodes, and require exogenous insulin delivery to keep their BG in healthy ranges. Glycemic control via glycemic management (GM) is associated with reduced mortality and morbidity in the ICU, but GM increases the cognitive load on clinicians. The availability of robust, accurate, and actionable clinical decision support (CDS) tools reduces this burden and assists in the decision-making process to improve health outcomes. Clinicians currently follow GM protocol flow charts for patient intravenous insulin delivery rate computations. We present a mechanistic model-based control algorithm that predicts the optimal intravenous insulin rate to keep BG within a target range; the goal is to develop this approach for eventual use within CDS systems. In this control framework, we employed a stochastic model representing BG dynamics in the ICU setting and used the linear quadratic Gaussian control methodology to develop a controller. We designed two experiments, one using virtual (simulated) patients and one using a real-world retrospective dataset. Using these, we evaluate the safety and efficacy of this model-based glycemic control methodology. The presented controller avoids hypoglycemia and hyperglycemia in virtual patients, maintaining BG levels in the target range more consistently than two existing GM protocols. Moreover, this methodology could theoretically prevent a large proportion of hypoglycemic and hyperglycemic events recorded in a real-world retrospective dataset., Comment: 26 pages, 4 figures, 5 tables

In this paper, we introduce the cyclic polygon plot, a representation based on a novel projection concept for multi-dimensional values. Cyclic polygon plots combine the typically competing requirements of quantitativeness, image-space efficiency, and readability. Our approach is complemented with a placement strategy based on its intrinsic features, resulting in a dimensionality reduction strategy that is consistent with our overall concept. As a result, our approach combines advantages from dimensionality reduction techniques and quantitative plots, supporting a wide range of tasks in multi-dimensional data analysis. We examine and discuss the overall properties of our approach, and demonstrate its utility with a user study and selected examples., Comment: 10 pages, 8 figures, 2 tables

Magnetic particle imaging is a tracer-based tomographic imaging technique that allows the concentration of magnetic nanoparticles to be determined with high spatio-temporal resolution. To reconstruct an image of the tracer concentration, the magnetization dynamics of the particles must be accurately modeled. A popular ensemble model is based on solving the Fokker-Plank equation, taking into account either Brownian or N\'eel dynamics. The disadvantage of this model is that it is computationally expensive due to an underlying stiff differential equation. A simplified model is the equilibrium model, which can be evaluated directly but in most relevant cases it suffers from a non-negligible modeling error. In the present work, we investigate an extended version of the equilibrium model that can account for particle anisotropy. We show that this model can be expressed as a series of Bessel functions, which can be truncated based on a predefined accuracy, leading to very short computation times, which are about three orders of magnitude lower than equivalent Fokker-Planck computation times. We investigate the accuracy of the model for 2D Lissajous magnetic particle imaging sequences and show that the difference between the Fokker-Planck and the equilibrium model with anisotropy is sufficiently small so that the latter model can be used for image reconstruction on experimental data with only marginal loss of image quality, even compared to a system matrix-based reconstruction., Comment: This work has been submitted to the IEEE for possible publication

Quality colormaps can help communicate important data patterns. However, finding an aesthetically pleasing colormap that looks "just right" for a given scenario requires significant design and technical expertise. We introduce Cieran, a tool that allows any data analyst to rapidly find quality colormaps while designing charts within Jupyter Notebooks. Our system employs an active preference learning paradigm to rank expert-designed colormaps and create new ones from pairwise comparisons, allowing analysts who are novices in color design to tailor colormaps to their data context. We accomplish this by treating colormap design as a path planning problem through the CIELAB colorspace with a context-specific reward model. In an evaluation with twelve scientists, we found that Cieran effectively modeled user preferences to rank colormaps and leveraged this model to create new quality designs. Our work shows the potential of active preference learning for supporting efficient visualization design optimization., Comment: CHI 2024. 12 pages/9 figures

Designers often create visualizations to achieve specific high-level analytical or communication goals. These goals require people to naturally extract complex, contextualized, and interconnected patterns in data. While limited prior work has studied general high-level interpretation, prevailing perceptual studies of visualization effectiveness primarily focus on isolated, predefined, low-level tasks, such as estimating statistical quantities. This study more holistically explores visualization interpretation to examine the alignment between designers' communicative goals and what their audience sees in a visualization, which we refer to as their comprehension. We found that statistics people effectively estimate from visualizations in classical graphical perception studies may differ from the patterns people intuitively comprehend in a visualization. We conducted a qualitative study on three types of visualizations -- line graphs, bar graphs, and scatterplots -- to investigate the high-level patterns people naturally draw from a visualization. Participants described a series of graphs using natural language and think-aloud protocols. We found that comprehension varies with a range of factors, including graph complexity and data distribution. Specifically, 1) a visualization's stated objective often does not align with people's comprehension, 2) results from traditional experiments may not predict the knowledge people build with a graph, and 3) chart type alone is insufficient to predict the information people extract from a graph. Our study confirms the importance of defining visualization effectiveness from multiple perspectives to assess and inform visualization practices., Comment: Accepted for publication in ACM CHI 2024

We introduce symplectic billiards for pairs of possibly non-convex polygons. After establishing basic properties, we give several criteria on pairs of polygons for the symplectic billiard map to be fully periodic, i.e. $\textit{every}$ orbit is periodic. First fully periodic examples were discovered by Albers-Tabachnikov [AT18] and Albers-Banhatti-Sadlo-Schwartz-Tabachnikov in [ABS+19]. Our criteria allow us to construct a plethora of new examples. Moreover, we provide an example of a pair of polygons where the symplectic billiard map is fully periodic while having orbits of arbitrarily large period. After giving a class of examples which provably have isolated periodic orbits (and are thus not fully periodic) we exhibit the first example without any periodic orbits at all. It is open whether being fully periodic with unbounded period or having no periodic orbits at all is possible in the single polygon setting. Finally, we prove that if one replaces polygons by smooth strictly convex curves then there are always infinitely many periodic orbits., Comment: 37 pages, 41 figures

This paper studies a meta-simplex concept and geometric embedding framework for multi-population replicator dynamics. Central results are two embedding theorems which constitute a formal reduction of multi-population replicator dynamics to single-population ones. In conjunction with a robust mathematical formalism, this provides a toolset for analyzing complex multi-population models. Our framework provides a unifying perspective on different population dynamics in the literature which in particular enables to establish a formal link between multi-population and multi-game dynamics.

The susceptible-infected-recovered (SIR) model and its variants form the foundation of our understanding of the spread of diseases. Here, each agent can be in one of three states (susceptible, infected, or recovered), and transitions between these states follow a stochastic process. The probability of an agent becoming infected depends on the number of its infected neighbors, hence all agents are correlated. A common mean-field theory of the same stochastic process however, assumes that the agents are statistically independent. This leads to a self-feedback effect in the approximation: when an agent infects its neighbors, this infection may subsequently travel back to the original agent at a later time, leading to a self-infection of the agent which is not present in the underlying stochastic process. We here compute the first order correction to the mean-field assumption, which takes fluctuations up to second order in the interaction strength into account. We find that it cancels the self-feedback effect, leading to smaller infection rates. In the SIR model and in the SIRS model, the correction significantly improves predictions. In particular, it captures how sparsity dampens the spread of the disease: this indicates that reducing the number of contacts is more effective than predicted by mean-field models.

The nuclear two-photon or double-gamma ($2\gamma$) decay is a second-order electromagnetic process whereby a nucleus in an excited state emits two gamma rays simultaneously. To be able to directly measure the $2\gamma$ decay rate in the low-energy regime below the electron-positron pair-creation threshold, we combined the isochronous mode of a storage ring with Schottky resonant cavities. The newly developed technique can be applied to isomers with excitation energies down to $\sim100$\,keV and half-lives as short as $\sim10$\,ms. The half-life for the $2\gamma$ decay of the first-excited $0^+$ state in bare $^{72}\mathrm{Ge}$ ions was determined to be $23.9\left(6\right)$\,ms, which strongly deviates from expectations., Comment: Submitted to Physical Review Letters, 8 pages, 3 figures, 2 tables, 7 equations

Induced magnetospheres form around planetary bodies with atmospheres through the interaction of the solar wind with their ionosphere. Induced magnetospheres are highly dependent on the solar wind conditions and have only been studied with single spacecraft missions in the past. This gap in knowledge could be addressed by a multi-spacecraft plasma mission, optimized for studying global spatial and temporal variations in the magnetospheric system around Venus, which hosts the most prominent example of an induced magnetosphere in our solar system. The MVSE mission comprises four satellites, of which three are identical scientific spacecraft, carrying the same suite of instruments probing different regions of the induced magnetosphere and the solar wind simultaneously. The fourth spacecraft is the transfer vehicle which acts as a relay satellite for communications at Venus. In this way, changes in the solar wind conditions and extreme solar events can be observed, and their effects can be quantified as they propagate through the Venusian induced magnetosphere. Additionally, energy transfer in the Venusian induced magnetosphere can be investigated. The scientific payload includes instrumentation to measure the magnetic field, electric field, and ion-electron velocity distributions. This study presents the scientific motivation for the mission as well as requirements and the resulting mission design. Concretely, a mission timeline along with a complete spacecraft design, including mass, power, communication, propulsion and thermal budgets are given. This mission was initially conceived at the Alpbach Summer School 2022 and refined during a week-long study at ESAs Concurrent Design Facility in Redu, Belgium, Comment: 23 pages, 5 figures, Submitted to Acta Astronautica

High-precision laser interferometric instruments require optical surfaces with a close to perfect contour, as well as low scattering and absorption. Especially point absorbers are problematic because they heat up at high optical intensities and locally deform the otherwise flat surface, resulting in correlations between absorption and contour. Here, we present a laser scanning microscopy approach for the reconstruction of the two complementary images of an optical surface. The 'phase image' is related to the surface profile including roughness. The 'loss image' localizes point absorbers. Our experiment achieves a sensitivity of up to (3.1 $\pm$ 1.4) fm/$\sqrt{\mathrm{Hz}}$ and a (5.29 $\pm$ 0.06) $\mathrm{\mu}$m lateral resolution. The two images show correlations for some features proving the particular strength of our tomographic approach, which should help further improving optical surfaces or to understand dynamic processes of surface physics.

The sensitivity of atom interferometers depends on their ability to realize long pulse separation times and prevent loss of contrast by limiting the expansion of the atomic ensemble within the interferometer beam through matter-wave collimation. Here we investigate the impact of atomic interactions on collimation by applying a lensing protocol to a $^{39}$K Bose-Einstein condensate at different scattering lengths. Tailoring interactions, we measure energies corresponding to $340 \pm 12$ pK in one direction. Our results are supported by an accurate simulation, which allows us to extrapolate a 2D ballistic expansion energy of $438 \pm 77$ pK. Based on our findings we propose an advanced scenario, which enables 3D expansion energies below $16$ pK by implementing an additional pulsed delta-kick. Our results pave the way to realize ensembles with more than $1\times10^5$ atoms and 3D energies in the two-digit pK range in typical dipole trap setups without the need for micro-gravity or long baseline environments.

We use cluster algebras to interpret Floer potentials of monotone Lagrangian tori in toric del Pezzo surfaces as cluster characters of quiver representations., Comment: 14 pages