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Physical phenomena such as chemical reactions, bond breaking, and phase transition require molecular dynamics (MD) simulation with ab initio accuracy ranging from milliseconds to microseconds. However, previous state-of-the-art neural network based MD packages such as DeePMD-kit can only reach 4.7 nanoseconds per day on the Fugaku supercomputer. In this paper, we present a novel node-based parallelization scheme to reduce communication by 81%, then optimize the computationally intensive kernels with sve-gemm and mixed precision. Finally, we implement intra-node load balance to further improve the scalability. Numerical results on the Fugaku supercomputer show that our work has significantly improved the time-to-solution of the DeePMD-kit by a factor of 31.7x, reaching 149 nanoseconds per day on 12,000 computing nodes. This work has opened the door for millisecond simulation with ab initio accuracy within one week for the first time., Comment: 11 pages, 11 figures, 3 tables, SC'24

Navigating complex environments requires Unmanned Aerial Vehicles (UAVs) and autonomous systems to perform trajectory tracking and obstacle avoidance in real-time. While many control strategies have effectively utilized linear approximations, addressing the non-linear dynamics of UAV, especially in obstacle-dense environments, remains a key challenge that requires further research. This paper introduces a Non-linear Model Predictive Control (NMPC) framework for the DJI Matrice 100, addressing these challenges by using a dynamic model and B-spline interpolation for smooth reference trajectories, ensuring minimal deviation while respecting safety constraints. The framework supports various trajectory types and employs a penalty-based cost function for control accuracy in tight maneuvers. The framework utilizes CasADi for efficient real-time optimization, enabling the UAV to maintain robust operation even under tight computational constraints. Simulation and real-world indoor and outdoor experiments demonstrated the NMPC ability to adapt to disturbances, resulting in smooth, collision-free navigation., Comment: This manuscript has 7 pages and 8 figures, detailing NMPC for UAV obstacle avoidance using DJI UAVs. It features simulations, experimental results, and uses CasADi for optimization with ROS integration. Code and media at https://github.com/larasupernovae/nmpc_flash_multi_obstacle

This research investigates the efficiency of Floyd algorithm for obstacle-free path planning for autonomous aerial vehicles (UAVs) or drones. Floyd algorithm is used to generate the shortest paths for UAVs to fly from any place to the destination in a large-scale field with obstacles which UAVs cannot fly over. The simulation results demonstrated that Floyd algorithm effectively plans the shortest obstacle-free paths for UAVs to fly to a destination. It is verified that Floyd algorithm holds a time complexity of O(n3). This research revealed a correlation of a cubic polynomial relationship between the time cost and the size of the field, no correlation between the time cost and the number of obstacles, and no correlation between the time cost and the number of UAVs in the tested field. The applications of the research results are discussed in the paper as well., Comment: 9 pages, 8 figures

Recent years have seen significant growth of quantum technologies, and specifically quantum sensing, both in terms of the capabilities of advanced platforms and their applications. One of the leading platforms in this context is nitrogen-vacancy (NV) color centers in diamond, providing versatile, high-sensitivity, and high-resolution magnetic sensing. Nevertheless, current schemes for spin resonance magnetic sensing (as applied by NV quantum sensing) suffer from tradeoffs associated with sensitivity, dynamic range, and bandwidth. Here we address this issue, and implement machine learning tools to enhance NV magnetic sensing in terms of the sensitivity/bandwidth tradeoff in large dynamic range scenarios. We experimentally demonstrate this new approach, reaching an improvement in the relevant figure of merit by a factor of up to 5. Our results promote quantum machine learning protocols for sensing applications towards more feasible and efficient quantum technologies., Comment: 12 pages including supplementary, 6 figures

In virtual Hand-Object Interaction (HOI) scenarios, the authenticity of the hand's deformation is important to immersive experience, such as natural manipulation or tactile feedback. Unrealistic deformation arises from simplified hand geometry, neglect of the different physics attributes of the hand, and penetration due to imprecise contact handling. To address these problems, we propose PhysHand, a novel hand simulation model, which enhances the realism of deformation in HOI. First, we construct a physiologically plausible geometry, a layered mesh with a "skin-flesh-skeleton" structure. Second, to satisfy the distinct physics features of different soft tissues, a constraint-based dynamics framework is adopted with carefully designed layer-corresponding constraints to maintain flesh attached and skin smooth. Finally, we employ an SDF-based method to eliminate the penetration caused by contacts and enhance its accuracy by introducing a novel multi-resolution querying strategy. Extensive experiments have been conducted to demonstrate the outstanding performance of PhysHand in calculating deformations and handling contacts. Compared to existing methods, our PhysHand: 1) can compute both physiologically and physically plausible deformation; 2) significantly reduces the depth and count of penetration in HOI., Comment: 11 pages

Directed graphs provide more subtle and precise modelling tools for optimization in road networks than simple graphs. In particular, they are more suitable in the context of alternative fuel vehicles and new automotive technologies, like electric vehicles. In this paper, we introduce the new general concept of a reachability digraph associated with a road network to model the placement of refuelling facilities in road networks as k-dominating sets in the reachability digraph. Two new greedy heuristics are designed and experimentally tested to search for small k-dominating sets in two types of digraphs, including the reachability digraphs. Refined greedy strategies are shown to be efficient, capable of finding good quality solutions, and suitable for application in very large digraphs and road networks. Also, a probabilistic method is used to prove a new upper bound on the k-domination number of a digraph, which informs the development of a new randomized heuristic to search for k-dominating sets in the digraph. Generalizing the randomized heuristic ideas, making the heuristic more flexible, tuning and combining it with the greedy strategies allows us to obtain even better results for the reachability digraphs. Computational experiments are conducted for a case study of road networks in the West Midlands (UK)., Comment: 27 pages, 1 figure, 7 tables; preliminary results are presented in a short conference paper and at the International Network Optimization Conference INOC 2024, University College Dublin (Ireland) https://inoc2024.sciencesconf.org/

Actuator saturation is a common nonlinearity. In wave energy conversion, force saturation conveniently limits drivetrain size and cost with minimal impact on energy generation. However, such nonlinear dynamics typically demand numerical simulation, which increases computational cost and diminishes intuition. This paper instead uses describing functions to approximate a force saturation nonlinearity as a linear impedance mismatch. In the frequency domain, the impact of controller impedance mismatch (such as force limit, finite bandwidth, or parameter error) on electrical power production is shown analytically and graphically for a generic nondimensionalized single degree of freedom wave energy converter in regular waves. Results are visualized with Smith charts. Notably, systems with a specific ratio of reactive to real mechanical impedance are least sensitive to force limits, a criteria which conflicts with resonance and bandwidth considerations. The describing function method shows promise to enable future studies such as large-scale design optimization and co-design., Comment: 6 pages, 7 figures. For code, see https://github.com/symbiotic-engineering/IFAC_CAMS_2024/ . To be presented at IFAC CAMS 2024 conference and to appear in IFAC-PapersOnLine

The way we engage with digital spaces and the digital world has undergone rapid changes in recent years, largely due to the emergence of the Metaverse. As technology continues to advance, the demand for sophisticated and immersive interfaces to interact with the Metaverse has become increasingly crucial. Haptic interfaces have been developed to meet this need and provide users with tactile feedback and realistic touch sensations. These interfaces play a vital role in creating a more authentic and immersive experience within the Metaverse. This article introduces the concept of MetaDigiHuman, a groundbreaking framework that combines blended digital humans and haptic interfaces. By harnessing cutting-edge technologies, MetaDigiHuman enables seamless and immersive interaction within the Metaverse. Through this framework, users can simulate the sensation of touching, feeling, and interacting with digital beings as if they were physically present in the environments, offering a more compelling and immersive experience within the Metaverse., Comment: 5 pages, 2 figures

The route to chaos and phase dynamics in a rotating shallow-water model were rigorously examined using a five-mode Galerkin truncated system with complex variables. This system is valuable for investigating how large/meso-scales destabilize and evolve into chaos. Two distinct transitions into chaotic behaviour were identified as energy levels increased. The initial transition occurs through bifurcations following the Feigenbaum sequence. The subsequent transition, at higher energy levels, shows a shift from quasi-periodic states to chaotic regimes. The first chaotic state is mainly due to inertial forces governing nonlinear interactions. The second chaotic state arises from the increased significance of free surface elevation in the dynamics. A novel reformulation using phase and amplitude representations for each truncated variable revealed that phase components exhibit a temporal piece-wise locking behaviour, maintaining a constant value for a prolonged interval before an abrupt transition of $\pm\pi$, while amplitudes remain chaotic. It was observed that phase stability duration decreases with increased energy, leading to chaos in phase components at high energy levels. This is attributed to the nonlinear term in the equations, where phase components are introduced through linear combinations of triads with different modes. When locking durations vary across modes, the dynamics result in a stochastic interplay of multiple $\pi$ phase shifts, creating a stochastic dynamic within the coupled phase triads, observable even at minimal energy injections., Comment: 31 pages, 13 figures, 55 references, 2 appendices

In a class of heterogeneous random networks, where each node dynamics is a random dynamical system, interacting with neighbor nodes via a random coupling function, we characterize the hub behavior as the mean-field, subject to statistically controlled fluctuations. In particular, we prove that the fluctuations are small over exponentially long time scales and obtain Berry-Esseen estimates for the fluctuation statistics at any fixed time. Our results provide a mathematical explanation for several numerical observations, including the scaling relation between system size and frequency of large fluctuations, as well as system size induced desynchronization. To our best knowledge, these are the first characterizations of mean-field fluctuations on networks with a degree distribution that follows a power-law, a common feature for many realistic systems., Comment: 40 pages, 7 figures

This paper presents the Customer Experience (CX) Simulator, a novel framework designed to assess the effects of untested web-marketing campaigns through user behavior simulations. The proposed framework leverages large language models (LLMs) to represent various events in a user's behavioral history, such as viewing an item, applying a coupon, or purchasing an item, as semantic embedding vectors. We train a model to predict transitions between events from their LLM embeddings, which can even generalize to unseen events by learning from diverse training data. In web-marketing applications, we leverage this transition prediction model to simulate how users might react differently when new campaigns or products are presented to them. This allows us to eliminate the need for costly online testing and enhance the marketers' abilities to reveal insights. Our numerical evaluation and user study, utilizing BigQuery Public Datasets from the Google Merchandise Store, demonstrate the effectiveness of our framework., Comment: 5 pages, 2 figures, 1 table, the 33rd ACM International Conference on Information and Knowledge Management (CIKM '24)

This draft article outlines a prediction challenge where the target is to forecast the number of fatalities in armed conflicts, in the form of the UCDP `best' estimates, aggregated to the VIEWS units of analysis. It presents the format of the contributions, the evaluation metric, and the procedures, and a brief summary of the contributions. The article serves a function analogous to a pre-analysis plan: a statement of the forecasting models made publicly available before the true future prediction window commences. More information on the challenge, and all data referred to in this document, can be found at https://viewsforecasting.org/research/prediction-challenge-2023., Comment: Forecasting competition, conflict forecasting, forecasting with uncertainty

The use of Virtual Reality (VR) technologies has been extensively researched in surgical and anatomical education. VR provides a lifelike and interactive environment where healthcare providers can practice and refresh their skills in a safe environment. VR has been shown to be as effective as traditional medical education teaching methods, with the potential to provide more cost-effective and convenient means of curriculum delivery, especially in rural and remote areas or in environments with limited access to hands-on training. In this sense, VR offers the potential to be used to support resuscitation training for healthcare providers such as the Neonatal Resuscitation Program (NRP). The NRP program is an evidence-based and standardized approach for training healthcare providers on the resuscitation of the newborn. In this article, we describe a VR simulation environment that was designed and developed to refresh the skills of NRP providers. To validate this platform, we compared the VR-NRP simulation with exposure to 360-degree immersive video. We found that both VR technologies were positively viewed by healthcare professionals and performed very similarly to each other. However, the VR simulation provided a significantly increased feeling of presence. Furthermore, participants found the VR simulation more useful, leading to improved experiential learning outcomes. Also, participants using VR simulation reported higher confidence in certain NRP skills, such as proper mask placement and newborn response evaluation. This research represents a step forward in understanding how VR and related extended reality (XR) technologies can be applied for effective, immersive medical education, with potential benefits for remote and rural healthcare providers.

A complete model for estimating the electric conductivity of combustion product gases, with added cesium (Cs) or potassium (K) vapor for ionization, is presented. Neutral carrier gases serve as the bulk fluid that carries the seed material, as well as the electrons generated by the partial thermal (equilibrium) ionization of the seed alkali metal. The model accounts for electron-neutral scattering, as well as electron-ion and electron-electron scattering. The model is tested through comparison with published data. The model is aimed at being utilized for the plasma within magnetohydrodynamic (MHD) channels, where direct power extraction from passing electrically conducting plasma gas enables electric power generation. The thermal ionization model is then used to estimate the electric conductivity of seeded combustion gases under complete combustion of three selected fuels, namely: hydrogen (H2), methane (CH4), and carbon (C). For each of these three fuels, two options for the oxidizer were applied, namely: air (21 % molecular oxygen, 79 % molecular nitrogen by mole), and pure oxygen (oxy-combustion). Two types of seeds (with 1 % mole fraction, based on the composition before ionization) were also applied for each of the six combinations of (fuel-oxidizer), leading to a total of 12 different MHD plasma cases. For each of these cases, the electric conductivity was computed for a range of temperatures from 2000 K to 3000 K. The smallest estimated electric conductivity was 0.35 S/m for oxy-hydrogen combustion at 2000 K, with potassium seeding. The largest estimated electric conductivity was 180.30 S/m for oxy-carbon combustion at 3000 K, with cesium seeding. At 2000 K, replacing potassium with cesium causes a gain in the electric conductivity by a multiplicative gain factor of about 3.6 regardless of the fuel and oxidizer. This gain factor declines to between 1.77 and 2.07 at 3000 K., Comment: 28 pages, 16 figures, 14 tables

Automated classification of electroencephalogram (EEG) signals is complex due to their high dimensionality, non-stationarity, low signal-to-noise ratio, and variability between subjects. Deep neural networks (DNNs) have shown promising results for EEG classification, but the above challenges hinder their performance. Euclidean Alignment (EA) and Data Augmentation (DA) are two promising techniques for improving DNN training by permitting the use of data from multiple subjects, increasing the data, and regularizing the available data. In this paper, we perform a detailed evaluation of the combined use of EA and DA with DNNs for EEG decoding. We trained individual models and shared models with data from multiple subjects and showed that combining EA and DA generates synergies that improve the accuracy of most models and datasets. Also, the shared models combined with fine-tuning benefited the most, with an overall increase of 8.41\% in classification accuracy., Comment: 8 pages, 4 figures, 2 tables, accepted at Eusipco 2024

The intrinsic dynamics of most proteins are central to their function. Protein tyrosine kinases such as Abl1 undergo significant conformational changes that modulate their activity in response to different stimuli. These conformational changes constitute a conserved mechanism for self-regulation that dramatically impacts kinases' affinities for inhibitors. Few studies have attempted to extensively sample the pathways and elucidate the mechanisms that underlie kinase inactivation. Seeking to bridge this knowledge gap, we present a thorough analysis of the ``DFG flip'' inactivation pathway in Abl1 kinase. By leveraging the power of the Weighted Ensemble methodology, which accelerates sampling without the use of biasing forces, we have comprehensively simulated DFG flip events in Abl1 and its inhibitor-resistant variants, revealing a rugged landscape punctuated by potentially druggable intermediate states. Through our strategy, we successfully simulated dozens of uncorrelated DFG flip events distributed along two principal pathways, identified the molecular mechanisms that govern them, and measured their relative probabilities. Further, we show that the compound Glu255Lys/Val Thr315Ile Abl1 variants owe their inhibitor resistance phenotype to an increase in the free energy barrier associated with completing the DFG flip. This barrier stabilizes Abl1 variants in conformations that can lead to loss of binding for Type-II inhibitors such as Imatinib or Ponatinib. Finally, we contrast our Abl1 observations with the relative state distributions and propensity for undergoing a DFG flip of evolutionarily-related protein tyrosine kinases with diverging Type-II inhibitor binding affinities. Altogether, we expect that our work will be of significant importance for protein tyrosine kinase inhibitor discovery., Comment: 34 pages, 10 figures

This paper explores the application of Artificial Intelligence (AI) techniques for generating the trajectories of fleets of Unmanned Aerial Vehicles (UAVs). The two main challenges addressed include accurately predicting the paths of UAVs and efficiently avoiding collisions between them. Firstly, the paper systematically applies a diverse set of activation functions to a Feedforward Neural Network (FFNN) with a single hidden layer, which enhances the accuracy of the predicted path compared to previous work. Secondly, we introduce a novel activation function, AdaptoSwelliGauss, which is a sophisticated fusion of Swish and Elliott activations, seamlessly integrated with a scaled and shifted Gaussian component. Swish facilitates smooth transitions, Elliott captures abrupt trajectory changes, and the scaled and shifted Gaussian enhances robustness against noise. This dynamic combination is specifically designed to excel in capturing the complexities of UAV trajectory prediction. This new activation function gives substantially better accuracy than all existing activation functions. Thirdly, we propose a novel Integrated Collision Detection, Avoidance, and Batching (ICDAB) strategy that merges two complementary UAV collision avoidance techniques: changing UAV trajectories and altering their starting times, also referred to as batching. This integration helps overcome the disadvantages of both - reduction in the number of trajectory manipulations, which avoids overly convoluted paths in the first technique, and smaller batch sizes, which reduce overall takeoff time in the second., Comment: 24 Pages, 9 Tables, 6 Figures

In this paper, we present an innovative technique for the path planning of flying robots in a 3D environment in Rough Mereology terms. The main goal was to construct the algorithm that would generate the mereological potential fields in 3-dimensional space. To avoid falling into the local minimum, we assist with a weighted Euclidean distance. Moreover, a searching path from the start point to the target, with respect to avoiding the obstacles was applied. The environment was created by connecting two cameras working in real-time. To determine the gate and elements of the world inside the map was responsible the Python Library OpenCV [1] which recognized shapes and colors. The main purpose of this paper is to apply the given results to drones., Comment: number of pages: 16, number of figures: 10

Finite difference (FD) approximation is a classic approach to stochastic gradient estimation when only noisy function realizations are available. In this paper, we first provide a sample-driven method via the bootstrap technique to estimate the optimal perturbation, and then propose an efficient FD estimator based on correlated samples at the estimated optimal perturbation. Furthermore, theoretical analyses of both the perturbation estimator and the FD estimator reveal that, {\it surprisingly}, the correlation enables the proposed FD estimator to achieve a reduction in variance and, in some cases, a decrease in bias compared to the traditional optimal FD estimator. Numerical results confirm the efficiency of our estimators and align well with the theory presented, especially in scenarios with small sample sizes. Finally, we apply the estimator to solve derivative-free optimization (DFO) problems, and numerical studies show that DFO problems with 100 dimensions can be effectively solved.

Inference methods for computing confidence intervals in parametric settings usually rely on consistent estimators of the parameter of interest. However, it may be computationally and/or analytically burdensome to obtain such estimators in various parametric settings, for example when the data exhibit certain features such as censoring, misclassification errors or outliers. To address these challenges, we propose a simulation-based inferential method, called the implicit bootstrap, that remains valid regardless of the potential asymptotic bias of the estimator on which the method is based. We demonstrate that this method allows for the construction of asymptotically valid percentile confidence intervals of the parameter of interest. Additionally, we show that these confidence intervals can also achieve second-order accuracy. We also show that the method is exact in three instances where the standard bootstrap fails. Using simulation studies, we illustrate the coverage accuracy of the method in three examples where standard parametric bootstrap procedures are computationally intensive and less accurate in finite samples.

We use the Multi Level Monte Carlo method to estimate uncertainties in a Henry-like salt water intrusion problem with a fracture. The flow is induced by the variation of the density of the fluid phase, which depends on the mass fraction of salt. We assume that the fracture has a known fixed location but an uncertain aperture. Other input uncertainties are the porosity and permeability fields and the recharge. In our setting, porosity and permeability vary spatially and recharge is time-dependent. For each realisation of these uncertain parameters, the evolution of the mass fraction and pressure fields is modelled by a system of non-linear and time-dependent PDEs with a jump of the solution at the fracture. The uncertainties propagate into the distribution of the salt concentration, which is an important characteristic of the quality of water resources. We show that the multilevel Monte Carlo (MLMC) method is able to reduce the overall computational cost compared to classical Monte Carlo methods. This is achieved by balancing discretisation and statistical errors. Multiple scenarios are evaluated at different spatial and temporal mesh levels. The deterministic solver ug4 is run in parallel to calculate all stochastic scenarios., Comment: 19 pages, 4 tables, 7 figures. arXiv admin note: text overlap with arXiv:2403.17018

The pattern of state changes in a biomedical time series can be related to health or disease. This work presents a principled approach for selecting a changepoint detection algorithm for a specific task, such as disease classification. Eight key algorithms were compared, and the performance of each algorithm was evaluated as a function of temporal tolerance, noise, and abnormal conduction (ectopy) on realistic artificial cardiovascular time series data. All algorithms were applied to real data (cardiac time series of 22 patients with REM-behavior disorder (RBD) and 15 healthy controls) using the parameters selected on artificial data. Finally, features were derived from the detected changepoints to classify RBD patients from healthy controls using a K-Nearest Neighbors approach. On artificial data, Modified Bayesian Changepoint Detection algorithm provided superior positive predictive value for state change identification while Recursive Mean Difference Maximization (RMDM) achieved the highest true positive rate. For the classification task, features derived from the RMDM algorithm provided the highest leave one out cross validated accuracy of 0.89 and true positive rate of 0.87. Automatically detected changepoints provide useful information about subject's physiological state which cannot be directly observed. However, the choice of change point detection algorithm depends on the nature of the underlying data and the downstream application, such as a classification task. This work represents the first time change point detection algorithms have been compared in a meaningful way and utilized in a classification task, which demonstrates the effect of changepoint algorithm choice on application performance., Comment: 24 pages, 2 figures

We present Alljoined1, a dataset built specifically for EEG-to-Image decoding. Recognizing that an extensive and unbiased sampling of neural responses to visual stimuli is crucial for image reconstruction efforts, we collected data from 8 participants looking at 10,000 natural images each. We have currently gathered 46,080 epochs of brain responses recorded with a 64-channel EEG headset. The dataset combines response-based stimulus timing, repetition between blocks and sessions, and diverse image classes with the goal of improving signal quality. For transparency, we also provide data quality scores. We publicly release the dataset and all code at https://linktr.ee/alljoined1., Comment: 8 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

Objective: The integration of Deep Learning (DL) algorithms on brain signal analysis is still in its nascent stages compared to their success in fields like Computer Vision. This is particularly true for BCI, where the brain activity is decoded to control external devices without requiring muscle control. Electroencephalography (EEG) is a widely adopted choice for designing BCI systems due to its non-invasive and cost-effective nature and excellent temporal resolution. Still, it comes at the expense of limited training data, poor signal-to-noise, and a large variability across and within-subject recordings. Finally, setting up a BCI system with many electrodes takes a long time, hindering the widespread adoption of reliable DL architectures in BCIs outside research laboratories. To improve adoption, we need to improve user comfort using, for instance, reliable algorithms that operate with few electrodes. Approach: Our research aims to develop a DL algorithm that delivers effective results with a limited number of electrodes. Taking advantage of the Augmented Covariance Method and the framework of SPDNet, we propose the Phase-SPDNet architecture and analyze its performance and the interpretability of the results. The evaluation is conducted on 5-fold cross-validation, using only three electrodes positioned above the Motor Cortex. The methodology was tested on nearly 100 subjects from several open-source datasets using the Mother Of All BCI Benchmark (MOABB) framework. Main results: The results of our Phase-SPDNet demonstrate that the augmented approach combined with the SPDNet significantly outperforms all the current state-of-the-art DL architecture in MI decoding. Significance: This new architecture is explainable and with a low number of trainable parameters.

We present a first study of Bayesian forecasting of electricity prices traded on the German continuous intraday market which fully incorporates parameter uncertainty. A particularly large set of endogenous and exogenous covariables is used, handled through feature selection with Orthogonal Matching Pursuit (OMP) and regularising priors. Our target variable is the IDFull price index, forecasts are given in terms of posterior predictive distributions. For validation we use the exceedingly volatile electricity prices of 2022, which have hardly been the subject of forecasting studies before. As a benchmark model, we use all available intraday transactions at the time of forecast creation to compute a current value for the IDFull. According to the weak-form efficiency hypothesis, it would not be possible to significantly improve this benchmark built from last price information. We do, however, observe statistically significant improvement in terms of both point measures and probability scores. Finally, we challenge the declared gold standard of using LASSO for feature selection in electricity price forecasting by presenting strong statistical evidence that OMP leads to better forecasting performance., Comment: 22 pages, 14 figures, 4 tables. Revised version with an added schematic figure. Under review for Applied Energy

This work highlights an approach for incorporating realistic uncertainties into scientific computing workflows based on finite elements, focusing on applications in computational mechanics and design optimization. We leverage Mat\'ern-type Gaussian random fields (GRFs) generated using the SPDE method to model aleatoric uncertainties, including environmental influences, variating material properties, and geometric ambiguities. Our focus lies on delivering practical GRF realizations that accurately capture imperfections and variations and understanding how they impact the predictions of computational models and the topology of optimized designs. We describe a numerical algorithm based on solving a generalized SPDE to sample GRFs on arbitrary meshed domains. The algorithm leverages established techniques and integrates seamlessly with the open-source finite element library MFEM and associated scientific computing workflows, like those found in industrial and national laboratory settings. Our solver scales efficiently for large-scale problems and supports various domain types, including surfaces and embedded manifolds. We showcase its versatility through biomechanics and topology optimization applications. The flexibility and efficiency of SPDE-based GRF generation empower us to run large-scale optimization problems on 2D and 3D domains, including finding optimized designs on embedded surfaces, and to generate topologies beyond the reach of conventional techniques. Moreover, these capabilities allow us to model geometric uncertainties of reconstructed submanifolds, such as the surfaces of cerebral aneurysms. In addition to offering benefits in these specific domains, the proposed techniques transcend specific applications and generalize to arbitrary forward and backward problems in uncertainty quantification involving finite elements., Comment: 38 pages, 21 figures

The aftermath of the Covid-19 pandemic saw more severe outcomes for racial minority groups and economically-deprived communities. Such disparities can be explained by several factors, including unequal access to healthcare, as well as the inability of low income groups to reduce their mobility due to work or social obligations. Moreover, senior citizens were found to be more susceptible to severe symptoms, largely due to age-related health reasons. Adapting vaccine distribution strategies to consider a range of demographics is therefore essential to address these disparities. In this study, we propose a novel approach that utilizes influence maximization (IM) on mobility networks to develop vaccination strategies which incorporate demographic fairness. By considering factors such as race, social status, age, and associated risk factors, we aim to optimize vaccine distribution to achieve various fairness definitions for one or more protected attributes at a time. Through extensive experiments conducted on Covid-19 spread in three major metropolitan areas across the United States, we demonstrate the effectiveness of our proposed approach in reducing disease transmission and promoting fairness in vaccination distribution., Comment: 10 pages, 4 figures

Social-ecological systems research aims to understand the nature of social-ecological phenomena, to find ways to foster or manage conditions under which desired phenomena occur or to reduce the negative consequences of undesirable phenomena. Such challenges are often addressed using dynamical systems models (DSM) or agent-based models (ABM). Here we develop an iterative procedure for combining DSM and ABM to leverage their strengths and gain insights that surpass insights obtained by each approach separately. The procedure uses results of an ABM as inputs for a DSM development. In the following steps, results of the DSM analyses guide future analysis of the ABM and vice versa. This dialogue, more than having a tight connection between the models, enables pushing the research frontier, expanding the set of research questions and insights. We illustrate our method with the example of poverty traps and innovation in agricultural systems, but our conclusions are general and can be applied to other DSM-ABM combinations., Comment: 16 pages, 8 figures

The square root velocity transformation provides a convenient and numerically efficient approach to functional and shape data analysis of curves. We study fundamental geometric properties of curves under this transformation. Moreover, utilizing natural geometric constructions, we employ the approach for intrinsic comparison within several classes of surfaces and augmented curves, which arise in the real world applications such as tubes, ruled surfaces, spherical strips, protein molecules and hurricane tracks.

Robotic harvesting has the potential to positively impact agricultural productivity, reduce costs, improve food quality, enhance sustainability, and to address labor shortage. In the rapidly advancing field of agricultural robotics, the necessity of training robots in a virtual environment has become essential. Generating training data to automatize the underlying computer vision tasks such as image segmentation, object detection and classification, also heavily relies on such virtual environments as synthetic data is often required to overcome the shortage and lack of variety of real data sets. However, physics engines commonly employed within the robotics community, such as ODE, Simbody, Bullet, and DART, primarily support motion and collision interaction of rigid bodies. This inherent limitation hinders experimentation and progress in handling non-rigid objects such as plants and crops. In this contribution, we present a plugin for the Gazebo simulation platform based on Cosserat rods to model plant motion. It enables the simulation of plants and their interaction with the environment. We demonstrate that, using our plugin, users can conduct harvesting simulations in Gazebo by simulating a robotic arm picking fruits and achieve results comparable to real-world experiments., Comment: Upon request, we are happy to share our GazeboPlants plugin open-source (MPL 2.0)

One of the main sources of electricity generation is power plants that use water (steam) to rotate turbines, which drive large electric generators. The steam can be generated from renewable or non-renewable energy sources, such as geothermal energy and nuclear fuels. Having an analysis tool for modeling the performance of such steam power plants can greatly help in reaching optimum designs, leading to less fuel consumption, reduced pollution, and cheaper electricity. It is further advantageous if such modeling tool is free to access, does not require many inputs from the user, and gives results in a very short time. These remarks establish a motivation for the current study. This article documents a computer code written in the Python programming language for numerically analysing the main processes in a steam power cycle with superheating. The code utilizes built-in thermodynamic properties for water in the open-source software package "Cantera". A validation case with a benchmarking example in the literature using an independent source of water properties suggests that the developed code is correct. The code can be viewed as an extension to the Python examples for thermodynamic and power generation applications. Cantera can handle both subcritical and supercritical types of superheating. In the subcritical superheating, the steam absolute pressure does not exceed 220.9 bar. In the supercritical superheating, water becomes in a special condition called supercritical fluid, with absolute pressures above 220.9 bar., Comment: 11 pages, 4 tables, journal paper

To extend the limited scope of autonomy used in prior missions for operation in distant and complex environments, there is a need to further develop and mature autonomy that jointly reasons over multiple subsystems, which we term system-level autonomy. System-level autonomy establishes situational awareness that resolves conflicting information across subsystems, which may necessitate the refinement and interconnection of the underlying spacecraft and environment onboard models. However, with a limited understanding of the assumptions and tradeoffs of modeling to arbitrary extents, designing onboard models to support system-level capabilities presents a significant challenge. In this paper, we provide a detailed analysis of the increasing levels of model fidelity for several key spacecraft subsystems, with the goal of informing future spacecraft functional- and system-level autonomy algorithms and the physics-based simulators on which they are validated. We do not argue for the adoption of a particular fidelity class of models but, instead, highlight the potential tradeoffs and opportunities associated with the use of models for onboard autonomy and in physics-based simulators at various fidelity levels. We ground our analysis in the context of deep space exploration of small bodies, an emerging frontier for autonomous spacecraft operation in space, where the choice of models employed onboard the spacecraft may determine mission success. We conduct our experiments in the Multi-Spacecraft Concept and Autonomy Tool (MuSCAT), a software suite for developing spacecraft autonomy algorithms., Comment: Project page: https://sites.google.com/stanford.edu/spacecraft-models. 20 pages, 8 figures. Accepted to the IEEE Conference on Aerospace (AeroConf) 2024

Electroencephalography (EEG) signals are frequently used for various Brain-Computer Interface (BCI) tasks. While Deep Learning (DL) techniques have shown promising results, they are hindered by the substantial data requirements. By leveraging data from multiple subjects, transfer learning enables more effective training of DL models. A technique that is gaining popularity is Euclidean Alignment (EA) due to its ease of use, low computational complexity, and compatibility with Deep Learning models. However, few studies evaluate its impact on the training performance of shared and individual DL models. In this work, we systematically evaluate the effect of EA combined with DL for decoding BCI signals. We used EA to train shared models with data from multiple subjects and evaluated its transferability to new subjects. Our experimental results show that it improves decoding in the target subject by 4.33% and decreases convergence time by more than 70%. We also trained individual models for each subject to use as a majority-voting ensemble classifier. In this scenario, using EA improved the 3-model ensemble accuracy by 3.7%. However, when compared to the shared model with EA, the ensemble accuracy was 3.62% lower., Comment: 14 pages and 10 figures

We show how to compute globally optimal solutions to inverse kinematics (IK) by formulating the problem as an indefinite quadratically constrained quadratic program. Our approach makes it feasible to solve IK instances of generic redundant manipulators. We demonstrate the performance on randomly generated designs and on real-world robots with up to ten revolute joints. The same technique can be used for manipulator design by introducing kinematic parameters as variables., Comment: This work has been submitted to the IEEE for possible publication

Better understanding the natural world is a crucial task with a wide range of applications. In environments with close proximity between humans and animals, such as zoos, it is essential to better understand the causes behind animal behaviour and what interventions are responsible for changes in their behaviours. This can help to predict unusual behaviours, mitigate detrimental effects and increase the well-being of animals. There has been work on modelling the dynamics behind swarms of birds and insects but the complex social behaviours of mammalian groups remain less explored. In this work, we propose a method to build behavioural models using causal structure discovery and graph neural networks for time series. We apply this method to a mob of meerkats in a zoo environment and study its ability to predict future actions and model the behaviour distribution at an individual-level and at a group level. We show that our method can match and outperform standard deep learning architectures and generate more realistic data, while using fewer parameters and providing increased interpretability., Comment: 9 pages, 7 figures, accepted as an extended abstract and poster at AAMAS 2024

By its nature, the so-called social cost of carbon (SCC(t)) will likely not cover the cost induced by climate change (damage cost and abatement cost) if it is used as a CO$_2$-price. It is a marginal price only. We define an implied CO$_2$-price that covers the climate change-induced costs. The price can be interpreted as a \textit{polluter pays principle}. A numerical analysis using a classical DICE model reveals that the cost-implied CO$_2$ price is around 500 \$/tCO$_2$, while the corresponding price associated with the SCC is about 50 \$/tCO$_2$. In addition, we define the internal rate of return of carbon abatement and calculate it for the classical DICE model. This rate is much higher than the model's discount rate, which may suggest the advantage of financing abatement by loans., Comment: 17 pages, 4 figures

We present an empirical model for auroral (90--150 km) electron--ion pair production rates, ionization rates for short, derived from SSUSI (Special Sensor Ultraviolet Spectrographic Imager) electron energy and flux data. Using the Fang et al., 2010 parametrization for mono-energetic electrons, and the NRLMSISE-00 neutral atmosphere model, the calculated ionization rate profiles are binned in 2-h magnetic local time (MLT) and 3.6$^{\circ}$ geomagnetic latitude to yield time series of ionization rates at 5-km altitude steps. We fit each of these time series to the geomagnetic indices Kp, PC, and Ap, the 81-day averaged solar F$_{\text{10.7}}$ radio flux index, and a constant term. The resulting empirical model can easily be incorporated into coupled chemistry--climate models to include particle precipitation effects., Comment: 17 pages, 5 figures, submitted to JGR Space Phys

In this work, we introduce AutoFragDiff, a fragment-based autoregressive diffusion model for generating 3D molecular structures conditioned on target protein structures. We employ geometric vector perceptrons to predict atom types and spatial coordinates of new molecular fragments conditioned on molecular scaffolds and protein pockets. Our approach improves the local geometry of the resulting 3D molecules while maintaining high predicted binding affinity to protein targets. The model can also perform scaffold extension from user-provided starting molecular scaffold., Comment: Accepted, NeurIPS 2023 Generative AI and Biology Workshop. OpenReview: https://openreview.net/forum?id=E3HN48zjam

Today's decisions on climate change mitigation affect the damage that future generations will bear. Discounting future benefits and costs of climate change mitigation is one of the most critical components of assessing efficient climate mitigation pathways. We extend the DICE model with stochastic discount rates to reflect the uncertain nature of discount rates. Stochastic rates give rise to a stochastic mitigation strategy, resulting in all model quantities becoming stochastic. We show that the classical calibration of the DICE model induces intergenerational inequality: future generations have to bear higher costs relative to GDP. Further, we show that considering stochastic discount rates and stochastic abatement policies, which can be interpreted as successive re-calibration, increases intergenerational inequality (and adds additional risks). Motivated by this, we consider additional financing risks by investigating two modifications of DICE. We find that allowing financing of abatement costs and considering non-linear financing effects for large damages improves intergenerational effort sharing. To conclude our discussion of options to improve intergenerational equity in an IAM, we propose a modified optimization to keep costs below 3% of GDP, resulting in more equal distribution of efforts between generations., Comment: 36 pages, 10 figures, arXiv admin note: text overlap with arXiv:2309.16186

Amazon Locker is a self-service delivery or pickup location where customers can pick up packages and drop off returns. A basic first-come-first-served policy for accepting package delivery requests to lockers results in lockers becoming full with standard shipping speed (3-5 day shipping) packages, and leaving no space left for expedited packages which are mostly Next-Day or Two-Day shipping. This paper proposes a solution to the problem of determining how much locker capacity to reserve for different ship-option packages. Yield management is a much researched field with popular applications in the airline, car rental, and hotel industries. However, Amazon Locker poses a unique challenge in this field since the number of days a package will wait in a locker (package dwell time) is, in general, unknown. The proposed solution combines machine learning techniques to predict locker demand and package dwell time, and linear programming to maximize throughput in lockers. The decision variables from this optimization provide optimal capacity reservation values for different ship options. This resulted in a year-over-year increase of 9% in Locker throughput worldwide during holiday season of 2018, impacting millions of customers., Comment: 22 pages, 10 figues

Magnetohydrodynamics (MHD) is a subject concerned with the dynamics of electrically conducting fluids (plasma) and can be applied in electric power generation. As a unique technology for producing direct-current electricity without moving parts, it can be utilized within a high-temperature topping power cycle to be combined with a traditional bottoming power cycle, forming a combined-cycle MHD system. This study presents governing equations for the electric field and current density field within a moving plasma subject to an applied magnetic field. The modeling equations are described at four descending levels of complexity. Starting with the first level of modeling, which is the most general case, where no assumptions are made regarding the electric field, plasma velocity field, applied magnetic field, or electrode geometry. In the second level of modeling, the magnetic field is treated as one-dimensional. In the third level of modeling, a specific Faraday-type magnetohydrodynamics plasma generator channel is considered, having two continuous electrodes acting as parallel constant-voltage terminals. In the fourth (and simplest) level of modeling, an additional approximation is made by setting the Hall parameter to zero and replacing all vector fields with scalar quantities. For that simplest model, a representative set of operation conditions (electric conductivity 20 S/m, temperature 2800 K, supersonic plasma gas speed 2000 m/s with Mach 2.134, and magnetic flux density 5 T) shows that the optimum idealized electric power that can be extracted from a unit volume of plasma is estimated as 500 MW/m3. This is a much larger volumetric power density than typical values encountered in reciprocating piston-type engines (0.2 MW/m3) or rotary gas turbine engines (0.5 MW/m3). Such an extremely high power density enables very compact power generation units., Comment: 13 pages, 5 figures, journal paper

Renewable energy has received strong attention and investment to replace fossil energy sources and reduce greenhouse gas emissions. Quite good and good wind speed areas have been invested in building large-capacity wind farms for many years. The low wind speed region occupies a very large on the world, which has been interested in the exploitation of wind energy in recent years. In this study, the original airfoil of S1010 operated at low wind speed was redesigned to increase the aerodynamic efficiency of the airfoil by using XFLR5 software. After, the new VAST-EPU-S1010 airfoil model was adjusted to the maximum thickness and the maximum thickness position. It was simulated in low wind speed conditions of 4-6 m/s by CFD simulation. The lift coefficient, drag coefficient and $C_{L}$/$C_{D}$ coefficient ratio were evaluated under the effect of the angle of attack and the maximum thickness by using the $k-\epsilon$ model. Simulation results show that the VAST-EPU-S1010 airfoil achieved the greatest aerodynamic efficiency at the angle of attack of $3\,^{\circ}$, the maximum thickness of 8\% and the maximum thickness position of 20.32\%. The maximum value of $C_{L}$/$C_{D}$ of the new airfoil at 6 m/s is higher than at the 4 m/s by about 6.25\%., Comment: 19 pages, 21 figures

Predicting human mobility holds significant practical value, with applications ranging from enhancing disaster risk planning to simulating epidemic spread. In this paper, we present the GeoFormer, a decoder-only transformer model adapted from the GPT architecture to forecast human mobility. Our proposed model is rigorously tested in the context of the HuMob Challenge 2023 -- a competition designed to evaluate the performance of prediction models on standardized datasets to predict human mobility. The challenge leverages two datasets encompassing urban-scale data of 25,000 and 100,000 individuals over a longitudinal period of 75 days. GeoFormer stands out as a top performer in the competition, securing a place in the top-3 ranking. Its success is underscored by performing well on both performance metrics chosen for the competition -- the GEO-BLEU and the Dynamic Time Warping (DTW) measures. The performance of the GeoFormer on the HuMob Challenge 2023 underscores its potential to make substantial contributions to the field of human mobility prediction, with far-reaching implications for disaster preparedness, epidemic control, and beyond., Comment: Accepted in the HuMob-Challenge '23: 1st International Workshop on the Human Mobility Prediction Challenge. Repository is available at https://github.com/avsolatorio/GeoFormer

This paper investigates a hypothesis proposed in previous research relating neutron star (NS) mass and its dark matter (DM) accumulation. As DM accumulates, NS mass decreases, predicting lower NS masses toward the Galactic center. Due to limited NSs data near the galactic center, we examine NSs located within DM clumps. Using the CLUMPY code simulations, we determine the DM clumps distribution, with masses from 10 to $10^{8}$ $M_{\odot}$ and scales from $10^{-3}$ to 10 kpc. These clumps' DM exhibit a peak at the center, tapering toward the outskirts, resembling our Galaxy's DM distribution. We analyse these DM clumps' NS mass variations, considering diverse DM particle masses and galaxy types. We find relatively stable NS mass within 0.01 to 5 kpc from the clump center. This stability supports the initial hypothesis, particularly for NSs located beyond 0.01 kpc from the clump center, where NS mass reaches a plateau around 0.1 kpc. Nevertheless, NS mass near the clump's periphery reveals spatial dependence: NS position within DM clumps influences its mass in Milky Way-type galaxies. Moreover, this dependence varies with the DM model considered. In summary, our study investigates the proposed link between NS mass and DM accumulation by examining NSs within DM clumps. While NS mass remains stable at certain distances from the clump center, spatial dependencies arise near the clump's outer regions, contingent on the specific DM model., Comment: 23 pages, 23 figures, 2 tables. arXiv admin note: text overlap with arXiv:1606.04898 by other authors

In this work, we introduce an efficient generation procedure to produce synthetic multi-modal datasets of fluid simulations. The procedure can reproduce the dynamics of fluid flows and allows for exploring and learning various properties of their complex behavior, from distinct perspectives and modalities. We employ our framework to generate a set of thoughtfully designed training datasets, which attempt to span specific fluid simulation scenarios in a meaningful way. The properties of our contributions are demonstrated by evaluating recently published algorithms for the neural fluid simulation and fluid inverse rendering tasks using our benchmark datasets. Our contribution aims to fulfill the community's need for standardized training data, fostering more reproducibile and robust research., Comment: 10 pages, 7 figures

Gray-box models offer significant benefit over black-box approaches for equipment emulator development for equipment since their integration of physics provides more confidence in the model outside of the training domain. However, challenges such as model nonlinearity, unmodeled dynamics, and local minima introduce uncertainties into grey-box creation that contemporary approaches have failed to overcome, leading to their under-performance compared with black-box models. This paper seeks to address these uncertainties by injecting noise into the training dataset. This noise injection enriches the dataset and provides a measure of robustness against such uncertainties. A dynamic model for a water-to-water heat exchanger has been used as a demonstration case for this approach and tested using a pair of real devices with live data streaming. Compared to the unprocessed signal data, the application of noise injection resulted in a significant reduction in modeling error (root mean square error), decreasing from 0.68 to 0.27{\deg}C. This improvement amounts to a 60% enhancement when assessed on the training set, and improvements of 50% and 45% when validated against the test and validation sets, respectively., Comment: 47 pages, 15 figures, initial manuscript self-archiving prior to submission to ADVEI

Assessing the costs of climate change is essential to finding efficient pathways for the transition to a net-zero emissions economy, which is necessary to stabilise global temperatures at any level. In evaluating the benefits and costs of climate change mitigation, the discount rate converting future damages and costs into net-present values influences the timing of mitigation. Here, we amend the DICE model with a stochastic interest rate model to consider the uncertainty of discount rates in the future. Since abatement reduces future damages, changing interest rates renders abatement investments more or less beneficial. Stochastic interest rates will hence lead to a stochastic abatement strategy. We introduce a simple stochastic abatement model and show that this can increase intergenerational inequality concerning cost and risk. Analysing the sensitivities of the model calibration analytically and numerically exhibits that intergenerational inequality is a consequence of the DICE model calibration (and maybe that of IAMs in general). We then show that introducing funding of abatement costs reduces the variation of future cash-flows, which occur at different times but are off-setting in their net-present value. This effect can be interpreted as improving intergenerational effort sharing, which might be neglected in classical optimisation. This mechanism is amplified, including dependence of the interest rate risk on the amount of debt to be financed, i.e. considering the limited capacity of funding sources. As an alternative policy optimisation method, we propose limiting the total cost of damages and abatement below a fixed level relative to GDP - this modification induces equality between generations compared to their respective economic welfare, inducing early and fast mitigation of climate change to keep the total cost of climate change below 3% of global GDP.

Corner case scenarios are an essential tool for testing and validating the safety of autonomous vehicles (AVs). As these scenarios are often insufficiently present in naturalistic driving datasets, augmenting the data with synthetic corner cases greatly enhances the safe operation of AVs in unique situations. However, the generation of synthetic, yet realistic, corner cases poses a significant challenge. In this work, we introduce a novel approach based on Heterogeneous Graph Neural Networks (HGNNs) to transform regular driving scenarios into corner cases. To achieve this, we first generate concise representations of regular driving scenes as scene graphs, minimally manipulating their structure and properties. Our model then learns to perturb those graphs to generate corner cases using attention and triple embeddings. The input and perturbed graphs are then imported back into the simulation to generate corner case scenarios. Our model successfully learned to produce corner cases from input scene graphs, achieving 89.9% prediction accuracy on our testing dataset. We further validate the generated scenarios on baseline autonomous driving methods, demonstrating our model's ability to effectively create critical situations for the baselines., Comment: The first two authors contributed equally to this work

Complex adaptive systems (CASs), from ecosystems to economies, are open systems and inherently dependent on external conditions. While a system can transition from one state to another based on the magnitude of change in external conditions, the rate of change -- irrespective of magnitude -- may also lead to system state changes due to a phenomenon known as a rate-induced transition (RIT). This study presents a novel framework that captures RITs in CASs through a local model and a network extension where each node contributes to the structural adaptability of others. Our findings reveal how RITs occur at a critical environmental change rate, with lower-degree nodes tipping first due to fewer connections and reduced adaptive capacity. High-degree nodes tip later as their adaptability sources (lower-degree nodes) collapse. This pattern persists across various network structures. Our study calls for an extended perspective when managing CASs, emphasizing the need to focus not only on thresholds of external conditions but also the rate at which those conditions change, particularly in the context of the collapse of surrounding systems that contribute to the focal system's resilience. Our analytical method opens a path to designing management policies that mitigate RIT impacts and enhance resilience in ecological, social, and socioecological systems. These policies could include controlling environmental change rates, fostering system adaptability, implementing adaptive management strategies, and building capacity and knowledge exchange. Our study contributes to the understanding of RIT dynamics and informs effective management strategies for complex adaptive systems in the face of rapid environmental change., Comment: 25 pages, 4 figures, 1 box, supplementary information