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In this paper, we introduce the concept of fractional integration for spatial autoregressive models. We show that the range of the dependence can be spatially extended or diminished by introducing a further fractional integration parameter to spatial autoregressive moving average models (SARMA). This new model is called the spatial autoregressive fractionally integrated moving average model, briefly sp-ARFIMA. We show the relation to time-series ARFIMA models and also to (higher-order) spatial autoregressive models. Moreover, an estimation procedure based on the maximum-likelihood principle is introduced and analysed in a series of simulation studies. Eventually, the use of the model is illustrated by an empirical example of atmospheric fine particles, so-called aerosol optical thickness, which is important in weather, climate and environmental science.

In this paper, we develop a domain-decomposition method for the generalized Poisson-Boltzmann equation based on a solvent-excluded surface which is widely used in computational chemistry. The solver requires to solve a generalized screened Poisson (GSP) equation defined in $\mathbb{R}^3$ with a space-dependent dielectric permittivity and an ion-exclusion function that accounts for Steric effects. Potential theory arguments transform the GSP equation into two-coupled equations defined in a bounded domain. Then, the Schwarz decomposition method is used to formulate local problems by decomposing the cavity into overlapping balls and only solving a set of coupled sub-equations in each ball in which, the spherical harmonics and the Legendre polynomials are used as basis functions in the angular and radial directions. A series of numerical experiments are presented to test the method.

We study scalable machine learning models for full event reconstruction in high-energy electron-positron collisions based on a highly granular detector simulation. Particle-flow (PF) reconstruction can be formulated as a supervised learning task using tracks and calorimeter clusters or hits. We compare a graph neural network and kernel-based transformer and demonstrate that both avoid quadratic memory allocation and computational cost while achieving realistic PF reconstruction. We show that hyperparameter tuning on a supercomputer significantly improves the physics performance of the models. We also demonstrate that the resulting model is highly portable across hardware processors, supporting Nvidia, AMD, and Intel Habana cards. Finally, we demonstrate that the model can be trained on highly granular inputs consisting of tracks and calorimeter hits, resulting in a competitive physics performance with the baseline. Datasets and software to reproduce the studies are published following the findable, accessible, interoperable, and reusable (FAIR) principles.

This study focuses on the use of model and data fusion for improving the Spalart-Allmaras (SA) closure model for Reynolds-averaged Navier-Stokes solutions of separated flows. In particular, our goal is to develop of models that not-only assimilate sparse experimental data to improve performance in computational models, but also generalize to unseen cases by recovering classical SA behavior. We achieve our goals using data assimilation, namely the Ensemble Kalman Filtering approach (EnKF), to calibrate the coefficients of the SA model for separated flows. A holistic calibration strategy is implemented via a parameterization of the production, diffusion, and destruction terms. This calibration relies on the assimilation of experimental data collected velocity profiles, skin friction, and pressure coefficients for separated flows. Despite using of observational data from a single flow condition around a backward-facing step (BFS), the recalibrated SA model demonstrates generalization to other separated flows, including cases such as the 2D-bump and modified BFS. Significant improvement is observed in the quantities of interest, i.e., skin friction coefficient ($C_f$) and pressure coefficient ($C_p$) for each flow tested. Finally, it is also demonstrated that the newly proposed model recovers SA proficiency for external, unseparated flows, such as flow around a NACA-0012 airfoil without any danger of extrapolation, and that the individually calibrated terms in the SA model are targeted towards specific flow-physics wherein the calibrated production term improves the re-circulation zone while destruction improves the recovery zone.

A challenging category of robotics problems arises when sensing incurs substantial costs. This paper examines settings in which a robot wishes to limit its observations of state, for instance, motivated by specific considerations of energy management, stealth, or implicit coordination. We formulate the problem of planning under uncertainty when the robot's observations are intermittent but their timing is known via a pre-declared schedule. After having established the appropriate notion of an optimal policy for such settings, we tackle the problem of joint optimization of the cumulative execution cost and the number of state observations, both in expectation under discounts. To approach this multi-objective optimization problem, we introduce an algorithm that can identify the Pareto front for a class of schedules that are advantageous in the discounted setting. The algorithm proceeds in an accumulative fashion, prepending additions to a working set of schedules and then computing incremental changes to the value functions. Because full exhaustive construction becomes computationally prohibitive for moderate-sized problems, we propose a filtering approach to prune the working set. Empirical results demonstrate that this filtering is effective at reducing computation while incurring only negligible reduction in quality. In summarizing our findings, we provide a characterization of the run-time vs quality trade-off involved.

High-order structures have been recognised as suitable models for systems going beyond the binary relationships for which graph models are appropriate. Despite their importance and surge in research on these structures, their random cases have been only recently become subjects of interest. One of these high-order structures is the oriented hypergraph, which relates couples of subsets of an arbitrary number of vertices. Here we develop the Erd\H{o}s-R\'enyi model for oriented hypergraphs, which corresponds to the random realisation of oriented hyperedges of the complete oriented hypergraph. A particular feature of random oriented hypergraphs is that the ratio between their expected number of oriented hyperedges and their expected degree or size is 3/2 for large number of vertices. We highlight the suitability of oriented hypergraphs for modelling large collections of chemical reactions and the importance of random oriented hypergraphs to analyse the unfolding of chemistry.

We propose a novel estimation approach for a general class of semi-parametric time series models where the conditional expectation is modeled through a parametric function. The proposed class of estimators is based on a Gaussian quasi-likelihood function and it relies on the specification of a parametric pseudo-variance that can contain parametric restrictions with respect to the conditional expectation. The specification of the pseudo-variance and the parametric restrictions follow naturally in observation-driven models with bounds in the support of the observable process, such as count processes and double-bounded time series. We derive the asymptotic properties of the estimators and a validity test for the parameter restrictions. We show that the results remain valid irrespective of the correct specification of the pseudo-variance. The key advantage of the restricted estimators is that they can achieve higher efficiency compared to alternative quasi-likelihood methods that are available in the literature. Furthermore, the testing approach can be used to build specification tests for parametric time series models. We illustrate the practical use of the methodology in a simulation study and two empirical applications featuring integer-valued autoregressive processes, where assumptions on the dispersion of the thinning operator are formally tested, and autoregressions for double-bounded data with application to a realized correlation time series.

This paper introduces a novel approach for human-to-robot motion retargeting, enabling robots to mimic human motion with precision while preserving the semantics of the motion. For that, we propose a deep learning method for direct translation from human to robot motion. Our method does not require annotated paired human-to-robot motion data, which reduces the effort when adopting new robots. To this end, we first propose a cross-domain similarity metric to compare the poses from different domains (i.e., human and robot). Then, our method achieves the construction of a shared latent space via contrastive learning and decodes latent representations to robot motion control commands. The learned latent space exhibits expressiveness as it captures the motions precisely and allows direct motion control in the latent space. We showcase how to generate in-between motion through simple linear interpolation in the latent space between two projected human poses. Additionally, we conducted a comprehensive evaluation of robot control using diverse modality inputs, such as texts, RGB videos, and key-poses, which enhances the ease of robot control to users of all backgrounds. Finally, we compare our model with existing works and quantitatively and qualitatively demonstrate the effectiveness of our approach, enhancing natural human-robot communication and fostering trust in integrating robots into daily life.

The joint design of the optical system and the downstream algorithm is a challenging and promising task. Due to the demand for balancing the global optimal of imaging systems and the computational cost of physical simulation, existing methods cannot achieve efficient joint design of complex systems such as smartphones and drones. In this work, starting from the perspective of the optical design, we characterize the optics with separated aberrations. Additionally, to bridge the hardware and software without gradients, an image simulation system is presented to reproduce the genuine imaging procedure of lenses with large field-of-views. As for aberration correction, we propose a network to perceive and correct the spatially varying aberrations and validate its superiority over state-of-the-art methods. Comprehensive experiments reveal that the preference for correcting separated aberrations in joint design is as follows: longitudinal chromatic aberration, lateral chromatic aberration, spherical aberration, field curvature, and coma, with astigmatism coming last. Drawing from the preference, a 10% reduction in the total track length of the consumer-level mobile phone lens module is accomplished. Moreover, this procedure spares more space for manufacturing deviations, realizing extreme-quality enhancement of computational photography. The optimization paradigm provides innovative insight into the practical joint design of sophisticated optical systems and post-processing algorithms.

Recently, deep learning-based methods achieved promising performance in nuclei detection and classification applications. However, training deep learning-based methods requires a large amount of pixel-wise annotated data, which is time-consuming and labor-intensive, especially in 3D images. An alternative approach is to adapt weak-annotation methods, such as labeling each nucleus with a point, but this method does not extend from 2D histopathology images (for which it was originally developed) to 3D immunofluorescent images. The reason is that 3D images contain multiple channels (z-axis) for nuclei and different markers separately, which makes training using point annotations difficult. To address this challenge, we propose the Label-efficient Contrastive learning-based (LECL) model to detect and classify various types of nuclei in 3D immunofluorescent images. Previous methods use Maximum Intensity Projection (MIP) to convert immunofluorescent images with multiple slices to 2D images, which can cause signals from different z-stacks to falsely appear associated with each other. To overcome this, we devised an Extended Maximum Intensity Projection (EMIP) approach that addresses issues using MIP. Furthermore, we performed a Supervised Contrastive Learning (SCL) approach for weakly supervised settings. We conducted experiments on cardiovascular datasets and found that our proposed framework is effective and efficient in detecting and classifying various types of nuclei in 3D immunofluorescent images.