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We collect robust proposals given in the field of regression models with heteroscedastic errors. Our motivation stems from the fact that the practitioner frequently faces the confluence of two phenomena in the context of data analysis: non--linearity and heteroscedasticity. The impact of heteroscedasticity on the precision of the estimators is well--known, however the conjunction of these two phenomena makes handling outliers more difficult. An iterative procedure to estimate the parameters of a heteroscedastic non--linear model is considered. The studied estimators combine weighted $MM-$regression estimators, to control the impact of high leverage points, and a robust method to estimate the parameters of the variance function.

Space exploration and establishing human presence on other planets demand advanced technology and effective collaboration between robots and astronauts. Efficient space resource utilization is also vital for extraterrestrial settlements. The Collaborative In-Situ Resources Utilisation (CISRU) project has developed a software suite comprising five key modules. The first module manages multi-agent autonomy, facilitating communication between agents and mission control. The second focuses on environment perception, employing AI algorithms for tasks like environment segmentation and object pose estimation. The third module ensures safe navigation, covering obstacle avoidance, social navigation with astronauts, and cooperation among robots. The fourth module addresses manipulation functions, including multi-tool capabilities and tool-changer design for diverse tasks in In-Situ Resources Utilization (ISRU) scenarios. Finally, the fifth module controls cooperative behaviour, incorporating astronaut commands, Mixed Reality interfaces, map fusion, task supervision, and error control. The suite was tested using an astronaut-rover interaction dataset in a planetary environment and GMV SPoT analogue environments. Results demonstrate the advantages of E4 autonomy and AI in space systems, benefiting astronaut-robot collaboration. This paper details CISRU's development, field test preparation, and analysis, highlighting its potential to revolutionize planetary exploration through AI-powered technology.

The CISRU project has focused on the development of a software suite for planetary (and terrestrial) robotics, fully abstracted from the robotic platform and enabling interaction between rovers and astronauts in complex tasks and non-structured scenarios. To achieve this, a high level of autonomy is required, powered by AI and multi-agent autonomous planning systems inherited from ERGO/ADE and the PERASPERA program. This communication presents the system developed in CISRU, focusing on the modules of AI-based perception and the interaction between astronauts and robots.

Persistent homology is a popular computational tool for detecting non-trivial topology of point clouds, such as the presence of loops or voids. However, many real-world datasets with low intrinsic dimensionality reside in an ambient space of much higher dimensionality. We show that in this case vanilla persistent homology becomes very sensitive to noise and fails to detect the correct topology. The same holds true for most existing refinements of persistent homology. As a remedy, we find that spectral distances on the $k$-nearest-neighbor graph of the data, such as diffusion distance and effective resistance, allow persistent homology to detect the correct topology even in the presence of high-dimensional noise. Furthermore, we derive a novel closed-form expression for effective resistance in terms of the eigendecomposition of the graph Laplacian, and describe its relation to diffusion distances. Finally, we apply these methods to several high-dimensional single-cell RNA-sequencing datasets and show that spectral distances on the $k$-nearest-neighbor graph allow robust detection of cell cycle loops.

Auroral classification plays a crucial role in polar research. However, current auroral classification studies are predominantly based on images taken at a single wavelength, typically 557.7 nm. Images obtained at other wavelengths have been comparatively overlooked, and the integration of information from multiple wavelengths remains an underexplored area. This limitation results in low classification rates for complex auroral patterns. Furthermore, these studies, whether employing traditional machine learning or deep learning approaches, have not achieved a satisfactory trade-off between accuracy and speed. To address these challenges, this paper proposes a lightweight auroral multi-wavelength fusion classification network, MLCNet, based on a multi-view approach. Firstly, we develop a lightweight feature extraction backbone, called LCTNet, to improve the classification rate and cope with the increasing amount of auroral observation data. Secondly, considering the existence of multi-scale spatial structures in auroras, we design a novel multi-scale reconstructed feature module named MSRM. Finally, to highlight the discriminative information between auroral classes, we propose a lightweight attention feature enhancement module called LAFE. The proposed method is validated using observational data from the Arctic Yellow River Station during 2003-2004. Experimental results demonstrate that the fusion of multi-wavelength information effectively improves the auroral classification performance. In particular, our approach achieves state-of-the-art classification accuracy compared to previous auroral classification studies, and superior results in terms of accuracy and computational efficiency compared to existing multi-view methods.

Implicit models for magnetic coenergy have been proposed by Pera et al. to describe the anisotropic nonlinear material behavior of electrical steel sheets. This approach aims at predicting magnetic response for any direction of excitation by interpolating measured of B--H curves in the rolling and transverse directions. In an analogous manner, an implicit model for magnetic energy is proposed. We highlight some mathematical properties of these implicit models and discuss their numerical realization, outline the computation of magnetic material laws via implicit differentiation, and discuss the potential use for finite element analysis in the context of nonlinear magnetostatics.

We consider the community recovery problem on a multilayer variant of the hypergraph stochastic block model (HSBM). Each layer is associated with an independent realization of a d-uniform HSBM on N vertices. Given the similarity matrix containing the aggregated number of hyperedges incident to each pair of vertices, the goal is to obtain a partition of the N vertices into disjoint communities. In this work, we investigate a semidefinite programming (SDP) approach and obtain information-theoretic conditions on the model parameters that guarantee exact recovery both in the assortative and the disassortative cases.

We study the canonical momentum based discretizations of a hybrid model with kinetic ions and mass-less electrons. Two equivalent formulations of the hybrid model are presented, in which the vector potentials are in different gauges and the distribution functions depend on canonical momentum (not velocity). Particle-in-cell methods are used for the distribution functions, and the vector potentials are discretized by the finite element methods in the framework of finite element exterior calculus. Splitting methods are used for the time discretizations. It is illustrated that the second formulation is numerically superior and the schemes constructed based on the anti-symmetric bracket proposed have better conservation properties, although the filters can be used to improve the schemes of the first formulation.

At least two, different approaches to define and solve statistical models for the analysis of economic systems exist: the typical, econometric one, interpreting the Gravity Model specification as the expected link weight of an arbitrary probability distribution, and the one rooted into statistical physics, constructing maximum-entropy distributions constrained to satisfy certain network properties. In a couple of recent, companion papers they have been successfully integrated within the framework induced by the constrained minimisation of the Kullback-Leibler divergence: specifically, two, broad classes of models have been devised, i.e. the integrated and the conditional ones, defined by different, probabilistic rules to place links, load them with weights and turn them into proper, econometric prescriptions. Still, the recipes adopted by the two approaches to estimate the parameters entering into the definition of each model differ. In econometrics, a likelihood that decouples the binary and weighted parts of a model, treating a network as deterministic, is typically maximised; to restore its random character, two alternatives exist: either solving the likelihood maximisation on each configuration of the ensemble and taking the average of the parameters afterwards or taking the average of the likelihood function and maximising the latter one. The difference between these approaches lies in the order in which the operations of averaging and maximisation are taken - a difference that is reminiscent of the quenched and annealed ways of averaging out the disorder in spin glasses. The results of the present contribution, devoted to comparing these recipes in the case of continuous, conditional network models, indicate that the annealed estimation recipe represents the best alternative to the deterministic one.