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In this paper, we study a suitable experimental design of electrochemical impedance spectroscopy (EIS) to reduce the number of frequency points while not significantly affecting the uncertainties of the estimated cell's equivalent circuit model (ECM) parameters. It is based on an E-optimal experimental design that aims to maximize the information about the ECM parameters collected by EIS measurements and, at the same time, minimize the overall uncertainty. In a numerical experiment, we first analyze to which extent reducing the number of measurement points at low frequencies affects the uncertainty of the estimated parameters. Secondly, we show that applying the frequency adjustments can lead to the same or even improved global uncertainty of ECM parameter estimates as with a higher number of measurements. This is numerically verified through a case study using the ECM parameters of a commercial battery cell.

Many systems of partial differential equations have been proposed as simplified representations of complex collective behaviours in large networks of neurons. In this survey, we briefly discuss their derivations and then review the mathematical methods developed to handle the unique features of these models, which are often nonlinear and non-local. The first part focuses on parabolic Fokker-Planck equations: the Nonlinear Noisy Leaky Integrate and Fire neuron model, stochastic neural fields in PDE form with applications to grid cells, and rate-based models for decision-making. The second part concerns hyperbolic transport equations, namely the model of the Time Elapsed since the last discharge and the jump-based Leaky Integrate and Fire model. The last part covers some kinetic mesoscopic models, with particular attention to the kinetic Voltage-Conductance model and FitzHugh-Nagumo kinetic Fokker-Planck systems.

Glucose oxidation is a key reaction in biosensing and energy conversion, with anodized copper electrodes showing great potential as catalysts for its enhancement. This study explores the relationship between anodization parameters and glucose oxidation on thin copper films, providing valuable insights for optimization. By adjusting anodization parameters, specific species such as Cu2O, Cu(OH)2, and CuO can be selectively formed, each exhibiting different catalytic activities. Applying polarization in 1 M KOH at 0 V (vs Ag|AgCl) generates a highly active CuO surface layer, leading to significant performance improvements over bare copper electrodes. Specifically, sensitivity increases by 55% in the 0.1 mM-0.5 mM range and 73% in the 0.75 mM-2 mM range. Additionally, the electrodes demonstrate an exceptionally low detection limit of just 0.004 mM. These results are attributed to scalable, reproducible manufacturing on cleanroom-compatible platforms. This study not only sheds light on the effects of thin copper film anodization on glucose oxidation but also provides a practical approach for enhancing the efficiency of copper-based systems in biosensing and energy conversion applications.

Quantum algorithms can potentially solve a handful of problems more efficiently than their classical counterparts. In that context, it has been discussed that Markov chains problems could be solved significantly faster using quantum computing. Indeed, previous work suggests that quantum computers could accelerate sampling from the stationary distribution of reversible Markov chains. However, in practice, certain physical processes of interest are nonreversible in the probabilistic sense and reversible Markov chains can sometimes be replaced by more efficient nonreversible chains targeting the same stationary distribution. This study uses modern quantum algorithmic techniques and Markov chain theory to sample from the stationary distribution of nonreversible Markov chains with faster worst-case runtime and without requiring the stationary distribution to be computed up to a multiplicative constant. Such an up-to-exponential quantum speedup goes beyond the predicted quadratic quantum acceleration for reversible chains and is likely to have a decisive impact on many applications ranging from statistics and machine learning to computational modeling in physics, chemistry, biology and finance.

We report our findings on a spectroscopic survey of seven unresolved DA+DB binary white dwarf candidates. We have discovered extreme spectroscopic variations in one of these candidates, SDSS J084716.21+484220.40. Previous analysis failed to reproduce the optical spectrum using a single object with a homogeneous atmosphere. Our time-resolved spectroscopy reveals a double-faced white dwarf that switches between a DBA and DA spectral type over 6.5 or 8.9 hours due to varying surface abundances. We also provide time-series spectroscopy of the magnetic DBA, SDSS J085618.94+161103.6 (LB 8915), and confirm an inhomogeneous atmosphere. We employ an atmosphere model with hydrogen caps and a helium belt that yields excellent fits to our time-resolved spectra. We use the oblique rotator model to derive the system geometry for both targets. With the addition of these two objects, the emerging class of double-faced white dwarfs now consists of seven members. We summarize the properties of this new class of objects, and discuss how magnetism impacts the convective processes and leads to the formation of double-faced white dwarfs. We identify cooler versions of white dwarfs with inhomogeneous atmospheres among the cool magnetic DA white dwarf sample, where the H$\alpha$ line is shallower than expected based on pure hydrogen atmosphere models., Comment: 14 pages, 9 figures, Accepted for publication in ApJ

The 2017 observing campaign of the Event Horizon Telescope (EHT) delivered the first very long baseline interferometry (VLBI) images at the observing frequency of 230 GHz, leading to a number of unique studies on black holes and relativistic jets from active galactic nuclei (AGN). In total, eighteen sources were observed: the main science targets, Sgr A* and M87 along with various calibrators. We investigated the morphology of the sixteen AGN in the EHT 2017 data set, focusing on the properties of the VLBI cores: size, flux density, and brightness temperature. We studied their dependence on the observing frequency in order to compare it with the Blandford-K\"onigl (BK) jet model. We modeled the source structure of seven AGN in the EHT 2017 data set using linearly polarized circular Gaussian components and collected results for the other nine AGN from dedicated EHT publications, complemented by lower frequency data in the 2-86 GHz range. Then, we studied the dependences of the VLBI core flux density, size, and brightness temperature on the frequency measured in the AGN host frame. We compared the observations with the BK jet model and estimated the magnetic field strength dependence on the distance from the central black hole. Our results indicate a deviation from the standard BK model, particularly in the decrease of the brightness temperature with the observing frequency. Either bulk acceleration of the jet material, energy transfer from the magnetic field to the particles, or both are required to explain the observations.

We introduce a novel framework to implement stochastic inflation on stochastic trees, modelling the inflationary expansion as a branching process. Combined with the $\delta N$ formalism, this allows us to generate real-space maps of the curvature perturbation that fully capture quantum diffusion and its non-perturbative backreaction during inflation. Unlike lattice methods, trees do not proceed on a fixed background since new spacetime units emerge dynamically as trees unfold, naturally incorporating metric fluctuations. The recursive structure of stochastic trees also offers remarkable numerical efficiency, and we develop the FOrtran Recursive Exploration of Stochastic Trees ($\texttt{FOREST}$) tool and demonstrate its performance. We show how primordial black holes blossom at unbalanced nodes of the trees, and how their mass distribution can be obtained while automatically accounting for the "cloud-in-cloud" effect. In the "quantum-well" toy model, we find broad mass distributions, with mild power laws terminated by exponential tails. We finally compare our results with existing approximations in the literature and discuss several prospects., Comment: 39 pages, 13 figures

Despite being the most common types of stars in the Galaxy, the physical properties of late M dwarfs are often poorly constrained. A trend of radius inflation compared to evolutionary models has been observed for earlier type M dwarfs in eclipsing binaries, possibly caused by magnetic activity. It is currently unclear whether this trend also extends to later type M dwarfs below the convective boundary. This makes the discovery of lower-mass, fully convective, M dwarfs in eclipsing binaries valuable for testing evolutionary models especially in longer-period binaries where tidal interaction between the primary and secondary is negligible. With this context, we present the discovery of the NGTS-EB-7 AB system, an eclipsing binary containing a late M dwarf secondary and an evolved G-type primary star. The secondary star has a radius of $0.125 \pm 0.006 R_\odot$ , a mass of $0.096 \pm 0.004 M_\odot$ and follows a highly eccentric $(e=0.71436 \pm 0.00085)$ orbit every $193.35875 \pm 0.00034$ days. This makes NGTS-EB-7 AB the third longest-period eclipsing binary system with a secondary smaller than $200 M_J$ with the mass and radius constrained to better than $5 \%$. In addition, NGTS-EB-7 is situated near the centre of the proposed LOPS2 southern field of the upcoming PLATO mission, allowing for detection of the secondary eclipse and measurement of the companion`s temperature. With its long-period and well-constrained physical properties - NGTS-EB-7 B will make a valuable addition to the sample of M dwarfs in eclipsing binaries and help in determining accurate empirical mass/radius relations for later M dwarf stars., Comment: Main body: 14 pages, 6 figures, 5 tables. Appendices: 7 pages, 5 figures, 5 tables

Endovascular navigation is a crucial aspect of minimally invasive procedures, where precise control of curvilinear instruments like guidewires is critical for successful interventions. A key challenge in this task is accurately predicting the evolving shape of the guidewire as it navigates through the vasculature, which presents complex deformations due to interactions with the vessel walls. Traditional segmentation methods often fail to provide accurate real-time shape predictions, limiting their effectiveness in highly dynamic environments. To address this, we propose SplineFormer, a new transformer-based architecture, designed specifically to predict the continuous, smooth shape of the guidewire in an explainable way. By leveraging the transformer's ability, our network effectively captures the intricate bending and twisting of the guidewire, representing it as a spline for greater accuracy and smoothness. We integrate our SplineFormer into an end-to-end robot navigation system by leveraging the condensed information. The experimental results demonstrate that our SplineFormer is able to perform endovascular navigation autonomously and achieves a 50% success rate when cannulating the brachiocephalic artery on the real robot., Comment: 8 pages

In this paper, we investigate on a bounded open set of $\mathbb{R}^N$ with smooth boundary, an eigenvalue problem involving the sum of nonlocal operators $(-\Delta)_p^{s_1}+ (-\Delta)_q^{s_2}$ with $s_1,s_2\in (0,1)$, $p,q\in (1,\infty)$ and subject to the corresponding homogeneous nonlocal $(p,q)$-Neumann boundary condition. A careful analysis of the considered problem leads us to a complete description of the set of eigenvalues as being the precise interval $\{0\}\cup(\lambda_{1}(s_2,q),\infty)$, where $\lambda_{1}(s_2,q)$ is the first nonzero eigenvalue of the homogeneous fractional $q$-Laplacian under nonlocal $q$-Neumann boundary condition. Furthermore, we establish that every eigenfunctions is globally bounded., Comment: 26 pages. arXiv admin note: text overlap with arXiv:2406.15825

Electromagnetic waves in the magnetosphere scatter electrons, causing them to precipitate deep into Earth's atmosphere, where they impart their temporal characteristics to diffuse aurorae. Using radar-observations of the ionospheric E-region and satellite observations from the magnetosphere, we demonstrate a close and unprecedented association between enhanced electrostatic cyclotron harmonic wave activity in the magnetosphere and the appearance of meter-scale ionospheric plasma turbulence observed a few seconds later in the lower ionosphere on nearby magnetic field lines., Comment: 10 pages, 6 figures

We report pattern formation in an otherwise non-uniform and unsteady flow arising in high-speed liquid entrainment conditions on the outer wall of a wide rotating drum. We show that the coating flow in this rotary drag-out undergoes axial modulations to form an array of roughly vertical thin liquid sheets which slowly drift from the middle of the drum towards its side walls. Thus, the number of sheets fluctuate in time such that the most probable rib spacing varies ever so slightly with the speed, and a little less weakly with the viscosity. We propose that these axial patterns are generated due to a primary instability driven by an adverse pressure gradient in the meniscus region of the rotary drag-out flow, similar to the directional Saffman-Taylor instability, as is well-known for ribbing in film-splitting flows. Rib spacing based on this mechanistic model turns out to be proportional to the capillary length, wherein the scaling factor can be determined based on existing models for film entrainment at both low and large Capillary numbers. In addition, we performed Direct Numerical Simulations, which reproduce the experimental phenomenology and the associated wavelength. We further include two numerical cases wherein either the liquid density, or the liquid surface tension are quadrupled while keeping all other parameters identical with experiments. The rib spacings of these cases are in agreement with the predictions of our model., Comment: in press for JFM

Large X-ray observatories such as Chandra and XMM-Newton have been delivering scientific breakthroughs in research fields as diverse as our Solar System, the astrophysics of stars, stellar explosions and compact objects, accreting super-massive black holes, and large-scale structures traced by the hot plasma permeating and surrounding galaxy groups and clusters. The recently launched observatory XRISM is opening in earnest the new observational window of non-dispersive high-resolution spectroscopy. However, several quests are left open, such as the effect of the stellar radiation field on the habitability of nearby planets, the Equation-of-State regulating matter in neutron stars, the origin and distribution of metals in the Universe, the processes driving the cosmological evolution of the baryons locked in the gravitational potential of Dark Matter and the impact of supermassive black hole growth on galaxy evolution, just to mention a few. Furthermore, X-ray astronomy is a key player in multi-messenger astrophysics. Addressing these quests experimentally requires an order-of-magnitude leap in sensitivity, spectroscopy and survey capabilities with respect to existing X-ray observatories. This paper succinctly summarizes the main areas where high-energy astrophysics is expected to contribute to our understanding of the Universe in the next decade and describes a new mission concept under study by the European Space Agency, the scientific community worldwide and two International Partners (JAXA and NASA), designed to enable transformational discoveries: NewAthena. This concept inherits its basic payload design from a previous study carried out until 2022, Athena., Comment: Published in Nature Astronomy. 9 pages, 4 figures

Charge transport in materials has an impact on a wide range of devices based on semiconductor, battery or superconductor technology. Charge transport in sliding Charge Density Waves (CDW) differs from all others in that the atomic lattice is directly involved in the transport process. To obtain an overall picture of the structural changes associated to the collective transport, the large coherent X-ray beam generated by an X-ray free-electron laser (XFEL) source was used. The CDW phase can be retrieved over the entire sample from diffracted intensities using a genetic algorithm. For currents below threshold, increasing shear deformation is observed in the central part of the sample while longitudinal deformation appears above threshold when shear relaxes. Shear thus precedes longitudinal deformation, with relaxation of one leading to the appearance of the other. Moreover, strain accumulates on surface steps in the sliding regime, demonstrating the strong pinning character of these surface discontinuities. The sliding process of nanometric CDW is based on an impressive spatial coherence involving the macroscopic sample dimensions., Comment: 20 pages, 5 figures

Accurate quantification of the extent of lung pathological patterns (fibrosis, ground-glass opacity, emphysema, consolidation) is prerequisite for diagnosis and follow-up of interstitial lung diseases. However, segmentation is challenging due to the significant class imbalance between healthy and pathological tissues. This paper addresses this issue by leveraging a diffusion model for data augmentation applied during training an AI model. Our approach generates synthetic pathological tissue patches while preserving essential shape characteristics and intricate details specific to each tissue type. This method enhances the segmentation process by increasing the occurence of underrepresented classes in the training data. We demonstrate that our diffusion-based augmentation technique improves segmentation accuracy across all pathological tissue types, particularly for the less common patterns. This advancement contributes to more reliable automated analysis of lung CT scans, potentially improving clinical decision-making and patient outcomes, Comment: accepted at ISBI 2025

During the 23 April 2023 geospace storm, we observed chorus wave-driven energetic particle precipitation on closed magnetic field lines in the dayside magnetosphere. Simultaneously and in the ionosphere's bottom-side, we observed signatures of impact ionization and strong enhancements in the ionospheric electric field strength, via radar-detection of meter-scale turbulence, and with matching temporal characteristics as that of the magnetospheric observations (correlation coefficient = 0.78). During geospace storms, then, turbulent structuring as well as fast electrodynamics in the dayside polar ionosphere can be driven by wave-particle interactions in the magnetosphere., Comment: 8 pages, 4 figures

This note studies phase transitions for the existence of unregularized M-estimators under proportional asymptotics where the sample size $n$ and feature dimension $p$ grow proportionally with $n/p \to \delta \in (0, \infty)$. We study the existence of M-estimators in single-index models where the response $y_i$ depends on covariates $x_i \sim N(0, I_p)$ through an unknown index $w \in R^p$ and an unknown link function. An explicit expression is derived for the critical threshold $\delta_\infty$ that determines the phase transition for the existence of the M-estimator, generalizing the results of Cand`es and Sur (2020) for binary logistic regression to other single-index linear models. Furthermore, we investigate the existence of a solution to the nonlinear system of equations governing the asymptotic behavior of the M-estimator when it exists. The existence of solution to this system for $\delta > \delta_\infty$ remains largely unproven outside the global null in binary logistic regression. We address this gap with a proof that the system admits a solution if and only if $\delta > \delta_\infty$, providing a comprehensive theoretical foundation for proportional asymptotic results that require as a prerequisite the existence of a solution to the system., Comment: 27 pages, 2 figures

Approximate Leave-One-Out Cross-Validation (ALO-CV) is a method that has been proposed to estimate the generalization error of a regularized estimator in the high-dimensional regime where dimension and sample size are of the same order, the so called ``proportional regime''. A new analysis is developed to derive the consistency of ALO-CV for non-differentiable regularizer under Gaussian covariates and strong-convexity of the regularizer. Using a conditioning argument, the difference between the ALO-CV weights and their counterparts in mean-field inference is shown to be small. Combined with upper bounds between the mean-field inference estimate and the leave-one-out quantity, this provides a proof that ALO-CV approximates the leave-one-out quantity as well up to negligible error terms. Linear models with square loss, robust linear regression and single-index models are explicitly treated.

This note develops an analysis of the Lasso \( \hat b\) in linear models without any sparsity or L1 assumption on the true regression vector, in the proportional regime where dimension \( p \) and sample \( n \) are of the same order. Under Gaussian design and covariance matrix with spectrum bounded away from 0 and $+\infty$, it is shown that the L2 risk is stochastically bounded if and only if the number of selected variables is bounded away from \( n \), in the sense that $$ (1-\|\hat b\|_0/n)^{-1} = O_P(1) \Longleftrightarrow \|\hat b- b^*\|_2 = O_P(1) $$ as \( n,p\to+\infty \). The right-to-left implication rules out constant risk for dense Lasso estimates (estimates with close to $n$ active variables), which can be used to discard tuning parameters leading to dense estimates. We then bring back sparsity in the picture, and revisit the precise phase transition characterizing the sparsity patterns of the true regression vector leading to unbounded Lasso risk -- or by the above equivalence to dense Lasso estimates. This precise phase transition was established by \citet{miolane2018distribution,celentano2020lasso} using fixed-point equations in an equivalent sequence model. An alternative proof of this phase transition is provided here using simple arguments without relying on the fixed-point equations or the equivalent sequence model. A modification of the well-known Restricted Eigenvalue argument allows to extend the analysis to any small tuning parameter of constant order, leading to a bounded risk on one side of the phase transition. On the other side of the phase transition, it is established the Lasso risk can be unbounded for a given sign pattern as soon as Basis Pursuit fails to recover that sign pattern in noiseless problems.

We construct and study new generalisations to rooted trees and forests of some properties of shuffles of words. First, we build a coproduct on rooted trees which, together with their shuffle, endow them with bialgebra structure. We then caracterize the coproduct dual to the shuffle product of rooted forests and build a product on rooted trees to obtain the bialgebra dual to the shuffle bialgebra. We then characterize and enumerate primitive trees for the dual coproduct. Finally, using modified shuffles of rooted forests, we prove a property in the category of Rota-Baxter algebras., Comment: 28 pages

We report on the electron spin resonance (ESR), heat capacity, magnetization, nuclear magnetic resonance (NMR), magnetic circular and linear dichroism (XMCD, XMLD), as well as the electrical resistivity of EuMn$_{2}$P$_{2}$ single crystals. Antiferromagnetic order of Eu was observed in several quantities at $T^{\rm Eu}_{\rm N}\,=\,18\,\rm K$. The temperature dependencies of ESR linewidth and resonance shift show, when approaching the Eu-ordered state, a divergence towards $T^{\rm Eu}_{\rm N}$, indicating the growing importance of magnetic correlations and the build-up of internal magnetic fields. An additional temperature scale of $\approx 47\,\rm K$ has considerable impact on linewidth, resonance field and intensity. This points to the presence of weak Mn-based ordering. The observed ESR line is interpreted as an Eu$^{2+}$ resonance, which probes the weak magnetic background of the Mn subsystem. Such picture is suggested by the lineshape which keeps to be Lorentzian across the $47\,\rm K$ scale and by the ESR intensity which can be described by the same Curie-Weiss temperature above and below $47\,\rm K$. In the same temperature range anomalies were observed at $48.5\,\rm K$ and $51\,\rm K$ in the heat capacity data as well as a pronounced broadening of the NMR signal of the EuMn$_{2}$P$_{2}$ samples. In XMCD and XMLD measurements, this weak magnetic order could not be detected in the same temperature range which might be due to the small magnetic moment, with a potential $c$-component or frustration.

End-to-end image and video codecs are becoming increasingly competitive, compared to traditional compression techniques that have been developed through decades of manual engineering efforts. These trainable codecs have many advantages over traditional techniques, such as their straightforward adaptation to perceptual distortion metrics and high performance in specific fields thanks to their learning ability. However, current state-of-the-art neural codecs do not fully exploit the benefits of vector quantization and the existence of the entropy gradient in decoding devices. In this paper, we propose to leverage these two properties (vector quantization and entropy gradient) to improve the performance of off-the-shelf codecs. Firstly, we demonstrate that using non-uniform scalar quantization cannot improve performance over uniform quantization. We thus suggest using predefined optimal uniform vector quantization to improve performance. Secondly, we show that the entropy gradient, available at the decoder, is correlated with the reconstruction error gradient, which is not available at the decoder. We therefore use the former as a proxy to enhance compression performance. Our experimental results show that these approaches save between 1 to 3% of the rate for the same quality across various pretrained methods. In addition, the entropy gradient based solution improves traditional codec performance significantly as well., Comment: Accepted in IEEE TRANSACTIONS ON IMAGE PROCESSING

Efforts towards endowing robots with the ability to speak have benefited from recent advancements in NLP, in particular large language models. However, as powerful as current models have become, they still operate on sentence or multi-sentence level input, not on the word-by-word input that humans operate on, affecting the degree of responsiveness that they offer, which is critical in situations where humans interact with robots using speech. In this paper, we review the literature on interactive systems that operate incrementally (i.e., at the word level or below it). We motivate the need for incremental systems, survey incremental modeling of important aspects of dialogue like speech recognition and language generation. Primary focus is on the part of the system that makes decisions, known as the dialogue manager. We find that there is very little research on incremental dialogue management, offer some requirements for practical incremental dialogue management, and the implications of incremental dialogue for embodied, robotic platforms., Comment: 16 pages

We introduce a solvable model of a measurement-induced phase transition (MIPT) in a deterministic but chaotic dynamical system with a positive Lyapunov exponent. In this setup, an observer only has a probabilistic description of the system but mitigates chaos-induced uncertainty through repeated measurements. Using a minimal representation via a branching tree, we map this problem to the directed polymer (DP) model on the Cayley tree, although in a regime dominated by rare events. By studying the Shannon entropy of the probability distribution estimated by the observer, we demonstrate a phase transition distinguishing a chaotic phase with reduced Lyapunov exponent from a strong-measurement phase where uncertainty remains bounded. Remarkably, the location of the MIPT transition coincides with the freezing transition of the DP, although the critical properties differ. We provide an exact universal scaling function describing entropy growth in the critical regime. Numerical simulations confirm our theoretical predictions, highlighting a simple yet powerful framework to explore measurement-induced transitions in classical chaotic systems., Comment: 14 pages, 5 figures

This paper describes RHP Friends, a social humanoid robot developed to enable assistive robotic deployments in human-coexisting environments. As a use-case application, we present its potential use in nursing by extending its capabilities to operate human devices and tools according to the task and by enabling remote assistance operations. To meet a wide variety of tasks and situations in environments designed by and for humans, we developed a system that seamlessly integrates the slim and lightweight robot and several technologies: locomanipulation, multi-contact motion, teleoperation, and object detection and tracking. We demonstrated the system's usage in a nursing application. The robot efficiently performed the daily task of patient transfer and a non-routine task, represented by a request to operate a circuit breaker. This demonstration, held at the 2023 International Robot Exhibition (IREX), conducted three times a day over three days., Comment: IEEE Robotics and Automation Magazine, In press

Molecular Dynamics simulations are essential tools for understanding the dynamic behavior of biomolecules, yet extracting meaningful molecular pathways from these simulations remains challenging due to the vast amount of generated data. In this work, we present Molecular Kinetics via Topology (MoKiTo), a novel approach that combines the ISOKANN algorithm to determine the reaction coordinate of a molecular system with a topological analysis inspired by the Mapper algorithm. Our strategy efficiently identifies and characterizes distinct molecular pathways, enabling the detection and visualization of critical conformational transitions and rare events. This method offers deeper insights into molecular mechanisms, facilitating the design of targeted interventions in drug discovery and protein engineering.

We Study versions of Cauchy formula in more general algebras than the complex case., Comment: 53 pages, in French language

The rapid expansion of citizen science initiatives has led to a significant growth of biodiversity databases, and particularly presence-only (PO) observations. PO data are invaluable for understanding species distributions and their dynamics, but their use in Species Distribution Models (SDM) is curtailed by sampling biases and the lack of information on absences. Poisson point processes are widely used for SDMs, with Maxent being one of the most popular methods. Maxent maximises the entropy of a probability distribution across sites as a function of predefined transformations of environmental variables, called features. In contrast, neural networks and deep learning have emerged as a promising technique for automatic feature extraction from complex input variables. In this paper, we propose DeepMaxent, which harnesses neural networks to automatically learn shared features among species, using the maximum entropy principle. To do so, it employs a normalised Poisson loss where for each species, presence probabilities across sites are modelled by a neural network. We evaluate DeepMaxent on a benchmark dataset known for its spatial sampling biases, using PO data for calibration and presence-absence (PA) data for validation across six regions with different biological groups and environmental covariates. Our results indicate that DeepMaxent improves model performance over Maxent and other state-of-the-art SDMs across regions and taxonomic groups. The method performs particularly well in regions of uneven sampling, demonstrating substantial potential to improve species distribution modelling. The method opens the possibility to learn more robust environmental features predicting jointly many species and scales to arbitrary large numbers of sites without an increased memory demand., Comment: Submitted to Methods in Ecology and Evolution

Recent advances in statistical learning theory have revealed profound connections between mutual information (MI) bounds, PAC-Bayesian theory, and Bayesian nonparametrics. This work introduces a novel mutual information bound for statistical models. The derived bound has wide-ranging applications in statistical inference. It yields improved contraction rates for fractional posteriors in Bayesian nonparametrics. It can also be used to study a wide range of estimation methods, such as variational inference or Maximum Likelihood Estimation (MLE). By bridging these diverse areas, this work advances our understanding of the fundamental limits of statistical inference and the role of information in learning from data. We hope that these results will not only clarify connections between statistical inference and information theory but also help to develop a new toolbox to study a wide range of estimators.

Covariant integral quantization is implemented for systems whose phase space is $Z_{d} \times Z_{d}$, i.e., for systems moving on the discrete periodic set $Z_d= \{0,1,\dotsc d-1$ mod$ d\}$. The symmetry group of this phase space is the periodic discrete version of the Weyl-Heisenberg group, namely the central extension of the abelian group $Z_d \times Z_d$. In this regard, the phase space is viewed as the left coset of the group with its center. The non-trivial unitary irreducible representation of this group, as acting on $L^2(Z_{N})$, is square integrable on the phase phase. We derive the corresponding covariant integral quantizations from (weight) functions on the phase space, and display their phase space portrait., Comment: 27 pages, 3 figures

Entropic optimal transport problems are regularized versions of optimal transport problems. These models play an increasingly important role in machine learning and generative modelling. For finite spaces, these problems are commonly solved using Sinkhorn algorithm (a.k.a. iterative proportional fitting procedure). However, in more general settings the Sinkhorn iterations are based on nonlinear conditional/conjugate transformations and exact finite-dimensional solutions cannot be computed. This article presents a finite-dimensional recursive formulation of the iterative proportional fitting procedure for general Gaussian multivariate models. As expected, this recursive formulation is closely related to the celebrated Kalman filter and related Riccati matrix difference equations, and it yields algorithms that can be implemented in practical settings without further approximations. We extend this filtering methodology to develop a refined and self-contained convergence analysis of Gaussian Sinkhorn algorithms, including closed form expressions of entropic transport maps and Schr\"odinger bridges., Comment: 68 pages

Since the discovery of heavy-fermion superconductivity in CeCu$_{2}$Si$_{2}$, the material has attracted great interest particularly with regard to the nature of the superconducting pairing and its mechanism. Consequently, it is essential to better understand the electronic Fermi surface topology and its role in strong antiferromagnetic fluctuations. The standard density functional theory method is insufficient to model the interplay of strong onsite Coulomb repulsion in localized 4{\it f}-electrons and their hybridization with itinerant ligand-orbital electrons. We have performed electronic ground state calculations on CeCu$_{2}$Si$_{2}$ using the Gutzwiller wavefunction approximation. The Gutzwiller approximation captures the quasiparticle band renormalization from the strong onsite Coulomb repulsion. We have performed an analysis of this effect on the electronic structure and the Fermi surface topology by varying the interaction strength and taking into account the crystal-field splitting. Using the de Haas van Alphen effect, the extremal Fermi surface cross-sectional areas were calculated to quantify the effects of quasiparticle mass renormalization on the Fermi surface. Our results confirm two Fermi surface sheets corresponding to the heavy (488m$_{e}$) and light (4.35m$_{e}$) quasiparticles, which is in close agreement with experimental measurements as well as the renormalized band method., Comment: 10 pages, 3 figures, 2 tables