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We propose a method for interpolating divergence-free continuous magnetic fields via vector potential reconstruction using Hermite interpolation, which ensures high-order continuity for applications requiring adaptive, high-order ordinary differential equation (ODE) integrators, such as the Dormand-Prince method. The method provides C(m) continuity and achieves high-order accuracy, making it particularly suited for particle trajectory integration and Poincar\'e section analysis under optimal integration order and timestep adjustments. Through numerical experiments, we demonstrate that the Hermite interpolation method preserves volume and continuity, which are critical for conserving toroidal canonical momentum and magnetic moment in guiding center simulations, especially over long-term trajectory integration. Furthermore, we analyze the impact of insufficient derivative continuity on Runge-Kutta schemes and show how it degrades accuracy at low error tolerances, introducing discontinuity-induced truncation errors. Finally, we demonstrate performant Poincar\'e section analysis in two relevant settings of field data collocated from finite element meshes, Comment: 21 pages, 9 figures

A calorimetric detector for minimally disruptive measurements of atomic hydrogen beams is described. The calorimeter measures heat released by the recombination of hydrogen atoms into molecules on a thin wire. As a demonstration, the angular distribution of a beam with a peak intensity of $\approx 10^{16} \,{\rm{atoms}}/{(\rm{cm}^2 \rm{s})}$ is measured by translating the wire across the beam. The data agree well with an analytic model of the beam from the thermal hydrogen atom source. Using the beam shape model, the relative intensity of the beam can be determined to 5% precision or better at any angle.

In this brief and speculative commentary, we explore ideas inspired by neural networks in machine learning, proposing that a simple neural XOR motif, involving both excitatory and inhibitory connections, may provide the basis for a relevant mode of plasticity in neural circuits of living organisms, with homeostasis as the sole guiding principle. This XOR motif simply signals the discrepancy between incoming signals and reference signals, thereby providing a basis for a loss function in learning neural circuits, and at the same time regulating homeostasis by halting the propagation of these incoming signals. The core motif uses a 4:1 ratio of excitatory to inhibitory neurons, and supports broader neural patterns such as the well-known 'winner takes all' (WTA) mechanism. We examined the prevalence of the XOR motif in the published connectomes of various organisms with increasing complexity, and found that it ranges from tens (in C. elegans) to millions (in several Drosophila neuropils) and more than tens of millions (in mouse V1 visual cortex). If validated, our hypothesis identifies two of the three key components in analogy to machine learning models: the architecture and the loss function. And we propose that a relevant type of biological neural plasticity is simply driven by a basic control or regulatory system, which has persisted and adapted despite the increasing complexity of organisms throughout evolution., Comment: 11 pages, 6 figures

This paper studies three different ways to assign weights to the lattice points of a convex polytope and discusses the algebraic and combinatorial properties of the resulting weighted Ehrhart functions and their generating functions and associated rings. These will be called $q$-weighted, $r$-weighted, and $s$-weighted Ehrhart functions, respectively. The key questions we investigate are \emph{When are the weighted Ehrhart series rational functions and which classical Ehrhart theory properties are preserved? And, when are the abstract formal power series the Hilbert series of Ehrhart rings of some polytope?} We prove generalizations about weighted Ehrhart $h^*$-coefficients of $q$-weighted Ehrhart series, and show $q$- and $s$-weighted Ehrhart reciprocity theorems. Then, we show the $q$- and $r$-weighted Ehrhart rings are the (classical) Ehrhart rings of weight lifting polytopes.

Robotic telescope networks play an important role in capturing early and bright optical afterglows, providing critical insights into the energetics and emission mechanisms of GRBs. In this study, we analyze GRB 230204B, an exceptionally energetic and multi-pulsed long GRB, detected by the Fermi GBM and MAXI detectors, with an isotropic equivalent gamma-ray energy exceeding 10$^{54}$ erg. Time-resolved spectral analysis reveals a transition in the prompt emission from hard (sub-photospheric dominated) spectra during early pulses to softer (synchrotron radiation dominated) spectra in later pulses, indicative of a hybrid jet composition. We report the discovery and characterization of the optical afterglow using the MASTER and BOOTES robotic telescope networks, alongside long-term radio observations extending to 335 days post-burst with the ATCA. At ~1.3 ks post-burst, the optical luminosity was exceptionally high, surpassing even other bright GRBs, such as GRB 221009A (the ``BOAT"). Multi-wavelength modeling, incorporating data from MASTER, BOOTES, DOT, Swift/XRT, and radio observations, was conducted using an external ISM forward-shock top-hat jet model with afterglowpy. The results reveal a narrow and highly collimated jet with a circumburst density of n$_{0}$ ~ 28.12 cm$^{-3}$, kinetic energy E$_{K}$ ~ 4.18 x 10$^{55}$ erg, and a relatively low value of $\epsilon_{B}$ = 2.14 x 10$^{-6}$, indicating shock-compression of the magnetic field in the surrounding interstellar medium. We constrained a low radiative efficiency of ~ 4.3 %. This study highlights the indispensable contribution of robotic networks to early afterglow observations and advances our understanding of GRB 230204B unique characteristics and underlying jet physics., Comment: 27 pages, 12 figures, 8 tables, submitted

The sum of quantum computing errors is the key element both for the estimation and control of errors in quantum computing and for its statistical study. In this article we analyze the sum of two independent quantum computing errors, $X_1$ and $X_2$, and we obtain the formula of the variance of the sum of these errors: $$ V(X_1+X_2)=V(X_1)+V(X_2)-\frac{V(X_1)V(X_2)}{2}. $$ We conjecture that this result holds true for general quantum computing errors and we prove the formula for independent isotropic quantum computing errors.

This work shows a study about the structure of the cycles contained in a Minimal Strong Digraph (MSD). The structure of a given cycle is determined by the strongly connected components (or strong components, SCs) that appear after suppressing the arcs of the cycle. By this process and by the contraction of all SCs into single vertices we obtain a Hasse diagram from the MSD. Among other properties, we show that any SC conformed by more than one vertex (non trivial SC) has at least one linear vertex (a vertex with indegree and outdegree equal to 1) in the MSD (Theorem 1); that in the Hasse diagram at least one linear vertex exists for each non trivial maximal (resp. minimal) vertex (Theorem 2); that if an SC contains a number $\lambda$ of vertices of the cycle then it contains at least $\lambda$ linear vertices in the MSD (Theorem 3); and, finally, that given a cycle of length $q$ contained in the MSD, the number $\alpha$ of linear vertices contained in the MSD satisfies $\alpha \geq \lfloor (q+1)/2 \rfloor$ (Theorem 4).

A mathematical modeling process for phenomena with a single state variable that attempts to be realistic must be given by a scalar nonautonomous differential equation $x'=f(t,x)$ that is concave with respect to the state variable $x$ in some regions of its domain and convex in the complementary zones. This article takes the first step towards developing a theory to describe the corresponding dynamics: the case in which $f$ is concave on the region $x\ge b(t)$ and convex on $x\le b(t)$, where $b$ is a $C^1$ map, is considered. The different long-term dynamics that may appear are analyzed while describing the bifurcation diagram for $x'=f(t,x)+\lambda$. The results are used to establish conditions on a concave-convex map $h$ and a nonnegative map $k$ ensuring the existence of a value $\rho_0$ giving rise to the unique critical transition for the parametric family of equations $x'=h(t,x)-\rho\,k(t,x)$, which is assumed to approach $x'=h(t,x)$ as time decreases, but for which no conditions are assumed on the future dynamics. The developed theory is justified by showing that concave-convex models fit correctly some laboratory experimental data, and applied to describe a population dynamics model for which a large enough increase on the peak of a temporary higher predation causes extinction., Comment: 45 pages, 10 figures

Autonomous vehicles (AVs) are poised to revolutionize modern transportation, offering enhanced safety, efficiency, and convenience. However, the increasing complexity and connectivity of AV systems introduce significant cybersecurity challenges. This paper provides a comprehensive survey of AV security with a focus on threat modeling frameworks, including STRIDE, DREAD, and MITRE ATT\&CK, to systematically identify and mitigate potential risks. The survey examines key components of AV architectures, such as sensors, communication modules, and electronic control units (ECUs), and explores common attack vectors like wireless communication exploits, sensor spoofing, and firmware vulnerabilities. Through case studies of real-world incidents, such as the Jeep Cherokee and Tesla Model S exploits, the paper highlights the critical need for robust security measures. Emerging technologies, including blockchain for secure Vehicle-to-Everything (V2X) communication, AI-driven threat detection, and secure Over-The-Air (OTA) updates, are discussed as potential solutions to mitigate evolving threats. The paper also addresses legal and ethical considerations, emphasizing data privacy, user safety, and regulatory compliance. By combining threat modeling frameworks, multi-layered security strategies, and proactive defenses, this survey offers insights and recommendations for enhancing the cybersecurity of autonomous vehicles.

We study the non-Gaussian tail of the curvature fluctuation, $\zeta$, in an inflationary scenario with a transient ultra slow-roll phase that generates a localized large enhancement of the spectrum of $\zeta$. To do so, we implement a numerical procedure that provides the probability distribution of $\zeta$ order by order in perturbation theory. The non-Gaussianities of $\zeta$ can be shown to arise from its non-linear relation to the inflaton fluctuations and from the intrinsic non-Gaussianities of the latter, which stem from its self interactions. We find that intrinsic non-Gaussianities, which have often been ignored to estimate the abundance of primordial black holes in this kind of scenario, are important. The relevance of the intrinsic contribution depends on the rapidity with which the transient ultra slow-roll phase occurs, as well as on its duration. Our method cannot be used accurately when the perturbative in-in formalism fails to apply, highlighting the relevance of developing fully non-perturbative approaches to the problem., Comment: 28 pages, 7 figures

We study ultrafilters from the perspective of the algebra in the \v{C}ech-Stone compactification of the natural numbers, and idempotent elements therein. The first two results that we prove establish that, if $p$ is a Q-point (resp. a selective ultrafilter) and $\mathscr F^p$ (resp. $\mathscr G^p$) is the smallest family containing $p$ and closed under iterated sums (resp. closed under Blass--Frol\'{\i}k sums and Rudin--Keisler images), then $\mathscr F^p$ (resp. $\mathscr G^p$) contains no idempotent elements. The second of these results about a selective ultrafilter has the following interesting consequence: assuming a conjecture of Blass, in models of the form $\mathbf{L}(\mathbb R)[p]$ where $\mathbf{L}(\mathbb R)$ is a Solovay model (of $\mathsf{ZF}$ without choice) and $p$ is a selective ultrafilter, there are no idempotent elements. In particular, the theory $\mathsf{ZF}$ plus the existence of a nonprincipal ultrafilter on $\omega$ does not imply the existence of idempotent ultrafilters, which answers a question of DiNasso and Tachtsis (Proc. Amer. Math. Soc. 146, 397-411). Following the line of obtaining independence results in $\mathsf{ZF}$, we finish the paper by proving that $\mathsf{ZF}$ plus "every additive filter can be extended to an idempotent ultrafilter" does not imply the Ultrafilter Theorem over $\mathbb R$, answering another question of DiNasso and Tachtsis from the same paper., Comment: 27 pages

We study the slices or sections of a convex polytope by affine hyperplanes. We present results on two key problems: First, we provide tight bounds on the maximum number of vertices attainable by a hyperplane slice of $d$-polytope (a sort of upper bound theorem) and discuss a new algorithm to find all sections. Second, we investigate the sequence of numbers of vertices produced by the different slices over all possible hyperplanes and analyze the gaps that arise in that sequence. We study these sequences for three-dimensional polytopes and for hypercubes. Our results were obtained with the help of large computational experiments, and we report on new data generated for hypercubes., Comment: 16 pages

In this paper, the stability of IMEX-BDF methods for delay differential equations (DDEs) is studied based on the test equation $y'(t)=-A y(t) + B y(t-\tau)$, where $\tau$ is a constant delay, $A$ is a positive definite matrix, but $B$ might be any matrix. First, it is analyzed the case where both matrices diagonalize simultaneously, but the paper focus in the case where the matrices $A$ and $B$ are not simultaneosly diagonalizable. The concept of field of values is used to prove a sufficient condition for unconditional stability of these methods and another condition which also guarantees their stability, but according to the step size. Several numerical examples in which the theory discussed here is applied to DDEs, but also parabolic problems given by partial delay differential equations with a diffusion term and a delayed term are presented., Comment: 25 pages

Searching for information on the internet and digital platforms to satisfy an information need requires effective retrieval solutions. However, such solutions are not yet available for Tetun, making it challenging to find relevant documents for text-based search queries in this language. To address these challenges, this study investigates Tetun text retrieval with a focus on the ad-hoc retrieval task. It begins by developing essential language resources -- including a list of stopwords, a stemmer, and a test collection -- which serve as foundational components for solutions tailored to Tetun text retrieval. Various strategies are then explored using both document titles and content to evaluate retrieval effectiveness. The results show that retrieving document titles, after removing hyphens and apostrophes without applying stemming, significantly improves retrieval performance compared to the baseline. Efficiency increases by 31.37%, while effectiveness achieves an average gain of 9.40% in MAP@10 and 30.35% in nDCG@10 with DFR BM25. Beyond the top-10 cutoff point, Hiemstra LM demonstrates strong performance across various retrieval strategies and evaluation metrics. Contributions of this work include the development of Labadain-Stopwords (a list of 160 Tetun stopwords), Labadain-Stemmer (a Tetun stemmer with three variants), and Labadain-Avaliad\'or (a Tetun test collection containing 59 topics, 33,550 documents, and 5,900 qrels).

In our previous study, we identified a shift in the synchrotron peak frequency of the blazar B2 1308$+$326 from 10$^{12.9}$ Hz to 10$^{14.8}$ Hz during a flare, suggesting it could be a changing-look blazar (CLB). In this work, we investigate the CL behaviour of B2 1308+326 by analysing a newly acquired optical spectrum and comparing it with an archival spectrum. We find that between the two epochs, the continuum flux increased by a factor of $\sim$4.4, while the Mg II emission line flux decreased by a factor of 1.4$\pm$0.2. Additionally, the equivalent width of the Mg II line reduced from $\sim 20$ \AA \ to $\sim 3$ \AA, indicating an apparent shift from a flat-spectrum radio quasar (FSRQ) class to a BL Lacertae (BL Lac) class. Despite this apparent change, the ratio of accretion disk luminosity to Eddington luminosity remains $>$ 10$^{-2}$ during both epochs, indicating efficient accretion persists in B2 1308$+$326. The measured black hole mass remains consistent with an average $\log M_{\rm BH} = 8.44$ M$_{\odot}$. Our findings suggest that B2 1308$+$326 is not a genuine CLB, but rather an intrinsic FSRQ that emerges as a BL Lac during high-flux states due to enhanced non-thermal emission., Comment: 8 pages, 4 figures, 2 tables, accepted for publication in The Astrophysical Journal

In this work, we investigate the formation of time-periodic solutions with a non-zero background that emulate rogue waves, known as Kuzentsov-Ma (KM) breathers, in physically relevant lattice nonlinear dynamical systems. Starting from the completely integrable Ablowitz-Ladik (AL) model, we demonstrate that the evolution of KM initial data is proximal to that of the non-integrable discrete Nonlinear Schr\"odinger (DNLS) equation for certain parameter values of the background amplitude and breather frequency. This finding prompts us to investigate the distance (in certain norms) between the evolved solutions of both models, for which we rigorously derive and numerically confirm an upper bound. Finally, our studies are complemented by a two-parameter (background amplitude and frequency) bifurcation analysis of numerically exact, KM-type breather solutions to the DNLS equation. Alongside the stability analysis of these waveforms reported herein, this work additionally showcases potential parameter regimes where such waveforms with a flat background may emerge in the DNLS setting., Comment: 21 pages, 7 figures

Image quality databases are used to train models for predicting subjective human perception. However, most existing databases focus on distortions commonly found in digital media and not in natural conditions. Affine transformations are particularly relevant to study, as they are among the most commonly encountered by human observers in everyday life. This Data Descriptor presents a set of human responses to suprathreshold affine image transforms (rotation, translation, scaling) and Gaussian noise as convenient reference to compare with previously existing image quality databases. The responses were measured using well established psychophysics: the Maximum Likelihood Difference Scaling method. The set contains responses to 864 distorted images. The experiments involved 105 observers and more than 20000 comparisons of quadruples of images. The quality of the dataset is ensured because (a) it reproduces the classical Pi\'eron's law, (b) it reproduces classical absolute detection thresholds, and (c) it is consistent with conventional image quality databases but improves them according to Group-MAD experiments.

Visual illusions in humans arise when interpreting out-of-distribution stimuli: if the observer is adapted to certain statistics, perception of outliers deviates from reality. Recent studies have shown that artificial neural networks (ANNs) can also be deceived by visual illusions. This revelation raises profound questions about the nature of visual information. Why are two independent systems, both human brains and ANNs, susceptible to the same illusions? Should any ANN be capable of perceiving visual illusions? Are these perceptions a feature or a flaw? In this work, we study how visual illusions are encoded in diffusion models. Remarkably, we show that they present human-like brightness/color shifts in their latent space. We use this fact to demonstrate that diffusion models can predict visual illusions. Furthermore, we also show how to generate new unseen visual illusions in realistic images using text-to-image diffusion models. We validate this ability through psychophysical experiments that show how our model-generated illusions also fool humans.

Context. The characterization of exoplanets requires a good description of the host star. Stellar activity acts as a source of noise which can alter planet radii as derived from the transit depth or atmospheric characterization. Aims. Here, we propose PAStar, a model to describe photospheric activity in the form of spots and faculae which could be applied to a wide range of stellar observations, from photometric to spectroscopic time series, to be able to correctly extract planetary and stellar properties. Methods. The adopted stellar atmosphere is a combination of three components, the quiet photosphere, spots and faculae. The model takes into account the effects of star inclination, doppler shifts due to stellar rotation as well as for limb darkening, independent for each component. Several synthetic products have been presented to show the capabilities of the model. Results. The model is able to retrieve the input surface inhomogeneities configuration through photometric or spectroscopic observations. The model has been validated against optical solar data and compared to alternative stellar surface activity models; e.g. SOAP code. The Sun is a unique laboratory to test stellar models because of the possibility to relate unambiguously flux variations to surface inhomogeneities configuration. This validation has been done by analyzing a photometric time series from the VIRGO photometer on board of SOHO mission. Results have been compared to real solar images from the HMI instrument on board of SDO to confirm the goodness of the results in terms of surface inhomogeneities position and dimensions. Conclusions. The description of stellar activity is a fundamental step in several astrophysical contexts and it is covered by the method we have presented. Our model offers a flexible and valuable tool to describe the activity of stars when it is dominated by spots and faculae., Comment: 17 pages, 16 figures; accepted for publication in Sect. 8. Stellar atmospheres of A&A; official acceptance date is 12/12/2024

Leveraging the large body of work devoted in recent years to describe redundancy and synergy in multivariate interactions among random variables, we propose a novel approach to quantify cooperative effects in feature importance, one of the most used techniques for explainable artificial intelligence. In particular, we propose an adaptive version of a well-known metric of feature importance, named Leave One Covariate Out (LOCO), to disentangle high-order effects involving a given input feature in regression problems. LOCO is the reduction of the prediction error when the feature under consideration is added to the set of all the features used for regression. Instead of calculating the LOCO using all the features at hand, as in its standard version, our method searches for the multiplet of features that maximize LOCO and for the one that minimize it. This provides a decomposition of the LOCO as the sum of a two-body component and higher-order components (redundant and synergistic), also highlighting the features that contribute to building these high-order effects alongside the driving feature. We report the application to proton/pion discrimination from simulated detector measures by GEANT., Comment: 11 pages, 3 figures

Segmentation models are typically constrained by the categories defined during training. To address this, researchers have explored two independent approaches: adapting Vision-Language Models (VLMs) and leveraging synthetic data. However, VLMs often struggle with granularity, failing to disentangle fine-grained concepts, while synthetic data-based methods remain limited by the scope of available datasets. This paper proposes enhancing segmentation accuracy across diverse domains by integrating Vision-Language reasoning with key strategies for Unsupervised Domain Adaptation (UDA). First, we improve the fine-grained segmentation capabilities of VLMs through multi-scale contextual data, robust text embeddings with prompt augmentation, and layer-wise fine-tuning in our proposed Foundational-Retaining Open Vocabulary Semantic Segmentation (FROVSS) framework. Next, we incorporate these enhancements into a UDA framework by employing distillation to stabilize training and cross-domain mixed sampling to boost adaptability without compromising generalization. The resulting UDA-FROVSS framework is the first UDA approach to effectively adapt across domains without requiring shared categories.

Finding players with similar profiles is an important problem in sports such as football. Scouting for new players requires a wealth of information about the available players so that similar profiles to that of a target player can be identified. However, information about the position of the players in the field is seldom used. For this reason, a novel approach based on spatial data analysis is introduced to produce a spatial similarity index that can help to identify similar players. The use of this new spatial similarity index is illustrated to identify similar players using spatial data from the Spanish competition "La Liga", season 2019-2020.

Artificial Intelligence is widely regarded as a transformative force with the potential to redefine numerous sectors of human civilization. While Artificial Intelligence has evolved from speculative fiction to a pivotal element of technological progress, its role as a truly transformative agent, or transformative Artificial Intelligence, remains a subject of debate. This work explores the historical precedents of technological breakthroughs, examining whether Artificial Intelligence can achieve a comparable impact, and it delves into various ethical frameworks that shape the perception and development of Artificial Intelligence. Additionally, it considers the societal, technical, and regulatory challenges that must be addressed for Artificial Intelligence to become a catalyst for global change. We also examine not only the strategies and methodologies that could lead to transformative Artificial Intelligence but also the barriers that could ultimately make these goals unattainable. We end with a critical inquiry into whether reaching a transformative Artificial Intelligence might compel humanity to adopt an entirely new ethical approach, tailored to the complexities of advanced Artificial Intelligence. By addressing the ethical, social, and scientific dimensions of Artificial Intelligence's development, this work contributes to the broader discourse on the long-term implications of Artificial Intelligence and its capacity to drive civilization toward a new era of progress or, conversely, exacerbate existing inequalities and risks., Comment: 100 pages, 6 Figures, 2 Tables

Human interactions and mobility shape epidemic dynamics by facilitating disease outbreaks and their spatial spread across regions. Traditional models often isolate commuting and random mobility as separate behaviors, focusing either on short, recurrent trips or on random, exploratory movements. Here, we propose a unified formalism that allows a smooth transition between commuting and exploratory behavior based on travel and return probabilities. We derive an analytical expression for the epidemic threshold, revealing a non-monotonic dependence on recurrence rates: while recurrence tends to lower the threshold by increasing agent concentration in high-contact hubs, it counterintuitively raises the invasion threshold in low-mobility scenarios, suggesting that allowing recurrence may foster local outbreaks while suppressing global epidemics. These results provide a comprehensive understanding of the interplay between human mobility patterns and epidemic spread, with implications for containment strategies in structured populations., Comment: 10 pages, 3 figures, 2 supplementary figures

In the present work we analyze two different models of interaction between dark energy and dark matter, also known as vacuum decay models or $\Lambda(t)$CDM models. In both models, when the $H_0$ parameter is constrained by the Planck distance priors, its value is compatible with a higher value of $H_0$, in agreement with SH0ES data, while simultaneously reducing the values of $\Omega_m$ and $\Omega_b$. In both models, we find $H_0=73.1\pm0.86$ at 68\% c.l. by combining Planck+SH0ES data. We also find the decay parameter to be $\varepsilon=0.0197^{+0.0032}_{-0.0027}$ for one model and $\varepsilon=0.0203\pm0.0034$ for the other one. From these analyses, a noninteracting model is excluded at least at $6\sigma$ c.l.! This shows that these types of models are promising in solving or at least alleviating the $H_0$ tension problem. Our analysis also shows a preference for the decay of vacuum into dark matter, in agreement to thermodynamic analyses., Comment: 13 pages, 2 figures

We introduce Condition-Aware Self-Supervised Learning Representation (CA-SSLR), a generalist conditioning model broadly applicable to various speech-processing tasks. Compared to standard fine-tuning methods that optimize for downstream models, CA-SSLR integrates language and speaker embeddings from earlier layers, making the SSL model aware of the current language and speaker context. This approach reduces the reliance on input audio features while preserving the integrity of the base SSLR. CA-SSLR improves the model's capabilities and demonstrates its generality on unseen tasks with minimal task-specific tuning. Our method employs linear modulation to dynamically adjust internal representations, enabling fine-grained adaptability without significantly altering the original model behavior. Experiments show that CA-SSLR reduces the number of trainable parameters, mitigates overfitting, and excels in under-resourced and unseen tasks. Specifically, CA-SSLR achieves a 10% relative reduction in LID errors, a 37% improvement in ASR CER on the ML-SUPERB benchmark, and a 27% decrease in SV EER on VoxCeleb-1, demonstrating its effectiveness., Comment: 38th Conference on Neural Information Processing Systems (NeurIPS 2024)

While deep learning models can learn human-like features at earlier levels, which suggests their utility in modeling human vision, few attempts exist to incorporate these features by design. Current approaches mostly optimize all parameters blindly, only constraining minor architectural aspects. This paper demonstrates how parametrizing neural network layers enables more biologically-plausible operations while reducing trainable parameters and improving interpretability. We constrain operations to functional forms present in human vision, optimizing only these functions' parameters rather than all convolutional tensor elements independently. We present two parametric model versions: one with hand-chosen biologically plausible parameters, and another fitted to human perception experimental data. We compare these with a non-parametric version. All models achieve comparable state-of-the-art results, with parametric versions showing orders of magnitude parameter reduction for minimal performance loss. The parametric models demonstrate improved interpretability and training behavior. Notably, the model fitted to human perception, despite biological initialization, converges to biologically incorrect results. This raises scientific questions and highlights the need for diverse evaluation methods to measure models' humanness, rather than assuming task performance correlates with human-like behavior.

Cough is a protective reflex conveying information on the state of the respiratory system. Cough assessment has been limited so far to subjective measurement tools or uncomfortable (i.e., non-wearable) cough monitors. This limits the potential of real-time cough monitoring to improve respiratory care. Objective: This paper presents a machine hearing system for audio-based robust cough segmentation that can be easily deployed in mobile scenarios. Methods: Cough detection is performed in two steps. First, a short-term spectral feature set is separately computed in five predefined frequency bands: [0, 0.5), [0.5, 1), [1, 1.5), [1.5, 2), and [2, 5.5125] kHz. Feature selection and combination are then applied to make the short-term feature set robust enough in different noisy scenarios. Second, high-level data representation is achieved by computing the mean and standard deviation of short-term descriptors in 300 ms long-term frames. Finally, cough detection is carried out using a support vector machine trained with data from different noisy scenarios. The system is evaluated using a patient signal database which emulates three real-life scenarios in terms of noise content. Results: The system achieves 92.71% sensitivity, 88.58% specificity, and 90.69% Area Under Receiver Operating Characteristic (ROC) curve (AUC), outperforming state-of-the-art methods. Conclusion: Our research outcome paves the way to create a device for cough monitoring in real-life situations. Significance: Our proposal is aligned with a more comfortable and less disruptive patient monitoring, with benefits for patients (allows self-monitoring of cough symptoms), practitioners (e.g., assessment of treatments or better clinical understanding of cough patterns), and national health systems (by reducing hospitalizations)., Comment: 12 pages, 11 figures, 5 tables

Ultrafast X-ray spectroscopy has been revolutionized in recent years due to the advent of fourth-generation X-ray facilities. In solid-state materials, core excitons determine the energy and line shape of absorption features in core-level spectroscopies such as X-ray absorption spectroscopy. The screening of core excitons is an inherent many-body process that can reveal insight into charge-transfer excitations and electronic correlations. Under non-equilibrium conditions such as after photoexcitation, however, core-exciton screening is still not fully understood. Here we demonstrate the dynamic Coulomb screening of core excitons induced by photoexcited carriers by employing X-ray transient absorption (XTA) spectroscopy with picosecond time resolution. Our interpretation is supported by state-of-the-art ab initio theory, combining constrained and real-time time-dependent density functional theory with many-body perturbation theory. Using ZnO as an archetypal wide band-gap semiconductor, we show that the Coulomb screening by photoexcited carriers at the Zn K-edge leads to a decrease in the core-exciton binding energy, which depends nonlinearly on both the excitation density and the distribution of photoexcited carriers in reciprocal space. The effect of Coulomb screening dominates over Pauli blocking in the XTA spectra. We show that dynamic core-exciton screening is also observed at other X-ray absorption edges and theoretically predict the effect of core-exciton screening on the femtosecond time scale for the case of ZnO, a major step towards hard X-ray excitonics. The results have implications for the interpretation of ultrafast X-ray spectra in general and their use in tracking charge carrier dynamics in complex materials on atomic length scales., Comment: 43 pages, 37 figures

This report presents a comprehensive response to the United Nation's Interim Report on Governing Artificial Intelligence (AI) for Humanity. It emphasizes the transformative potential of AI in achieving the Sustainable Development Goals (SDGs) while acknowledging the need for robust governance to mitigate associated risks. The response highlights opportunities for promoting equitable, secure, and inclusive AI ecosystems, which should be supported by investments in infrastructure and multi-stakeholder collaborations across jurisdictions. It also underscores challenges, including societal inequalities exacerbated by AI, ethical concerns, and environmental impacts. Recommendations advocate for legally binding norms, transparency, and multi-layered data governance models, alongside fostering AI literacy and capacity-building initiatives. Internationally, the report calls for harmonising AI governance frameworks with established laws, human rights standards, and regulatory approaches. The report concludes with actionable principles for fostering responsible AI governance through collaboration among governments, industry, academia, and civil society, ensuring the development of AI aligns with universal human values and the public good., Comment: Submitted to United Nations. 23 pages. All the Authors Contributed Equally

Single-molecule localization microscopy generates point clouds corresponding to fluorophore localizations. Spatial cluster identification and analysis of these point clouds are crucial for extracting insights about molecular organization. However, this task becomes challenging in the presence of localization noise, high point density, or complex biological structures. Here, we introduce MIRO (Multimodal Integration through Relational Optimization), an algorithm that uses recurrent graph neural networks to transform the point clouds in order to improve clustering efficiency when applying conventional clustering techniques. We show that MIRO supports simultaneous processing of clusters of different shapes and at multiple scales, demonstrating improved performance across varied datasets. Our comprehensive evaluation demonstrates MIRO's transformative potential for single-molecule localization applications, showcasing its capability to revolutionize cluster analysis and provide accurate, reliable details of molecular architecture. In addition, MIRO's robust clustering capabilities hold promise for applications in various fields such as neuroscience, for the analysis of neural connectivity patterns, and environmental science, for studying spatial distributions of ecological data.

We present a method for solving loop integrals in dimensional regularization that is particularly useful in the context of inflation. We apply this method to the calculation of the tensor power spectrum induced by scalar fluctuations in slow-roll inflation.

Radial Moore graphs are approximations of Moore graphs that preserve the distance-preserving spanning tree for its central vertices. One way to classify their resemblance with a Moore graph is the status measure. The status of a graph is defined as the sum of the distances of all pairs of ordered vertices and equals twice the Wiener index. In this paper we study upper bounds for both the maximum number of central vertices and the status of radial Moore graphs. Finally, we present a family of radial Moore graphs of diameter $3$ that is conjectured to have maximum status.

Cellular networks rely on handovers (HOs) as a fundamental element to enable seamless connectivity for mobile users. A comprehensive analysis of HOs can be achieved through data from Mobile Network Operators (MNOs); however, the vast majority of studies employ data from measurement campaigns within confined areas and with limited end-user devices, thereby providing only a partial view of HOs. This paper presents the first countrywide analysis of HO performance, from the perspective of a top-tier MNO in a European country. We collect traffic from approximately 40M users for 4 weeks and study the impact of the radio access technologies (RATs), device types, and manufacturers on HOs across the country. We characterize the geo-temporal dynamics of horizontal (intra-RAT) and vertical (inter-RATs) HOs, at the district level and at millisecond granularity, and leverage open datasets from the country's official census office to associate our findings with the population. We further delve into the frequency, duration, and causes of HO failures, and model them using statistical tools. Our study offers unique insights into mobility management, highlighting the heterogeneity of the network and devices, and their effect on HOs.

The production of silicon monoxide (SiO) can be considered as a fingerprint of shock interaction. In this work, we use high-sensitivity observations of the SiO (2-1) and H$^{13}$CO$^{+}$ (1-0) emission to investigate the broad and narrow SiO emission toward 146 massive star-forming regions in the ATOMS survey. We detected SiO emission in 136 regions and distinguished broad and narrow components across the extension of 118 sources (including 58 UC $H_{II}$ regions) with an average angular resolution of 2.5$^{\prime}$$^{\prime}$. The derived SiO luminosity ($L_{SiO}$) across the whole sample shows that the majority of $L_{SiO}$ (above 66$\%$) can be attributed to broad SiO, indicating its association with strong outflows. The comparison of the ALMA SiO images with the filamentary skeletons identified from H$^{13}$CO$^{+}$ and in the infrared data (at 4.5, 8, and 24 $mu$m), further confirms that most SiO emission originates from outflows. However, note that for nine sources in our sample, the observed SiO emission may be generated by expanding UC $H_{II}$ regions. There is a moderate positive correlation between the bolometric luminosity ($L_{bol}$) and $L_{SiO}$ for both components (narrow and broad). The UC $H_{II}$ sources show a weaker positive correlation between $L_{bol}$ and $L_{SiO}$ and higher $L_{SiO}$ compared to the sources without UC $H_{II}$ regions. These results imply that the SiO emission from UC $H_{II}$ sources might be affected by UV-photochemistry induced by UC $H_{II}$ regions., Comment: 23 pages, 14 figures

Astronomers have found more than a dozen planets transiting 10-40 million year old stars, but even younger transiting planets have remained elusive. A possible reason for the lack of such discoveries is that newly formed planets are not yet in a configuration that would be recognized as a transiting planet or cannot exhibit transits because our view is blocked by a protoplanetary disk. However, we now know that many outer disks are warped; provided the inner disk is depleted, transiting planets may thus be visible. Here we report the observations of the transiting planet IRAS 04125+2902 b orbiting a 3 Myr, 0.7 M$_\odot$, pre-main sequence star in the Taurus Molecular Cloud. IRAS 04125+2902 hosts a nearly face-on (i $\sim$ 30$^\circ$) transitional disk and a wide binary companion. The planet has a period of 8.83 days, a radius of 10.9 R$_\oplus$ (0.97R$_J$), and a 95%-confidence upper limit on its mass of 90M$_\oplus$ (0.3M$_J$) from radial velocity measurements, making it a possible precursor of the super-Earths and sub-Neptunes that are commonly found around main-sequence stars. The rotational broadening of the star and the orbit of the wide (4", 635 AU) companion are both consistent with edge-on orientations. Thus, all components of the system appear to be aligned except the outer disk; the origin of this misalignment is unclear. Given the rare set of circumstances required to detect a transiting planet at ages when the disk is still present, IRAS 04125+2902 b likely provides a unique window into sub-Neptunes immediately following formation., Comment: Initial version submitted to Nature. Stellar, and hence planetary, parameters slightly differ from final version. Published version available at https://www.nature.com/articles/s41586-024-08123-3

The propagation of light that undergoes multiple-scattering by resonant atomic vapor can be described as a L\'evy flight. L\'evy flight is a random walk with heavy tailed step-size (r) distribution, decaying asymptotically as $P(r)\sim r^{-1-\alpha}$, with $\alpha<2$. The large steps, typical of L\'evy flights, have its origins in frequency redistribution of the light scattered by the vapor. We calculate the frequency redistribution function and the step-size distribution for light diffusion in atomic vapor. From the step-size distribution we extract a L\'evy parameter $\alpha$ that depends on the step's size. We investigate how the frequency redistribution function and step-size distribution are influenced by the finite size of the vapor and the many-level structure typical for alkali vapors. Finite size of the vapor introduces cutoff on the light scattered spectrum and thus in the size of steps. Multi-level structure introduces oscillations in $P(r)$ slope. Both effects might have an impact on measurables related to the L\'evy flight random walk., Comment: 37 pages, 12 figures

In this study, we present a comprehensive numerical analysis of blood flow within human left ventricle models, with particular emphasis on optimizing simulation conditions to enhance the realism and computational efficiency of heart flow dynamics. The objective is to determine the most effective mesh configurations, flow conditions, and boundary settings necessary for accurately capturing the formation and behavior of the vortex ring, a pivotal element in ventricular flow dynamics. Utilizing a computational fluid mechanics approach, we review the influence of both idealized and patient specific geometries on simulation outcomes. It is imperative to consider the necessity of dynamic wall motion and the precise calibration of inlet and outlet boundary conditions, which must be designed to mimic physiological conditions as accurately as possible. These factors are of paramount importance in achieving a balance between computational resource demands and the fidelity of the simulations, thereby providing valuable insights for future cardiovascular modeling efforts., Comment: 13 pages, 7 figures, 3 table

In the realm of cardiovascular medicine, medical imaging plays a crucial role in accurately classifying cardiac diseases and making precise diagnoses. However, the field faces significant challenges when integrating data science techniques, as a significant volume of images is required for these techniques. As a consequence, it is necessary to investigate different avenues to overcome this challenge. In this contribution, we offer an innovative tool to conquer this limitation. In particular, we delve into the application of a well recognized method known as the EigenFaces approach to classify cardiac diseases. This approach was originally motivated for efficiently representing pictures of faces using principal component analysis, which provides a set of eigenvectors (aka eigenfaces), explaining the variation between face images. As this approach proven to be efficient for face recognition, it motivated us to explore its efficiency on more complicated data bases. In particular, we integrate this approach, with convolutional neural networks (CNNs) to classify echocardiography images taken from mice in five distinct cardiac conditions (healthy, diabetic cardiomyopathy, myocardial infarction, obesity and TAC hypertension). Performing a preprocessing step inspired from the eigenfaces approach on the echocardiography datasets, yields sets of pod modes, which we will call eigenhearts. To demonstrate the proposed approach, we compare two testcases: (i) supplying the CNN with the original images directly, (ii) supplying the CNN with images projected into the obtained pod modes. The results show a substantial and noteworthy enhancement when employing SVD for pre-processing, with classification accuracy increasing by approximately 50%., Comment: 16 pages, 9 figures, 3 tables

In this work, a data-driven, modal decomposition method, the higher order dynamic mode decomposition (HODMD), is combined with a convolutional neural network (CNN) in order to improve the classification accuracy of several cardiac diseases using echocardiography images. The HODMD algorithm is used first as feature extraction technique for the echocardiography datasets, taken from both healthy mice and mice afflicted by different cardiac diseases (Diabetic Cardiomyopathy, Obesity, TAC Hypertrophy and Myocardial Infarction). A total number of 130 echocardiography datasets are used in this work. The dominant features related to each cardiac disease were identified and represented by the HODMD algorithm as a set of DMD modes, which then are used as the input to the CNN. In a way, the database dimension was augmented, hence HODMD has been used, for the first time to the authors knowledge, for data augmentation in the machine learning framework. Six sets of the original echocardiography databases were hold out to be used as unseen data to test the performance of the CNN. In order to demonstrate the efficiency of the HODMD technique, two testcases are studied: the CNN is first trained using the original echocardiography images only, and second training the CNN using a combination of the original images and the DMD modes. The classification performance of the designed trained CNN shows that combining the original images with the DMD modes improves the results in all the testcases, as it improves the accuracy by up to 22%. These results show the great potential of using the HODMD algorithm as a data augmentation technique., Comment: 12 pages, 6 figures, 2 tables

Spiking Neural Networks (SNNs) offer potential advantages in energy efficiency but currently trail Artificial Neural Networks (ANNs) in versatility, largely due to challenges in efficient input encoding. Recent work shows that direct coding achieves superior accuracy with fewer timesteps than traditional rate coding. However, there is a lack of specialized hardware to fully exploit the potential of direct-coded SNNs, especially their mix of dense and sparse layers. This work proposes the first hybrid inference architecture for direct-coded SNNs. The proposed hardware architecture comprises a dense core to efficiently process the input layer and sparse cores optimized for event-driven spiking convolutions. Furthermore, for the first time, we investigate and quantify the quantization effect on sparsity. Our experiments on two variations of the VGG9 network and implemented on a Xilinx Virtex UltraScale+ FPGA (Field-Programmable Gate Array) reveal two novel findings. Firstly, quantization increases the network sparsity by up to 15.2% with minimal loss of accuracy. Combined with the inherent low power benefits, this leads to a 3.4x improvement in energy compared to the full-precision version. Secondly, direct coding outperforms rate coding, achieving a 10% improvement in accuracy and consuming 26.4x less energy per image. Overall, our accelerator achieves 51x higher throughput and consumes half the power compared to previous work. Our accelerator code is available at: https://github.com/githubofaliyev/SNN-DSE/tree/DATE25

We present tonalli, a spectroscopic analysis python code that efficiently predicts effective temperature, stellar surface gravity, metallicity, $\alpha$-element abundance, and rotational and radial velocities for stars with effective temperatures between 3200 and 6250 K, observed with the Apache Point Observatory Galactic Evolution Experiment 2 (APOGEE-2). tonalli implements an asexual genetic algorithm to optimise the finding of the best comparison between a target spectrum and the continuum-normalised synthetic spectra library from the Model Atmospheres with a Radiative and Convective Scheme (MARCS), which is interpolated in each generation. Using simulated observed spectra and the APOGEE-2 solar spectrum of Vesta, we study the performance, limitations, accuracy and precision of our tool. Finally, a Monte Carlo realisation was implemented to estimate the uncertainties of each derived stellar parameter. The ad hoc continuum-normalised library is publicly available on Zenodo (DOI 10.5281/zenodo.12736546)., Comment: 35 pages, 22 figures. Accepted to RASTI. Supplemental continuum-normalised library available at: 10.5281/zenodo.12736546

We examine boundary regularity for a fully nonlinear free transmission problem. We argue using approximation methods, comparing the operators driving the problem with a limiting profile. Working natural conditions on the data of the problem, we produce regularity estimates in Sobolev and $C^{1,{\rm Log-Lip}}$-spaces. Our findings extend recent developments in the literature to the free boundary setting.

Supporting multiple partial computations efficiently at each of the workers is a keystone in distributed coded computing in order to speed up computations and to fully exploit the resources of heterogeneous workers in terms of communication, storage, or computation capabilities. Multivariate polynomial coding schemes have recently been shown to deliver faster results for distributed matrix-matrix multiplication compared to conventional univariate polynomial coding schemes by supporting multiple partial coded computations at each worker at reduced communication costs. In this work, we extend multivariate coding schemes to also support arbitrary matrix partitions. Generalized matrix partitions have been proved useful to trade-off between computation speed and communication costs in distributed (univariate) coded computing. We first formulate the computation latency-communication trade-off in terms of the computation complexity and communication overheads required by coded computing approaches as compared to a single server uncoded computing system. Then, we propose two novel multivariate coded computing schemes supporting arbitrary matrix partitions. The proposed schemes are shown to improve the studied trade-off as compared to univariate schemes., Comment: 5 pages, 2 figures, presented at ITW'24

Recent advances in semiconductor spin qubits have achieved linear arrays exceeding ten qubits. Moving to two-dimensional (2D) qubit arrays is a critical next step to advance towards fault-tolerant implementations, but it poses substantial fabrication challenges, particularly because enabling control of nearest-neighbor entanglement requires the incorporation of interstitial exchange gates between quantum dots in the qubit architecture. In this work, we present a 2D array of silicon metal-oxide-semiconductor (MOS) quantum dots with tunable interdot coupling between all adjacent dots. The device is characterized at 4.2 K, where we demonstrate the formation and isolation of double-dot and triple-dot configurations. We show control of all nearest-neighbor tunnel couplings spanning up to 30 decades per volt through the interstitial exchange gates and use advanced modeling tools to estimate the exchange interactions that could be realized among qubits in this architecture. These results represent a significant step towards the development of 2D MOS quantum processors compatible with foundry manufacturing techniques., Comment: 9 pages, 5 figures

The field of visual and physiological optics is undergoing continuous significant advancements, driven by a deeper understanding of the human visual system and the development of cutting-edge optical technologies. This Roadmap, authored by leading experts, delves into critical areas such as corneal biomechanical properties, keratoconus, and advancements in corneal imaging and elastography. It explores the intricate structure-function relationship within the eye lens, offering new perspectives through lens models and ray tracing techniques. The document also covers advancements in retinal imaging, highlighting the current state and future directions, and the role of adaptive optics in evaluating retinal structure and function in both healthy and diseased eyes. Furthermore, it addresses the modelling of ocular surfaces using different mathematical functions and examines the factors affecting peripheral image quality in the human eye, emphasizing the importance of these aspects in visual performance. Additional topics include schematic and functional models of the human eye, the impact of optical and chromatic aberrations, and the design of contact, and intraocular lenses. Finally, the Roadmap addresses the intersection of neurosciences with vision health, presenting a comprehensive overview of current research and future trends aimed at improving visual health and optical performance. Ultimately, this Roadmap aims to serve as a valuable resource for ophthalmologists, optometrists, vision scientists, and engineers dedicated to advancing the field of visual and physiological optics., Comment: This is the pre-peer-review and pre-editing version of the article, as submitted by the author to Journal of Optics

Customer demand, regulatory pressure, and engineering efficiency are the driving forces behind the industry-wide trend of moving from siloed engines and services that are optimized in isolation to highly integrated solutions. This is confirmed by the wide adoption of open formats, shared component libraries, and the meteoric success of integrated data lake experiences such as Microsoft Fabric. In this paper, we study the implications of this trend to Query Optimizer (QO) and discuss our experience of building Calcite and extending Cascades into QO components of Microsoft SQL Server, Fabric Data Warehouse (DW), and SCOPE. We weigh the pros and cons of a drastic change in direction: moving from bespoke QOs or library-sharing (\`a la Calcite) to rewriting the QO stack and fully embracing Query Optimizer as a Service (QOaaS). We report on some early successes and stumbles as we explore these ideas with prototypes compatible with Fabric DW and Spark. The benefits include centralized workload-level optimizations, multi-engine federation, and accelerated feature creation, but the challenges are equally daunting. We plan to engage CIDR audience in a debate on this exciting topic.

The number $n_s$ of clusters (per site) of size $s$, a central quantity in percolation theory, displays at criticality an algebraic scaling behavior of the form $n_s\simeq s^{-\tau}\, A\, (1+B s^{-\Omega})$. For the Fortuin--Kasteleyn representation of the $Q$-state Potts model in two dimensions, the Fisher exponent $\tau$ is known as a function of the real parameter $0\le Q\le4$, and, for bond percolation (the $Q\rightarrow 1$ limit), the correction-to-scaling exponent is derived as $\Omega=72/91$. We theoretically derive the exact formula for the correction-to-scaling exponent $\Omega=8/[(2g+1)(2g+3)]$ as a function of the Coulomb-gas coupling strength $g$, which is related to $Q$ by $Q=2+2\cos(2 \pi g)$. Using an efficient Monte Carlo cluster algorithm, we study the O($n$) loop model on the hexagonal lattice, which is in the same universality class as the $Q=n^2$ Potts model, and has significantly suppressed finite-size corrections and critical slowing-down. The predictions of the above formula include the exact value for percolation as a special case, and agree well with the numerical estimates of $\Omega$ for both the critical and tricritical branches of the Potts model., Comment: The document contains the paper (pdflatex, 14 pages), and 6 pdf figures

Building pluralistic AI requires designing models that are able to be shaped to represent a wide range of value systems and cultures. Achieving this requires first being able to evaluate the degree to which a given model is capable of reflecting various personas. To this end, we propose a benchmark for evaluating the steerability of model personas as a function of prompting. Our design is based on a formal definition of prompt steerability, which analyzes the degree to which a model's joint behavioral distribution can be shifted from its baseline behavior. By defining steerability indices and inspecting how these indices change as a function of steering effort, we can estimate the steerability of a model across various persona dimensions and directions. Our benchmark reveals that the steerability of many current models is limited -- due to both a skew in their baseline behavior and an asymmetry in their steerability across many persona dimensions. We release an implementation of our benchmark at https://github.com/IBM/prompt-steering.

Using PREM as a reference model for the Earth density distribution we investigate the sensitivity of the Hyper-Kamiokande (HK) detector to deviations of the Earth i) core average density $\bar{\rho}_C$, ii) lower mantle average density $\bar{\rho}_{lman}$) and iii) upper mantle average density $\bar{\rho}_{uman}$, from their respective PREM densities. The analysis is performed by studying the effects of the Earth matter on the oscillations of atmospheric $\nu_{\mu}$, $\nu_e$, $\bar{\nu}_\mu$ and $\bar{\nu}_e$. We implement the constraints on the variations of $\rho_C$, $\rho_{lman}$ and $\rho_{uman}$ following from the precise knowledge of the Earth mass $M_\oplus$ and moment of inertia $I_\oplus$, as well as from the requirement that the Earth be in hydrostatic equilibrium (EHE). These constraints limit in the case of the three layer Earth density structure we are considering the maximal positive deviation of $\bar{\rho}_C$ from its PREM value to $10\%$. Considering the case of normal ordering (NO) of neutrino masses, we present results which illustrate the dependence of sensitivity to the core, lower and upper mantle average densities on the energy and zenith angle resolutions, on whether or not the prospective systematic errors are accounted for and on the value of $\theta_{23}$. We show, in particular, that in the ''nominal'' case of neutrino energy resolution $E_{res} = 30\%$ and zenith angle resolution $\theta_{zres} = 20^\circ$ and for, e.g., $\sin^2\theta_{23}=0.45~(0.58)$, HK can determine the average core density $\bar{\rho}_C$ at $2\sigma$ C.L. after 6500 days of operation with an uncertainty of (-14.5\%)/+39.5\% ((-9.3\%/+31.7\%). In the ''more favorable'' case of $E_{res}= 20\%$ and $\theta_{zres} = 10^\circ$, and if $\sin^2\theta_{23}=0.58~(0.45)$, the core density would be determined at $2\sigma$ C.L. with an uncertainty of (-8.3\%)/+9.8\% ((-9.2\%)/+11.3\%)., Comment: arXiv admin note: text overlap with arXiv:2111.13048