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According to the well established hierarchical framework for galaxy evolution, galaxies grow through mergers with other galaxies and the LambdaCDM cosmological model predicts that the stellar halos of galaxies are rich in remnants from minor mergers. The Stellar Streams Legacy Survey has provided a first release of a catalogue with a statistically significant sample of stellar streams in the Local Universe that can be used to study minor mergers and test the cosmological models. The main objective is to compare the results of the observations of stellar tidal streams with the predictions of state-of-the-art cosmological simulations regarding the formation of stellar streams up to a redshift z < 0.02, according to the LambdaCDM model. We use the predictions of the cosmological simulations Copernicus Complexio, TNG50 of the IllustrisTNG project and Auriga to generate 225 mock-images of nearby halos at a distance of 70 Mpc, and search for stellar streams. We compare the obtained stream frequency and characteristics with those obtained from the Stellar Streams Legacy Survey. We find good agreement between the results of analysing real images from the Dark Energy Survey and mock-images from cosmological simulations. We obtained predictions for the detection rate of stellar streams to a surface brightness limit of 35 mag arcsec^-2. The cosmological simulations predict that for a surface brightness limit of 32 mag arcsec^-2 a frequency of almost 70% in the detection of streams around galaxies can be achieved., Comment: 18 pages, 17 figures

Temporal cavity solitons, or dissipative Kerr solitons (DKS) in integrated microresonators, are essential for deployable metrology technologies. Such applications favor the lowest noise state, typically the single-DKS state where one soliton is in the resonator. Other multi-DKS states can also be reached, offering better conversion efficiency and thermal stability, potentially simplifying DKS-based technologies. Yet they exhibit more noise due to relative soliton jitter, and are usually not compatible with targeted applications. We demonstrate that Kerr-induced synchronization, an all-optical trapping technique, can azimuthally pin the multi-DKS state to a common reference field. This method ensures repetition rate noise independent of the number of solitons, making a multi-DKS state indistinguishable from a single-DKS state in that regard, akin to trapped-soliton molecule behavior. Supported by theoretical analysis and experimental demonstration in an integrated microresonator, this approach provides metrological capacity regardless of the number of cavity solitons, benefiting numerous DKS-based metrology applications.

Over the past decade and more, S-matrix-based calculational methods have experienced a resurgence, proving to be both an elegant and powerful tool for extracting physical quantities without the need for an underlying Lagrangian formulation. In this work, we critically review and further develop the formalism introduced by Dashen, Ma, and Bernstein, which connects the thermodynamics of relativistic systems to the information contained in their scattering amplitudes. As a demonstration, we revisit the computation of the QCD equation of state to leading order in the strong coupling, showcasing the advantages of this method over traditional Thermal Field Theory techniques. Additionally, we apply these tools to the effective theory of a long confining Flux Tube in D dimensions, analyzing thermal effects up to and including NNLO contributions. Our results are compared with those obtained using the Thermodynamic Bethe Ansatz method. We also discuss how these techniques enable the inclusion of non-universal effects in the study of Flux Tubes, while relying solely on the S-matrix as input., Comment: 27 pages + appendices

Cryo-electron microscopy (cryo-EM) is a powerful technique for determining high-resolution 3D biomolecular structures from imaging data. As this technique can capture dynamic biomolecular complexes, 3D reconstruction methods are increasingly being developed to resolve this intrinsic structural heterogeneity. However, the absence of standardized benchmarks with ground truth structures and validation metrics limits the advancement of the field. Here, we propose CryoBench, a suite of datasets, metrics, and performance benchmarks for heterogeneous reconstruction in cryo-EM. We propose five datasets representing different sources of heterogeneity and degrees of difficulty. These include conformational heterogeneity generated from simple motions and random configurations of antibody complexes and from tens of thousands of structures sampled from a molecular dynamics simulation. We also design datasets containing compositional heterogeneity from mixtures of ribosome assembly states and 100 common complexes present in cells. We then perform a comprehensive analysis of state-of-the-art heterogeneous reconstruction tools including neural and non-neural methods and their sensitivity to noise, and propose new metrics for quantitative comparison of methods. We hope that this benchmark will be a foundational resource for analyzing existing methods and new algorithmic development in both the cryo-EM and machine learning communities.

Stellar tidal streams are a key tracer of galaxy evolution and have the potential to provide an indirect means for tracing dark matter. For the Local Group, many diffuse substructures have been identified and their link to galaxy evolution has been traced. However, an analysis of a larger sample is required to better probe the frequency and characteristics of these streams to verify the predictions of the Lambda-CDM model and its implementation in cosmological simulations. For that purpose, we are carrying out the first systematic survey of faint stellar debris from tidally disrupted dwarf satellites around nearby galaxies up to a distance of 100 Mpc. In this paper, we present a catalogue with the results of the first harvest of stellar tidal streams found by visual inspection in deep images of ~ 700 galaxies from the Dark Energy Survey (DES). We include a photometric characterisation of the streams obtained by measuring their surface brightnesses and colours. We found a total of 63 streams in our sample at distances between 40 and 100 Mpc, including 59 which were not previously reported. We measured their average surface brightness for the grz bands, to be 28.35+/-0.20, 27.81+/-0.13 and 27.62+/-0.09 mag arcsec^-2, respectively. By applying a statistical analysis to our findings, we obtained a stream detection frequency of 9.1% +/- 1.1% , in agreement with previous studies. We identified stream progenitors in 5-14% of our stream sample, depending on the confidence level. The first catalogue of streams in the Local Universe presented here will be complemented by future stream surveys within the Stellar Stream Legacy Survey. In this work we have learnt that the faintest measured stream surface brightness can be significantly brighter than the surface brightness limit of an image measured at pixel level, mainly due to correlated noise present in the images., Comment: 20 pages with 16 figures, plus Appendices: 27 pages in total

Generative Artificial Intelligence has grown exponentially as a result of Large Language Models (LLMs). This has been possible because of the impressive performance of deep learning methods created within the field of Natural Language Processing (NLP) and its subfield Natural Language Generation (NLG), which is the focus of this paper. Within the growing LLM family are the popular GPT-4, Bard and more specifically, tools such as ChatGPT have become a benchmark for other LLMs when solving most of the tasks involved in NLG research. This scenario poses new questions about the next steps for NLG and how the field can adapt and evolve to deal with new challenges in the era of LLMs. To address this, the present paper conducts a review of a representative sample of surveys recently published in NLG. By doing so, we aim to provide the scientific community with a research roadmap to identify which NLG aspects are still not suitably addressed by LLMs, as well as suggest future lines of research that should be addressed going forward.

Crop yield forecasting plays a significant role in addressing growing concerns about food security and guiding decision-making for policymakers and farmers. When deep learning is employed, understanding the learning and decision-making processes of the models, as well as their interaction with the input data, is crucial for establishing trust in the models and gaining insight into their reliability. In this study, we focus on the task of crop yield prediction, specifically for soybean, wheat, and rapeseed crops in Argentina, Uruguay, and Germany. Our goal is to develop and explain predictive models for these crops, using a large dataset of satellite images, additional data modalities, and crop yield maps. We employ a long short-term memory network and investigate the impact of using different temporal samplings of the satellite data and the benefit of adding more relevant modalities. For model explainability, we utilize feature attribution methods to quantify input feature contributions, identify critical growth stages, analyze yield variability at the field level, and explain less accurate predictions. The modeling results show an improvement when adding more modalities or using all available instances of satellite data. The explainability results reveal distinct feature importance patterns for each crop and region. We further found that the most influential growth stages on the prediction are dependent on the temporal sampling of the input data. We demonstrated how these critical growth stages, which hold significant agronomic value, closely align with the existing literature in agronomy and crop development biology.

Communication network engineering in enterprise environments is traditionally a complex, time-consuming, and error-prone manual process. Most research on network engineering automation has concentrated on configuration synthesis, often overlooking changes in the physical network topology. This paper introduces GeNet, a multimodal co-pilot for enterprise network engineers. GeNet is a novel framework that leverages a large language model (LLM) to streamline network design workflows. It uses visual and textual modalities to interpret and update network topologies and device configurations based on user intents. GeNet was evaluated on enterprise network scenarios adapted from Cisco certification exercises. Our results demonstrate GeNet's ability to interpret network topology images accurately, potentially reducing network engineers' efforts and accelerating network design processes in enterprise environments. Furthermore, we show the importance of precise topology understanding when handling intents that require modifications to the network's topology.

The goal of this paper is to establish a new and efficient characterization of quasi-homogeneous isolated singularities of free curves and nearly free curves $C$ in $\mathbb{P}^2$. The criterion will be in terms of the first syzygy matrix associated with the Jacobian ideal of $f$ where $f=0$ is the equation of the plane curve $C$., Comment: 20 pages, 4 figures

Sample Return Capsules (SRCs) entering Earth's atmosphere at hypervelocity from interplanetary space are a valuable resource for studying meteor phenomena. The 24 September 2023 arrival of the OSIRIS-REx (Origins, Spectral Interpretation, Resource Identification, and Security-Regolith Explorer) SRC provided an unprecedented chance for geophysical observations of a well-characterized source with known parameters, including timing and trajectory. A collaborative effort involving researchers from 16 institutions executed a carefully planned geophysical observational campaign at strategically chosen locations, deploying over 400 ground-based sensors encompassing infrasound, seismic, distributed acoustic sensing (DAS), and GPS technologies. Additionally, balloons equipped with infrasound sensors were launched to capture signals at higher altitudes. This campaign (the largest of its kind so far) yielded a wealth of invaluable data anticipated to fuel scientific inquiry for years to come. The success of the observational campaign is evidenced by the near-universal detection of signals across instruments, both proximal and distal. This paper presents a comprehensive overview of the collective scientific effort, field deployment, and preliminary findings. The early findings have the potential to inform future space missions and terrestrial campaigns, contributing to our understanding of meteoroid interactions with planetary atmospheres. Furthermore, the dataset collected during this campaign will improve entry and propagation models as well as augment the study of atmospheric dynamics and shock phenomena generated by meteoroids and similar sources., Comment: 87 pages, 14 figures

For artinian Gorenstein algebras in codimension four and higher, it is well known that the Weak Lefschetz Property (WLP) does not need to hold. For Gorenstein algebras in codimension three, it is still open whether all artinian Gorenstein algebras satisfy the WLP when the socle degree and the Sperner number are both higher than six. We here show that all artinian Gorenstein algebras with socle degree $d$ and Sperner number at most $d+1$ satisfy the WLP, independent of the codimension. This is a sharp bound in general since there are examples of artinian Gorenstein algebras with socle degree $d$ and Sperner number $d+2$ that do not satisfy the WLP for all $d\ge 3$.

Jupiter's Grat Red Spot (GRS) is the largest and longest-lived vortex of all solar system planets but its lifetime is debated and its formation mechanism remains hidden. G. D. Cassini discovered in 1665 the presence of a dark oval at the GRS latitude, known as the "Permanent Spot" (PS) that was observed until 1713. We show from historical observations of its size evolution and motions that PS is unlikely to correspond to the current GRS, that was first observed in 1831. New numerical simulations rule out that the GRS formed by the merging of vortices or by a superstorm, but most likely formed from a flow disturbance between the two opposed Jovian zonal jets north and south of it. If so, the aearly GRS should have had a low tangential velocity so that its rotation velocity has increased over time as it shrunk.

Current clinical decision support systems (DSS) are trained and validated on observational data from the target clinic. This is problematic for treatments validated in a randomized clinical trial (RCT), but not yet introduced in any clinic. In this work, we report on a method for training and validating the DSS using the RCT data. The key challenges we address are of missingness -- missing rationale for treatment assignment (the assignment is at random), and missing verification evidence, since the effectiveness of a treatment for a patient can only be verified (ground truth) for treatments what were actually assigned to a patient. We use data from a multi-armed RCT that investigated the effectiveness of single- and combination- treatments for 240+ tinnitus patients recruited and treated in 5 clinical centers. To deal with the 'missing rationale' challenge, we re-model the target variable (outcome) in order to suppress the effect of the randomly-assigned treatment, and control on the effect of treatment in general. Our methods are also robust to missing values in features and with a small number of patients per RCT arm. We deal with 'missing verification evidence' by using counterfactual treatment verification, which compares the effectiveness of the DSS recommendations to the effectiveness of the RCT assignments when they are aligned v/s not aligned. We demonstrate that our approach leverages the RCT data for learning and verification, by showing that the DSS suggests treatments that improve the outcome. The results are limited through the small number of patients per treatment; while our ensemble is designed to mitigate this effect, the predictive performance of the methods is affected by the smallness of the data. We provide a basis for the establishment of decision supporting routines on treatments that have been tested in RCTs but have not yet been deployed clinically.

Designing active-flow-control (AFC) strategies for three-dimensional (3D) bluff bodies is a challenging task with critical industrial implications. In this study we explore the potential of discovering novel control strategies for drag reduction using deep reinforcement learning. We introduce a high-dimensional AFC setup on a 3D cylinder, considering Reynolds numbers ($Re_D$) from $100$ to $400$, which is a range including the transition to 3D wake instabilities. The setup involves multiple zero-net-mass-flux jets positioned on the top and bottom surfaces, aligned into two slots. The method relies on coupling the computational-fluid-dynamics solver with a multi-agent reinforcement-learning (MARL) framework based on the proximal-policy-optimization algorithm. MARL offers several advantages: it exploits local invariance, adaptable control across geometries, facilitates transfer learning and cross-application of agents, and results in a significant training speedup. For instance, our results demonstrate $21\%$ drag reduction for $Re_D=300$, outperforming classical periodic control, which yields up to $6\%$ reduction. To the authors' knowledge, the present MARL-based framework represents the first time where training is conducted in 3D cylinders. This breakthrough paves the way for conducting AFC on progressively more complex turbulent-flow configurations., Comment: Under review in Nature Engineering Communications

This study presents novel active-flow-control (AFC) strategies aimed at achieving drag reduction for a three-dimensional cylinder immersed in a flow at a Reynolds number based on freestream velocity and cylinder diameter of (Re_D=3900). The cylinder in this subcritical flow regime has been extensively studied in the literature and is considered a classic case of turbulent flow arising from a bluff body. The strategies presented are explored through the use of deep reinforcement learning. The cylinder is equipped with 10 independent zero-net-mass-flux jet pairs, distributed on the top and bottom surfaces, which define the AFC setup. The method is based on the coupling between a computational-fluid-dynamics solver and a multi-agent reinforcement-learning (MARL) framework using the proximal-policy-optimization algorithm. Thanks to the acceleration in training facilitated by exploiting the local invariants with MARL, a drag reduction of (8\%) was achieved, with a mass cost efficiency two orders of magnitude lower than those of the existing classical controls in the literature. This development represents a significant advancement in active flow control, particularly in turbulent regimes critical to industrial applications., Comment: Under review in "Special Issue": Progress in Engineering Turbulence Modelling, Simulation and Measurements

This paper describes the numerical implementation in a high-performance computing environment of an open-source library for model order reduction in fluid dynamics. This library, called pyLOM, contains the algorithms of proper orthogonal decomposition (POD), dynamic mode decomposition (DMD) and spectral proper orthogonal decomposition (SPOD), as well as, efficient SVD and matrix-matrix multiplication, all of them tailored for supercomputers. The library is profiled in detail under the MareNostrum IV supercomputer. The bottleneck is found to be in the QR factorization, which has been solved by an efficient binary tree communications pattern. Strong and weak scalability benchmarks reveal that the serial part (i.e., the part of the code that cannot be parallelized) of these algorithms is under 10% for the strong scaling and under 0.7% for the weak scaling. Using pyLOM, a POD of a dataset containing 1.14 x 108 gridpoints and 1808 snapshots that takes 6.3Tb of memory can be computed in 81.08 seconds using 10368 CPUs. Additioally, the algorithms are validated using the datasets of a flow around a circular cylinder at ReD = 100 and ReD = 1 x 104, as well as the flow in the Stanford diffuser at Reh = 1 x 104.

In this paper, we determine the maximum $h_{max}$ and the minimum $h_{min}$ of the Hilbert vectors of Perazzo algebras $A_F$, where $F$ is a Perazzo polynomial of degree $d$ in $n+m+1$ variables. These algebras always fail the Strong Lefschetz Property. We determine the integers $n,m,d$ such that $h_{max}$ (resp. $h_{min}$) is unimodal, and we prove that $A_F$ always fails the Weak Lefschetz Property if its Hilbert vector is maximum, while it satisfies the Weak Lefschetz Property if it is minimum, unimodal, and satisfies an additional mild condition. We determine the minimal free resolution of Perazzo algebras associated to Perazzo threefolds in $\mathbb P^4$ with minimum Hilbert vectors. Finally we pose some open problems in this context. Dedicated to Enrique Arrondo on the occasion of his $60^{th}$ birthday., Comment: 24 pages, to be published in Rendiconti del Circolo Matematico di Palermo Series 2

Euclid is poised to make significant advances in the study of nearby galaxies in the local Universe. Here we present a first look at 6 galaxies observed for the Nearby Galaxy Showcase as part of the Euclid Early Release Observations acquired between August and November, 2023. These targets, 3 dwarf galaxies (HolmbergII, IC10, NGC6822) and 3 spirals (IC342, NGC2403, NGC6744), range in distance from about 0.5 Mpc to 8.8 Mpc. Our assessment of the surface brightness depths in the stacked Euclid images confirms previous estimates in 100 arcsec^2 regions of 1sigma=30.5 mag/arcsec^2 for VIS, but slightly deeper than previous estimates for NISP with 1sigma=29.2-29.4 mag/arcsec^2. By combining Euclid HE, YE, and IE into RGB images, we illustrate the large field-of-view covered by a single Reference Observing Sequence, together with exquisite detail on parsec scales in these nearby galaxies. Radial surface brightness and color profiles demonstrate galaxy colors in agreement with stellar population synthesis models. Standard stellar photometry selection techniques find approximately 1.3 million stars across the 6 galaxy fields. Euclid's resolved stellar photometry allows us to constrain the star-formation histories of these galaxies, by disentangling the distributions of young stars, as well as asymptotic giant branch and red giant branch stellar populations. We finally examine 2 galaxies individually for surrounding satellite systems. Our analysis of the ensemble of dwarf satellites around NGC6744 reveals a new galaxy, EDwC1, a nucleated dwarf spheroidal at the end of a spiral arm. Our new census of the globular clusters around NGC2403 yields 9 new star-cluster candidates, 8 of which with colors indicative of evolved stellar populations. In summary, our investigation of the 6 Showcase galaxies demonstrates that Euclid is a powerful probe of the anatomy of nearby galaxies [abridged]., Comment: 36 pages; 20 figures in main text; 4 Appendices. Submitted to A&A, as part of the A&A special issue `Euclid on Sky', which contains Euclid key reference papers and first results from the Euclid Early Release Observations

The Euclid ERO showcase Euclid's capabilities in advance of its main mission, targeting 17 astronomical objects, from galaxy clusters, nearby galaxies, globular clusters, to star-forming regions. A total of 24 hours observing time was allocated in the early months of operation, engaging the scientific community through an early public data release. We describe the development of the ERO pipeline to create visually compelling images while simultaneously meeting the scientific demands within months of launch, leveraging a pragmatic, data-driven development strategy. The pipeline's key requirements are to preserve the image quality and to provide flux calibration and photometry for compact and extended sources. The pipeline's five pillars are: removal of instrumental signatures; astrometric calibration; photometric calibration; image stacking; and the production of science-ready catalogues for both the VIS and NISP instruments. We report a PSF with a full width at half maximum of 0.16" in the optical and 0.49" in the three NIR bands. Our VIS mean absolute flux calibration is accurate to about 1%, and 10% for NISP due to a limited calibration set; both instruments have considerable colour terms. The median depth is 25.3 and 23.2 AB mag with a SNR of 10 for galaxies, and 27.1 and 24.5 AB mag at an SNR of 5 for point sources for VIS and NISP, respectively. Euclid's ability to observe diffuse emission is exceptional due to its extended PSF nearly matching a pure diffraction halo, the best ever achieved by a wide-field, high-resolution imaging telescope. Euclid offers unparalleled capabilities for exploring the LSB Universe across all scales, also opening a new observational window in the NIR. Median surface-brightness levels of 29.9 and 28.3 AB mag per square arcsec are achieved for VIS and NISP, respectively, for detecting a 10 arcsec x 10 arcsec extended feature at the 1 sigma level., Comment: Submitted to A&A, 44 pages, 36 figures - Part of the A&A special issue `Euclid on Sky', which contains Euclid key reference papers and first results from the Euclid Early Release Observations

Phase-coherent pulsed driving of passive optical fiber resonators enable the generation of ultrashort dissipative Raman solitons with durations well below 100~fs. The existence and characteristics of such solitons critically depends on the desynchronisation between the pulsed driving source and the resonator roundtrip time, yet the full mechanism through which these dependencies arise remains unclear. Here, we numerically demonstrate that Raman solitons can exist even under conditions of continuous wave driving, and by numerically examining the existence and characteristics of Raman solitons under such conditions, we elucidate the role of desynchronisation in pulse-driven systems. In addition to providing new insights on the existence and characteristics of ultrashort Raman solitons, our analysis yields a qualitative explanation for the range of desynchronisations over which the solitons can exist.

The increasing reliance on Deep Learning models, combined with their inherent lack of transparency, has spurred the development of a novel field of study known as eXplainable AI (XAI) methods. These methods seek to enhance the trust of end-users in automated systems by providing insights into the rationale behind their decisions. This paper presents a novel approach for measuring user trust in XAI systems, allowing their refinement. Our proposed metric combines both performance metrics and trust indicators from an objective perspective. To validate this novel methodology, we conducted a case study in a realistic medical scenario: the usage of XAI system for the detection of pneumonia from x-ray images.

Incorporating a monolayer of WS$_2$ via interface engineering enhances the overall physical properties of a FAPbI3 perovskite based heterostructure. FAPbI$_3$/WS$_2$/TiO$_2$/ITO and FAPbI$_3$/TiO$_2$/ITO heterostructures were analyzed by UV-Vis spectroscopy, X-ray diffraction, scanning electron microscopy and atomic force microscopy. The configuration with WS$_2$ interlayer presents higher absorption in the visible region with a bandgap of {\aprox} 1.44 eV. WS$_2$ also enhances the deposition process of FAPbI$_3$, resulting in the formation of pure photoactive $\alpha$-phase without the non-photoactive $\delta$-phase nor residual plumbates. The incorporation of the monolayer improves the crystalline structure of the FAPbI$_3$, promoting a preferential growth in the [100] direction. The smooth surface of WS$_2$ favors a homogeneous morphology and an increase of the grain size to ~4.5 $\mu$m, the largest reported for similar structures. Furthermore, the work function obtained lets us propose an enhance an adequate energy band alignment between FAPbI$_3$ and the n-type layers for the electron flux to the cathode. These findings strongly suggest that the interfacial coupling of FAPbI$_3$/WS$_2$ could be a promising candidate in photovoltaic applications., Comment: 13 pages, 4 figures

National Security Letters (NSLs) are similar to administrative subpoenas and can be issued directly by elements of the executive branch without requiring prior approval from a court or grand jury. Importantly, NSLs authorize the imposition of nondisclosure orders (aka "gag orders") on the receiving party. Controversy about potential abuses of this authority has driven a range of legal and policy discussions. To address these concerns, both the public sector and the private sector have sought to document the usage of NSLs in aggregated form. However, each data source is limited in scope, time, and kind. In this paper, we consolidate the available data around NSLs and answer two questions: (1) what can the public effectively learn from the reported data and does this information suffice to assess the NSL usage? (2) how accessible is this data collection? We show that longitudinal trends in the usage of NSLs can be observed. For instance, we find a significant increase in NSL requests for non-US persons and that the policy reforms to decrease the mandated nondisclosure period appear to be effective. The observed trends suggest that the current transparency mechanisms are viable safeguards against the excessive use of NSLs. However, aggregating and normalizing the data requires manual reviewing, parsing, and validating. We even find inconsistencies within and across official data sources. Overall, the laborious data collection process hinders external and internal auditing efforts and demonstrates the need for a unified and more usable dataset for NSLs., Comment: Accepted as short presentation at CSLAW 2024 (not in proceeding): https://computersciencelaw.org/2024/accepted-papers/

Mukai proved that the moduli space of simple sheaves on a smooth projective K3 surface is symplectic, and in \cite{FM2} we gave two constructions allowing one to construct new locally closed Lagrangian/isotropic subspaces of the moduli from old ones. In this paper, we extend both Mukai's result and our construction to reduced projective K3 surfaces; for the former we need to restrict our attention to perfect sheaves. There are two key points where we cannot get a straightforward generalization. In each, we need to prove that a certain differential form on the moduli space of simple, perfect sheaves vanishes, and we introduce a smoothability condition to complete the proof., Comment: Comments and remarks are welcome

We deal with Perazzo hypersurfaces $X=V(f)$ in $\PP^{n+2}$ defined by a homogeneous polynomial $f(x_0,x_1,\dots,x_n,u,v)=p_0(u,v)x_0+p_1(u,v)x_1+\cdots +p_n(u,v)x_n+g(u,v)$, where $p_0,p_1,\dots ,p_n$ are algebraically dependent but linearly independent forms of degree $d-1$ in $K[u,v]$ and $g$ is a form in $K[u,v]$ of degree $d$. Perazzo hypersurfaces have vanishing hessian and, hence, the associated graded artinian Gorenstein algebra $A_f$ fails the strong Lefschetz property. In this paper, we first determine the maximum and minimum Hilbert function of $A_f$, we prove that the Hilbert function of $A_f$ is always unimodal and we determine when $A_f$ satisfies the weak Lefschetz property. We illustrate our results with many examples and we show that our results do not generalize to Perazzo hypersurfaces $X=V(f)$ in $\PP^{n+3}$ defined by a homogeneous polynomial $f(x_0,x_1,\dots,x_{n},u,v,w)=p_0(u,v,w)x_0+p_1(u,v,w)x_1+\cdots +p_{n}(u,v,w)x_{n}+g(u,v,w)$, where $p_0,p_1,\dots ,p_{n}$ are algebraically dependent but linearly independent forms of degree $d-1$ in $K[u,v,w]$ and $g$ is a form in $K[u,v,w]$ of degree $d$., Comment: To be published in Journal of Algebra

Accurate crop yield prediction is of utmost importance for informed decision-making in agriculture, aiding farmers, and industry stakeholders. However, this task is complex and depends on multiple factors, such as environmental conditions, soil properties, and management practices. Combining heterogeneous data views poses a fusion challenge, like identifying the view-specific contribution to the predictive task. We present a novel multi-view learning approach to predict crop yield for different crops (soybean, wheat, rapeseed) and regions (Argentina, Uruguay, and Germany). Our multi-view input data includes multi-spectral optical images from Sentinel-2 satellites and weather data as dynamic features during the crop growing season, complemented by static features like soil properties and topographic information. To effectively fuse the data, we introduce a Multi-view Gated Fusion (MVGF) model, comprising dedicated view-encoders and a Gated Unit (GU) module. The view-encoders handle the heterogeneity of data sources with varying temporal resolutions by learning a view-specific representation. These representations are adaptively fused via a weighted sum. The fusion weights are computed for each sample by the GU using a concatenation of the view-representations. The MVGF model is trained at sub-field level with 10 m resolution pixels. Our evaluations show that the MVGF outperforms conventional models on the same task, achieving the best results by incorporating all the data sources, unlike the usual fusion results in the literature. For Argentina, the MVGF model achieves an R2 value of 0.68 at sub-field yield prediction, while at field level evaluation (comparing field averages), it reaches around 0.80 across different countries. The GU module learned different weights based on the country and crop-type, aligning with the variable significance of each data source to the prediction task.

The use of eXplainable Artificial Intelligence (XAI) systems has introduced a set of challenges that need resolution. Herein, we focus on how to correctly select an XAI method, an open questions within the field. The inherent difficulty of this task is due to the lack of a ground truth. Several authors have proposed metrics to approximate the fidelity of different XAI methods. These metrics lack verification and have concerning disagreements. In this study, we proposed a novel methodology to verify fidelity metrics, using a well-known transparent model, namely a decision tree. This model allowed us to obtain explanations with perfect fidelity. Our proposal constitutes the first objective benchmark for these metrics, facilitating a comparison of existing proposals, and surpassing existing methods. We applied our benchmark to assess the existing fidelity metrics in two different experiments, each using public datasets comprising 52,000 images. The images from these datasets had a size a 128 by 128 pixels and were synthetic data that simplified the training process. All metric values, indicated a lack of fidelity, with the best one showing a 30 \% deviation from the expected values for perfect explanation. Our experimentation led us to conclude that the current fidelity metrics are not reliable enough to be used in real scenarios. From this finding, we deemed it necessary to development new metrics, to avoid the detected problems, and we recommend the usage of our proposal as a benchmark within the scientific community to address these limitations.

The connected sum construction, which takes as input Gorenstein rings and produces new Gorenstein rings, can be considered as an algebraic analogue for the topological construction having the same name. We determine the graded Betti numbers for connected sums of graded Artinian Gorenstein algebras. Along the way, we find the graded Betti numbers for fiber products of graded rings; an analogous result was obtained in the local case by Geller. We relate the connected sum construction to the doubling construction, which also produces Gorenstein rings. Specifically, we show that a connected sum of doublings is the doubling of a fiber product ring.

We develop the theory of Hamiltonian Truncation (HT) to systematically study RG flows that require the renormalization of coupling constants. This is a necessary step towards making HT a fully general method for QFT calculations. We apply this theory to a number of QFTs defined as relevant deformations of $d=1+1$ CFTs. We investigated three examples of increasing complexity: the deformed Ising, Tricritical-Ising, and non-unitary minimal model $M(3,7)$. The first two examples provide a crosscheck of our methodologies against well established characteristics of these theories. The $M(3,7)$ CFT deformed by its $Z_2$-even operators shows an intricate phase diagram that we clarify. At a boundary of this phase diagram we show that this theory flows, in the IR, to the $M(3,5)$ CFT., Comment: Published version with corrected typos, 42 pages, 12 figures

We critically assess to what extent it makes sense to bound the Wilson coefficients of dimension-six operators. In the context of Higgs physics, we establish that a closely related observable, $c_H$, is well-defined and satisfies a two-sided bound. $c_H$ is derived from the low momentum expansion of the scattering amplitude, or the derivative of the amplitude at the origin with respect to the Mandelstam variable $s$, expressed as $M(H_iH_i\rightarrow H_jH_j)=c_H s +O(g_\text{SM}, s^{-2})$ where $g_\text{SM}$ represents all Standard Model couplings. This observable is non-dispersive and, as a result, not sign-definite. We also determine the conditions under which the bound on $c_H$ is equivalent to a bound on the dimension-six operator $O_H=\partial| H|^2 \partial |H|^2$., Comment: 8 pages + appendices

Let $\varphi: F\longrightarrow G$ be a graded morphism between free $R$-modules of rank $t$ and $t+c-1$, respectively, and let $I_j(\varphi)$ be the ideal generated by the $j \times j$ minors of a matrix representing $\varphi$. In this short note: (1) We show that the canonical module of $R/I_j(\varphi)$ is up to twist equal to a suitable Schur power $\Sigma ^I M$ of $M=\coker (\varphi ^*)$; thus equal to $\wedge ^{t+1-j}M$ if $c=2$ in which case we find a minimal free $R$-resolution of $\wedge ^{t+1-j}M$ for any $j$, (2) For $c = 3$, we construct a free $R$-resolution of $\wedge ^2M$ which starts almost minimally (i.e. the first three terms are minimal up to a precise summand), and (3) For $c \ge 4$, we construct under a certain depth condition the first three terms of a free $R$-resolution of $\wedge ^2M$ which are minimal up to a precise summand. As a byproduct we answer the first open case of a question posed by Buchsbaum and Eisenbud.

Goal-conditioned planning benefits from learned low-dimensional representations of rich observations. While compact latent representations typically learned from variational autoencoders or inverse dynamics enable goal-conditioned decision making, they ignore state reachability, hampering their performance. In this paper, we learn a representation that associates reachable states together for effective planning and goal-conditioned policy learning. We first learn a latent representation with multi-step inverse dynamics (to remove distracting information), and then transform this representation to associate reachable states together in $\ell_2$ space. Our proposals are rigorously tested in various simulation testbeds. Numerical results in reward-based settings show significant improvements in sampling efficiency. Further, in reward-free settings this approach yields layered state abstractions that enable computationally efficient hierarchical planning for reaching ad hoc goals with zero additional samples., Comment: Accepted at ICML 2024

The study of the Lefschetz properties of Artinian graded algebras was motivated by the hard Lefschetz theorem for a smooth complex projective variety, a breakthrough in algebraic topology and geometry. Over the last few years, this topic has attracted increasing attention from mathematicians in various areas. Here, we suggest some important open problems about or related to Lefschetz properties of Artinian graded algebras with the ultimate aim to attract the attention of young researchers from different areas., Comment: To appear in The Proceedings of the Cortona's meeting; "Lefschetz Properties: Current and New Directions"

The evaluation of the fidelity of eXplainable Artificial Intelligence (XAI) methods to their underlying models is a challenging task, primarily due to the absence of a ground truth for explanations. However, assessing fidelity is a necessary step for ensuring a correct XAI methodology. In this study, we conduct a fair and objective comparison of the current state-of-the-art XAI methods by introducing three novel image datasets with reliable ground truth for explanations. The primary objective of this comparison is to identify methods with low fidelity and eliminate them from further research, thereby promoting the development of more trustworthy and effective XAI techniques. Our results demonstrate that XAI methods based on the backpropagation of output information to input yield higher accuracy and reliability compared to methods relying on sensitivity analysis or Class Activation Maps (CAM). However, the backpropagation method tends to generate more noisy saliency maps. These findings have significant implications for the advancement of XAI methods, enabling the elimination of erroneous explanations and fostering the development of more robust and reliable XAI.

The Eclipse Layout Kernel (ELK) is a collection of graph drawing algorithms that supports compound graph layout and ports as explicit anchor points of edges. It is available as open-source library under an EPL license. Since its beginning, ELK has served both as a research vehicle for graph drawing algorithms, and as a practical tool for solving real-world problems. ELK and its transpiled JavaScript cousin elkjs are now included in numerous academic and commercial projects. Most of the algorithms realized in ELK are described in a series of publications. In this paper, the technical description concentrates on the key features of the flag-ship algorithm ELK Layered, the algorithm architecture, and usage. However, the main purpose of this paper is to give the broader view that is typically left unpublished. Specifically, we review its history, give a brief overview of technical papers, discuss lessons learned over the past fifteen years, and present example usages. Finally, we reflect on potential threats to open-source graph drawing libraries.

This paper presents for the first time successful results of active flow control with multiple independently controlled zero-net-mass-flux synthetic jets. The jets are placed on a three-dimensional cylinder along its span with the aim of reducing the drag coefficient. The method is based on a deep-reinforcement-learning framework that couples a computational-fluid-dynamics solver with an agent using the proximal-policy-optimization algorithm. We implement a multi-agent reinforcement-learning framework which offers numerous advantages: it exploits local invariants, makes the control adaptable to different geometries, facilitates transfer learning and cross-application of agents and results in significant training speedup. In this contribution we report significant drag reduction after applying the DRL-based control in three different configurations of the problem., Comment: ETMM14 2023 conference proceeding paper

We introduce a simple yet effective early fusion method for crop yield prediction that handles multiple input modalities with different temporal and spatial resolutions. We use high-resolution crop yield maps as ground truth data to train crop and machine learning model agnostic methods at the sub-field level. We use Sentinel-2 satellite imagery as the primary modality for input data with other complementary modalities, including weather, soil, and DEM data. The proposed method uses input modalities available with global coverage, making the framework globally scalable. We explicitly highlight the importance of input modalities for crop yield prediction and emphasize that the best-performing combination of input modalities depends on region, crop, and chosen model., Comment: 4 pages, 1 figure, 3 tables, IEEE IGARSS 2023