Recurrent neural networks with balanced excitation and inhibition exhibit irregular asynchronous dynamics, which is fundamental for cortical computations. Classical balance mechanisms require strong external inputs to sustain finite firing rates, raising concerns about their biological plausibility. Here, we investigate an alternative mechanism based on short-term synaptic depression (STD) acting on excitatory-excitatory synapses, which dynamically balances the network activity without the need of external inputs. By employing numerical simulations and theoretical investigations we characterize the dynamics of a massively coupled network made up of $N$ rate-neuron models. Depending on the synaptic strength $J_0$, the network exhibits two distinct regimes: at sufficiently small $J_0$, it converges to a homogeneous fixed point, while for sufficiently large $J_0$, it exhibits Rate Chaos. For finite networks, we observe several different routes to chaos depending on the network realization. The width of the transition region separating the homogeneous stable solution from Rate Chaos appears to shrink for increasing $N$ and eventually to vanish in the thermodynamic limit. The characterization of the Rate Chaos regime performed by employing Dynamical Mean Field approaches allow us on one side to confirm that this novel balancing mechanism is able to sustain finite irregular activity even in the thermodynamic limit, and on the other side to reveal that the balancing occurs via dynamic cancellation of the input correlations generated by the massive coupling. Our findings show that STD provides an intrinsic self-regulating mechanism for balanced networks, sustaining irregular yet stable activity without the need of biologically unrealistic inputs. This work extends the balanced network paradigm, offering insights into how cortical circuits could maintain robust dynamics via synaptic adaptation.

Quantum error correction code discovery has relied on algebraic constructions with predetermined structure or computational search lacking mechanistic interpretability. We introduce a game-theoretic framework recasting code optimization as strategic interactions between competing objectives, where Nash equilibria systematically generate codes with desired properties. We validate the framework by demonstrating it rediscovers the optimal $[\![15,7,3]\!]$ quantum Hamming code (Calderbank-Shor-Steane 1996) from competing objectives without predetermined algebraic structure, with equilibrium analysis providing transparent mechanistic insights into why this topology emerges. Applied across six objectives -- distance maximization, hardware adaptation, rate-distance optimization, cluster-state generation, surface-like topologies, and connectivity enhancement -- the framework generates distinct code families through objective reconfiguration rather than algorithm redesign. Scalability to hardware-relevant sizes is demonstrated at $n=100$ qubits, discovering codes including $[\![100,50,4]\!]$ with distance-4 protection and 50\% encoding rate, with tractable $O(n^3)$ per-iteration complexity enabling discovery in under one hour. This work opens research avenues at the intersection of game theory and quantum information, providing systematic, interpretable frameworks for quantum system design.

We report on the observation and measurement of astrometry, photometry, morphology, and activity of the interstellar object 3I/ATLAS, also designated C/2025 N1 (ATLAS), with the NSF-DOE Vera C. Rubin Observatory. The third interstellar object, comet 3I/ATLAS, was first discovered on UT 2025 July 1. Serendipitously, the Rubin Observatory collected imaging in the area of the sky inhabited by the object during regular commissioning activities. We successfully recovered object detections from Rubin visits spanning UT 2025 June 21 (10 days before discovery) to UT 2025 July 7. Facilitated by Rubin's high resolution and large aperture, we report on the detection of cometary activity as early as June 21st, and observe it throughout. We measure the location and magnitude of the object on 37 Rubin images in r, i, and z bands, with typical precision of about 20 mas (100 mas, systematic) and about 10 mmag, respectively. We use these to derive improved orbit solutions, and to show there is no detectable photometric variability on hourly timescales. We derive a V-band absolute magnitude of H_V = (13.7 +/- 0.2) mag, and an equivalent effective nucleus radius of around (5.6 +/- 0.7) km. These data represent the earliest observations of this object by a large (8-meter class) telescope reported to date, and illustrate the type of measurements (and discoveries) Rubin's Legacy Survey of Space and Time (LSST) will begin to provide once operational later this year.

Despite major advances in artificial intelligence (AI) for medicine and healthcare, the deployment and adoption of AI technologies remain limited in real-world clinical practice. In recent years, concerns have been raised about the technical, clinical, ethical and legal risks associated with medical AI. To increase real world adoption, it is essential that medical AI tools are trusted and accepted by patients, clinicians, health organisations and authorities. This work describes the FUTURE-AI guideline as the first international consensus framework for guiding the development and deployment of trustworthy AI tools in healthcare. The FUTURE-AI consortium was founded in 2021 and currently comprises 118 inter-disciplinary experts from 51 countries representing all continents, including AI scientists, clinicians, ethicists, and social scientists. Over a two-year period, the consortium defined guiding principles and best practices for trustworthy AI through an iterative process comprising an in-depth literature review, a modified Delphi survey, and online consensus meetings. The FUTURE-AI framework was established based on 6 guiding principles for trustworthy AI in healthcare, i.e. Fairness, Universality, Traceability, Usability, Robustness and Explainability. Through consensus, a set of 28 best practices were defined, addressing technical, clinical, legal and socio-ethical dimensions. The recommendations cover the entire lifecycle of medical AI, from design, development and validation to regulation, deployment, and monitoring. FUTURE-AI is a risk-informed, assumption-free guideline which provides a structured approach for constructing medical AI tools that will be trusted, deployed and adopted in real-world practice. Researchers are encouraged to take the recommendations into account in proof-of-concept stages to facilitate future translation towards clinical practice of medical AI.

Starting from Greg Moore's description about Physical Mathematics, a framework is proposed in order to understand it, based on Gilles Châtelet's philosophy. It will be argued that Châtelet's ideas of inverting, splitting, augmenting and virtuality are crucial in the discussion about the nature of Physical Mathematics. Along this line, it will be proposed that mirror symmetry is a natural study case to test Châtelet's ideas in this context. This should be considered as a first step in a long term project aiming to study the relations among mathematics, physics and philosophy in the construction of a global understanding of the structure of the universe, as it was envisioned by Grothendieck in the late 80's of the last century and it was started to be developed independently by Châtelet in the beginning of the 90's. The main suggestion of the essay is that it is in the relations between mathematics, physics and philosophy that new knowledge arises.

We present \textit{JWST} NIRSpec and MIRI MRS observations of the central kiloparsec of M58 (NGC 4579), a nearby LINER galaxy hosting a low-luminosity AGN (LLAGN; $L_\mathrm{bol} \sim 10^{42}$ erg s$^{-1}$) with a low-power jet. These data provide an unprecedented view of the warm molecular gas phase and reveal clear signatures of feedback. We detect 44 H$_2$ lines, including bright pure rotational lines (S(1)-S(18)) and rovibrational lines up to $\nu=2$, probing a wide range of excitation conditions. Excitation diagrams show that rotational lines follow a power-law temperature distribution with an exponential cutoff, consistent with heating by low-velocity shocks. H$_2$ rovibrational lines deviate from thermal models primarily because of sub-thermal excitation at low density. Additionally, there may be a 10% contribution by AGN X-ray heating in the nucleus. The dust lanes associated with the spiral inflow appear dynamically undisturbed but show signs of shock heating, while the inner $\sim$200 pc exhibits turbulent kinematics produced by outflowing molecular gas. These results reveal the subtle yet measurable impact of LLAGN feedback on the interstellar medium, demonstrating that even weak, vertically oriented jets and low radiative accretion rates can perturb molecular gas and regulate nuclear reservoirs. This study highlights JWST's transformative ability to uncover hidden modes of AGN feedback.

The mechanisms leading to the formation of disks around young stellar objects (YSOs) and to the launching of the associated jets are crucial to the understanding of the earliest stages of star and planet formation. HH 212 is a privileged laboratory to study a pristine jet-disk system. Therefore we investigate the innermost region (<100 AU) around the HH 212-MM1 protostar through ALMA band\,7 observations of methanol. The 8 GHz bandwidth spectrum towards the peak of the continuum emission of the HH 212 system reveals at least 19 transitions of methanol. Several of these lines (among which several vibrationally excited lines in the v$_{\rm t}=1,2$ states) have upper energies above 500 K. They originate from a compact (<135 AU in diameter), hot ($\sim 295$ K) region elongated along the direction of the SiO jet. We performed a fit in the $uv$ plane of various velocity channels of the strongest high-excitation lines. The blue- and red-shifted velocity centroids are shifted roughly symmetrically on either side of the jet axis, indicating that the line-of-sight velocity beyond 0.7 km s$^{-1}$ from systemic is dominated by rotational motions. The velocity increases moving away from the protostar further indicating that the emission of methanol is not associated with a Keplerian disk or rotating-infalling cavity, and it is more likely associated with outflowing gas. We speculate that CH$_3$OH traces a disk wind gas accelerated at the base. The launching region would be at a radius of a few astronomical units from the YSO.

Self-supervised learning (SSL) models have recently demonstrated remarkable performance across various tasks, including image segmentation. This study delves into the emergent characteristics of the Self-Distillation with No Labels (DINO) algorithm and its application to Synthetic Aperture Radar (SAR) imagery. We pre-train a vision transformer (ViT)-based DINO model using unlabeled SAR data, and later fine-tune the model to predict high-resolution land cover maps. We rigorously evaluate the utility of attention maps generated by the ViT backbone and compare them with the model's token embedding space. We observe a small improvement in model performance with pre-training compared to training from scratch and discuss the limitations and opportunities of SSL for remote sensing and land cover segmentation. Beyond small performance increases, we show that ViT attention maps hold great intrinsic value for remote sensing, and could provide useful inputs to other algorithms. With this, our work lays the groundwork for bigger and better SSL models for Earth Observation.

In this essay we give a general picture about the evolution of Grohendieck's ideas regarding the notion of space. Starting with his fundamental work in algebraic geometry, where he introduces schemes and toposes as generalizations of classical notions of spaces, passing through tame topology and ending with the formulation of a geometry of forms, we show how the ideas of Grothendieck evolved from pure mathematical considerations to physical and philosophical questions about the nature and structure of space and its mathematical models.

Considering the flexibility and applicability of Bayesian modeling, in this work we revise the main characteristics of two hierarchical models in a regression setting. We study the full probabilistic structure of the models along with the full conditional distribution for each model parameter. Under our hierarchical extensions, we allow the mean of the second stage of the model to have a linear dependency on a set of covariates. The Gibbs sampling algorithms used to obtain samples when fitting the models are fully described and derived. In addition, we consider a case study in which the plant size is characterized as a function of nitrogen soil concentration and a grouping factor (farm).

We present Galaxy-Galaxy Lensing measurements obtained by cross-correlating spectroscopically observed galaxies from the first data release of the Dark Energy Spectroscopic Instrument (DESI) with source galaxies from the Hyper Suprime-Cam Subaru Strategic Survey, the Kilo-Degree Survey, the Sloan Digital Sky Survey, and the Dark Energy Survey. Specifically, we measure the excess surface mass density $\Delta\Sigma$ and tangential shear $\gamma_\mathrm{t}$ for the Bright Galaxy Sample and Luminous Red Galaxies measured within the first year of observations with DESI. To ensure robustness, we test the measurements for systematic biases, finding no significant trends related to the properties of the \acrshort{desi} lens galaxies. We identify a significant trend with the average redshift of source galaxies, however, this trend vanishes once we apply shifts to the Hyper Suprime-Cam Subaru Strategic Survey redshift distributions that are also favored by their fiducial cosmology analysis. Additionally, we compare the observed scatter in the measurements with the theoretical covariance and find excess scatter, driven primarily by small-scale measurements of $r\leq 1 \, \mathrm{Mpc}/h$; measurements on larger scales are consistent at the $2\,\sigma$ level. We further present the projected clustering measurements $w_p$ of the galaxy samples in the the first data release of DESI. These measurements, which will be made publicly available, serve as a foundation for forthcoming cosmological analyses.

Studying molecular gas in nearby galaxies using hydrogen cyanide (HCN) as a tracer for higher densities than CO emission still poses a significant challenge. Even though several galaxies have HCN maps on a few kpc scales, higher-resolution maps are still required. Our goal is to examine the contrast in intensity between two tracers that probe different density regimes - HCN(1-0)/CO(2-1) ratio - and their kinematics across NGC 253. By utilizing the advanced capabilities of the Atacama Large Millimeter/submillimeter Array (ALMA), we can map these features at high resolution across a large field of view and uncover the nature of such dense gas in extragalactic systems. We present new ALMA Atacama Compact Array and Total Power (ACA+TP) observations of the HCN emission across NGC 253, covering the inner 8.6' of the galaxy disk at 300 pc scales. We analyze the integrated intensity and mean velocity of HCN and CO along each line of sight and use SCOUSE software to perform spectral decomposition, which considers each velocity component separately. Molecular gas traced by HCN piles up in a ring-like structure at a radius of 2 kpc. The HCN emission is enhanced by 2 orders of magnitude in the central 2 kpc regions, beyond which its intensity decreases with increasing galactocentric distance. The number of components in the HCN spectra shows a robust environmental dependence, with multiple velocity features across the center and bar. We have identified an increase in the HCN/CO ratio in these regions, corresponding to a velocity component likely associated with a molecular outflow. We have also discovered that the ratio between the total infrared luminosity and dense gas mass, which indicates the star formation efficiency of dense gas, is anti-correlated with the molecular gas surface density up to approximately 200 Msul/pc^2. In contrast, beyond this point, the ratio starts to increase.

Recent JWST/NIRCam imaging taken for the ultra-deep UNCOVER program reveals a very red dropout object at $z_{\mathrm{phot}}\simeq7.6$, triply imaged by the galaxy cluster Abell 2744 ($z_{\mathrm{d}}=0.308$). All three images are very compact, i.e. unresolved, with a de-lensed size upper-limit of $r_{e}\lesssim35$ pc. The images have apparent magnitudes of $m_{\mathrm{F444W}}\sim25-26$ AB, and the magnification-corrected absolute UV magnitude of the source is $M_{\mathrm{UV},1450}=-16.81\pm0.09$. From the sum of observed fluxes and from a spectral energy distribution (SED) analysis, we obtain estimates of the bolometric luminosities of the source of $L_{\mathrm{bol}}\gtrsim10^{43} \frac{\mathrm{erg}}{\mathrm{s}}$ and $L_{\mathrm{bol}}\sim10^{44}-10^{46} \frac{\mathrm{erg}}{\mathrm{s}}$, respectively. Based on its compact, point-like appearance, its position in color-color space and the SED analysis, we tentatively conclude that this object is a UV-faint dust-obscured quasar-like object, i.e. an active galactic nucleus (AGN) at high redshift. We also discuss other alternative origins for the object's emission features, including a massive star cluster, Population III, supermassive, or dark stars, or a direct-collapse black hole. Although populations of red galaxies at similar photometric redshifts have been detected with JWST, this object is unique in that its high-redshift nature is corroborated geometrically by lensing, that it is unresolved despite being magnified -- and thus intrinsically even more compact -- and that it occupies notably distinct regions in both size-luminosity and color-color space. Planned UNCOVER JWST/NIRSpec observations, scheduled in Cycle 1, will enable a more detailed analysis of this object.

This paper explores the versatility and depth of Bayesian modeling by presenting a comprehensive range of applications and methods, combining Markov chain Monte Carlo (MCMC) techniques and variational approximations. Covering topics such as hierarchical modeling, spatial modeling, higher-order Markov chains, and Bayesian nonparametrics, the study emphasizes practical implementations across diverse fields, including oceanography, climatology, epidemiology, astronomy, and financial analysis. The aim is to bridge theoretical underpinnings with real-world applications, illustrating the formulation of Bayesian models, elicitation of priors, computational strategies, and posterior and predictive analyses. By leveraging different computational methods, this paper provides insights into model fitting, goodness-of-fit evaluation, and predictive accuracy, addressing computational efficiency and methodological challenges across various datasets and domains.

This study examines the impact of $CP$-violation on the signal strength $\mu^{Z\gamma}$, which was reported as $2.2\pm 0.7$ by the LHC. We obtain constraints on the real and absorptive parts of the $CP$-violating form factor $h_3^{Z\gamma}$ and find that they are less than 1.15 GeV. Additionally, we revisit the leading order Standard Model contributions to the $H\rightarrow Z\gamma$ decay and calculate contributions to $h_3^{Z\gamma}$ from FCNC complex couplings mediated by the $Z$ and $H$ bosons. By using the current bounds on such couplings, we find that the FCNC contribution to $h_3^{Z\gamma}$ with top and charm quarks in the loop is of order $10^{-5}$ GeV. While in a model with new quarks that preserves the SM predictions on Higgs decays, the $CP$-violating form factor $h_3^{Z\gamma}$ can be of order $10^{-1}$ GeV and could explain the excess on the signal strength $\mu^{Z\gamma}$.

We introduce version 3 of NetKet, the machine learning toolbox for many-body quantum physics. NetKet is built around neural-network quantum states and provides efficient algorithms for their evaluation and optimization. This new version is built on top of JAX, a differentiable programming and accelerated linear algebra framework for the Python programming language. The most significant new feature is the possibility to define arbitrary neural network ansätze in pure Python code using the concise notation of machine-learning frameworks, which allows for just-in-time compilation as well as the implicit generation of gradients thanks to automatic differentiation. NetKet 3 also comes with support for GPU and TPU accelerators, advanced support for discrete symmetry groups, chunking to scale up to thousands of degrees of freedom, drivers for quantum dynamics applications, and improved modularity, allowing users to use only parts of the toolbox as a foundation for their own code.

This article introduces a spherical latent space model for social network analysis, embedding actors on a hypersphere rather than in Euclidean space as in standard latent space models. The spherical geometry facilitates the representation of transitive relationships and community structure, naturally captures cyclical patterns, and ensures bounded distances, thereby mitigating degeneracy issues common in traditional approaches. Bayesian inference is performed via Markov chain Monte Carlo methods to estimate both latent positions and other model parameters. The approach is demonstrated using two benchmark social network datasets, yielding improved model fit and interpretability relative to conventional latent space models.