In this paper, we propose a new mathematical optimization model for multiclass classification based on arrangements of hyperplanes. Our approach preserves the core support vector machine (SVM) paradigm of maximizing class separation while minimizing misclassification errors, and it is computationally more efficient than a previous formulation. We present a kernel-based extension that allows it to construct nonlinear decision boundaries. Furthermore, we show how the framework can naturally incorporate alternative geometric structures, including classification trees, $\ell_p$-SVMs, and models with discrete feature selection. To address large-scale instances, we develop a dynamic clustering matheuristic that leverages the proposed MIP formulation. Extensive computational experiments demonstrate the efficiency of the proposed model and dynamic clustering heuristic, and we report competitive classification performance on both synthetic datasets and real-world benchmarks from the UCI Machine Learning Repository, comparing our method with state-of-the-art implementations available in scikit-learn.

The Milky Way's inner region is dominated by a stellar bar and a boxy-peanut shaped bulge. However, which stellar populations inhabit the inner Galaxy or how star formation proceeded there is still unknown. The difficulty in studying these stars stems from their location in dense regions that are strongly impacted by extinction and crowding effects. In this work, we use star formation histories computed in the solar neighbourhood using Gaia Colour-Magnitude Diagram fitting to shed light onto the evolution of the central regions of our Galaxy. For that, we have obtained precise age distributions for the non-negligible amount of super metal-rich stars ([M/H] $\sim$ 0.5) in the solar neighbourhood (more than 5$\%$ of the total stars within 400 pc of the plane). Assuming that these stars were born in the inner Galaxy and migrated outwards, those distributions should be indicative of the true stellar age distribution in the inner Galaxy. Surprisingly, we find that these age distributions are not continuous but show clear signs of episodic star formation ($\sim$~13.5, 10.0, 7.0, 4.0, 2.0 and less than 1~Gyr ago). Interestingly, with the exception of the 4~Gyr event, the timings of the detected events coincide with the formation of the primitive Milky Way and with known merging events or satellite encounters (Gaia-Enceladus-Sausage, Sagittarius dwarf galaxy, and the Magellanic Clouds), suggesting that these could have induced enhanced and global star-forming episodes. These results are compatible with a scenario in which Gaia-Enceladus-Sausage is responsible for the formation of the bar 10 Gyr ago. However, we cannot associate any accretion counterpart with the 4-Gyr-ago event, leaving room for a late formation of the bar, as previously proposed. A qualitative comparison with the Auriga Superstars simulations suggesting a possible link to bar dynamics and satellite accretion. [Abridged]

This paper investigates some aspects of a recently proposed nonlinear mathematical model of opinion dynamics. The main objective is to identify the network structures that maximize the average equilibrium opinion (HMO). We prove that consensus is not generally attainable for populations with heterogeneous convictions, and that the highest mean does not necessarily correspond to consensus. Our analysis includes a necessary and sufficient condition for achieving the HMO, description of an algorithm for constructing optimal connectivity matrices, and strategies for pruning agents when heterogeneity obstructs mean optimization.

We present cosmological constraints on deviations from general relativity (GR) from the first-year of clustering observations from Dark Energy Spectroscopic Instrument (DESI) in combination with other datasets. We first consider $\mu(a,k)$-$\Sigma(a,k)$ modified gravity (MG) parametrization (as well as $\eta(a,k)$) in flat $\Lambda$CDM and $w_0 w_a$CDM backgrounds. Using a functional form for time-only evolution gives $\mu_0=0.11^{+0.44}_{-0.54}$ from DESI(FS+BAO)+BBN and a wide prior on $n_{s}$. Using DESI(FS+BAO)+CMB+DESY3+DESY5-SN, we obtain $\mu_0=0.05\pm 0.22$ and $\Sigma_0=0.008\pm 0.045$ in the $\Lambda$CDM background. In $w_0 w_a$CDM, we obtain $\mu_0=-0.24^{+0.32}_{-0.28}$ and $\Sigma_0=0.006\pm 0.043$, consistent with GR, and still find a preference for dynamical dark energy with w_0>-1 and w_a<0. We then use binned forms in the 2 backgrounds starting with 2 bins in redshift and then adding 2 bins in scale for a total of 4 and 8 MG parameters, respectively. All MG parameters are found consistent with GR. We also find that the tension reported for $\Sigma_0$ with GR from Planck PR3 goes away when using LoLLiPoP+HiLLiPoP likelihoods. As noted previously, this seems to indicate the tension is related to CMB lensing anomaly in PR3 which is also resolved when using these likelihoods. We then constrain the class of Horndeski theory in both EFT-basis and $\alpha$-basis. Assuming a power law for the non-minimal coupling function $\Omega$, we obtain $\Omega_0=0.012^{+0.001}_{-0.012}$ and $s_0=0.996^{+0.54}_{-0.20}$ from DESI(FS+BAO)+DESY5SN+CMB in a $\Lambda$CDM background, consistent with GR. Using the $\alpha$-basis with no-braiding ($\alpha_B=0$) gives c_M<1.14, in agreement with GR. However, we see a mild yet consistent indication for c_B>0 when $\alpha_B$ is varied which will require further study to determine whether this is due to systematics or new physics. [Abridged]

The asymmetry between heating and cooling in open quantum systems is a hallmark of nonequilibrium dynamics, yet its thermodynamic origin has remained unclear. Here, we investigate the thermalization of a quantum system weakly coupled to a thermal bath, focusing on the entropy production rate and the quantum thermokinetic uncertainty relation (TKUR). We derive an analytical expression for the entropy production rate, showing that heating begins with a higher entropy production, which drives faster thermalization than cooling. The quantum TKUR links this asymmetry to heat current fluctuations, demonstrating that larger entropy production suppresses fluctuations, making heating more stable than cooling. Our results reveal the thermodynamic basis of asymmetric thermalization and highlight uncertainty relations as key to nonequilibrium quantum dynamics.

Cosmic rays reaching the atmosphere of an astrophysical object produce showers of secondary particles that may then scape into space. Here we obtain the flux of gammas and neutrinos of energy $E>10$ GeV emited by the Sun, Jupiter and Earth. We show that, while the solar magnetic field induces an albedo flux of gammas from all the points in the Sun's surface, the dipolar magnetic field in the planets implies gammas only from the very peripheral region. Neutrinos, in contrast, can cross these objects and emerge from any point in their surface. The emission from these astrophysical objects is above the diffuse flux from cosmic ray interactions with the interstellar medium and has a distinct spectrum and gamma to neutrino ratio.

This is the second paper in the HOWLS (higher-order weak lensing statistics) series exploring the usage of non-Gaussian statistics for cosmology inference within \textit{Euclid}. With respect to our first paper, we develop a full tomographic analysis based on realistic photometric redshifts which allows us to derive Fisher forecasts in the ($\sigma_8$, $w_0$) plane for a \textit{Euclid}-like data release 1 (DR1) setup. We find that the 5 higher-order statistics (HOSs) that satisfy the Gaussian likelihood assumption of the Fisher formalism (1-point probability distribution function, $\ell$1-norm, peak counts, Minkowski functionals, and Betti numbers) each outperform the shear 2-point correlation functions by a factor $2.5$ on the $w_0$ forecasts, with only marginal improvement when used in combination with 2-point estimators, suggesting that every HOS is able to retrieve both the non-Gaussian and Gaussian information of the matter density field. The similar performance of the different estimators\inlinecomment{, with a slight preference for Minkowski functionals and 1-point probability distribution function,} is explained by a homogeneous use of multi-scale and tomographic information, optimized to lower computational costs. These results hold for the $3$ mass mapping techniques of the \textit{Euclid} pipeline: aperture mass, Kaiser--Squires, and Kaiser--Squires plus, and are unaffected by the application of realistic star masks. Finally, we explore the use of HOSs with the Bernardeau--Nishimichi--Taruya (BNT) nulling scheme approach, finding promising results towards applying physical scale cuts to HOSs.

We introduce SpectraPyle, a versatile spectral stacking pipeline developed for the Euclid mission's NISP spectroscopic surveys, aimed at extracting faint emission lines and spectral features from large galaxy samples in the Wide and Deep Surveys. Designed for computational efficiency and flexible configuration, SpectraPyle supports the processing of extensive datasets critical to Euclid's non-cosmological science goals. We validate the pipeline using simulated spectra processed to match Euclid's expected final data quality. Stacking enables robust recovery of key emission lines, including Halpha, Hbeta, [O III], and [N II], below individual detection limits. However, the measurement of galaxy properties such as star formation rate, dust attenuation, and gas-phase metallicity are biased at stellar mass below log10(M*/Msol) ~ 9 due to the flux-limited nature of Euclid spectroscopic samples, which cannot be overcome by stacking. The SFR-stellar mass relation of the parent sample is recovered reliably only in the Deep survey for log10(M*/Msol) > 10, whereas the metallicity-mass relation is recovered more accurately over a wider mass range. These limitations are caused by the increased fraction of redshift measurement errors at lower masses and fluxes. We examine the impact of residual redshift contaminants that arises from misidentified emission lines and noise spikes, on stacked spectra. Even after stringent quality selections, low-level contamination (< 6%) has minimal impact on line fluxes due to the systematically weaker emission of contaminants. Percentile-based analysis of stacked spectra provides a sensitive diagnostic for detecting contamination via coherent spurious features at characteristic wavelengths. While our simulations include most instrumental effects, real Euclid data will require further refinement of contamination mitigation strategies.

Robust inference methods are essential for parameter estimation and model selection in stochastic modeling approaches, which provide interpretable frameworks for describing time series of complex phenomena. However, applying such methods is often challenging, as they typically demand either high-frequency observations or access to the model's analytical solution, resources that are rarely available in practice. Here, we address these limitations by designing a novel Monte Carlo method based on full-path statistics and bridge processes, which optimize sampling efforts and performance even under coarse sampling. We systematically investigate how experimental design -- particularly sampling frequency and dataset size -- shapes inference accuracy, revealing optimal sampling regimes and the fundamental limits of model distinguishability. We validate our approach on four datasets -- optical tweezers, human microbiome, topic mentions in social media, and forest population dynamics -- where resolution-dependent limits to inference emerge, offering fresh insight into ongoing debates about the dominant sources of noise in these systems. Overall, this work shows how combining minimal stochastic models with path-inference tools and model selection can guide the experimental design of optimized strategies in data collection and clarify the boundaries of model-based understanding in complex systems.

This article explains a program to study complete and properly embedded minimal surfaces in $\mathbb{R}^3$ developed jointly with W.H. Meeks and A. Ros in the last three decades. It follows closely the structure of my invited ICM talk with the same title and supplies details and references to the original papers. After recalling the role of the classical Riemann minimal examples in minimal surface theory, we explain our four-step classification of properly embedded minimal surfaces of genus zero and infinite topology in $\mathbb{R}^3$: the periodic case, the quasi-periodicity of the two-limit-ended case, the non-existence of one-limit-ended examples, and the final classification. We then review the lamination techniques (limit-leaf stability, local removable singularity, and singular structure theorems), the dynamics theorem, bounds on topology and index for complete embedded minimal surfaces of finite total curvature, and the resolution of the embedded Calabi-Yau problem for finite genus and countably many ends. Throughout we emphasize the interaction between topology, flux, curvature estimates, and the structure of related moduli spaces. We end this article with a list of some open problems.

Studying the impact of new-physics models on low-energy observables necessitates matching to effective field theories at the relevant mass thresholds. We introduce the first public version of Matchete, a computer tool for matching weakly-coupled models at one-loop order. It uses functional methods to directly compute all matching contributions in a manifestly gauge-covariant manner, while simplification methods eliminate redundant operators from the output. We sketch the workings of the program and provide examples of how to match simple Standard Model extensions. The package, documentation, and example notebooks are publicly available at this https URL

Euclid is expected to establish new state-of-the-art constraints on extensions beyond the standard LCDM cosmological model by measuring the positions and shapes of billions of galaxies. Specifically, its goal is to shed light on the nature of dark matter and dark energy. Achieving this requires developing and validating advanced statistical tools and theoretical prediction software capable of testing extensions of the LCDM model. In this work, we describe how the Euclid likelihood pipeline, Cosmology Likelihood for Observables in Euclid (CLOE), has been extended to accommodate alternative cosmological models and to refine the theoretical modelling of Euclid primary probes. In particular, we detail modifications made to CLOE to incorporate the magnification bias term into the spectroscopic two-point correlation function of galaxy clustering. Additionally, we explain the adaptations made to CLOE's implementation of Euclid primary photometric probes to account for massive neutrinos and modified gravity extensions. Finally, we present the validation of these CLOE modifications through dedicated forecasts on synthetic Euclid-like data by sampling the full posterior distribution and comparing with the results of previous literature. In conclusion, we have identified in this work several functionalities with regards to beyond-LCDM modelling that could be further improved within CLOE, and outline potential research directions to enhance pipeline efficiency and flexibility through novel inference and machine learning techniques.

We investigate the potential for observing gravitational waves from cosmological phase transitions with LISA in light of recent theoretical and experimental developments. Our analysis is based on current state-of-the-art simulations of sound waves in the cosmic fluid after the phase transition completes. We discuss the various sources of gravitational radiation, the underlying parameters describing the phase transition and a variety of viable particle physics models in this context, clarifying common misconceptions that appear in the literature and identifying open questions requiring future study. We also present a web-based tool, PTPlot, that allows users to obtain up-to-date detection prospects for a given set of phase transition parameters at LISA.

This work presents single-differential electron-neutrino charged-current cross sections on argon measured using the MicroBooNE detector at the Fermi National Accelerator Laboratory. The analysis uses data recorded when the Neutrinos at the Main Injector beam was operating in both neutrino and antineutrino modes, with exposures of $2 \times 10^{20}$ and $5 \times 10^{20}$ protons on target, respectively. A selection algorithm targeting electron-neutrino charged-current interactions with at least one proton, one electron, and no pions in the final topology is used to measure differential cross sections as a function of outgoing electron energy, total visible energy, and opening angle between the electron and the most energetic proton. The interaction rate as a function of proton multiplicity is also reported. The total cross section is measured as [4.1 $\pm$ 0.4 (stat.) $\pm$ 1.2 (syst.)]$\,$$\times \,10^{-39} \mathrm{cm}^{2}/\,\mathrm{nucleon}$. The unfolded cross-section measurements are compared to predictions from neutrino event generators commonly employed in the field. Good agreement is seen across all variables within uncertainties.

Hybrid neuro-evolutionary algorithms may be inspired on Darwinian or Lamarckian evolu- tion. In the case of Darwinian evolution, the Baldwin effect, that is, the progressive incorporation of learned characteristics to the genotypes, can be observed and leveraged to improve the search. The purpose of this paper is to carry out an exper- imental study into how learning can improve G-Prop genetic search. Two ways of combining learning and genetic search are explored: one exploits the Baldwin effect, while the other uses a Lamarckian strategy. Our experiments show that using a Lamarckian op- erator makes the algorithm find networks with a low error rate, and the smallest size, while using the Bald- win effect obtains MLPs with the smallest error rate, and a larger size, taking longer to reach a solution. Both approaches obtain a lower average error than other BP-based algorithms like RPROP, other evolu- tionary methods and fuzzy logic based methods

We present methods to achieve NLL+NLO accurate parton showering for processes with two coloured legs: neutral- and charged-current Drell-Yan, and Higgs production in $pp$ collisions, as well as DIS and $e^+e^-$ to jets. The methods include adaptations of existing approaches, as well as a new NLO matching scheme, ESME, that is positive-definite by construction. Our implementations of the methods within the PanScales framework yield highly competitive NLO event generation speeds. We validate the fixed-order and combined resummation accuracy with tests in the limit of small QCD coupling and briefly touch on phenomenological comparisons to standard NLO results and to Drell-Yan data. The progress reported here is an essential step towards showers with logarithmic accuracy beyond NLL for processes with incoming hadrons.

The neural model introduced by Sompolinsky, Crisanti, and Sommers (SCS) nearly four decades ago has become a paradigmatic framework for studying complex dynamics in random recurrent networks. In its original formulation, with balanced positive and negative couplings, the model exhibits two phases: a quiescent regime, where all activity ceases, and a regime of ongoing irregular collective activity, termed asynchronous chaos (AC), in which state variables fluctuate strongly in time and across units but average to zero across the network. Building on recent work, we analyze an extension of the SCS model that breaks this coupling balance, yielding a richer phase diagram. In addition to the classical quiescent and AC phases, two additional regimes emerge, marked by spontaneous symmetry breaking. In the persistent-activity (PA) phase, each unit settles into a distinct, stable activation state. In the synchronous-chaotic (SC) phase, dynamics remain irregular and chaotic but fluctuate around a nonzero mean, generating sustained long-time autocorrelations. Using analytical techniques based on dynamical mean-field theory, complemented by extensive numerical simulations, we show how structural disorder gives rise to symmetry and ergodicity breaking. Remarkably, the resulting phase diagram closely parallels that of the Sherrington-Kirkpatrick spin-glass model, with the onset of the SC phase coinciding with the transition associated with replica-symmetry breaking. All key features of spin glasses, including ergodicity breaking, have clear counterparts in this recurrent network context, albeit with crucial idiosyncratic differences, highlighting a unified perspective on complexity in disordered systems.

Energy storage is a basic physical process with many applications. When considering this task at the quantum scale, it becomes important to optimise the non-equilibrium dynamics of energy transfer to the storage device or battery. Here, we tackle this problem using the methods of quantum feedback control. Specifically, we study the deposition of energy into a quantum battery via an auxiliary charger. The latter is a driven-dissipative two-level system subjected to a homodyne measurement whose output signal is fed back linearly into the driving field amplitude. We explore two different control strategies, aiming to stabilise either populations or quantum coherences in the state of the charger. In both cases, linear feedback is shown to counteract the randomising influence of environmental noise and allow for stable and effective battery charging. We analyse the effect of realistic control imprecisions, demonstrating that this good performance survives inefficient measurements and small feedback delays. Our results highlight the potential of continuous feedback for the control of energetic quantities in the quantum regime.