In this work, we describe how to construct matrices and block right-hand sides that exhibit a specified restarted block \gmres convergence pattern, such that the eigenvalues and Ritz values at each iteration can be chosen independent of the specified convergence behavior. This work is a generalization of the work in [Meurant and Tebbens, Num.~Alg.~2019] in which the authors do the same for restarted non-block \gmres. We use the same tools as were used in [Kubínová and Soodhalter, SIMAX 2020], namely to analyze block \gmres as an iteration over a right vector space with scalars from the $^\ast$-algebra of matrices. To facilitate our work, we also extend the work of Meurant and Tebbens and offer alternative proofs of some of their results, that can be more easily generalized to the block setting.

We compute the full Tamarkin-Tsygan calculus of a Koszul algebra whose global dimension exceeds the number of generators. Our results show that even for algebras possessing an economic presentation and agreeable homological properties, the Hochschild (co)homology, as well as the structure of the Tamarkin--Tsygan calculus may exhibit a rather intricate behavior.

Radon and its progeny constitute a major source of background in rare-event physics experiments, such as those searching for dark matter, neutrinos, and neutrinoless double beta decay, due to their origin as unavoidable decay products of natural uranium. In particular, $^{222}$Rn and its long-lived daughter $^{210}$Pb can diffuse from detector material surfaces, resulting in sustained background contributions. To investigate this process, a system was developed using a controlled radon source, a vacuum chamber with a high electric field, and a thin Nylon-6 film to enable deposition of radon progeny onto the film surface. Nylon-6 was selected for the initial measurement given its history in low-background experiments. We intend to systematically study diffusion in various polymers in the future. Our setup allowed for controlled study of the diffusion behavior of $^{210}$Pb and its daughter $^{210}$Po under varying humidity conditions. Our results show that both $^{210}$Pb and $^{210}$Po diffuse significantly in nylon under high relative humidity, which can potentially lead to internal contamination and increased background in low-background detectors. The diffusivity of $^{210}$Pb was found to be lower than 1.14 $\times$ 10$^{-15}$ cm$^2$/s at 40$\%$ relative humidity (RH), and to be (4.03 $\pm$ 1.01) $\times$ 10$^{-13}$ cm$^2$/s at 95$\%$ RH. The diffusivity of $^{210}$Po at 95$\%$ RH was measured to be (3.94 $\pm$ 0.98) $\times$ 10$^{-13}$ cm$^2$/s. These findings underscore the importance of controlling environmental humidity and material exposure to radon in the design of ultra-low background experiments.

This study investigates long-term investment decisions in distributed photovoltaic panels by individual investors. We consider a setting where investment decisions are driven by expected revenue from participating in short-term electricity markets over the panel lifespan. These revenues depend on short-term market equilibria, i.e., prices and allocations, which are influenced by aggregate invested panel capacity participating in the markets. We model the interactions among investors by a non-atomic game and develop a framework that links short-term market equilibria to the resulting long-term investment equilibrium. Then, within this framework, we analyze three market mechanisms: (a) a single-product real-time energy market, (b) a product-differentiated real-time energy market that treats solar energy and grid energy as different products, and (c) a contract-based panel market that trades claims/rights to the production of certain panel capacity ex-ante, rather than the realized solar production ex-post. For each, we derive expressions for short-term equilibria and the associated expected revenues, and analytically characterize the corresponding long-term Nash equilibrium aggregate capacity. We compare the solutions of these characterizing equations under different conditions and theoretically establish that the product-differentiated market always supports socially optimal investment, while the single-product market consistently results in under-investment. We also establish that the contract-based market leads to over-investment when the extra valuations of users for solar energy are small. Finally, we validate our theoretical results through numerical experiments.

This paper studies affine algebraic varieties parametrized by sine and cosine functions, generalizing algebraic Lissajous figures in the plane. We show that, up to a combinatorial factor, the degree of these varieties equals the volume of a polytope. We deduce defining equations from rank constraints on a matrix with polynomial entries. We discuss applications of Lissajous varieties in dynamical systems, in particular the Kuramoto model. This leads us to study connections with convex optimization and Lissajous discriminants.

We have investigated vacuum polarization of a quantized charged massive scalar field in the presence of a magnetic topological defect, modeled as an impenetrable tube of finite thickness carrying magnetic flux. At the tube's surface, we imposed a general Robin boundary condition. Our analysis demonstrates that, in flat space-time, the total induced vacuum energy is independent of the coupling $ξ$ of the scalar field's interaction with the space-time curvature only in the special cases of Dirichlet and Neumann boundary conditions. For general Robin boundary conditions, however, the total induced vacuum energy depends on the coupling $ξ$ in a flat space-time and exhibits a nontrivial dependence on the parameter of the Robin boundary condition. We investigated the dependence of this effect not only on Robin's boundary condition parameter, but also on the tube thickness and the space-time dimensionality. We conclude that careful measurements of vacuum polarization effects in flat space-time may, in principle, provide an independent way to probe the $ξ$ coupling.

The measurement of $Σ^{+}$ production in pp collisions at $\sqrt{s}=13$ TeV is presented. The measurement is performed at midrapidity in both minimum-bias and high-multiplicity pp collisions at $\sqrt{s}=13$ TeV. The $Σ^{+}$ is reconstructed via its weak-decay topology in the decay channel $Σ^{+} \rightarrow \rm{p} + π^{0}$ with $π^{0} \rightarrow γ+ γ$. In a novel approach, the neutral pion is reconstructed by combining photons that convert in the detector material with photons measured in the calorimeters. The transverse-momentum ($p_{\rm T}$) distributions of the $Σ^{+}$ and its rapidity densities ${\rm d}N$/${\rm d}y$ in both event classes are reported. The $p_{\rm T}$ spectrum in minimum-bias collisions is compared to QCD-inspired event generators. The ratio of $Σ^{+}$ to previously measured $Λ$ baryons is in good agreement with calculations from the Statistical Hadronization Model. The high efficiency and purity of the novel reconstruction method for $Σ^{+}$ presented here will enable future studies of the interaction of $Σ^{+}$ with protons in the context of femtoscopic measurements, which could be crucial for understanding the equation of state of neutron stars.

We investigate the problem of work extraction from a cavity-based quantum battery that is remotely charged via a transmission line composed of an array of coupled single-mode cavities. For uniform coupling along the line, we show that the ergotropy of the battery, evaluated at the point of maximum power transfer, decreases with the length of the charging line and vanishes beyond a critical size. By carefully engineering the initial state of the charger, nonzero ergotropy can still be harvested even beyond this critical length. We further examine scenarios in which the charging line is initialized in an entangled state, as well as configurations with nonuniform, parabolically varying coupling strengths. In the latter case, we demonstrate that high ergotropy values can be restored, highlighting the potential of spatially engineered interactions to enhance quantum battery performance.

We establish analytic linearization of s-proper analytic groupoids around invariant submanifolds. We apply this result to show that any such groupoid admits a holomorphic extension.

We generalize the $2$-tensor paraproduct decomposition result of [arXiv:2503.12629] to $d$-tensors. In particular, we show that for $A \in C^{d}(\mathbb{R}), f \in Λ_α([0,1]^d)$, $A(f)$ can be approximated by $\tilde{A}_{(N_i)_{i=0}^d}(f) = (\sum_{β=1}^d A^β(P^{j_1,j_2, \ldots, j_d}(f)) \tilde{\mathbf{v}}^β(f) ) $ with the residual $Δ_{(N_i)_{i=1}^d}(A,f) = \tilde{A}_{(N_i)_{i=1}^d}(f) - A(f) \in Λ_{2α}([0,1]^d)$. Our theoretical findings are supported by a computational example for d=3.

The geometric median, a notion of center for multivariate distributions, has gained recent attention in robust statistics and machine learning. Although conceptually distinct from the mean (i.e., expectation), we demonstrate that both are very close in high dimensions when the dependence between the distribution components is suitably controlled. Concretely, we find an upper bound on the distance that vanishes with the dimension asymptotically, and derive a rate-matching first order expansion of the geometric median components. Simulations illustrate and confirm our results.

The gravitational wave event GW231123 detected by the LIGO interferometers during their fourth observing run features two black holes with source-frame masses of $137^{+23}_{-18} M_\odot$ and $101^{+22}_{-50} M_\odot$ -- in the range of the pair-instability black hole mass gap predicted by standard stellar evolution theory. Both black holes are also inferred to be rapidly spinning ($χ_1 \simeq 0.9$, $χ_2 \simeq 0.8$). The primary object in GW231123 is the heaviest stellar mass black hole detected to date, which, together with its extreme rotation, raises questions about its astrophysical origin. Accounting for the unusually large spin of $\sim 0.9$ with hierarchical mergers requires some degree of fine tuning. We investigate whether such a massive, highly spinning object could plausibly form from the collapse of a single rotating massive star. We simulate stars with an initial core mass of $160\,M_\odot$ -- sufficient to produce BH masses at the upper edge of the 90\% credible interval for $m_1$ in GW231123 -- across a range of rotation rates and $^{12}\mathrm{C}(α,γ)^{16}\mathrm{O}$ reaction rates. We allow for differential rotation to explore the high-spin regime. In this limit of weak angular momentum transport, we find that: (i) rotation shifts the pair-instability mass gap to higher masses, introducing an important correlation between masses and spins in gravitational wave predictions; and (ii) highly spinning BHs with masses $\gtrsim 150 \rm M_\odot$ can form above the mass gap. Our results suggest that the primary object of GW231123 may be the first directly observed black hole that formed via direct core collapse following the photodisintegration instability.

Financial models do not merely analyse markets, but actively shape them. This effect, known as performativity, describes how financial theories and the subsequent actions based on them influence market processes, by creating self-fulfilling prophecies. Although discussed in the literature on economic sociology, this deeply rooted phenomenon lacks mathematical formulation in financial markets. Our paper closes this gap by breaking down the canonical separation of diffusion processes between the description of the market environment and the financial model. We do that by embedding the model in the process itself, creating a closed feedback loop, and demonstrate how prices change towards greater conformity to the prevailing financial model used in the market. We further show, with closed-form solutions and machine learning, how a performative market maker can reverse engineer the current dominant strategies in the market and effectively arbitrage them while maintaining competitive quotes and superior P&L.

Spatial point process (SPP) models are commonly used to analyze point pattern data in many fields, including presence-only data in ecology. Existing exact Bayesian methods for fitting these models are computationally expensive because they require approximating an intractable integral each time parameters are updated and often involve algorithm supervision (i.e., tuning in the Bayesian setting). We propose a flexible, efficient, and exact multi-stage recursive Bayesian approach to fitting SPP models that leverages parallel computing resources to obtain realizations from the joint posterior, which can then be used to obtain inference on derived quantities. We outline potential extensions, including a framework for analyzing study designs with compact observation windows and a neural network basis expansion for increased model flexibility. We demonstrate this approach and its extensions using a simulation study and analyze data from aerial imagery surveys to improve our understanding of spatially explicit abundance of harbor seal (Phoca vitulina) pups in Johns Hopkins Inlet, a protected tidewater glacial fjord in Glacier Bay National Park, Alaska.

Higher rank gauge theories are generalizations of electromagnetism where, in addition to overall charge conservation, there is also conservation of higher rank multipoles such as the total dipole moment. In this work we study a four dimensional lattice tensor gauge theory coupled to bosonic matter which has second rank tensor electric and magnetic fields and charge conservation on individual planes. Starting from the Hamiltonian, we derive the lattice action for the gauge fields coupled to $q=1,2$ charged scalars. We use the action formulation to carry out Monte Carlo simulations to map the phase diagram as a function of the gauge ($β$) and matter ($κ$) couplings. We compute the nature of correlators at strong and weak coupling in the pure gauge theory and compare the results to numerical simulations. Simulations show that the naive weak coupling regime (small $κ$, large $β$) does not survive in the thermodynamic limit. Instead, the strong coupling confined phase, spans the whole phase diagram. It is a proliferation of instantons that destroys the weak coupling phase and we show, via a duality transformation, that the expected strong confinement is present in the analog of Wilson line correlators. For finite matter coupling at $q=1$ we find a single thermodynamic phase albeit with a first order phase transition terminating in a critical endpoint.For $q=2$ it is known that the the X-cube model with $\mathbb{Z}_2$ fractonic topological order is recovered deep in the Higgs regime. The simulations indeed reveal a distinct Higgs phase in this case.

The origin of a number of proton-rich isotopes in the solar system has been a long-standing puzzle. A promising explanation is the $νp$-process, which is posited to operate in the neutrino-driven outflows that form inside core-collapse supernovae after shock revival. While recent studies have analyzed several relevant physical effects that influence the efficiency of this process, the impact of General Relativity (GR) on it remains unexplored. We perform a comparative analysis of the time-integrated $νp$-process yields in Newtonian and fully GR calculations, using detailed models of time-evolving outflow profiles. The GR effects are seen to suppress the production of seed nuclei, significantly boosting the resulting $p$-nuclide abundances. Our reference GR model, with an 18~$M_\odot$ progenitor, reproduces both the relative and absolute solar system abundances of the entire set of the $p$ nuclides in the mass range $74\leq A\leq102$. The yields are suboptimal in our 12.75~$M_\odot$ GR model, where the outflow transitions to the supersonic regime several seconds into the explosion, suppressing further $p$-nuclide production. In both models, most of the production of the crucial $^{92,94}{\rm Mo}$ and $^{96,98}{\rm Ru}$ $p$ isotopes occurs relatively early, 1--3 seconds after shock revival. In contrast, a large fraction of the shielded isotope $^{92}{\rm Nb}$ is produced in the subsequent ejecta. The impact of GR on this isotope is especially large, with its final abundance boosted by a factor of 25 compared to a Newtonian calculation. In summary, with the GR effects taken into account, the $νp$-process in a sufficiently massive progenitor can provide a unifying explanation for the origin of all $p$ nuclei in the solar system up to $^{102}$Pd.

The current transit universe model is a precise solution to the equations of a new type of gravity theory called metric-affine $f(R,T,Q,T_m)$ gravity proposed in [Herko et al. \textit{Phys. Dark Univ.} \textbf{34} (2021) 100886]. This theory is the maximal extension of the most successful theory, ``General Relativity," by including the scalars, Ricci curvature $R$, torsion $T$, nonmetricity $Q$, and trace $T_{m}$ of the matter-energy-momentum tensor using a generalized connection called the ``metric-affine" connection. We obtain the modified field equations for a linear form of the $f(R,T,Q,T_m)$ function and for a flat, homogeneous, and isotropic FLRW spacetime universe. We find a hyperbolic solution and determine the constrained values of the model parameters using the latest observational data. We examine how certain cosmological factors, like the deceleration parameter $q(z)$, effective equation of state parameter $ω_{\rm eff}$, and dark energy equation of state parameter $ω_{\rm de}$, vary over time to explain the properties of the observable universe. We perform the $Om$ diagnostic test for the model, and it represents the phantom scenarios of the model. The behavior of the dark energy EoS parameter $ω_{\rm de}$ reveals the quintom-A-type universe characteristics.

Aqueous foams are subject to coarsening, whereby gas from the bubbles diffuses through the liquid phase. Gas is preferentially transported from small to large bubbles, resulting in a gradual decrease of the number of bubbles and an increase in the average bubble size. Coarsening foams are expected to approach a scaling state at late times in which their statistical properties are invariant. However, a model predicting the experimentally observed bubble-size distribution in the scaling state of foams with moderate liquid content, as a function of the liquid fraction $ϕ$, has not yet been developed. To this end, we propose a three-dimensional mean-field bubble growth law for foams without inter-bubble adhesion, validated against bubble-scale simulations, and use it to derive a prediction of the scaling-state bubble-size distribution for any $ϕ$ from zero up to the unjamming transition $ϕ_\text{c} \approx 36\%$. We verify that the derived scaling state is approached from a variety of initial conditions using mean-field simulations implementing the proposed growth law. Comparing our predicted bubble-size distribution with previous simulations and experimental results, we likewise find a large population of small bubbles when $ϕ> 0$, but there are qualitative differences from prior results which we attribute to the absence of rattlers, i.e. bubbles not pressed into contact with their neighbours, in our model.

Gaussian quantum probes have been widely used in quantum metrology and thermometry, where the goal is to estimate the temperature of an environment with which the probe interacts. It was recently shown that introducing initial position-momentum (PM) correlations in such probes can enhance the estimation precision compared to standard, uncorrelated Gaussian states. Motivated by these findings, we investigate whether PM correlations can also be advantageous in a simultaneous estimation setting, specifically, when estimating both the PM correlations themselves and the effective environment temperature that interacts with the probe. Using the Quantum Fisher Information Matrix, we derive new precision bounds for this joint estimation task. Additionally, we demonstrate that such correlations can serve as a resource to improve temperature estimation within this multiparameter context. Finally, we analyze the compatibility between the two parameters, establishing conditions under which the derived bounds can be saturated.

While large transformer models have been successfully used in many real-world applications such as natural language processing, computer vision, and speech processing, scaling transformers for recommender systems remains a challenging problem. Recently, Generative Recommenders framework was proposed to scale beyond typical Deep Learning Recommendation Models (DLRMs). Reformulation of recommendation as sequential transduction task led to improvement of scaling properties in terms of compute. Nevertheless, the largest encoder configuration reported by the HSTU authors amounts only to ~176 million parameters, which is considerably smaller than the hundreds of billions or even trillions of parameters common in modern language models. In this work, we present a recipe for training large transformer recommenders with up to a billion parameters. We show that autoregressive learning on user histories naturally decomposes into two subtasks, feedback prediction and next-item prediction, and demonstrate that such a decomposition scales effectively across a wide range of transformer sizes. Furthermore, we report a successful deployment of our proposed architecture on a large-scale music platform serving millions of users. According to our online A/B tests, this new model increases total listening time by +2.26% and raises the likelihood of user likes by +6.37%, constituting (to our knowledge) the largest improvement in recommendation quality reported for any deep learning-based system in the platform's history.

Bosonic systems, particularly in quantum optics and atomic physics, are leading platforms for achieving quantum enhanced precision in parameter estimation. By exploiting properties such as mode and particle entanglement, it is possible to attain precisions that surpass the shot noise limit with respect to key resources like probe number or energy. Yet the mechanisms by which these bosonic resources enable quantum enhancement remain unclear. Consequently, the design of optimal probes and evolutions often relies on case by case analyses, where continuous and discrete variable regimes are treated separately and their connection is still unclear. We develop a comprehensive framework for quantum metrology that unifies all known precision enhancement mechanisms based on bosonic systems. Our approach employs a superselection rule compliant representation of the electromagnetic field that explicitly includes the phase reference, thereby enforcing total particle number conservation and bridging the discrete and continuous limits of quantum optics and symmetric massive systems. Within this unified formalism, of which established results emerge as special cases, we identify the distinct roles of mode and particle entanglement for quantum enhanced precision. The framework further provides general measurement optimization strategies for arbitrary multimode entangled probe states and naturally incorporates noise and non-unitary dynamics, ensuring applicability to realistic experimental conditions.

The transverse momentum spectra and integrated yields of anti-$Σ$ hyperons ($\overlineΣ^{\pm}$) have been measured in pp and p-Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV with the ALICE experiment. Measurements are performed via the newly accessed decay channel $\overlineΣ^{\pm} \rightarrow {\rm\overline{n}}π^{\pm}$. A new method of antineutron reconstruction with the PHOS electromagnetic spectrometer is developed and applied to this analysis. The $p_{\rm T}$ spectra of $\overlineΣ^{\pm}$ are measured in the range $0.5 < p_{\rm T} < 3$ GeV/$c$ and compared to predictions of the PYTHIA 8, DPMJET, PHOJET, EPOS LHC and EPOS4 models. The EPOS LHC and EPOS4 models provide the best descriptions of the measured spectra both in pp and p-Pb collisions, while models which do not account for multiparton interactions provide a considerably worse description at high $p_{\rm T}$. The total yields of $\overlineΣ^{\pm}$ in both pp and p-Pb collisions are compared to predictions of the Thermal-FIST model and dynamical models PYTHIA 8, DPMJET, PHOJET, EPOS LHC and EPOS4. All models reproduce the total yields in both colliding systems within uncertainties. The nuclear modification factors $R_\mathrm{pPb}$ for both $\overlineΣ^{+}$ and $\overlineΣ^{-}$ are evaluated and compared to those of protons, $Λ$ and $Ξ$ hyperons, and predictions of EPOS LHC and EPOS4 models. No deviations of $R_\mathrm{pPb}$ for $\overlineΣ^{\pm}$ from the model predictions or measurements for other hadrons are found within uncertainties.

The model organism Physarum polycephalum is known to perform decentralised problem solving despite absence of nervous system. Experimental evidence and modelling studies have linked these abilities, and in particular maze-solving, to some sort of memory and adaptation. However, despite compelling hypotheses, it is still not clear whether the tasks are solved optimally, and which key dynamical mechanisms enable Physarum's impressive abilities. Here, we employ a circuital network model for the foraging behaviour of Physarum polycephalum to prove that threshold sensing yields the emergence of unique and optimal paths that connect food sources and solve mazes. We also prove which conditions lead to alternative paths, thus elucidating how the organism achieves flexibility and adaptation in a self-organised manner. These findings are aligned with experimental evidences and provide insight into the evolution of primitive intelligence. Our results can also inspire the development of threshold-based algorithms for computing applications.

We show that the gravitational Green-Schwarz (GS) transformation becomes trivial in the non-relativistic (NR) limit of ten-dimensional heterotic supergravity with four-derivative corrections. This constitutes an important step towards establishing the trivialization of the GS mechanism in this limit. In this work, we perform a NR expansion of the Kalb-Ramond field and identify the finite Green-Schwarz transformation in this limit, which can be interpreted as a non-covariant $SO(8)$ transformation. We then construct an explicit field redefinition such that the redefined two-form is invariant under this symmetry. This result is compared with the previously reported trivialization of the gauge GS mechanism under the same limit. Both field redefinitions can be implemented simultaneously, and the associated Chern-Simons terms are exact, arising directly from the redefinition structure, and leading to a trivial Bianchi identity. These results support the expectation that anomaly cancellation becomes automatic in the NR regime, and therefore we discuss their potential implications.

The ICARUS liquid argon TPC detector is taking data on the Booster (BNB) and Main Injector (NuMI) Neutrino beam lines at Fermilab with a trigger system based on the scintillation light produced by charged particles in coincidence with the proton beam extraction from the accelerators. The architecture and the deployment of the trigger system in the first two runs for physics are presented, as well as the triggered event rates. The event recognition efficiency has been evaluated as a function of the deposited energy and the position of cosmic muons stopping inside the detector.

Biological organisms are adaptive, able to function in unpredictably changing environments. Drawing on recent nonequilibrium physics, we show that in adaptation, fitness has two components parameterized by observable coordinates: a static Generalism component characterized by state distributions, and a dynamic Tracking component sustained by nonequilibrium fluxes. Our findings: (1) General Theory: We prove that tracking gain scales strictly with environmental variability and switching time-scales; near-static or fast-switching environments are not worth tracking. (2) Optimal Strategies: We explain optimal bet-hedging and phenotypic memory as the interplay between these components. (3) Control: We demonstrate, with an example, how to suppress pathogens by independently attacking their Generalism robustness (via environmental time fractions) and Tracking capabilities (via environmental switching speed). This work provides a physical framework for understanding and controlling adaptivity.

The formation of black holes by the gravitational collapse of stars is known to spontaneously excite particle pairs out of the quantum vacuum. For the canonical vacuum state at past null infinity, the expected number of particles received at future null infinity can be obtained in full closed form at sufficiently late times. However, for intermediate times, or for more complicated astrophysical processes (e.g. binary black hole mergers), the problem is technically challenging and has not yet been resolved. We develop here a numerical approach to study scattering problems of massless quantum fields in asymptotically flat spacetimes, based on the hyperboloidal slice method used in numerical relativity and perturbation theory. This promising approach can reach both past and future null infinities, and therefore it has the potential to address the Hawking scattering problem more rigorously than evolution on the usual Cauchy slices. We test this approach with some dynamical toy models in Minkowski using effective potentials that mimic the effects of gravity, and compute the spectrum of particles received at future null infinity. We finally discuss future prospects for applying this framework in more relevant gravitational scenarios.

We show that for every $C^\infty$ diffeomorphism of a closed Riemannian manifold, if there exists a positive volume set of points which admit some expansion with a positive Lyapunov exponent (in a weak sense) then there exists an invariant probability measure with a disintegration by absolutely continuous conditionals on smoothly embedded disks subordinated to unstable leaves. As an application, we prove a strong version of the Viana conjecture in any dimension. Our methods include developing a quantitative approach to high-dimensional Yomdin theory which allows to control the geometry of disks, and introducing a notion of ``measured disks" in order to provide a disintegration by absolutely continuous conditionals. In particular, we provide also a new proof for the case of surfaces (a previous result by the second author) proving directly the absolute continuity of conditionals rather than mere entropy estimates.

In the framework of scalar-on-function regression models, in which several functional variables are employed to predict a scalar response, we propose a methodology for selecting relevant functional predictors while simultaneously providing accurate smooth (or, more generally, regular) estimates of the functional coefficients. We suppose that the functional predictors belong to a real separable Hilbert space, while the functional coefficients belong to a specific subspace of this Hilbert space. Such a subspace can be a Reproducing Kernel Hilbert Space (RKHS) to ensure the desired regularity characteristics, such as smoothness or periodicity, for the coefficient estimates. Our procedure, called SOFIA (Scalar-On-Function Integrated Adaptive Lasso), is based on an adaptive penalized least squares algorithm that leverages functional subgradients to efficiently solve the minimization problem. We demonstrate that the proposed method satisfies the functional oracle property, even when the number of predictors exceeds the sample size. SOFIA's effectiveness in variable selection and coefficient estimation is evaluated through extensive simulation studies and a real-data application to GDP growth prediction.

We present a comprehensive investigation into the anomalous magnetic dipole moment ($a_τ$) and electric dipole moment ($d_τ$) of the $τ$ lepton using the $γγ\to τ^+τ^-$ process at future lepton colliders, with the Super Tau-Charm Facility serving as a benchmark. By employing transverse-momentum-dependent factorization, we introduce novel observables derived from $\cos2ϕ$, $\sin2ϕ$, and $\cos4ϕ$ azimuthal asymmetries to precisely probe the $τ$ lepton's electromagnetic structure. Our analysis significantly enhances the precision of $a_τ$ constraints within the photon-photon fusion process, yielding $\mathrm{Re}(a_τ) \in [-4.6, 7.0] \times 10^{-3}$ at the $2σ$ confidence level, which approaches the precision of the Standard Model prediction. These findings highlight the considerable potential of azimuthal asymmetry measurements for high-precision determinations of fundamental particle properties at future lepton colliders.