The long-standing question of whether the residual entropy of hexagonal ice ($S_h$) equals that of cubic ice ($S_c$) remains unresolved despite decades of research on ice-type models. While analytical studies have established the inequality $S_h \geq S_c$, numerical investigations suggest that the two values are very close. In this work, we revisit this problem using high-precision tensor-network methods. In Monte Carlo approaches the residual entropy cannot be directly obtained by sampling the ground-state degeneracy space, however, the tensor-network framework enables an explicit encoding of the "ice rule'' into local tensors, and then the residual entropy is transformed into finding the largest eigenvalue of a transfer operator in the form of a projected entangled-pair operator, which allows high-accuracy numerical evaluation. Meanwhile, we propose a new perspective based on analyzing the normality of the transfer operator, and demonstrate that if the operator is normal, the equality $S_h = S_c$ follows directly. Then the variational tensor network methods are employed to numerically verify this normality. Finally both residual entropies are directly computed by using our recently developed split corner transfer matrix renormalization group algorithm, providing a rigorous evidence supporting the equality between $S_h$ and $S_c$.

The rapid advancement of location-based services (LBSs) in three-dimensional (3D) domains, such as smart cities and intelligent transportation, has raised concerns over 3D spatiotemporal trajectory privacy protection. However, existing research has not fully addressed the risk of attackers exploiting the spatiotemporal correlation of 3D spatiotemporal trajectories and the impact of height information, both of which can potentially lead to significant privacy leakage. To address these issues, this paper proposes a personalized 3D spatiotemporal trajectory privacy protection mechanism, named 3DSTPM. First, we analyze the characteristics of attackers that exploit spatiotemporal correlations between locations in a trajectory and present the attack model. Next, we exploit the complementary characteristics of 3D geo-indistinguishability (3D-GI) and distortion privacy to find a protection location set (PLS) that obscures the real location for all possible locations. To address the issue of privacy accumulation caused by continuous trajectory queries, we propose a Window-based Adaptive Privacy Budget Allocation (W-APBA), which dynamically allocates privacy budgets to all locations in the current PLS based on their predictability and sensitivity. Finally, we perturb the real location using the allocated privacy budget by the PF (Permute-and-Flip) mechanism, effectively balancing privacy protection and Quality of Service (QoS). Simulation results demonstrate that the proposed 3DSTPM effectively reduces QoS loss while meeting the user's personalized privacy protection needs.

The dynamics of a spinning colored particle in a background non-Abelian Yang-Mills field is of broad interest in many areas of physics. A physically important application arises in relativistic heavy-ion collisions, where hard probes such as heavy quarks and jets propagate through the strong early-time classical color fields collectively referred to as the glasma. The standard framework for describing the classical dynamics of colored particles in a background Yang-Mills field is provided by the Wong equations, but it does not incorporate spin degrees of freedom. Although several extensions of the Wong equations have been proposed to include spin, they generally fail to satisfy all the necessary requirements simultaneously, such as Lorentz covariance, allowance for an arbitrary chromomagnetic moment, and preservation of the required physical constraints. In this work, we extend the framework of a relativistic classical spinning particle in an electromagnetic field to describe spin-1/2 quarks propagating in a generic background non-Abelian Yang-Mills field. By systematically applying the Dirac-Bergmann algorithm, we derive a self-consistent set of equations of motion for the particle's coordinates, momenta, spin, and color charge that satisfies all these requirements. This formalism provides a more complete and physically consistent description of spinning colored particles in background Yang-Mills fields, and offers a suitable framework for studying momentum diffusion and spin polarization phenomena of hard probes in heavy-ion collisions, particularly in the glasma.

We extend based cluster algebras from the finite rank case to the infinite rank case. By extending (quantum) cluster algebras whose initial seeds are associated with signed words (arising from double Bott-Samelson cells), we recover infinite rank cluster algebras arising from representations of (shifted) quantum affine algebras. As a main application, we show that the fundamental variables of the cluster algebras arising from double Bott-Samelson cells can be computed via a braid group action when the Cartan matrix is of finite type. We also obtain the equality A=U for the associated infinite rank (quantum) cluster algebras. Additionally, several conjectures regarding quantum virtual Grothendieck rings due to Jang-Lee-Oh and Oh-Park follow as consequences. Finally, we show that the cluster algebras arising from representations of shifted quantum affine algebras, discovered by Geiss-Hernandez-Leclerc, admit natural quantizations.

We study wavepackets that propagate across (a) topological interfaces in quantum spin systems exhibiting non-invertible symmetries and (b) duality defects coupling dual theories. We demonstrate that the transmission is always perfect, and that a particle traversing the interface is converted into a nonlocal string-like excitation. We give a systematic way of constructing such a defect by identifying its Hilbert space with the virtual bond dimension of the matrix product operator representing defect lines. Our work both gives an operational meaning to topological interfaces, and provides a lattice analogue of recent results solving the monopole paradox in quantum field theory.

Purpose: To demonstrate the feasibility of performing in-vivo imaging and quantitative relaxation mapping of soft and hard tissues using a low-cost, portable MRI scanner, and to establish the methodological foundations for zero echo time (ZTE) imaging in systems affected by strong field inhomogeneities. Methods: A complete framework for artifact-free ZTE imaging at low field was developed, including: (i) RF pulse pre/counteremphasis calibration to minimize ring-down and electronics switching time; (ii) an extension of a recent single-point double-shot (SPDS) protocol for simultaneous B0 and B1 mapping; and (iii) a model-based reconstruction incorporating these field maps into the encoding matrix. ZTE imaging and variable flip angle (VFA) T1 mapping were performed on phantoms and in-vivo human knees and ankles, and benchmarked against standard RARE and STIR acquisitions. Results: The optimized PETRA sequence produced 3D images of knees and ankles within clinically compatible times (< 15 min), revealing hard tissues such as ligaments, tendons, cartilage, and bone that are invisible in spin-echo sequences. The extended SPDS method enabled accurate field mapping, while the VFA approach provided the first in-vivo T1 measurements of hard tissues at B0 < 0.1 T. Conclusions: The proposed framework broadens the range of pulse sequences feasible in portable low-field MRI and demonstrates the potential of ZTE for quantitative and structural imaging of musculoskeletal tissues in affordable Halbach-based systems.

The discovery of ambient-pressure superconductivity with $T_{c,\text{onset}} > 40$ K in La$_3$Ni$_2$O$_7$ (LNO) thin films grown on the SrLaAlO$_4$ (SLAO) substrate with compressive ($\varepsilon\approx-2\%$) epitaxial strain provides a unique platform for investigating the superconducting mechanism in nickelate superconductors. Here, we use resonant inelastic X-ray scattering (RIXS) to unveil the dispersive spin excitations in the LNO/SLAO thin film and establish the strain dependence of the electronic and spin excitations in LNO thin films with strain ranging from $\varepsilon\approx-2\%$ to $+1.9\%$. Compared with bulk LNO, LNO/SLAO exhibits similar $dd$ excitations and spin dynamics, but with a larger spin-excitation bandwidth, whereas tensile-strained LNO/SrTiO$_3$ exhibits a marked suppression of both the spin excitations and the Ni $3d_{z^2}$-derived $dd$ excitations. This evolution reflects a strain-tuned interlayer exchange interaction $J_z$ and Ni $3d_{z^2}$-O 2$p_z$ hybridization. Our results demonstrate how epitaxial strain modulates the interlayer magnetic coupling and are consistent with scenarios in which the interlayer antiferromagnetic superexchange interaction promotes interlayer pairing in bilayer nickelates.

We present an analytical 1D axisymmetric model describing the evolution of the dynamic z-pinch. This model is capable of predicting the trajectories of the imploding sheath's magnetic piston and preceding shock front, along with the velocity, pressure, density, and magnetic field profiles, for any time-dependent current, spatially varying initial density profile, and weak initial axial field. The implosion is divided into stages, with each stage described by a set of coupled ordinary differential equations derived from the ideal MHD equations. Comparisons with experimental data from the COBRA pulsed-power facility are quite promising and imply this model could prove useful in designing and analyzing future pulsed-power experiments.

This is the manuscript of my "Habilitation à diriger des recherches", where I present the research work that I have done after my PhD, defended in 2009. The manuscript is divided in two parts. The first one is dedicated to atomic-structure calculations with neutral and trivalent lanthanides, in the contexts of ultracold gases and rare-earth doped solids. The second part deals with long-range interactions in ultracold gases of alkali-metal atoms and diatomic molecules, as well as lanthanide atoms. The detailed description of long-range interactions serves to characterize ultralow-temperature phenomena, like photoassociation and collisional shielding.

In this note, we answer positively a question of Yau by proving the existence of closed minimal surfaces with negative induced curvature in any sphere of large dimension. The proof follows the strategy of Song, applying it to closed Riemann surfaces with large automorphism groups, and obtaining almost hyperbolic minimal surfaces.

Topological gauge theories constitute a framework for understanding strongly correlated quantum matter in terms of weakly interacting composite degrees of freedom. Their topological properties become evident when these theories are realized on a space of non-trivial topology. Here, we propose a scheme to realize a one-dimensional topological gauge theory, the so-called chiral BF theory, on a ring geometry. We obtain such a theory by dimensionally reducing Chern-Simons theory on a disk to the chiral BF theory defined on the ring. Then, we encode the theory into a Hamiltonian with a coupling between angular momentum and density, and we propose and numerically benchmark its realization in an optically-dressed Bose gas confined in a ring-shaped trap. There, the topological properties of the underlying theory manifest themselves through a magnetic flux variable that is density-dependent. We quantify such density-dependent magnetic flux in terms of the ground-state angular momentum and the chiral properties of the system through a Bogoliubov analysis. Our proposal enables the observation of topological features of the chiral BF theory that become manifest due to the non-trivial topology of the ring geometry.

In \cite{Cha1}, the leading order term of the free energy of $\text{U(N)}$ lattice Yang-Mills theory in $Λ_n=\{0,\ldots,n\}^d\subset \mathbb{Z}^d$ was determined, for every $N\geq 1$ and $d\geq 2$. The formula is explicit apart from a contribution $K_d$ which corresponds to the limiting free energy of lattice Maxwell theory with boundary conditions induced by the axial gauge. By suitably adjusting the boundary conditions, we provide an equivalent characterization of $K_d$ that admits its explicit computation.

We introduce the Courant algebroid lift, a new construction that takes a Courant algebroid together with a vector bundle connection and produces, when the connection is flat in the image of the anchor, a Courant algebroid. In general, this lift produces a Courant-like structure that we call a curved Courant algebroid. We start by establishing a hierarchy of Courant algebroid properties and their associated structures. In this setting, we introduce curved Courant algebroids, which we show to be related to connections with torsion and curved differential graded Lie algebras. We use this to provide a classification of exact curved Courant algebroids. We show that the Courant algebroid lift of an exact Courant algebroid yields a natural link between the Patterson-Walker metric and generalized geometry. By lifting non-exact Courant algebroids, we establish a relation of these lifts to Lie algebras, Poisson and special complex geometry. Finally, we show that Courant algebroid lifts provide a large class of examples of Courant algebroid actions.

Geothermal field development typically involves complex processes that require multi-disciplinary expertise in each process. Thus, decision-making often demands the integration of geological, geophysical, reservoir engineering, and operational data under tight time constraints. We present Geothermal Analytics and Intelligent Agent, or GAIA, an AI-based system for automation and assistance in geothermal field development. GAIA consists of three core components: GAIA Agent, GAIA Chat, and GAIA Digital Twin, or DT, which together constitute an agentic retrieval-augmented generation (RAG) workflow. Specifically, GAIA Agent, powered by a pre-trained large language model (LLM), designs and manages task pipelines by autonomously querying knowledge bases and orchestrating multi-step analyses. GAIA DT encapsulates classical and surrogate physics models, which, combined with built-in domain-specific subroutines and visualization tools, enable predictive modeling of geothermal systems. Lastly, GAIA Chat serves as a web-based interface for users, featuring a ChatGPT-like layout with additional functionalities such as interactive visualizations, parameter controls, and in-context document retrieval. To ensure GAIA's specialized capability for handling complex geothermal-related tasks, we curate a benchmark test set comprising various geothermal-related scenarios and rigorously evaluate the system's performance. Beyond task-level automation, GAIA is a unified framework that tightly couples physics-based modeling with agentic reasoning, which enables both domain-infused agentic evolutionary algorithm (meta-evolution) and end-to-end geothermal data processing within a single system. This integration highlights GAIA's potential not only as an assistive tool but as a platform for accelerating scientific discovery and enabling more autonomous, data-driven geothermal field development.

We revisit the Standard Model description of the recently measured rare decays $D^0\toπ^+π^-\ell^+\ell^-$. Because of the effectiveness of the Glashow-Iliopoulos-Maiani mechanism in charm flavour-changing neutral currents, those decays are driven by non-local insertions of four-quark operators. Following previous work, we consider the mediation of resonances both for the dipion and dilepton pairs. For the first time, we incorporate the effect of the cascade-type topology $D^0\to π^- a_1^+(1260)(\toπ^+ρ^0(\to\ell^+\ell^-))$, which manifests distinctly in the invariant-mass and angular distributions. We find that this partial amplitude comprises one of the largest contributions to the decay rate and obtain an unprecedented agreement of the Standard Model prediction with the available LHCb data. Finally, we compare to the available CLEO-c, LHCb, and BESIII amplitude analyses for the analogous four-body hadronic decays and find that similar values of the hadronic parameters of our model successfully describe the two classes of decays.

We present a new model of the dark sector involving Dirac fermion dark matter, with axial coupling to a dark photon which provides a portal to Standard Model particles. In the non-relativistic limit, this implies that the dominant effective operator relevant to direct detection is ${\cal O}_8$. The resulting event rate for direct detection is suppressed by either the dark matter velocity or the momentum transfer. In this scenario there are much wider regions of the dark parameter space that are consistent with all of the existing constraints associated with thermal relic density, direct detection and collider searches.

Distribution theory is a cornerstone of the theory of partial differential equations. We report on the progress of formalizing the theory of tempered distributions in the interactive proof assistant Lean, which is the first formalization in any proof assistant. We give an overview of the mathematical theory and highlight key aspects of the formalization that differ from the classical presentation. As an application, we prove that the Fourier transform extends to a linear isometry on $L^2$ and we define Sobolev spaces via the Fourier transform on tempered distributions.

Privacy preservation has served as a key metric in designing Nash equilibrium (NE) computation algorithms. Although differential privacy (DP) has been widely employed for privacy guarantees, it does not exploit prior distributional knowledge of datasets and is ineffective in assessing information leakage for correlated datasets. To address these concerns, we establish a pointwise maximal leakage (PML) framework when computing NE in aggregative games. By incorporating prior knowledge of players' cost function datasets, we obtain a precise and computable upper bound of privacy leakage with PML guarantees. In the entire view, we show PML refines DP by offering a tighter privacy guarantee, enabling flexibility in designing NE computation with prior knowledge. Also, in the individual view, we reveal that the lower bound of PML can exceed the upper bound of DP by constructing specific correlated datasets. The results emphasize that PML is a more proper privacy measure than DP since the latter fails to adequately capture privacy leakage in correlated datasets. Moreover, we conduct experiments with adversaries who attempt to infer players' private information to illustrate the effectiveness.

Let $H_n$ be the row space of a signed adjacency matrix of a $C_4$-free bipartite bi-regular graph in which one part has degree $d(n)\to\infty$ and the other part has degree $k+1$ where $k\geq 1$ is a fixed integer. We show that the local limit as $n\to \infty$ of the determinantal process corresponding to the orthogonal projection on $H_n$ is a variant of a Poisson$(k)$ branching process conditioned to survive. This setup covers a wide class of determinantal processes such as uniform spanning trees, Kalai's determinantal hypertrees, hyperforests in regular polytopal complexes, discrete Grassmanians and incidence matroids, as long as their degree tends to $\infty$.

In this paper, we investigate the application of multivariate sampling Kantorovich (SK) operators for image reconstruction, with a particular focus on gap filling and speckle noise reduction. To understand the accuracy performances of the proposed algorithms, we first derive a quantitative estimate in $C(\R^n)$ for the error of approximation using the Euler-Maclaurin summation formula, under weak regularity conditions. We also establish a convergence result and a quantitative estimate with respect to the dissimilarity index measured by the continuous SSIM for functions in Lebesgue spaces. Additionally, we prove a multidimensional linear prediction result, which is used to design a new SK-based reconstruction algorithm to handle missing data, that we call LP-SK algorithm. To address speckle noise, we integrate SK operators into a newly proposed Down-Up scaling approach. Numerical tests are presented on synthetic and real SAR images to validate the proposed methods. Performance is assessed using similarity metrics such as SSIM and PSNR, along with speckle-specific indexes. Comparative analysis with state-of-the-art techniques highlights the effectiveness of the proposed approaches.

The interplay between band topology and material nonlinearity gives rise to a variety of novel phenomena, such as topological solitons and nonlinearity-induced topological phase transitions. However, most previous studies fall within the Hermitian regime, leaving the impact of nonlinearity on non-Hermitian topology seldom explored. Here, we investigate the effects of nonlinearity on the non-Hermitian skin effect, a well-known non-Hermitian phenomenon induced by the point-gap topology unique to non-Hermitian systems. Interestingly, we discover a nonlinearity-induced point-gap topological phase transition accompanied by a reversal of the skin mode localization, which is distinct from previous nonlinearity-induced line-gap topological phases. This phenomenon is experimentally demonstrated in a nonlinear microwave metamaterial, where electromagnetic waves are localized around one end of the sample under a low-intensity pump, whereas at a high-intensity pump, the waves are localized around the other end. Our results open a new route towards nonlinear topological physics in non-Hermitian systems and are promising for reconfigurable topological wave manipulation.

Automated code optimization improves program performance through refactoring, and recent studies leverage LLMs for this purpose. Existing approaches mine optimization commits from open-source codebases to build large-scale knowledge bases, then employ retrieval techniques such as BM25 to obtain relevant examples for hotspot code, guiding LLMs in optimization. However, semantically equivalent optimizations often appear in syntactically dissimilar code, so current retrieval methods fail to identify pertinent examples, leading to suboptimal results. To address these limitations, we propose SemOpt, a framework that leverages static program analysis to identify code segments, retrieve optimization strategies, and generate optimized results. SemOpt has three LLM-powered components: (1) a strategy library builder that extracts and clusters strategies from code modifications, (2) a rule generator that produces Semgrep static analysis rules to capture each strategy's applicability, and (3) an optimizer that generates optimized code using the strategy library. On a benchmark of 151 C/C++ and 150 Python optimization tasks, SemOpt shows consistent improvements across different LLMs, increasing successful optimizations by 1.38 to 28 times on C/C++ and 4.60 to 6.33 times on Python versus the baseline. On large-scale projects, SemOpt improves performance metrics by 5.04% to 218.07% on C/C++ and 61.77% to 479.90% on Python, showing cross-language generalization and practical effectiveness.

High-frequency gravitational waves (GWs), spanning frequencies from the microwave to the optical band, remain experimentally unexplored despite strong motivation from early-Universe dynamics, high-energy cosmology, and exotic compact objects. We propose a detection framework in which an incident GW excites an eigenmode of a high-$Q$ resonator in the presence of a static magnetic field through GW-induced electromagnetic mode conversion; the resulting cavity field is then read out using atomic sensors placed outside the magnetized volume. We analyze two concrete architectures: microwave detection based on Rydberg transitions and optical/near-infrared Raman schemes. For each, we derive projected strain sensitivities achievable with realistic, though ambitious, magnetic fields, cavity parameters, and atomic ensembles. Under optimistic assumptions on cavity performance, signal coherence, and technical noise, optical Raman implementations could approach benchmark narrowband coherent strain sensitivities relevant for speculative high frequency GW scenarios, while microwave systems may probe benchmark sensitivities in an otherwise unexplored frequency range. These setups motivate advances in high-$Q$ cavities, strong-field magnets, and quantum-limited atomic sensors, with broader implications for quantum instrumentation and fundamental physics.

Chiral active materials are abundant in nature, including the cytoskeleton with attached motor proteins, rotary clusters of bacterial flagella, and self-spinning starfish embryos. These materials break both time reversal and mirror-image (parity) symmetries due to injection of torques at the microscale. It was recently discovered that chiral active materials show a new type of elastic response termed `odd' elasticity. Currently, odd elasticity is understood microscopically only in ordered structures, e.g., lattice designs of metamaterials. It remains to explore how odd elasticity emerges in natural or biological systems, which are usually disordered. To address this, we propose a minimal generic model for disordered `odd solids', using micropolar (Cosserat) elasticity in the presence of local active torques. We find that odd elasticity naturally emerges as a nonlinear effect of internal particle rotations. Exploring the viscoelasticity of such a solid, when immersed in an odd fluid, we discover new dynamically unstable regions driven by the odd solid-fluid coupling, and, in the underdamped regime, also by inertia. Remarkably, in the overdamped limit, this odd solid-fluid coupling allows for bulk wave propagation near these unstable regions.

The future circular $e^+e^-$ collider (FCC-ee or CEPC) will provide unprecedented sensitivity to indirect new physics signals emerging as small deviations from the Standard Model predictions in electroweak precision tests. Assuming new physics scenarios containing a dark matter candidate and a $t$-channel mediator, we analyse the synergy and interplay of future Tera-$Z$ factories and non-collider tests conducted through direct and indirect searches of dark matter. Our results highlight the excellent prospect for a Tera-$Z$ run to indirectly probe the presence and nature of dark matter.

Recurrent Neural Networks (RNNs) have shown remarkable performances in system identification, particularly in nonlinear dynamical systems such as thermal processes. However, stability remains a critical challenge in practical applications: although the underlying process may be intrinsically stable, there may be no guarantee that the resulting RNN model captures this behavior. This paper addresses the stability issue by deriving a sufficient condition for Input-to-State Stability based on the infinity-norm (ISS$_{\infty}$) for Long Short-Term Memory (LSTM) networks. The obtained condition depends on fewer network parameters compared to prior works. A ISS$_{\infty}$-promoted training strategy is developed, incorporating a penalty term in the loss function that encourages stability and an ad hoc early stopping approach. The quality of LSTM models trained via the proposed approach is validated on a thermal system case study, where the ISS$_{\infty}$-promoted LSTM outperforms both a physics-based model and an ISS$_{\infty}$-promoted Gated Recurrent Unit (GRU) network while also surpassing non-ISS$_{\infty}$-promoted LSTM and GRU RNNs.

The SHIFT@LHC proposal introduced a novel shifted gaseous fixed-target concept at the LHC to search for exotic particles. In this letter, we explore an entirely different physics opportunity enabled by this setup: the observation of neutrinos in general-purpose LHC detectors. Using simulations of proton-gas collisions, hadron propagation, and neutrino interactions, we estimate that $O(10^4)$ muon-neutrino and $O(10^3)$ electron-neutrino interactions, with energies from 20 GeV to 1 TeV, would occur in the CMS and ATLAS detectors with 1% of the LHC Run 4 integrated luminosity ($\approx4\cdot10^{25}$ protons-on-target). This unique configuration provides access to hadron production in the pseudorapidity range $5<η<8$, complementary to existing LHC detectors. If realized, this would mark the first detection of neutrinos in a hadron collider detector, demonstrating the feasibility of such measurements in this experimental environment.

Symmetry plays a crucial role in the design and analysis of quantum protocols. This result shows a canonical circuit decomposition of a $(G\times H)$-invariant quantum comb for compact groups $G$ and $H$ using the corresponding Clebsch--Gordan transforms, which naturally extends to the $G$-covariant quantum comb. By using this circuit decomposition, we propose a parametrized quantum comb with group symmetry, and derive the optimal quantum comb which transforms an unknown unitary operation $U\in \mathrm{SU}(d)$ into its inverse $U^\dagger$ or transpose $U^\top$. From numerics, we find a deterministic and exact unitary transposition protocol for $d=3$ with $7$ queries to $U$. This protocol improves upon the protocol shown in the previous work, which requires $13$ queries to $U$.

We study methods for efficient preparation of approximate ground states of $SU(3)$ lattice gauge theory on quantum hardware. Working in a variant of the electric basis, we introduce a refinement of the irrep truncation based on the energy density of site singlets, which provides a finer gradation of simulation complexity. Using strong-coupling perturbation theory as a guide, we develop simple ansatz circuits for ground state preparation and test them via classical simulation on small lattices, including the $2\times 2$ plaquette lattice in $d=2$ and the cube in $d=3$. We contrast state fidelities and resource requirements of variational methods against adiabatic state preparation and introduce a method that hybridizes the two approaches. Finally, we report on the public release of \texttt{ymcirc} -- a package of tools for building $SU(3)$ circuits and processing measurements -- and \texttt{pyclebsch}, a package for efficiently computing $SU(N)$ Clebsch-Gordan coefficients.

Identifying frail older adults in an ageing population is essential for improving healthcare services. This study proposes a composite indicator to assess individual frailty levels using administrative healthcare data. Given the complex and multidimensional nature of frailty, a multi-outcome approach is adopted. Following an extensive literature review, a set of adverse health events is selected as proxies for frailty. These events were modelled using logistic classifiers, with frailty determinants (associated to adverse health events, selected using a gradient tree boosting) serving as covariates. The sensitivity and specificity of each classifier is used to compose their combined likelihood. From this, we derive an indicator capable of quantifying frailty across the population. The indicator shows robust performance across multiple outcomes and over time. Its primary innovation lies in allowing the use of diverse and outcome-specific sets of frailty determinants without any structural constraint. Overall, we offer an effective tool for quantifying frailty among older adults, potentially supporting health authorities in the prevention of frailty-related adverse events.