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Gaussian Mixture Model with unknown diagonal covariances via continuous sparse regularization
No full textThis paper addresses the statistical estimation of Gaussian Mixture Models (GMMs) with unknown diagonal covariances from independent and identically distributed samples. We employ the Beurling-LASSO (BLASSO), a convex optimization framework that promotes sparsity in the space of measures, to simultaneously estimate the number of components and their parameters. Our main contribution extends the BLASSO methodology to multivariate GMMs with component-specific unknown diagonal covariance matrices. This setting is significantly more flexible than previous approaches, which required known and identical covariances. We establish non-asymptotic recovery guarantees with nearly parametric convergence rates for component means, diagonal covariances, and weights, as well as for density prediction. A key theoretical contribution is the identification of an explicit separation condition on mixture components that enables the construction of non-degenerate dual certificates—essential tools for establishing statistical guarantees for the BLASSO. Our analysis leverages the Fisher-Rao geometry of the statistical model and introduces a novel semi-distance adapted to our framework, providing new insights into the interplay between component separation, parameter space geometry, and achievable statistical recovery
MEGATRON: the impact of non-equilibrium effects and local radiation fields on the circumgalactic medium at cosmic noon
No full textInternational audienceWe present three cosmological radiation-hydrodynamic zoom simulations of the progenitor of a Milky Way-mass galaxy from the MEGATRON suite. The simulations combine on-the-fly radiative transfer with a detailed non-equilibrium thermochemical network (81 ions and molecules), resolving the cold and warm gas in the circumgalactic medium (CGM) on spatial scales down to 20 pc and on average 200 pc at cosmic noon. Comparing our full non-equilibrium calculation with local radiation to traditional post-processed photoionization equilibrium (PIE) models assuming a uniform UV background (UVB), we find that non-equilibrium physics and local radiation fields fundamentally impact the thermochemistry of the CGM. Recombination lags and local radiation anisotropy shift ions away from their PIE+UVB values and modify covering fractions (for example, HI damped Ly absorbers differ by up to 40%). In addition, a resolution study with cooling-length refinement allows us to double the resolution in the cold and warm CGM gas, reaching 120 pc on average. When refining on cooling length, the mass of the lightest cold clumps decreases tenfold to , their boundary layers develop sharper ion stratification, and the warm gas is better resolved, boosting the abundance of warm gas tracers such as CIV and OIII. Together, these results demonstrate that non-equilibrium thermochemistry coupled to radiative transfer, combined with physically motivated resolution criteria, is essential to predict circumgalactic absorption and emission signatures and to guide the design of targeted observations with existing and upcoming facilities
Multiple Mellin-Barnes integrals with polygamma functions
No full textInternational audienceMellin-Barnes (MB) integrals appear in various branches of physics and mathematics and are, in particular, used as a standard tool for evaluating multi-loop, multi-scale Feynman integrals both analytically and numerically. Recent geometric approaches based on conic hulls and triangulations provide a systematic framework for computing multiple MB integrals in terms of multivariate series. These approaches have so far been limited to MB integrals whose integrands are ratios of products of Euler's gamma functions only. However, in Feynman integral calculus, MB integrals with polygamma functions naturally arise, for instance, after resolving singularities in the dimensional-regularisation parameter and expanding the MB integrand in powers of , as done by the public codes MB.m and MBresolve.m. In this paper, we extend the conic hull and triangulation methods to the computation of MB integrals having polygamma functions in their integrand. We show that the arguments of polygamma functions can be treated in a similar way to the arguments of gamma functions when applying the conic hull and triangulation techniques to identify poles that would contribute to different series solutions. However, since the singularity structure of the polygamma function is different from that of the gamma function, we propose two different ways to compute MB integrals involving polygamma functions, depending on whether the MB integral has straight or non-straight contours. We have implemented these algorithms in an updated version of the Mathematica package MBConicHulls.wl, which can be found at https://github.com/SumitBanikGit/MBConicHulls/, and we illustrate their use with a set of examples from Feynman integral calculus
Preoperative flexion contracture does not impair outcomes or early revision rates following robotic total knee arthroplasty with functional alignment
No full textInternational audienceAbstract Purpose Preoperative flexion contracture remains a challenging deformity in total knee arthroplasty (TKA). This study aimed to evaluate whether the presence of preoperative flexion contracture influences outcomes and early revision rates following robotic‐assisted TKA performed with functional alignment (FA) principles. Methods This retrospective comparative study analysed 190 patients who underwent robotic‐assisted TKA using a computed tomography‐based FA strategy. Patients were grouped based on intraoperative measurement of flexion contracture: ≥10° (study group; 43 patients) and <10° (control group; 147 patients). Clinical outcomes, intraoperative data, and early revision rates were assessed at a minimum 24‐month follow‐up. Results The study group exhibited significantly more varus alignment intraoperatively and required greater lateral tibial and posterior medial femoral resections. Preoperative knee flexion was lower in the contracture group (110° vs. 120°, p = 0.0018), and postoperative flexion remained slightly reduced (120° vs. 130°, p = 0.05). Flexion contracture at follow‐up was 1° in the study group versus 0° in controls ( p = 0.04). However, no significant differences were observed in Knee Society Scores, Forgotten Joint Score, Kujala score, or early revision rates. All‐cause revision rates were similar (97.67% vs. 98.64%, p = 0.66), with a hazard ratio of 1.85 (95% CI: 0.12–27.72). Aseptic survivorship was 100% in the contracture group versus 99.32% in controls ( p = 0.59). Conclusion Patients with preoperative flexion contracture ≥ 10° achieved comparable mid‐term outcomes and early survivorship to those without contracture following robotic‐assisted TKA using FA. These findings support FA as a reliable strategy to manage complex deformities without the need for soft tissue releases. Level of Evidence Level III
-structures through quotient by torus actions
No full textWe show that if is a Kähler manifold with an -structure and a Hamiltonian holomorphic action of a compact torus , then the usual symplectic quotient inherits an -structure provided the existence of special 1-forms on X, called twist forms. We then give several applications of our results: on complex projective spaces, on cones over Fano Kähler-Einstein manifold and on toric bundles. We also study the geometry behind these structures in the case of
A Cahn--Hilliard--Willmore phase field model for non-oriented interfaces
No full textInternational audienceWe investigate a new phase field model for representing non-oriented interfaces, approximating their area and simulating their area-minimizing flow. Our contribution is related to the approach proposed in arXiv:2105.09627 that involves ad hoc neural networks. We show here that, instead of neural networks, similar results can be obtained using a more standard variational approach that combines a Cahn-Hilliard-type functional involving an appropriate non-smooth potential and a Willmore-type stabilization energy. We show some properties of this phase field model in dimension and, for radially symmetric functions, in arbitrary dimension. We propose a simple numerical scheme to approximate its -gradient flow. We illustrate numerically that the new flow approximates fairly well the mean curvature flow of codimension or interfaces in dimensions and
Search for resonances decaying to an anomalous jet and a Higgs boson in proton-proton collisions at = 13 TeV
No full textInternational audienceThis paper presents a search for new physics through the process where a new massive particle, X, decays into a Higgs boson and a second particle, Y. The Higgs boson subsequently decays into a bottom quark-antiquark pair, reconstructed as a single large-radius jet. The decay products of Y are also assumed to produce a single large-radius jet. The identification of the Y particle is enhanced by computing the anomaly score of its candidate jet using an autoencoder, which measures deviations from typical QCD multijet jets. This allows a simultaneous search for multiple Y decay scenarios within a single analysis. In the main benchmark process, Y is a scalar particle that decays into WW. Two other benchmark processes are also considered, where Y is a scalar particle decaying into a light quark-antiquark pair, or into a top quark-antiquark pair. The last benchmark considers Y as a hadronically decaying top quark, arising from the decay of a vector-like quark into a top quark and a Higgs boson. Data recorded by the CMS experiment at a center-of-mass energy of 13 TeV in 20162018, and corresponding to an integrated luminosity of 138 fb, are analyzed. No significant excess is observed, and upper limits on the benchmark signal cross section for various masses of X and Y, at 95% confidence level, are placed
ZTF SN Ia DR2 follow-up: Exploring the origin of the Type Ia supernova host galaxy step through Si II velocities
No full textInternational audienceThe relationship between Type Ia supernovae (SNe Ia) and their host galaxy stellar masses is well documented. In particular, Hubble residuals display a luminosity shift based on host mass, known as the mass step, which is often used as an extra correction in the standardisation of SN Ia luminosities. Here we investigate Hubble residuals and the mass step in the context of Si II velocities, using 277 near-peak SNe Ia from ZTF DR2. We divide the sample into high-velocity (HV) and normal-velocity (NV) SNe Ia, separated at 12,000 km/s, resulting in 70 HV and 207 NV objects. We then examine links between Si II 6355 velocities, light-curve stretch , colour , and host properties to explore potential environmental and/or progenitor-related effects. Although we only find a marginal difference between the Hubble residuals of HV and NV SNe Ia, the NV mass step is mag (), while HV SNe Ia show mag (), consistent with zero. The NV-HV mass-step difference is . The clearest subtype difference is seen in central regions (), while NV SNe show stronger environmental trends. Thus, NV SNe Ia appear more environmentally sensitive, especially in central, likely metal-rich and older regions, while HV SNe Ia show weaker, subset-dependent trends, and applying a universal mass-step correction could introduce biases. Refined classifications or environment-dependent factors may improve future cosmological analyses beyond standard and cuts
First exclusive reconstruction of the B, B, and B mesons and precise measurement of their masses
No full textInternational audienceUsing proton-proton collision data collected by the CMS experiment at = 13 TeV in 20162018, corresponding to an integrated luminosity of 140 fb, the first full reconstruction of the three vector B meson states, B, B, and B, is performed. The mass differences between the excited mesons and their corresponding ground states are measured to be = 45.277 0.039 0.027 MeV, = 45.471 0.056 0.028 MeV, and = 49.407 0.132 0.041 MeV, where the first uncertainties are statistical and the second are systematic. These results improve on the precision of previous measurements by an order of magnitude
The Dark Energy Bedrock All-Sky Supernova Program: Cross Calibration, Simulations, and Cosmology Forecasts
No full textInternational audienceType Ia supernovae (SNe Ia) have been essential for probing the nature of dark energy; however, most SN analyses rely on the same low-redshift sample, which may lead to shared systematics. In a companion paper (arXiv:2508.10878), we introduce the Dark Energy Bedrock All-Sky Supernova (DEBASS) program, which has already collected more than 500 low-redshift SNe Ia on the Dark Energy Camera (DECam), and present an initial release of 77 SNe Ia within the Dark Energy Survey (DES) footprint observed between 2021 and 2024. Here, we examine the systematics, including photometric calibration and selection effects. We find agreement at the 10 millimagnitude level among the tertiary standard stars of DEBASS, DES, and Pan-STARRS1. Our simulations reproduce the observed distributions of DEBASS SN light-curve properties, and we measure a bias-corrected Hubble residual scatter of mag, which, while small, is found in 10% of our simulations. We compare the DEBASS SN distances to the Foundation sample and find consistency with a median residual offset of mag. Selection effects have negligible impacts on distances, but a different photometric calibration solution shifts the median residual mag, highlighting calibration sensitivity. Using conservative simulations, we forecast that replacing historical low-redshift samples with the full DEBASS sample (>400 SNe Ia) will improve the statistical uncertainties on dark energy parameters and by 30% and 24% respectively, enhance the dark energy Figure of Merit by up to 60%, and enable a measurement of at the 25% level