We investigate the capability of the J-PAS survey to constrain the primordial power spectrum using a non-parametric Bayesian method. Specifically, we analyze simulated power spectra generated by a local oscillatory primordial feature template motivated by non-standard inflation. The feature is placed within the range of scales where the signal-to-noise ratio is maximized, and we restrict the analysis to $k \in [0.02,0.2] \text{ h} \text{ Mpc}^{-1}$, set by the expected J-PAS coverage and the onset of non-linear effects. Each primordial power spectrum is reconstructed by linearly interpolating $N$ knots in the $\{\log k, \log P_{\mathcal{R}}(k)\}$ plane, which are sampled jointly with the cosmological parameters $\{H_0,Ω_b h^2, Ω_c h^2\}$ using PolyChord. To test the primordial features, we apply two statistical tools: the Bayes factor and a hypothesis test that localizes the scales where features are detected. We assess the recovery under different J-PAS specifications, including redshift binning, tracer type, survey area, and filter strategy. Our results show that combining redshift bins and tracers allows the detection of oscillatory features as small as 2\%.

Let $ξ$ be a real number and $b \ge 2$ an integer. We study the relationship between the irrationality exponent of $ξ$ and the subword complexity $p(n, \mathbf{x})$ of the $b$-ary expansion $\mathbf{x}$ of $ξ$, where $p(n, \mathbf{x})$ counts the number of distinct blocks of length $n$ in $\mathbf{x}$, for $n \ge 1$. If the irrationality exponent of $ξ$ is equal to $2$, which is the case for almost all real numbers $ξ$, we show that the limit superior of the sequence $(p(n, \mathbf{x}) / n)_{n \ge 1}$ is at least equal to 4/3. The proof is based on a careful study of the evolution of the Rauzy graphs of infinite words of low complexity.

We investigate the interplay between chirality and confinement in harmonically trapped active particles. The circular character of chiral motion combines with the radial symmetry of the potential to create distinctive non-equilibrium behavior. Chirality induces oscillatory cross-correlations between positional components that vanish in the absence of torque while the harmonic potential generates a finite delay between orientation and velocity - a signature of time-reversal symmetry breaking distinct from inertial delay mechanisms. The delay function exhibits characteristic temporal evolution with depth and persistence controlled by trap strength and rotational noise. The stationary probability distribution displays strongly non-Maxwellian characteristics, transitioning from broad annuli to compact localized peaks as confinement increases with the distribution radius governed by the competition between chiral propulsion and trap strength. These features emerge from the interplay between chiral swimming and the restoring force of the trap, revealing how confinement and activity jointly shape particle dynamics and transport properties in nonequilibrium steady states.

We show how crystalline inversion symmetry can be dynamically broken by optical phonons with generic, hardening Kerr-like non-linearities. The symmetry-broken state is reached through a parametric instability that can be accessed by driving close to half the phonon resonance. After the onset of the instability, the system settles to a steady state with inversion-symmetry breaking phonon trajectories and strong second harmonic generation. The time averaged positions of the atoms are displaced relative to equilibrium, resulting in a ferroelectric rectification of the driving signal.

We investigate electron pairing in a super clean kagome superconductor CsV3Sb5 with a residual resistivity ratio (RRR) of 290. By using the dilution-refrigerator-based scanning tunneling microscopy (STM) at the Synergetic Extreme Condition User Facility (SECUF), we find that the pairing gap exhibits chiral 2x2 modulations, and their chirality can be controlled by magnetic field training. We introduce nonmagnetic impurities to observe the complete suppression of 2x2 pairing modulations in presence of persistent 2x2 charge order. This nonmagnetic pair-breaking effect provides phase-sensitive evidence for pair-density-wave (PDW) induced pairing modulations. Our results support switchable chiral 2x2 PDW in this super clean kagome superconductor.

The remote dipole and quadrupole fields (RDF/RQF) encode information about the observable universe as seen from remote places within our past light cone. Sensitive to the superhorizon inhomogeneites, they provide a unique way to probe physics at the largest scales, bypassing the limitations of cosmic variance inherent in the primary cosmic microwave background (CMB). In this work, we focus on the bubble collision predicted by the eternal inflation theory, which can leave distinct azimuthally symmetric patterns on the superhorizon scales, potentially detectable through the RDF and RQF. We present the first analytic expression of the RQF signal induced by bubble collision and validate it against numerical calculations performed with $\texttt{RemoteField}$, a new public software tool we developed, finding excellent agreement between the two. Combining our new RQF calculation with the corresponding RDF signal calculated by prior work, we forecast the constraining power on bubble collision parameters using RDF/RQF reconstruction. We find that, for an CMB-S4-like and an LSST-like experiment, the RDF reconstruction can provide comparable constraining power as that from the primary CMB alone; and the RQF reconstruction can improve the constraining power by about an order of magnitude. We argue that these constraints can be improved further by including more RDF/RQF multipoles included and by using tomographic techniques to mitigate the standard $Λ$CDM signal. We anticipate the framework we developed in this work to be broadly applicable to probe other superhorizon-scale physics, such as cosmic topology and domain walls.

We present a family of analytic solutions for the nearly-equatorial motion of a test particle with precessing spin in Kerr spacetime. We solve the equations of motion up to linear order in the small body's spin for periodic and homoclinic orbits. At zero order, the particle moves along equatorial geodesics. The spin-curvature force introduces post-geodesic corrections which, for generic spin orientations, cause the precession of the orbital plane. We derive the solutions for eccentric orbits in terms of Legendre elliptic integrals and Jacobi elliptic functions for generic referential geodesics (known as ``spin gauges"). Our analytical solutions perfectly match the numerical trajectories obtained by Drummond and Hughes in Phys. Rev. D 105, 124041 (2022), and Piovano et al. in Phys. Rev. D 111, 044009 (2025). Furthermore, we present, for the first time, the solutions for homoclinic orbits for a spinning particle in Kerr spacetime, and the spin-corrections to the location of the separatrix. The homoclinic trajectories are described in closed form using elementary functions. Finally, we introduce a novel parametrization for the motion of a spinning particle, called ``fixed eccentricity spin gauge". This is the only spin gauge in which the corrections to periodic orbits are finite at the geodesic separatrix, and continuously reduce to the last stable orbits under appropriate limits. Our results will be useful for modeling the inspiral and transition-to-plunge phases of asymmetric mass binaries within the two-time-scale framework.

We propose a multiscale method for mixed-dimensional elliptic problems with highly heterogeneous coefficients arising, for example, in the modeling of fractured porous media. The method is based on the Localized Orthogonal Decomposition (LOD) framework and constructs locally supported, problem-adapted basis functions on a coarse mesh that does not need to resolve the coefficient oscillations. These basis functions are obtained in parallel by solving localized fine-scale problems. Our a priori error analysis shows that the method achieves optimal convergence with respect to the coarse mesh size, independent of the coefficient regularity, with an exponentially decaying localization error. Numerical experiments validate these theoretical findings and demonstrate the computational viability of the method.

This work investigates the performance of numerical optimization algorithms applied to the State-Averaged Orbital-Optimized Variational Quantum Eigensolver for the H2 molecule under various quantum noise conditions. The goal is to assess the stability, accuracy, and computational efficiency of commonly used gradient-based, gradient-free, and global optimization strategies within the Noisy Intermediate-Scale Quantum regime. We systematically compare six representative optimizers, BFGS, SLSQP, Nelder-Mead, Powell, COBYLA, and iSOMA, under ideal, stochastic, and decoherence noise models, including phase damping, depolarizing, and thermal relaxation channels. Each optimizer was tested over multiple noise intensities and measurement settings to characterize convergence behavior and sensitivity to noise-induced landscape distortions. The results show that BFGS consistently achieves the most accurate energies with minimal evaluations, maintaining robustness even under moderate decoherence. COBYLA performs well for low-cost approximations, while SLSQP exhibits instability in noisy regimes. Global approaches such as iSOMA show potential but are computationally expensive. These findings provide practical guidance for selecting suitable optimizers in variational quantum simulations, highlighting the importance of noise-aware optimization strategies for reliable and efficient quantum chemistry computations on current hardware.

We propose a variant of the approximate Bregman proximal gradient (ABPG) algorithm for minimizing the sum of a smooth nonconvex function and a nonsmooth convex function. ABPG is known to converge globally to a stationary point even when the smooth part of the objective function does not have a globally Lipschitz continuous gradient, and its iterates can often be expressed in closed form. However, ABPG relies on an Armijo line search to guarantee global convergence, which can slow down its practical performance. To address this issue, we propose a variant of ABPG with a variable metric Armijo--Wolfe line search. Under the variable metric Armijo--Wolfe condition, we establish global subsequential convergence of the algorithm. Moreover, assuming the Kurdyka--Łojasiewicz property, we also prove that the algorithm globally converges to a stationary point. Numerical experiments on $\ell_p$-regularized least squares problems and nonnegative linear inverse problems demonstrate that the proposed algorithm outperforms existing algorithms.

We prove a new sample complexity result for divergence regularized optimal transport. Our bound holds for probability measures on~$\mathbb{R}^d$ with exponential tail decay and for radial cost functions that satisfy a local Lipschitz condition. It is sharp up to logarithmic factors, and captures the intrinsic dimension of the marginal distributions through a generalized covering number of their supports. Examples that fit into our framework include subexponential and subgaussian distributions and radial cost functions $c(x,y)=|x-y|^p$ for $p\ge 1$ with logarithmic entropy or polynomial $α$-divergence.

Silicon nitride microresonators driven by strong pump pulses can generate squeezed light in a dominant spectral-temporal mode, a central resource for continuous-variable quantum computation. In the high parametric gain regime, several effects, including self- and cross-phase modulation as well as time-ordering corrections, become significant and can degrade source performance. In this work, we comprehensively investigate the generation of squeezed light from a silicon nitride resonator under pulsed pumping, spanning from low to high parametric gain up to 16 photons/pulse. We experimentally study how the average photon number and the first- and second- order correlations of the squeezed marginal modes evolve with increasing pulse energy, across various frequency detunings and pulse durations. Furthermore, we analyze the errors introduced by multi-pair emissions in estimating the joint temporal intensity via time-resolved coincidence measurements. We propose and demonstrate an error-correction strategy based on the marginal distributions of time-resolved multi-photon events. Our results provide a practical strategy for optimizing the gain and the temporal mode structure of pulsed squeezed light sources in microresonators, elucidating the physical mechanisms and limitations that govern source performance in the high gain regime.

We introduce a site-wise domination criterion for local percolation models, which enables the comparison of one-arm probabilities even in the absence of stochastic domination. The method relies on a local-to-global principle: if, at each site, one model is more likely than the other to connect to a subset of its neighbors, for all nontrivial such subsets, then this advantage propagates to connectivity events at all scales. In this way, we obtain a robust alternative to stochastic domination, applicable in all cases where the latter works and in many where it does not. As a main application, we compare classical Bernoulli bond percolation with degree-constrained models, showing that degree constraints enhance percolation, and obtain asymptotically optimal bounds on critical parameters for degree-constrained models.

Understanding how individuals perceive their living environment is a complex task, as it reflects both personal and contextual determinants. In this paper, we address this task by analyzing the environmental module of the Italian nationwide health surveillance system PASSI (Progressi delle Aziende Sanitarie per la Salute in Italia), integrating it with contextual information at the municipal level, including socio-economic indicators, pollution exposure, and other geographical characteristics. Methodologically, we adopt a penalized semi-parallel cumulative ordinal regression model to analyze how subjective perceptions are shaped by both personal and territorial determinants. The approach balances flexibility and interpretability by allowing both parallel and non-parallel effects while regularizing estimates to address multicollinearity and separation issues. We use the model as an analytical tool to uncover the determinants of positivity and neutrality in environmental perceptions, defined as factors that contribute the most to improving perception or increasing the sense of neutrality. The results are diverse. First, results reveal significant heterogeneity across Italian territories, indicating that local characteristics strongly shape environmental perception. Second, various individual factors interact with contextual influences to shape perceptions. Third, hazardous environmental factors, such as higher PM2.5 levels, appear to be associated with poorer environmental perception, suggesting a tendency among respondents to recognize specific environmental issues. Overall, the approach demonstrates strong potential for application and provides useful insights for environmental policy planning.

The appearance of highly anisotropic planes of satellites around the Milky Way and other galaxies was long considered a challenge to the standard cosmological model. Some recent simulations have found flattened satellite systems to be common, but these have been described as either "transient", short-lived alignments, or "persistent", long-lived structures. Here we analyse Milky Way analogue systems in the cosmological simulation TNG-50 to resolve this apparent contradiction. We show that, as the satellite populations of individual hosts rapidly change, the observed spatial anisotropies of their satellite systems are invariably short-lived, with lifetimes of no more than a few hundred million years. However, when the progenitors of the same satellites are traced backwards, we find examples where those identified to form a plane at the present day have retained spatial coherence over several billion years. The two ostensibly conflicting predictions for the lifetimes of satellite planes can be reconciled as two perspectives on the same phenomenon.

A measurement is presented of the electroweak vector boson scattering production of ZV (V = W, Z) boson pairs associated with two jets in proton-proton collisions at a center-of-mass energy of 13 TeV. The data, corresponding to an integrated luminosity of 138 fb$^{-1}$, were collected at the CERN LHC with the CMS detector during the 2016$-$2018 data-taking period. The analysis targets final states with a pair of isolated electrons or muons from Z boson decays and three or four jets, depending on the momentum of the vector boson that decays into quarks. Signal strength is measured for events characterized by a large invariant mass of two forward jets with a wide pseudorapidity gap between them. The electroweak production of ZV in association with two jets is measured with an observed (expected) significance of 1.3 (1.8) standard deviations. A combination of the analyses of ZV channel and the previously published WV channel in the lepton plus jets final state places constraints on effective field theory parameters that describe anomalous electroweak production of WW, WZ, and ZZ boson pairs in association with two jets. Several world best limits are set on anomalous quartic gauge couplings in terms of dimension-8 standard model effective field theory operators.

We consider the problem of fully Bayesian posterior estimation and uncertainty quantification in undirected Gaussian graphical models via Markov chain Monte Carlo (MCMC) under recently-developed element-wise graphical priors, such as the graphical horseshoe. Unlike the conjugate Wishart family, these priors are non-conjugate; but have the advantage that they naturally allow one to encode a prior belief of sparsity in the off-diagonal elements of the precision matrix, without imposing a structure on the entire matrix. Unfortunately, for a graph with $p$ nodes and with $n$ samples, the state-of-the-art MCMC approaches for the element-wise priors achieve a per iteration complexity of ${O}(p^4),$ which is prohibitive when $p\gg n$. In this regime, we develop a suitably reparameterized MCMC with per iteration complexity of ${O}(p^3)$, providing a one order of magnitude improvement, and consequently bringing the per iteration computational cost at par with the conjugate Wishart family, which is also ${O}(p^3)$ due to a use of the classical Bartlett decomposition, but this decomposition does not apply outside the Wishart family. Importantly, the proposed benefit is obtained solely due to our reparameterization in an MCMC scheme targeting the true posterior, that reverses the recently developed telescoping block decomposition of Bhadra et al. (2024), in a suitable sense. There is no variational or any other approximate Bayesian computation scheme considered in this paper that compromises targeting the true posterior. Simulations and the analysis of a breast cancer data set confirm both the correctness and better algorithmic scaling of the proposed reverse telescoping sampler.

FESTIM is an open-source finite element framework for modelling the transport of hydrogen isotopes in materials. It provides a flexible and extensible tool for simulating diffusion, trapping, surface interactions, and other processes that govern hydrogen behaviour. This paper presents FESTIM v2.0, a major release that broadens both the physical scope and the software infrastructure of the framework. On the physics side, the formulation adopts a modular structure that supports multi-species transport, advanced trapping and reaction schemes, isotope exchange, decay, and advection. Interface and boundary conditions have been generalised, and interoperability with external solvers enables multiphysics workflows, including coupling with fluid dynamics and neutron transport codes. On the software side, FESTIM v2.0 has been migrated to DOLFINx, the next-generation FEniCS platform, providing improved performance, interoperability, and long-term sustainability. Taken together, these advances position FESTIM v2.0 as a versatile platform for investigating hydrogen transport in materials across scientific and engineering applications.

Short-range correlations in electrolyte solutions lead to oscillatory profiles of water polarization and ionic concentration at electrode-electrolyte interfaces. The recently developed density-potential-polarization functional theory (DPPFT) provides a comprehensive framework to incorporate these short-range correlation effects. In the present work, the parameters describing short-range solvent-solvent and ion-solvent correlations in DPPFT are determined from the wavenumber-dependent dielectric susceptibility spectrum of pure water and from ion solvation energies derived within nonlocal electrostatics, respectively. The experimental ionic-radius-dependent hydration energies of alkali metal cations and halide anions are well reproduced by the solvation model. The charge hydration asymmetry is explained as the stronger short-range repulsion between cations and water molecules compared to that between anions and water molecules. Using these parameters, DPPFT is then applied to investigate short-range correlation effects at the Ag(111)-NaF aqueous electrolyte interface. The water polarization profiles obtained from DPPFT calculations agree with AIMD simulations. Furthermore, as the strength of short-range ion-solvent repulsion increases, the peaks of anionic/layers shift from regions near centers of positive/negative polarization charges toward those of opposite sign, thereby preserving solvation configurations similar to those in bulk solution. This work develops a consistent procedure for parameterizing short-range correlation effects within the DPPFT framework, thereby enabling a more quantitative and computationally efficient description of atomic-scale phenomena at electrochemical interfaces.

Mössbauer spectroscopy is widely used to study structure and dynamics of matter with remarkably high energy resolution, provided by the narrow nuclear resonance line widths. However, the narrow width implies low count rates, such that experiments commonly average over extended measurement times or many x-ray pulses (``shots''). This averaging impedes the study of non-equilibrium phenomena. It has been suggested that X-ray free-electron lasers (XFELs) could enable Mössbauer single-shot measurements without averaging, and a proof-of-principle demonstration has been reported. However, so far, only a tiny fraction of all shots resulted in signal-photon numbers which are sufficiently high for a single-shot analysis. Here, we demonstrate coherent nuclear-forward-scattering of self-seeded XFEL radiation, with up to 900 signal-photons per shot. We develop a sorting approach which allows us to include all data on a single-shot level, independent of the signal content of the individual shots. It utilizes the presence of different dynamics classes, i.e. different nuclear evolutions after each excitation. Each shot is assigned to one of the classes, which can then be analyzed separately. Our approach determines the classes from the data without requiring theory modeling nor prior knowledge on the dynamics, making it also applicable to unknown phenomena. We envision that our approach opens up new grounds for Mössbauer science, enabling the study of out-of-equilibrium transient dynamics of the nuclei or their environment.

We present the discovery of three new low-latitude (|b| ~ 20$^{\circ}$) Milky Way satellites: Yasone-1, Yasone-2, and Yasone-3. They were identified in our search for compact stellar overdensities in the Panoramic Survey Telescope and Rapid Response System 1, supported by follow-up deep photometric imaging from the Gran Telescopio Canarias OSIRIS instrument and Gaia astrometric data. These three new Milky Way satellites are found as compact stellar overdensities that exhibit structural and photometric properties consistent with old, metal-poor populations. All three are best described by isochrone fits corresponding to an age of ~12 Gyr and subsolar metallicities: [Fe/H] ~ -1.5 for Yasone-1 and Yasone-2, and [Fe/H] ~ -2.0 for Yasone-3. Yasone-1, located at a heliocentric distance of 12 kpc, has a physical half-light radius of 1.40 pc, an absolute V-band magnitude of +2.36, and a total stellar mass of 18.2 M$_{\odot}$. Yasone-2, at a distance of 20 kpc, has a slightly larger size of 2.44 pc, a brighter V-band magnitude of +1.83, and a higher mass of 28.0 M$_{\odot}$. Yasone-3, located at 15 kpc, is the faintest and least massive of the three, with M$_{V}$ = +2.52, a stellar mass of 14.4 M$_{\odot}$, and a half-light radius of 2.09 pc. We also report a fourth (Yasone-4), lower-confidence hypercompact candidate located at Galactic latitude (b ~ 48$^{\circ}$), identified by replicating our search using the photometric catalogue of the Hyper Suprime-Cam Subaru Strategic Program Public Release. Finally, we present the discovery of sixteen (Yasone-5 to Yasone-20) new hypercompact cluster candidates in the Galactic disc. We discuss the possibility that any of the Yasone clusters may host an intermediate-mass black hole, and we advocate for follow-up spectroscopic observations to further constrain their nature.

We prove quantitative scattering for the three-dimensional defocusing energy-critical quintic wave equation on a class of asymptotically flat, possibly non-stationary perturbations of Minkowski space, by establishing the first explicit global $L^8_{t,x}$ bound in this variable-coefficient setting. Earlier work in this setting proved scattering only qualitatively. For \[ Pu=u^5,\qquad P=\partial_α(g^{αβ}\partial_β), \] we show that, under smallness, decay, and regularity assumptions on the metric, and assuming a priori $\dot H^5\times\dot H^4$ and $L^2\times\dot H^{-1}$ bounds on the solution, the critical spacetime norm $\|u\|_{L^8_{t,x}(\mathbb R\times\mathbb R^3)}$ satisfies an explicit exponential-type estimate in terms of the energy and the a priori bound. This upgrades the qualitative scattering theory in this setting to a quantitative one. The main difficulty is to control geometric error terms over long times. We handle this by splitting the Duhamel history into recent past and remote past. For the recent past, we prove a variable-coefficient interaction Morawetz estimate that yields, on every sufficiently long interval, a time at which the recent nonlinear contribution is small. For the remote past, we prove a dispersive estimate from integrated local energy decay together with a transfer of pointwise decay from large radius to large time. Combining these estimates gives the explicit global $L^8_{t,x}$ bound.

We show that the existence of a strictly compatible pair of control Lyapunov and control barrier functions is equivalent to the existence of a single smooth Lyapunov function that certifies both asymptotic stability and safety. This characterization complements existing literature on converse Lyapunov functions by establishing a partial differential equation (PDE) characterization with prescribed boundary conditions on the safe set, ensuring that the safe set is exactly certified by this Lyapunov function. The result also implies that if a safety and stability specification cannot be certified by a single Lyapunov function, then any pair of control Lyapunov and control barrier functions necessarily leads to a conflict and cannot be satisfied simultaneously in a robust sense.

Zero forcing is an iterative graph coloring process studied for its wide array of applications. In this process, the vertices of the graph are initially designated as blue or white, and a zero forcing set is a set of initially blue vertices that results in all vertices becoming blue after repeated application of a color change rule. The zero forcing number of a graph is the minimum cardinality of a zero forcing set. The zero forcing number has motivated the introduction of a host of variants motivated by linear-algebraic or graph-theoretic contexts. We define a variant we term the $k$-fault tolerant zero forcing number, which is the minimum cardinality of a set $B$ such that every subset of $B$ of cardinality $|B|-k$ is a zero forcing set. We study the values of this parameter on various graph families, the behavior under several graph operations, and characterize the 1-fault tolerant zero forcing number of trees.

In this paper, we give an explicit form for the dual of the algebraic geometry code $C_e(a,b)$ defined on an Hirzebruch surface $\mathcal{H}_e$ and parametrized by the divisor $aS_e + bF_e$, where $a,b\in\mathbb{N}$ and $S_e$ and $F_e$ generate the Picard group $\mathrm{Pic}( \mathcal{H}_e)$. Notably, we compute a lower bound for the minimum distance of $C_e(a,b)^\perp$. One of the main ingredient for our study is a new explicit form of the code $C_e(a,b)$ which we provide at the beginning of the paper. We also investigate some puncturing of $C_e(a,b)$, recovering other previously studied AG codes from toric surfaces. Finally, we provide a sufficient condition for orthogonal inclusions between the codes $C_e(a,b)$, and construct CSS quantum codes from them.

We construct a sequence of simple non-discrete totally disconnected locally compact (tdlc) groups separated by finiteness properties; that is, for every positive integer $n$ there exists a simple non-discrete tdlc group that is of type $F_{n-1}$ but not of type $F_n$. This generalizes a result for discrete groups of Skipper--Witzel--Zaremsky. Furthermore, we construct a simple non-discrete tdlc group that is of type $FP_2$ over $\mathbb{Z}$ but not compactly presented. Our examples arise as Smith universal groups $\mathcal{U}(M, N)$ associated to permutation groups $M$ and $N$. We generalize a theorem of Haglund--Wise to tdlc groups and show that under mild conditions on $M$ and $N$ the finiteness properties of $\mathcal{U}(M, N)$ reflect those of its local actions $M$ and $N$.

Two projective varieties are said to be Cremona equivalent if there is a Cremona modification sending one onto the other. In the last decade, Cremona equivalence has been investigated widely, and we now have a complete theory for non-divisorial reduced schemes. The case of irreducible divisors is completely different, and not much is known besides the case of plane curves and a few classes of surfaces. In particular, for plane curves it is a classical result that an irreducible plane curve is Cremona equivalent to a line if and only if its log-Kodaira dimension is negative. This can be interpreted as the log version of Castelnuovo's rationality criterion for surfaces. One expects that a similar result for surfaces in projective space should not be true, as it is false, the generalization in higher dimensions of Castelnuovo's Rationality Theorem. In this paper, the first example of such behaviour is provided, exhibiting a rational surface in the projective space with negative log-Kodaira dimension, which is not Cremona equivalent to a plane. This can be thought of as a sort of log Iskovkikh-Manin, Clemens-Griffith, Artin-Mumford example. Using this example, it is then possible to show that Cremona equivalence to a plane is neither open nor closed among log pairs with negative Kodaira dimension.

Confidentiality for business data is an understudied area of disclosure avoidance, where legacy methods struggle to provide acceptable results. Standard formal privacy techniques for person-level data, like differential privacy, are designed to protect against membership inference and hence do not provide suitable confidentiality/utility trade-offs due to the highly skewed nature of business data and because extreme outlier records are often important contributors to query answers. Prior proposals, therefore, took a personalized differential privacy approach that allowed privacy parameters to degrade for the outlying records -- larger establishments get weaker membership inference guarantees. However, providing guarantees to some entities that are strictly weaker than guarantees for others is problematic from a policy standpoint. In this paper, we propose a novel confidentiality framework for business data with a focus on interpretability for policy makers. Instead of protecting against membership inference, which is often not a concern in business data, we protect against attribute inferences that are too precise. In our framework, data curators specify a neighbor function that is used to define uncertainty interval bands around an establishment's attribute values and the privacy parameters govern the strength of indistinguishability between values within the same uncertainty interval.We propose two query-answering mechanisms under this framework and evaluate them on: (1) a confidential Quarterly Census of Employment and Wages (QCEW) dataset produced by the U.S. Bureau of Labor Statistics (this was done through a cooperative agreement), and (2) a substitute dataset that we created from public sources (and will publicly release).

A model-agnostic search for Beyond the Standard Model physics is presented, targeting final states with at least four light leptons (electrons or muons). The search regions are separated by event topology and unsupervised machine learning is used to identify anomalous events in the full 140 fb$^{-1}$ of proton-proton collision data collected with the ATLAS detector during Run 2. No significant excess above the Standard Model background expectation is observed. Model-agnostic limits are presented in each topology, along with limits on several benchmark models including vector-like leptons, wino-like charginos and neutralinos, or smuons. Limits are set on the flavourful vector-like lepton model for the first time.

Motivated by the challenge of analyzing the dynamics of weekly sea border crossings in the Mediterranean (2015-2025) and the English Channel (2018-2025), we develop a Bayesian dynamic framework for modeling heteroskedastic count time series. Building on theoretical considerations and empirical stylized facts, our approach utilizes a Poisson random walk model that allows for heavy-tailed innovations or stochastic volatility dynamics, while incorporating an explicit mechanism to separate structural from sampling zeros. Posterior inference is carried out via a straightforward Markov chain Monte Carlo algorithm. Applying this methodology to Mediterranean and English Channel data, we compare alternative model specifications through a comprehensive out-of-sample forecasting exercise. Using log predictive scores and empirical coverage at predictive quantiles to evaluate each model, we find strong evidence for stochastic volatility in migration innovations. These models deliver the strongest out-of-sample forecasts with empirical coverage close to nominal levels up to the 99th percentile. Our framework can be used to develop risk indicators with direct policy implications for improving governance and preparedness for migration surges. More broadly, the methodology extends to other zero-inflated non-stationary count time series applications, including epidemiological surveillance and public safety incident monitoring.