The Growth-at-Risk (GaR) framework has garnered attention in recent econometric literature, yet current approaches implicitly assume a constant Pareto exponent. We introduce novel and robust econometrics to estimate the tails of GaR based on a rigorous theoretical framework and establish validity and effectiveness. Simulations demonstrate consistent outperformance relative to existing alternatives in terms of predictive accuracy. We perform a long-term GaR analysis that provides accurate and insightful predictions, effectively capturing financial anomalies better than current methods.

The quantum geometric tensor and quantum Fisher information have recently been shown to provide a unified geometric description of the linear response of many-body systems. However, a similar geometric description of higher-order perturbative phenomena including nonlinear response in generic quantum systems is lacking. In this work, we develop a general framework for the time-dependent quantum geometry of many-body systems by treating external perturbing fields as coordinates on the space of density matrices. We use the Bures distance between the initial and time-evolved density matrix to define geometric quantities through a perturbative expansion. To lowest order, we derive a time-dependent generalization of the Bures metric related to the spectral density of linear response functions, unifying previous results for the quantum metric in various limits and providing a geometric interpretation of Fermi's golden rule. At next order in the expansion, we define a time-dependent Bures-Levi-Civita connection for general many-body systems. We show that the connection is the sum of one contribution that is related to a second-order nonlinear response function, and a second contribution that captures the higher geometric structure of first-order perturbation theory. We show that in the quasistatic, zero-temperature limit for noninteracting fermions, this Bures connection reduces to the known expression for band-theoretic Christoffel symbols. Our work provides a systematic framework to explore many-body quantum geometry beyond the quantum metric and highlights how higher-order correlation functions can probe this geometry.

Wildlife-vehicle collisions (WVC) threaten both biodiversity and human safety worldwide. Despite empirical efforts to characterize the major determinants of WVC risk and optimize mitigation strategies, we still lack a theoretical framework linking traffic, landscape, and individual movement features to collision risk. Here, we introduce such a framework by leveraging recent advances in movement ecology and reaction-diffusion stochastic processes with partially absorbing boundaries. Focusing on range-resident terrestrial mammals -- responsible for most fatal WVCs -- we model interactions with a single linear road and derive exact expressions for key survival statistics, including mean collision time and road-induced lifespan reduction. These quantities are expressed in terms of measurable parameters, such as traffic intensity or road width, and movement parameters that can be robustly estimated from relocation data, such as home-range crossing times, home-range sizes, or distance between home-range center and road. Therefore, our work provides an effective theoretical framework integrating movement and road ecology, laying the foundation for data-driven, evidence-based strategies to mitigate WVCs and promote safer, more sustainable transportation networks.

We propose high-spin $Σ$-state polar molecules assembled from ultracold atoms to probe charge-parity violating physics beyond the Standard Model. We identify YbCr as a prime candidate to search for the electric dipole moment of the electron. We show that the combination of relativistic ytterbium and high-spin chromium, amenable to magneto-association, leads to molecules with easy-to-polarize parity doublets and large intramolecular electric fields. Based on \textit{ab initio} results for molecular constants, we predict a sensitivity of $δd_{\textrm{e}}= ( 6 \times 10^{-31} / \sqrt{n_{\mathrm{day}}})\,e\,\mathrm{cm}$ via standard spin-precession measurements, we assess the experimental feasibility, and discuss potential extensions to more advanced quantum control as well as searches of the nuclear magnetic quadrupole moment. This work paves the way to next-generation searches for new physics with ultracold molecules in both the leptonic and hadronic sectors.

The design of control systems for the spatial self-organization of mobile agents is an open challenge across several engineering domains, including swarm robotics and synthetic biology. Here, we propose a bio-inspired leader-follower solution, which is aware of energy constraints of mobile agents and is apt to deal with large swarms. Akin to many natural systems, control objectives are formulated for the entire collective, and leaders and followers are allowed to plastically switch their role in time. We frame a density control problem, modeling the agents' population via a system of nonlinear partial differential equations. This approach allows for a compact description that inherently avoids the curse of dimensionality and improves analytical tractability. We derive analytical guarantees for the existence of desired steady-state solutions and their local stability for one-dimensional and higher-dimensional problems. We numerically validate our control methodology, offering support to the effectiveness, robustness, and versatility of our proposed bio-inspired control strategy.

We investigate the ultrafast magnetization dynamics of semiconducting antiferromagnetic CrSBr using real-time time-dependent density functional theory. In zero magnetic field, laser excitation modifies only the magnetization along the easy axis, leaving transverse components unaffected. We find that below-gap, low-fluence pulses enhance the local magnetic moments via spin transfer from nonmagnetic to magnetic atoms, increasing the Neel vector. In contrast, high-fluence pulses drive interlayer spin transfer between magnetic atoms, producing strong demagnetization and reducing the Neel vector, while S and Br atoms exhibit primarily charge transfer with weak opposite contribution to the demagnetization. An applied magnetic field qualitatively alters the response, enabling both magnitude changes and ultrafast reorientation of the magnetization. We show that the resulting layer-resolved reorientation respects a twofold rotation about the x-axis, exciting coherent optical magnons even under this symmetry, which modulate the relative angle between neighboring layers and periodically tune electronic properties. These results reveal a microscopic pathway for coherent magnon excitation in van der Waals magnets and establish a framework for controlling their coupled spin-charge dynamics on femtosecond timescales.

We discuss static, spherically symmetric solutions to the 5D Einstein-Maxwell equations (belonging to wide classes of multidimensional solutions known at least from the 1990s) and select among them those which must observationally look like local objects whose surface reflects back particles or signals getting there, the so-called mirror stars (also called ``topological stars'' by some authors). Their significant parameters are the Schwarzschild mass $m$ and the magnetic charge $q$, such that $q^2 > 3m^2$, while the radius of their mirror surface is $r_b = 2q^2/(3m) > 2m$. We also discuss their black hole counterparts for which $q^2 \leq 3m^2$. For both these objects, we study spherically symmetric time-dependent perturbations and determine the stability regions in their parameter spaces. Thus, mirror stars turn out to be stable only at $r_b < r_b^{\rm crit} \approx 4.004\,m$, while the black holes prove to be stable in the whole range of their parameters. We calculate the fundamental frequencies and decay rates of black hole perturbations using the WKB and time domain methods. Our stability results disagree with some of those previously announced in the literature.

The differential radial flow fluctuation $v_0(p_{\mathrm{T}})$ has emerged as a new probe of the quark-gluon plasma. However, its characteristic rise-and-fall pattern with $p_{\mathrm{T}}$, resembling anisotropic flow, remains unexplained. I introduce a momentum rescaling framework that factorizes $v_0(p_{\mathrm{T}})$ into kinematic and dynamical components: $v_0(p_{\mathrm{T}})/v_0 = -[d\ln\langle n(p_{\mathrm{T}})\rangle/d\ln p_{\mathrm{T}} + 1] \times g(p_{\mathrm{T}})$. The first factor, determined by spectral shape, generates the rise-and-fall pattern as the spectra transition from exponential to power-law behavior. The dynamical component $g(p_{\mathrm{T}})$ isolates $p_{\mathrm{T}}$-dependent dynamics: $<1$ signals suppressed fluctuations, $>1$ indicates enhancement. Analysis of LHC data reveals $g(p_{\mathrm{T}})$ deviates from unity by 20-40% in central collisions. Predictions for RHIC show that spectral shape alone generates the rise-and-fall baseline pattern with substantial energy dependence. This framework enables tighter medium property constraints by separating kinematic from dynamical effects, with broad applications to anisotropic flow and higher-order radial flow fluctuations.

Compositional data, such as regional shares of economic sectors or property transactions, are central to understanding structural change in economic systems across space and time. This paper introduces a spatiotemporal multivariate autoregressive model tailored for panel data with composition-valued responses at each areal unit and time point. The proposed framework enables the joint modelling of temporal dynamics and spatial dependence under compositional constraints, and is estimated via a quasi-maximum likelihood approach. We build on recent theoretical advances to establish the identifiability and asymptotic properties of the estimator as both the number of regions and the number of time points grow. The utility and flexibility of the model are demonstrated through two applications: analysing property transaction compositions in an intra-city housing market (Berlin), and regional sectoral compositions in Spain's economy. These case studies highlight how the proposed framework captures key features of spatiotemporal economic processes that are often missed by conventional methods.

Pressure isotropy, i.e., equality between radial and tangential pressure, is often assumed when studying neutron stars. However, mechanisms such as pion/kaon condensation, magnetic fields, and dark matter clustering can lead to pressure anisotropy. This work presents a comprehensive measurement of pressure anisotropy in neutron stars. Our analysis incorporates an extensive set of nuclear experimental constraints and multi-messenger astrophysical observations. We find that the Bayes factor for anisotropy against isotropy $\gtrsim 3 : 1$, when the anisotropy is allowed to vary between individual stars. The posterior indicates a population-wide preference for negative anisotropy, primarily driven by PSR J0740+6620. Due to the lack of radius measurements for $2M_\odot$ neutron stars, we cannot rule out density-scale-dependent anisotropy. Therefore, both phase transitions and density-scale-independent mechanisms, such as magnetic fields, dark matter clustering, or deviations from general relativity are viable explanations. While the evidence for anisotropy remains inconclusive, these results demonstrate that pressure anisotropy can be utilized as a tool for identifying missing physics in neutron star modeling or revealing novel physics in the era of multi-messenger astronomy.

We present the first fixed-parameter tractable (FPT) algorithms for exact computation of generalized hypertree width (ghw) and fractional hypertree width (fhw). Our algorithms are parameterized by the target width, the rank, and the maximum degree of the input hypergraph. More generally, we show that testing f-width is in FPT for a broad class of width functions that we call manageable. This class contains the edge cover number $ρ$ and its fractional relaxation $ρ^*$, and thus covers both generalized and fractional hypertree width. We additionally extend our framework to also obtain an fpt algorithm for computing a discretized version of adaptive width. Our approach extends a recent algorithm for treewidth (Bojańcyk & Pilipczuk, LMCS 2022) that utilises monadic second-order transductions. To extend this idea beyond treewidth we develop new combinatorial machinery around elimination forests in hypergraphs, culminating in a structural normal form for optimal witnesses that makes transduction-based optimisation applicable in the much more general context of manageable width functions. This yields the first exact FPT algorithms for these measures under any nontrivial parameterisation and provides structural tools that may enable more direct optimisation algorithms

We present results from a global fit of Standard Model parameters and dimension-6 SMEFT Wilson coefficients that includes electroweak, Drell-Yan, Higgs-boson, top-quark, and flavour observables. Fits obtained by floating individual coefficients are also discussed. The leading-order scale dependence of the SMEFT Wilson coefficients is consistently included in the evolution from the UV scale to the electroweak scale and the low-energy scale of flavour observables. In defining the SMEFT set of active operators we consider both the $U(3)^5$ and the $U(2)^5$ flavour symmetric limits. All fits are obtained within the $\texttt{HEPfit}$ framework and are based on the most recent experimental results and state-of-the-art theoretical predictions for all the observables considered.

We discuss the problem of optimizing the distance function from a given point, subject to polynomial constraints. A key algebraic invariant that governs its complexity is the Euclidean distance degree, which pertains to first-order tangency. We focus on the data locus of points possessing at least one critical point of the distance function that is normal to a higher-order osculating space. We study the higher-order distance degree of a morphism as an intersection-theoretic invariant involving jet bundles and higher-order polar loci. Our approach builds on foundational definitions and results developed by Piene, particularly regarding higher-order polar loci. We give closed formulas for generic maps, Veronese embeddings, and toric embeddings. We place particular emphasis on the Bombieri-Weyl metric, revealing that the chosen metric profoundly influences both the degree and birationality of the higher-order projection maps. Additionally, we introduce a tropical framework that represents these degrees as stable intersections with Bergman fans, facilitating effective combinatorial computation in toric settings.

We analyze the convergence rate of the monotone accelerated proximal gradient method, which can be used to solve structured convex composite optimization problems. A linear convergence rate is established when the smooth part of the objective function is strongly convex, without knowledge of the strong convexity parameter. This is the fastest convergence rate known for this algorithm. As a byproduct, we also establish the boundedness of the iterates in the convex setting, and prove that the limit points of the iterates are all minimizers of the objective function.

Systematic comparisons across theoretical predictions for the properties of dense matter, nuclear physics data, and astrophysical observations (also called meta-analyses) are performed. Existing predictions for symmetric nuclear and neutron matter properties are considered, and they are shown in this paper as an illustration of the present knowledge. Asymmetric matter is constructed assuming the isospin asymmetry quadratic approximation. It is employed to predict the pressure at twice saturation energy-density based only on nuclear-physics constraints, and we find it compatible with the one from the gravitational-wave community. To make our meta-analysis transparent, updated in the future, and to publicly share our results, the Python toolkit \texttt{nucleardatapy} is described and released here. Hence, this paper accompanies \texttt{nucleardatapy}, which simplifies access to nuclear-physics data, including theoretical calculations, experimental measurements, and astrophysical observations. This Python toolkit is designed to easily provide data for: i) predictions for uniform matter (from microscopic or phenomenological approaches); ii) correlation among nuclear properties induced by experimental and theoretical constraints; iii) measurements for finite nuclei (nuclear chart, charge radii, neutron skins or nuclear incompressibilities, etc.) and hypernuclei (single particle energies); and iv) astrophysical observations. This toolkit provides data in a unified format for easy comparison and provides new meta-analysis tools. It will be continuously developed, and we expect contributions from the community in our endeavor.

The ordered allocation sampler is a Gibbs sampler designed to explore the posterior distribution in nonparametric mixture models. It encompasses both infinite mixtures and finite mixtures with random number of components, and it has be shown to possess mixing properties that pair well with collapsed, or marginal, samplers that integrate out the mixing distribution. The main advantage is that it adapts to mixing priors that do not enjoy tractable predictive structures needed for the implementation of marginal sampling methods. Thus it is as widely applicable as other conditional samplers while enjoying better algorithmic performances. In this paper we provide a modification of the ordered allocation sampler that enhances its performances in a substantial way while easing its implementation. In addition, exploiting the similarity with marginal samplers, we are able to adapt to the new version of the sampler the split-merge moves of Jain and Neal. Simulation studies confirm these findings.

We describe a general quantum receiver protocol that maps laser-light-modulated classical communications signals into quantum processors for decoding with quantum logic. The quantum logic enables joint quantum measurements over a codeword to achieve the quantum limit of communications capacity. Our receiver design requires only logarithmically increasing qubit resources with the size of the codeword and accommodates practically relevant coherent-state modulation containing multiple photons per pulse. Focusing on classical-quantum polar codes, we outline the necessary quality of quantum operations and codeword lengths to demonstrate a quantum processing-enhanced communications rate surpassing that of any known classical optical receiver-decoder pair. Specifically, we show that a small quantum receiver of 4 qubits with operational errors of $\sim 0.2\%$ can already provide a $5$ percent gain in the communications rate in the weak signal limit. Additionally, we outline a possible hardware implementation of the receiver where efficient spin-photon interfaces such as cavity-coupled diamond color centers or atomic qubits are used to input the received photonic signal to a small scale quantum processor for decoding. Our results outline a new, promising route for potential quantum advantage in classical communication with near-term, small-scale quantum computers.

Recently using Scanning Josephson Tunneling Microscopy (SJTM) in the group of Séamus Davis a super-modulation of the superconducting order parameter induced by super-modulation of the distance $δ$ between planar Cu and apical O was observed in [O'Mahony et. al., PNAS Vol. 119(37), e2207449119 (2022)]. The authors conclude that: "concurrence of prediction from strong correlation theory ... with these observations indicates that ... super-exchange is the electron pairing mechanism of Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$". In our current theoretical study we use the LCAO approximation, Hilbert space spanned on 5 atomic orbitals: Cu$4s$, Cu$3d_{x^2-y^2}$, O$2p_x$, O$2p_y$, O$2p_z$. For the only super-exchange amplitude $J_{sd}$ we use the Kondo double electron exchange between Cu$4s$ and Cu$3d_{x^2-y^2}$ orbitals and its anti-ferromagnetic sign is determined by adjacent to the Cu ion in-plane O orbitals. Within this approximations we have calculated: "Measured dependence of \dots electron-pair density $n_p$ on the displacement $δ$ of the apical O atoms from the planar Cu atoms" depicted in Fig. 5(C) of O'Mahony \textit{et. al.} and obtained an acceptable accuracy. As a whole, the analyzed SJTM experiment is one of the best confirmations of J. Röhler [J. Röhler, Physica B: Cond. Matter Vol. 284-288, 104 (2000)] idea that hybridization of Cu4$s$ with conduction band leads to increasing of $T_c$. The lack of an alternative explanations for SJTM data $n_p$ versus $δ$ and shape-$T_{c,max}$ correlations for the description of the critical temperature of optimally doped cuprates for several decades on the background of a simple view gives a hint that the long sought pairing mechanism has possibly been found and the Kondo exchange interaction as a property of strongly correlated quantum matter deserves further attention in the physics of layered cuprates.

We prove Lindelöf-on-average upper bounds on the cubic moment of central values of $L$-functions over certain families of $\operatorname{PGL}_2/\mathbb{Q}$ automorphic representations $π$ given by specifying the local representation $π_p$ of $π$ at finitely many primes. Such bounds were previously known in the case that $π_p$ belongs to the principal series or is a ramified quadratic twist of the Steinberg representation; here we handle the supercuspidal case. Crucially, we use new Petersson/Bruggeman-Kuznetsov forumulas for supercuspidal local component families recently developed by the authors. As corollaries, we derive Weyl-strength subconvex bounds for central values of $\operatorname{PGL}_2$ $L$-functions in the square-full aspect, and in the depth aspect, or in a hybrid of these two situations. A special case of our results is the Weyl-subconvex bound for all cusp forms of level $p^2$. Previously, such a bound was only known for forms that are twists from level $p$, which cover roughly half of the level $p^2$ forms.

Let $\mathcal{F}$ be a singular holomorphic foliation of dimension $k>1$ on a projective $n$-manifold $X$. Assume that the determinant of the normal sheaf of $\mathcal{F}$ is ample (as is always the case when $X=\mathbb{P}^{n}$), and that the singular set $Sing(\mathcal{F})$ has dimension $\leq k-1$. We show that the union of those irreducible components of $Sing(\mathcal{F})$ of dimension exactly $k-1$ is necessarily connected. Consequently, we obtain a Bott-type topological obstruction to the integrability of singular holomorphic distributions, echoing Bott's vanishing theorem, and we answer a question of Cerveau for codimension-one foliations on $\mathbb{P}^{3}$.

We establish a connection between dependence structures and subclasses of distortion riskmetrics under which the latter are additive. A new notion of positive dependence, called partial comonotonicity, is developed, which nests the existing concepts of comonotonicity and single-point concentration. For two random variables, being comonotonic with a third one does not imply that they are comonotonic; instead, this defines an instance of partial comonotonicity. Any specific instance of partial comonotonicity uniquely characterizes a class of distortion riskmetrics through additivity under this dependence structure. An implication of this result is the characterization of the Expected Shortfall using single-point concentration.

We study hyperbolicity for quasi-projective varieties where the boundary divisor consists of n+1 numerically parallel effective divisors on a complex projective variety of dimension n, allowing non-empty intersection. Under explicit local conditions on beta constants or intersection multiplicities, we prove that all entire curves are algebraically degenerate. Our approach extends the method of Levin-Huang-Xiao to higher dimensions, establishing a second main theorem for regular sequences of closed subschemes. This also yields a GCD-type estimate in the same geometric setting.

Consider a population that is expanding in two-dimensional space. Suppose we collect data from a sample of individuals taken at random either from the entire population, or from near the outer boundary of the population. A quantity of interest in population genetics is the site frequency spectrum, which is the number of mutations that appear on $k$ of the $n$ sampled individuals, for $k = 1, \dots, n-1$. As long as the mutation rate is constant, this number will be roughly proportional to the total length of all branches in the genealogical tree that are on the ancestral line of $k$ sampled individuals. While the rigorous literature has primarily focused on models without any spatial structure, in many natural settings, such as tumors or bacteria colonies, growth is dictated by spatial constraints. Many such two dimensional growth models are expected to fall in the KPZ universality class. In this article we adopt the perspective that for population models in the KPZ universality class, the genealogical tree can be approximated by the tree formed by the infinite upward geodesics in the directed landscape, a universal scaling limit constructed in \cite{dov22}, starting from $n$ randomly chosen points. Relying on geodesic coalescence, we prove new asymptotic results for the lengths of the portions of these geodesics that are ancestral to $k$ of the $n$ sampled points and consequently obtain exponents driving the site frequency spectrum as predicted in \cite{fgkah16}. An important ingredient in the proof is a new tight estimate of the probability that three infinite upward geodesics stay disjoint up to time $t$, i.e., a sharp quantitative version of the well studied N3G problem, which is of independent interest.

High-energy, heavy-ion collisions can create local domains of chirality-imbalanced quarks, reflecting the topological features of quantum chromodynamics. The chiral magnetic effect (CME) predicts an electric charge separation of quarks in such topological domains along the magnetic field ($\vec{B}$) generated by the passing of two high-$Z$ nuclei. We use a correlation observable $Δγ^{112}$ between charged meson pairs to detect the CME-induced charge separation and a novel event shape selection (ESS) method to mitigate the background effects related to elliptic flow ($v_2$). The ESS method classifies events based on the emission pattern of final-state particles and determines $Δγ^{112}_{\rm ESS}$ from the zero-flow limit. We reconstruct the $\vec{B}$ field direction from the spectator nucleons, which minimizes backgrounds unrelated to the collective motion of the system. In this work, we report the measurements of $Δγ^{112}$ and a background indicator $Δγ^{132}$ in Au+Au collisions from the RHIC Beam Energy Scan phase II and at the top RHIC energy. After background suppression, $Δγ^{132}_{\rm ESS}$ aligns with zero, and $Δγ^{112}_{\rm ESS}$ is reduced to no more than 20\% of $Δγ^{112}$. We observe a finite residual charge separation with $2.6σ$, $3.1σ$, and $3.3σ$ significance in the 20\%--50\% centrality range of Au+Au collisions at 11.5, 14.6, and 19.6 GeV. The results at 17.3 and 27 GeV also show positive values but with a lower significance of $1.3σ$ and $1.1σ$, respectively. The corresponding $Δγ^{112}_{\rm ESS}$ values at 7.7, 9.2, and 200 GeV are consistent with zero within uncertainties.

Future third-generation gravitational wave detectors like the Einstein Telescope (ET) and Cosmic Explorer (CE) are expected to detect millions of binary black hole (BBH) mergers. Alongside these advances, upcoming radio surveys, such as the Square Kilometer Array Observatory (SKAO) will provide new sets of cosmological tracers. These include mapping the large-scale distribution of neutral hydrogen (\hi) using intensity mapping (IM) and \hi\ and radio continuum galaxies. In this work, we will investigate synergies between gravitational waves (GW) and radio tracers through a multi-tracer approach. We first forecast the precision on the clustering bias of GWs by cross-correlating data from an ET-like detector with an SKAO IM survey. Our results indicate that this approach can constrain the GW clustering bias to within $2\%$ up to $z = 2.5$. Additionally, we explore the potential of a triple cross-correlation using GWs, IM, and photometric galaxies from a survey like the Vera Rubin Observatory's Legacy Survey of Space and Time (LSST). This multi-tracer method enhances constraints on the magnification lensing effect, achieving percent-level precision, and allows for a measurement of the Doppler effect with approximately $15\%$ uncertainty. Furthermore we show for the first time that this method could achieve the precision required to measure subdominant gravitational potential contributions to the relativistic corrections, which had thought to be below cosmic variance. Our analysis highlights the potential of cross-correlations between GWs and radio tracers to improve constraints on astrophysical properties of BBHs, measure relativistic effects, and perform null tests of GR in cosmological scales.

This paper presents the first large-scale analysis of public-facing chatbots on Character$.$AI, a rapidly growing social media platform where users create and interact with chatbots. Character$.$AI is distinctive in that it merges generative AI with user-generated content, enabling users to build bots for others to engage with. It is also popular, with over 20 million monthly active users, and impactful, with headlines detailing significant issues with youth engagement on the site. Character$.$AI is thus of interest to study both substantively and conceptually. To this end, we present a descriptive overview using a dataset of 2.1 million English-language prompts (or "greetings") from chatbots on the site, created by around 1 million users. Our work explores the prevalence of different fandoms on the site, broader tropes that persist across fandoms, and how dynamics of power intersect with gender within greetings. Overall, our findings illuminate an emerging form of online (para)social interaction at a unique and important intersection between generative AI and user-generated content.

Bilevel optimization (BLO) becomes fundamentally more challenging when the lower-level objective admits multiple minimizers. Beyond the unique-minimizer setting, two difficulties arise: (1) evaluating the hyper-objective $F_{\max}$ requires minima selection, i.e., optimizing over a potentially topologically disconnected set; (2) $F_{\max}$ can be discontinuous without structural assumptions. We show both can be circumvented under a local Polyak--Lojasiewicz (PL) condition (PL$^\circ$) on the lower-level objective. Under PL$^\circ$, $F_{\max}$ is Lipschitz continuous and, for every upper-level variable, the set of lower-level minimizers is topologically connected and a closed embedded submanifold of common intrinsic dimension $k$. This intrinsic dimension $k$, rather than the ambient one, governs BLO complexity. We give a method that finds an $(ε,ρ)$-Goldstein stationary point of $F_{\max}$ with at most $\mathcal{O}(m^{8k+11}ε^{-2}(ερ)^{-8k-10})$ gradient-oracle queries, where $m$ is the upper-level dimension. The key is a Superquantile--Gibbs relaxation that turns minima selection into a sampling problem solvable via Langevin dynamics. To our knowledge, this is the first work to rigorously treat minima selection in BLO and quantify how its complexity scales with the intrinsic dimensionality of the lower-level problem.

We demonstrate a strontium thermal beam atom interferometer gyroscope (AIG) on a rotation table using the $^{1\!}S_0$-$ ^{3\!}P_1$ intercombination line, and measure large rotation rates exceeding 6 rad/s. Our demonstration relies upon a transit-time-resonant (TTR), phase modulation technique for detecting the AIG phase which rejects signal background and variations in fringe amplitude.

Verification of programs operating on heap-allocated data structures, for instance lists or trees, poses significant challenges due to the potentially unbounded size of such data structures. We present time-indexed heap invariants, a novel invariant-based heap encoding leveraging uninterpreted predicates and prophecy variables to reduce verification of heap-manipulating programs to verification of programs over integers only. Our encoding of heap is general and agnostic to specific data structures. To the best of our knowledge, our approach is the first heap invariant-based method that achieves both soundness and completeness. We provide formal proofs establishing the correctness of our encodings. Through an experimental evaluation, we demonstrate that time-indexed heap invariants significantly extend the capability of existing verification tools, allowing automatic verification of programs with heap that were previously out of reach for state-of-the-art tools.

We study the decays of $B_{(s)}$ mesons into light pseudoscalar mesons under the $SU(3)$ flavour symmetry. Assuming exact $SU(3)$ symmetry at the level of the amplitudes leads to a simple parameterization. Using the available experimental data and, for the first time, mixing effects in the $B_s^0$ decays, we find that the data cannot be described with this assumption. We improve this parametrization by including {\it factorizable} $SU(3)_\mathrm{F}$-breaking effects. This new approach allows for an excellent description of the data, with a fit $p$ value of $32.3\%$. We provide posterior predictions for all observables and identify several decay channels that would significantly impact our analysis. Finally, we briefly compare our results with the predictions of QCD factorization, paving the way to a more detailed analysis which could provide insights into QCD effects at low energy scales.