We present updated constraints on cosmic string and superstring parameters derived from Cosmic Microwave Background (CMB) anisotropies. The constraints are obtained via Markov Chain Monte Carlo (MCMC) analyses of the full \textit{Planck} temperature and polarization data combined with the Atacama Cosmology Telescope (ACT) Data Release 6 (DR6). For ordinary cosmic strings, we constrain the string tension $Gμ$, the string wiggliness parameter $α$, and the self-chopping efficiency $\tilde{c}$. For cosmic superstrings, we constrain the fundamental string tension $Gμ_F$, the string coupling $g_s$, and a parameter $w$ describing the volume of the compact extra dimensions. In both cases, we find significantly tighter bounds on the string tension compared to previous analyses, obtaining $2σ$ upper limits of $Gμ< 3.66\times10^{-8}$ and $Gμ_F < 1.38\times10^{-8}$. We also discuss the significant prior-dependence of these results. The computational pipeline used in this work, including a modified version of \texttt{CAMB} capable of computing CMB anisotropies sourced by any active network described via unequal-time correlators, is released publicly as \texttt{CAMBactive} \cite{Raidal_CAMBactive_CAMB_extension_2026}.

This paper develops Kolmogorov-type maximal inequalities for sums of Negative Binomial random variables under both independence and dependence structures. For independent heterogeneous Negative Binomial variables we derive sharp Markov-type deviation inequalities and Kolmogorov-type bounds expressed in terms of Tweedie dispersion parameters, providing explicit control limits for NB2 generalized linear model monitoring. For dependent count data arising through a shared Gamma mixing variable, we establish a \emph{sub-exponential Bernstein-type refinement} that exploits the Poisson-Gamma hierarchical structure to yield exponentially decaying tail probabilities -- this refinement is new in the literature. Through moment-matched Monte Carlo experiments ($n=20$, 2{,}000 replications), we document a 55\% reduction in mean maximum deviation under appropriate dependence structures, a stabilization effect we explain analytically. A concrete epidemiological application with NB2 parameters calibrated from COVID-19 surveillance data demonstrates practical utility. These results materially advance the applicability of classical maximal inequalities to overdispersed and dependent count data prevalent in public health, insurance, and ecological modeling.

Disc galaxies exhibit radial metallicity gradients in both their stellar and gaseous components. The star-forming gas (SFG) in HII regions and young stars (YSs) trace the recent evolutionary history of the galaxy. We aim to assess the extent to which the joint analysis of metallicity gradient alignment in YSs and SFG can constrain the recent evolutionary history of galaxies. Using the high-resolution run of the EAGLE project, we derived radial, azimuthally averaged oxygen abundance profiles for YSs (age < 2 Gyr) and SFG and measured their gradients as the slopes of linear fits to these profiles. We classified galaxies into four groups based on the signs (N for negative and P for positive) of the slopes: NN, NP, PP, and PN (the first letter is for YSs and the second for SFG). We found that galaxies with NN, NP, PP, and PN combinations of metallicity profiles reflect different evolutionary paths over the past ~ 2 Gyr. NN galaxies exhibit sustained inside-out growth accompanied by high star formation efficiency, whereas NP and PP systems show evidence of recent or ongoing feedback-driven disruption, with PP galaxies likely being predominantly shaped by supernova feedback. PN galaxies, by contrast, show evidence of past violent events followed by gradient recovery, highlighting the interplay between inflows, feedback, and gas cooling in shaping metallicity distributions. The degree of alignment between the stellar and gas metallicity gradients provides a way to time the occurrence of significant events in the evolutionary history of galaxies, which contribute through a combination of gas inflows, star formation triggering, and metal mixing. They could also serve as probes of sub-grid physics when observations provide suitable comparison datasets. [Abridged]

Density functional theory (DFT) underpins modern atomistic simulations of transition-metal surfaces. It can predict key properties linked to catalytic performance, such as adsorption energies and barrier heights, enabling new paradigms in rational catalyst design. These applications require reliable density functionals, however achieving transition-metal chemical accuracy (13 kJ/mol) on these properties remains challenging. We introduce a framework for designing new functionals tailored to catalytic processes on transition-metal surfaces, building on recent non-self-consistent approaches. Within this framework, we develop a hybrid and a double-hybrid functional that achieve unprecedented accuracy, with the latter reaching transition-metal chemical accuracy on average across 39 experimental adsorption reactions. In addition, both functionals demonstrate balanced performance for 17 barrier heights and correct qualitative failures of standard functionals, including CO adsorption on Pt(111) and graphene on Ni(111). They are computationally efficient, readily integrated into existing DFT codes, and supported by open-source workflows to facilitate adoption. More broadly, this framework provides a systematic route towards improved functionals for heterogeneous catalysis and complex materials.

We investigate the interaction between Arens products on the bidual of a Banach algebra and structural regularity properties of functionals on the algebra. Building on the classical characterization of weakly almost periodic functionals via Arens regularity, we prove new analogous criteria for Asplund and tame functionals. We establish a systematic correspondence between geometric properties of orbit sets in the dual -- namely weak compactness, fragmentability, and absence of $\ell^1$-sequences -- and structural properties of the corresponding bidual orbits under the Arens products, such as weak compactness, separability, and co-tameness. In particular, we obtain bidual characterizations of right Asplund and right tame functionals analogous to the classical weakly almost periodic theory. We then apply the theory to the group algebra $L^{1}(G)$ of a locally compact group $G$. In this setting, we derive concrete characterizations of Asplund and tame elements of $L^{\infty}(G)$ using orbits of finitely additive $\{0, 1\}$-valued measures. For characteristic functions over countable discrete groups, this yields a simple criterion based on countability of the orbit, generalizing a result of Glasner and Megrelishvili for $\ell^1(\mathbb{Z})$.

In this paper, in residue characteristic 2 and 3, we extend the construction of epipelagic representations of Reeder--Yu to produce new supercuspidals of higher depth, building on work of Gastineau. In particular, we produce examples of epipelagic representations that do not arise from the construction of Reeder--Yu.

In this paper, we establish the interior Hessian estimates for $2$-convex solutions to $\frac{σ_2}{σ_1} (D^2 u) = ψ(x,u)$ in dimension three. In higher dimensions ($n \geq 4$), we prove the interior Hessian estimates for semi-convex solutions. We provide a new method to prove the doubling inequality for smooth solutions in dimensions three and four. In higher dimensions ($n\geq 5$) the doubling inequality is proved under an additional dynamic semi-convexity condition which is the same to that in \cite{SY2025}. The method also applies to the equation $σ_2 (D^2 u) = ψ(x, u, \nabla u)$.

Frontier AI systems are being adopted across Africa, yet most AI safety evaluations are designed and validated in Western environments. In this paper, we argue that the portability gap can leave Africa-centric pathways to severe harm untested when frontier AI systems are embedded in materially constrained and interdependent infrastructures. We define severe AI risks as material risks from frontier AI systems that result in critical harm, measured as the grave injury or death of thousands of people or economic loss and damage equivalent to five percent of a country's GDP. To support AI safety evaluation design, we develop a taxonomy for identifying Africa-centric severe AI risks. The taxonomy links outcome thresholds to process pathways that model risk as the intersection of hazard, vulnerability, and exposure. We distinguish severe risks by amplification and suddenness, where amplification requires that frontier AI be a necessary magnifier of latent danger and suddenness captures harms that materialise rapidly enough to overwhelm ordinary coping and governance capacity. We then propose threat modelling strategies for African contexts, surveying reference class forecasting, structured expert elicitation, scenario planning, and system theoretic process analysis, and tailoring them to constraints of limited resources, poor connectivity, limited technical expertise, weak state capacity, and conflict. We also examine AI misalignment risk, concluding that Africa is more likely to expose universal failure modes through distributional shift than to generate distinct pathways of misalignment. Finally, we offer practical guidance for running evaluations under resource constraints, emphasising open and extensible tooling, tiered evaluation pipelines, and sharing methods and findings to broaden evaluation scope.

We study a special class of holomorphic vertex operator algebras (VOAs) that we call \emph{balanced}.\ For a balanced, holomorphic VOA $V=\mathbb{C}\mathbf{1}\oplus V_1\oplus\dots$ with $c=32$ or $40$ we show that the Virasoro vectors of $V$ and the subVOA generated by $V_1$ coincide and use this result to provide a Schellekens-type list of possible root systems that may occur.

We identify the critical deviation scale governing Bayesian evidence accumulation in regular parametric testing. Under integrated Bayes risk with zero-one loss, the risk-optimal rejection boundary lies in a moderate deviation regime, with a square-root logarithmic inflation relative to the usual local asymptotic normal scale. Under Cramer regularity, local prior smoothness at the null, and symmetric loss, we derive the sharp threshold and show that its leading logarithmic term is universal across regular priors, while lower-order constants depend on the local prior density, Fisher information, and prior model odds. The result extends to one-parameter exponential families through local asymptotic normality and places Jeffreys' testing threshold, the Bayesian information criterion penalty, and Chernoff-Stein type error-exponent arguments within a common asymptotic moderate deviation framework.

We show that, for uniformly locally finite metric spaces $X$ and $Y$ with isomorphic uniform Roe algebras $C^*_u(X)$ and $C^*_u(Y)$, the existence of a bijective coarse equivalence $f \colon X \to Y$ is equivalent to the injectivity of the $0$th comparison map appearing in the HK conjecture for coarse groupoids. We further prove that the $0$th comparison map is injective unconditionally. Moreover, if the underlying space is coarsely connected, this map is in fact split-injective.

In this work, we obtain constraints on the intercepts of the Regge pole tra jectories (which we believe to have definite C-parity) based on the heuristic argument that C-even exchanges correspond to attractive forces between hadrons undergo ing elastic scattering, and C-odd exchanges correspond to attractive forces in the case of particle-antiparticle scattering and repulsive forces in the case of particle-particle scattering.

In a recent contribution [Fishman, V.; Lesiuk, M.; Martin, J.M.L.; Boese, A.D., J. Chem. Theory Comput. 2025, 21, 2311-2324], we introduced another angle at benchmarking non-covalent interactions by not just benchmarking interaction energies of different species, but by considering the evolution of interaction energies with increasing system size. Here, we extend the benchmark set to more species, such as electrostatically bound borazine dimers as well as the minima structures of parallel displaced acene and coronene dimers. While the minimum structures of the parallel displaced acene dimers yield similar results to previously published sandwich-structured acenes, the borazine dimers behave vastly different, yielding yet a more complete picture on non-covalent interactions and their scalability. In contrast, the polycyclic aromatic hydrocarbon structures -- coronenes sandwich-stacked and coronenes parallel displaced -- give results consistent with those obtained for both types of the polyacene series, resulting in an updated estimate for the coronene dimer energy.

We construct a family of non-geometric Bridgeland stability conditions on certain wrapped Fukaya categories, using homological mirror symmetry and categorical Künneth formulae. These stability conditions correspond to certain holomorphic volume forms, under which we prove that every stable object admits a special Lagrangian representative. This provides the first higher-dimensional examples of stability conditions away from the large complex structure limit for which ``stable implies special Lagrangian" is proved.

We investigate whether late-time modifications of gravity in the teleparallel framework can impact the current tension in the Hubble constant $H_0$, focusing on $f(T)$ cosmology as a minimal and well-controlled extension of General Relativity. We consider three representative $f(T)$ parametrisations that recover the teleparallel equivalent of General Relativity at early times and deviate from it only at late epochs. The models are confronted with unanchored Pantheon+ Type~Ia supernovae, DESI DR2 baryon acoustic oscillations, compressed Planck cosmic microwave background distance priors, and redshift-space distortion data, allowing us to jointly probe the background expansion and the growth of cosmic structures. Two of the three models partially shift the inferred value of $H_0$ towards local measurements, while the third worsens the discrepancy. This behaviour is directly linked to the effective torsional dynamics, with phantom-like regimes favouring higher $H_0$ and quintessence-like regimes producing the opposite effect. A global statistical comparison shows that the minimal $f(T)$ extensions considered here are not favoured over $Λ$CDM by the combined data. Nevertheless, our results demonstrate that late-time torsional modifications can non-trivially redistribute current cosmological tensions among the background and growth sectors.

CMB limits on cold-dark-matter isocurvature are often interpreted as excluding the simultaneous realization of high-scale inflation and large QCD axion decay constants in pre-inflationary Peccei--Quinn (PQ) scenarios. This conclusion can be evaded by exploiting \emph{field-space geometry}. For a minimal complex PQ scalar with a $U(1)$-symmetric potential and a nonlinear sigma-model kinetic term $dσ^{2}=dR^{2}+f^{2}(R)\,dθ^{2}$, the observable axion fluctuation is $δθ\sim H_{\rm inf}/f(R)$, so an enhanced effective decay constant $f(R)$ suppresses isocurvature without explicit PQ breaking, extreme radial displacements, or additional couplings. We specialize to a hyperbolic metric $f(R)\propto \sinh(R/L)$ with curvature scale $L$. The same geometry also induces a time-dependent $\mathcal{O}(H_{\rm inf})$ effective mass for the canonical axial mode during radial slow-roll, and fixing the tilt and running of isocurvature. Thus, CMB-scale isocurvature is suppressed while a characteristic blue-tilted spectrum is generated. As a result, inflationary Hubble scales as large as $H_{\rm inf}\sim 10^{13}\,\mathrm{GeV}$ can be compatible with $f_a\sim 10^{14}$--$10^{16}\,\mathrm{GeV}$, reopening parameter space usually regarded as excluded. We present `observable' benchmarks and a semi-analytic template that relates the scale-dependence of isocurvature to the geometric lever arm $R/L$, providing a direct phenomenological probe on PQ field-space geometry.

This paper presents the first optimal-rate $p$-th order methods with $p\geq 1$ for finding first and second-order stationary points of non-convex smooth objective functions over Riemannian manifolds. In contrast to the geodesically convex setting, we definitively establish that the optimal oracle complexity of non-convex optimization over manifolds matches that over Euclidean space. In parallel with the complexity analysis, we introduce a general framework for systematically studying higher-order regularity on Riemannian manifolds that characterizes its joint dependence on the objective function and the chosen retraction. To the best of our knowledge, this framework constitutes the first known application in optimization of pullback connections and the Sasaki metric to the study of retraction-based pullbacks of the objective function. We provide clean derivative bounds based on a new covariant Faà di Bruno formula derived within our framework. For $p=3$, our methods are fully implementable via a new Krylov-based framework for minimizing quartically regularized cubic polynomials. This is the first Krylov method for this class of polynomials and may be of independent interest beyond Riemannian optimization.

This paper introduces a version of decoupling and randomization to establish concentration inequalities for double-indexed permutation statistics. The results yield, among other applications, a new combinatorial Hanson-Wright inequality and a new combinatorial Bennett inequality. Several illustrative examples from rank-based statistics, graph-based statistics, and causal inference are also provided.

We develop a theory of variable elliptic structures on planar domains, in which the imaginary unit $i(x,y)$ is a moving generator of a rank-two real algebra bundle defined by a smoothly varying quadratic relation. Differentiating this relation produces an intrinsic obstruction $G = i_x + i\, i_y$ that governs all deviations from the constant-coefficient theory, such as the inhomogeneity of the generalized Cauchy-Riemann system and the forcing of a universal complex inviscid Burgers equation satisfied by the spectral parameter. The vanishing of $G$ -- rigidity -- selects the conservative regime of this transport law and simultaneously restores a coherent function theory: Cauchy-Pompeiu representation, covariant holomorphicity with gauge structure, a similarity principle, and a factorization of the variable Laplacian. A rigidity-flatness theorem shows that the only structure that is both rigid and Riemannian-flat is the constant one. Translated into Beltrami coordinates, the rigidity condition becomes $μ_{\bar{z}} = μ\, μ_z$: the structure map satisfies its own Beltrami equation, a self-dilatation property in the Poincaré disk. The central result is the Fundamental Independence Theorem: the Beltrami modulus $\|μ\|_{C^0}$ (zeroth order) and the transport obstruction $\|R(μ)\|_{C^{0,α}}$ (first order) are independently prescribable.

The exploration of cosmic rays, which are high-energy particles originate from space and the atmosphere, has historically been associated with particle physics and astrophysics. In the last 20 years, these particles have evolved into valuable tools for observing Earth's systems. This review compiles the use of cosmic rays in three primary areas: (1) particle physics and atmospheric processes, which include cosmic-ray-induced cascades, ionization, and their impact on atmospheric chemistry and radiation; (2) geosciences, where cosmogenic radionuclides assist in the dating of geological materials and cosmic-ray neutrons are used for large-scale monitoring of soil moisture and snow water equivalents; and (3) urban science, where cosmic-ray muons are employed for non-invasive subsurface imaging and, when paired with distributed sensors, serve as the basis for smart city monitoring. The review places particular emphasis on integrating these methods with remote sensing and geographic information systems (GIS), which helps close the persistent scale gap between point measurements and satellite observations, thereby enabling three-dimensional digital representations of subsurfaces. The review concludes by discussing the data standards, their integration into operational Earth observation workflows, and future research directions.

Tilings of a surface of negative Euler characteristic by n-gons with n\ge 7 is a finite problem. One extreme of the finite problem is single tile tilings. We develop the algorithm for finding all the single tile tilings and present the results for surfaces of small genus.

We provide an ${\rm Ext}$-quiver and relations presentation for the basic algebra of the anti-spherical Hecke categories of isotropic Grassmannians, $H_{(D_n, A_{n-1})}$, in terms of cup-cap meta Kazhdan--Lusztig combinatorics and Temperley--Lieb diagrammatics.

During the High Luminosity phase of LHC, up to 200 proton-proton collisions per bunch crossing will bring severe challenges for event reconstruction. To mitigate pileup effects, an extended upgrade program of the CMS experiment is expected. A new timing layer, the MIP Timing Detector (MTD), will be integrated between the tracker and the calorimeters. With a time resolution of 30-60 ps, the MTD will enable 4D vertexing and it will bring significant improvements in track-to-vertex association and object identification. The MTD is composed of two subsystems based on different technologies: the Barrel Timing Layer (BTL) consists of LYSO:Ce scintillating crystals readout by SiPMs and the Endcap Timing Layer (ETL) is made of Low Gain Avalanche Detectors. The BTL is currently under production, while ETL sensor prototyping and validation are ongoing. Recent system tests have confirmed the performance of the full acquisition chain. This talk will provide an overview of the MTD design, along with the physics motivation and the current status of BTL construction and ETL development.

Dicke states serve as a critical resource in quantum metrology, communication, and computation. However, unitary preparation of Dicke states is limited to logarithmic depth in standard circuit models and existing constant-depth protocols require measurement and feed-forward. In this work, we present the first unitary, constant-depth protocols for exact Dicke state preparation. We overcome the logarithmic-depth barrier by moving beyond the standard circuit model and leveraging global interactions (native to architectures such as neutral atoms and trapped ions). Specifically, utilizing unbounded CZ gates (i.e. within the QAC$^0$ circuit class), we offer circuits for exact computation of constant-weight Dicke states, using polynomial ancillae, and approximation of weight-1 Dicke states (i.e. $W$ states), using only constant ancillae. Granted additional access to the quantum FAN-OUT operation (i.e. upgrading to the QAC$_f^0$ circuit class), we also achieve exact and clean preparation of arbitrary-weight Dicke states, with polynomial ancillae. These protocols distinguish the constant-depth capabilities of quantum architectures based on connectivity and offer a novel path toward resolving a long-standing quantum complexity conjecture.

We have observed Hong-Ou-Mandel interference of high-brightness synchrotron x-rays with a Mach-Zehnder interferometer, yielding two-photon states of potential interest for x-ray quantum optics.

Using a gap-free, millennial-resolution ice-core record spanning the last 130,000 years, we identify the feedback architecture between Antarctic temperature and atmospheric CO$_2$. The series are found to be cointegrated, justifying estimation with a Vector Error Correction Model (VECM). The estimated long-run relationship yields a temperature change of 13.0 K per CO$_2$ doubling. Structural identification combining Milankovitch-cycle instrumental variables with the VECM residuals yields a contemporaneous carbon response (CCR) of 5.77 ppm/K, whereas the contemporaneous temperature response (CTR) is statistically indistinguishable from zero. Accounting for lagged feedbacks, the cumulative temperature response within one millennium of CO$_2$ doubling reaches 11.8 K.

We present a systematic study of the leading- and next-to-leading-twist light-cone distribution amplitudes (LCDAs) of ground-state pseudoscalar and vector quarkonium within the light-front quark model (LFQM). By implementing the replacement $M \to M_0$, we analyze the longitudinal and transverse structures of the LCDAs, together with their Gegenbauer moments, $ξ$-moments, and transverse momentum moments. We show that charge-conjugation symmetry enforces the exact vanishing of all odd Gegenbauer moments and odd $ξ$-moments. For pseudoscalar quarkonium, the twist-2 and twist-3 LCDAs become identical, which leads to the same Gegenbauer moments, $ξ$-moments, and transverse momentum moments. For vector quarkonium, although the twist-2 and twist-3 LCDAs differ in the case of finite quark masses, they progressively converge as the quark mass increases. In the heavy-quark limit, all quarkonium LCDAs satisfy $ϕ^A_{2} = ϕ^P_{3} \simeq ϕ^{\parallel}_{2} \simeq ϕ^{\perp}_{3}$, demonstrating an emergent twist-independence of quarkonium distribution amplitudes. We further find that the LCDAs become increasingly peaked and narrower with increasing quark mass, indicating that the meson system becomes increasingly close to a nonrelativistic bound state, with a more uniform and stable distribution of internal longitudinal momentum. For all quarkonium, the peak value exhibits a simple phenomenological scaling behavior governed by the ratio $m/β$. The transverse momentum moments increase with the meson mass, indicating a progressively more compact bound-state structure. These results reveal a universal and systematic evolution of quarkonium LCDAs driven by the quark mass.

Direct access asks for the retrieval of query answers by their ranked position, given a query and a desired order. While the time complexity of data structures supporting such accesses has been studied in depth, and efficient algorithms for many queries and common orders are known, their practical performance has received little attention. We provide an implementation covering a wide range of queries and orders; it allows us to investigate intriguing practical aspects, including the comparative performance of database systems and the relationship between direct access and its single-access counterpart.

In this lecture, I discuss measurements of the properties of the Higgs boson and related observables in the era of Higgs factories. This highly motivated experimental program is the challenge for the next generation of particle physicists.

We observed comet C/2025 A6 with the Five-hundred-meter Aperture Spherical radio Telescope (FAST) equipped with the ultra-wideband receiver from 2025 October 23 to November 8, and it was the first detection for this comet with FAST.Through trapezoidal fitting of the OH line profiles, we derived the expansion velocities of the water which showed an increase from 1.5$\pm$0.3 km s$^{-1}$ at the heliocentric distance of 0.65 AU to 3.0$\pm$0.9 km s$^{-1}$ at 0.54 AU. Based on these results, we estimated the OH production rates of C/2025 A6 for October 23, October 26, November 4 and November 5 which were (1.0$\pm$0.1)$\times$10$^{29}$, (1.2$\pm$0.1)$\times$10$^{29}$, (1.4$\pm$0.3)$\times$10$^{29}$, and (1.5$\pm$0.4)$\times$10$^{29}$ s$^{-1}$ respectively. The results show a significant upward trend.