We investigate the geometric albedos of hot Jupiters by comparing observational data from space telescopes TESS, Kepler, CoRoT, and CHEOPS against theoretical models. The study aims to understand the distribution of observed geometric albedos across different bandpasses and how these observations align with or deviate from model predictions. We have curated a comprehensive sample of observed geometric albedos, using either existing Spitzer secondary eclipse measurements or a scaling law between the equilibrium and dayside temperature to remove any contaminating thermal planetary emission. We then utilised hierarchical Bayesian modelling to identify trends with planetary properties such as equilibrium temperature, gravity, and stellar metallicity. On a population level, we found no statistical difference in the distributions of geometric albedos measured by TESS compared to those by Kepler, CoRoT and CHEOPS. We confront the geometric albedo sample with a simple, but first principles, model that includes Rayleigh scattering by molecular hydrogen and absorption by sodium, water and titanium oxide and vanadium oxide. We find that the abundance of sodium and water are the key absorbers that influence the geometric albedos of hot Jupiters, whilst the addition of titanium oxide and vanadium oxide (in the absence of condensation) results in vanishing geometric albedos that are inconsistent with the observed distributions.

We study whether a logic based on team semantics can be enriched with a conditional satisfying minimal requirements, such as preservation of the closure property of the logic, Modus Ponens, and the Deduction Theorem. We show that such well-behaved conditionals exist for downward or upward closed logics, but do not typically exist for union closed, convex or intersection closed logics. We also briefly investigate conditionals satisfying weaker requirements.

We present a novel, practical approach to speed up sparse matrix-vector multiplication (SpMVM) on GPUs. The novel key idea is to apply lossless entropy coding to further compress the sparse matrix when stored in one of the commonly supported formats. Our method is based on dtANS, our new lossless compression method that improves the entropy coding technique of asymmetric numeral systems (ANS) specifically for fast parallel GPU decoding when used in tandem with SpMVM. We apply dtANS on the widely used CSR format and present extensive benchmarks on the SuiteSparse collection of matrices against the state-of-the-art cuSPARSE library. On matrices with at least 2^(15) entries and at least 10 entries per row on average, our compression reduces the matrix size over the smallest cuSPARSE format (CSR, COO and SELL) in almost all cases and up to 11.77 times. Further, we achieve an SpMVM speedup for the majority of matrices with at least 2^(25) nonzero entries. The best speedup is 3.48x. We also show that we can improve over the AI-based multi-format AlphaSparse in an experiment that is limited due to its extreme computation overhead. We provide our code as an open source C++/CUDA header library, which includes both compression and multiplication kernels.

6G will require on-device antenna systems to operate at ultra-high frequency bands, achieve robust beamforming on the compact user devices, and be blockage-robust. Conventional edge-mounted antennas on devices have limited apertures, suffer from the 'death grip' caused by user-induced blockage, and have poor scalability at mmWave and sub-THz bands. To address these issues, motivated by the rapid evolution of transparent materials and antennas, we propose ScreenAnt in this work--which integrates a transparent antenna array onto the screens of future mobile devices. Specifically, we propose using a transparent on-screen uniform planar array and develop a framework to model its electromagnetic property, spatial configuration, and blockage robustness under realistic user-induced blockage. We also design a gradient-ascent-based algorithm to efficiently optimize power and phase control of on-screen antennas to maximize ScreenAnt's spectral efficiency. Our thorough simulations show that the proposed ScreenAnt can increase the uplink spectral efficiency by over 50% compared to edge-mounted antennas at 28 GHz, and by more than 150% at 300 GHz. ScreenAnt also demonstrates strong robustness against user-induced blockage, paving the way for practical and high-capacity 6G user device designs.

We compare the sensitivity of the upcoming long-baseline neutrino experiments Protvino to Super-ORCA (P2SO) and the Deep Underground Neutrino Experiment (DUNE) to non-unitarity (NU) of the leptonic mixing matrix in a model-independent framework. NU can arise in theories beyond the Standard Model that include heavy neutral leptons. These effects can modify neutrino oscillation probabilities and introduce new sources of CP violation, which may affect precision measurements of neutrino parameters. We find that DUNE provides stronger bounds on $α_{11}$ and $|α_{21}|$, while P2SO shows better sensitivity to $α_{22}$ and $α_{33}$, mainly due to its longer baseline and stronger matter effects. Our results show that DUNE (P2SO) will be able to improve the current bounds of $α_{11}$ ($α_{33}$). We further examine correlations with standard oscillation parameters and quantify the impact of NU on mass hierarchy, octant, and CP-violation sensitivities. Our results show that these sensitivities depend upon NU in a non-trivial way interconnecting the parameter degeneracies and matter effects. Our results demonstrate the complementarity of P2SO and DUNE in probing NU and show that NU can significantly influence next-generation precision oscillation studies.

Let $M$ be a compact oriented $3$-manifold with boundary consisting of tori, and let $G$ be a semisimple algebraic group. We define the adjoint torsion function on the moduli stack of $G$-local systems on $M$ satisfying a certain regularity condition, extending the construction by Porti for $G = \mathrm{SL}_2$. When $M$ is a cusped hyperbolic manifold, we prove that the local system associated with the image of the complete hyperbolic structure via a principal embedding $\mathrm{PGL}_2 \to G$ satisfies the regularity condition. Moreover, we provide a formula expressing its adjoint torsion as a product of $\mathrm{PGL}_2$-torsions associated with the simple $\mathrm{PGL}_2$-modules with multiplicity given by the exponents of the Lie algebra of $G$. We compute the adjoint $\mathrm{PGSp}_4$-torsions of the figure-eight knot complement for two boundary-unipotent local systems, one is arising from the complete hyperbolic structure via a principal embedding, and the other is defined over a number field of degree $6$ and not arising from any $\mathrm{PGL}_2$-local system via principal embeddings.

We present the quark weak-mixing component of a Froggatt--Nielsen program, with one flavon and three messengers, in which a single hierarchy parameter $B$ (with $ε\equiv 1/B$) and a rational-exponent ``$B$-lattice'' organize fermion Yukawa textures. Building on companion mass-fit work, we translate the lattice into predictions for quark mixing. The four-magnitude parameterization serves as a practical interface between the flavon Yukawa textures and quark weak mixing observables. The lattice exponent structure, together with a four-phase multi-messenger coefficient model, simultaneously reproduces all four CKM magnitudes, the full $3\times 3$ CKM matrix, and the CP-violating Jarlskog invariant, providing a stringent overdetermination test of the single-$B$ hypothesis. The same lattice parameter that organizes quark mixing also fixes the charged-lepton mass ratio $m_μ/m_τ=c_μ\,ε^{5/3}$, yielding the striking integer-exponent identity $|V_{ub}|\simeq(m_μ/m_τ)^{2}$, which connects the smallest CKM magnitude to the charged-lepton spectrum with no free parameters and agrees with the measured value at about the $6\%$ level. An equivalent cross-sector form $|V_{ub}|\simeq\sin^3θ_{13}$ ties the smallest CKM magnitude directly to the smallest PMNS magnitude; the two routes agree at the few-percent level, providing complementary determinations of the same ninths-lattice quantity from the quark and lepton sectors.

Material with metallic $σ$-bonding bands is expected to be a high-temperature superconductor, due to the sensitivity of $σ$ electrons to lattice vibration. Based on the first-principles calculations, electronic structures of hydrogenated BC$_3$ monolayers (H$_n$-B$_2$C$_6$ with $n$=1-8) are systematically investigated. At high coverage of hydrogen, the monolayer stabilizes in chair-like $sp^3$-hybridized configurations, leading to the metallization of $σ$ bands, especially in H$_7$-B$_2$C$_6$ and H$_8$-B$_2$C$_6$. This metallicity originates from the electron deficiency of boron, compared with insulating graphane. Utilizing Wannier interpolation, the electron-phonon coupling strengths for metallic phases of H$_n$-B$_2$C$_6$ are determined. As expected, strong couplings are identified between the conducting $σ$ electrons and low-frequency phonon modes. By solving the anisotropic Eliashberg equations, we confirm that H$_7$-B$_2$C$_6$ and H$_8$-B$_2$C$_6$ are single-gap superconductors with critical temperature being 87 K, exceeding the boiling point of liquid nitrogen. Considering that monolayer BC$_3$ has been synthesized in experiment, our results demonstrate that hydrogenation of two-dimensional BC$_3$ provides a viable pathway to achieve high-temperature superconductivity at ambient pressure.

[...] We observed XTE J1810-197 between 29 September 2022 and 14 July 2023 with the radio telescopes at the Argentine Institute of Radioastronomy (IAR). We searched for single pulses in time series at a DM range of 100-400 pc cm-3 , with a threshold in signal-to-noise ratio (S/N) of 8. [...] We found 249 giant pulses at a DM mean value of 178.8$\pm$0.1 pc cm-3 . We measured peak flux densities up to 119 Jy, and fluences up to 58 Jy ms. We fitted a power law distribution to the flux density, obtaining an index of -4.0$\pm$0.3. We observed a maximum rate of approximately 15 pulses per hour on 20 February 2023, followed by an abrupt disappearance of transient radio emission, indicating a transition to a less active state. The brightest single pulses are limited to a $\sim$2$\%$ of the rotational phase and have similar fluence values to the reported intermediate FRB-like bursts of SGR 1935+2154. No significant X-ray activity in the MAXI data was detected during the radio observing period. This is the first study of single radio pulses of a magnetar using IAR data, showing the potential of the upgraded telescopes for investigating the transient radio sky. The properties of the single pulses detected here show the magnetar transient nature and capability to emit high-luminosity pulses. We compared the detected emission to FRB-like bursts and single pulses emitted by SGR 1935+2154. Even though the mechanism producing all the events should be coherent, the luminosity of the events, features on the dynamic spectra, and the difference between being phase confined or not, indicate that XTE J1810-197 presents GP emission, while SGR 1935+2154 only shows normal single pulses or FRB bursts. This could indicate that the conditions for producing each type of event differ.

Cell-free massive-multiple-input-multiple-output (CFmMIMO) is a key enabler for sixth-generation (6G) wireless communication networks, where distributed access points (APs) jointly serve user equipments (UEs). In commonly adopted channel models for CFmMIMO networks, inter-AP channel correlation is assumed to be absent, thereby eliminating the potential benefits of centralized processing. However, by carefully designing the pilot transmission phase, the AP received signals during pilot transmission can become correlated, and thus, centralization can improve channel estimation performance, despite the absence of inter-AP channel correlation. In this paper, we propose a channel estimation scheme, termed master-assisted channel estimation (MACE), that aims to leverage inter-AP signal correlation by means of partially centralized processing and hence improve channel estimation performance. In MACE, a subset of APs fuse and forward their received pilot signals to a master AP, which then performs channel estimation using the fused signals together with its locally received signals. This scheme strikes a balance between local and fully centralized processing by leveraging inter-AP signal correlation, while reducing fronthaul signaling and computational complexity. Numerical experiments demonstrate that MACE consistently outperforms local channel estimation, where inter-AP signal correlation is neglected.

In Einstein-scalar-Maxwell theories with a coupling between the scalar field $ϕ$ and the electromagnetic field strength $F$ of the form $μ(ϕ) F$, we investigate the existence of exotic compact objects (ECOs) and their observational signatures in photon and massive-particle dynamics. For $μ(ϕ)$ diverging at the origin while all physical quantities remain finite, we demonstrate the existence of electrically charged ECOs with a shell-like structure whose density peaks at an intermediate radius. We compute their mass and radius, together with the scalar and vector field profiles, on a static and spherically symmetric background. We then examine the existence of light rings and place bounds on a model parameter by requiring the absence of a linearly stable light ring. Under this condition, photon echoes from ECOs are absent. We also compute the gravitational-lensing deflection angle and show that it attains a maximum for an impact parameter of the same order as the ECO radius. Finally, we study the parameter space in which innermost stable circular orbits of massive particles exist.

It has long been suggested that X-ray transients are produced at periastron of stellar-compact object binaries with eccentric orbits. Recoil of matter evaporated from the star by X-rays from matter transferred at periastron increases the orbital semi-major axis and eccentricity. After periastrons the object would be a transient X-ray source, a Galactic analogue of a tidal disruption event (TDE), but recurrent with a gradually increasing period rather than catastrophic.

We present the optical follow-up of SNe 2022ywf and 2023zgx, two examples from the Iax subclass of thermonuclear supernova (SN) events. With peak absolute magnitudes of $M_\mathrm{V} = -13.7$ and $-14.4$ mag, respectively, both objects belong to the extremely low-luminosity (EL) population of the class. A common origin of SNe in the Iax subclass is still under debate since the distribution of certain observables may indicate that the extremely low-luminosity explosions form a distinct population. We aim to estimate the physical properties of the two EL objects, including mapping the ejecta structure. We perform spectral tomography on the spectral series of SNe 2022ywf and 2023zgx around their maxima to map the physical properties of the ejecta. Together with the analysis of BgVriz photometry, a wide range of observables can be studied to investigate their distribution against luminosity. The constrained chemical abundances of the ejecta are compared to the predictions of the hydrodynamic simulations with similar peak luminosities. Constant abundances provide a good match for the distribution of chemical elements for both SNe 2022ywf and 2023zgx. The discrepancies compared to the least luminous pure deflagration model N5def_hybrid are minor, especially at post-maximum epochs. The two SNe also share similar characteristics in their constrained density structures, as well as the evolution of the photosphere. The analysis supports the assumption that pure deflagration models can reproduce the main characteristics of SNe Iax, even for the EL population. The presented indirect observational evidence indicates that these objects show similar intrinsic properties to the relatively luminous Iax sample and fit into the velocity distribution of the subclass.

We propose an approach to construct three-dimensional lattice models using line defects in state integral models on shaped triangulations of 3-manifolds. The Boltzmann weights for these models satisfy a variant of the tetrahedron equation, which implies integrability under suitable assumptions on R-matrices and transfer matrices. As an explicit example, we present a solution produced by Teichmüller TQFT.

Cosmological simulations suggest that various galaxy properties depend on their location within the cosmic web. Yet direct observational evidence of the dependence of star formation activity on distance to filaments remains scarce and is missing at z>1. We investigate how starburst, main-sequence (MS), and quenched galaxies are distributed with respect to cosmic web filaments, and how this distribution evolves with redshift. We first use the SIMBA cosmological simulation to predict the redshift evolution of the mean distance to the closest filament from z=3 to z=0 for different galaxy populations after removing stellar-mass dependencies. We then measure the corresponding signal in the COSMOS field, using COSMOS2020 and COSMOS-Web data, where accurate photometric redshifts enable reconstruction of the projected cosmic web from z=2 to z=0.5, and starbursts are identified through far-infrared spectral energy distribution fitting. In agreement with the results from SIMBA, starburst galaxies are found closer to filaments at z>1 and at larger distances at z<1, MS galaxies occupy intermediate environments with little evolution, and quenched galaxies show progressively shorter distances to filaments toward low redshift, with a crossing between starburst and MS populations around z~1. In COSMOS-Web, the relative evolution in the average distance to filaments between starburst and MS galaxies is detected at a significance level of at least 5σ. We show that a minimal toy model in which the only environmental ingredient is the sSFR-filament distance modulation measured in simulations is sufficient to reproduce the observed differential evolution of the average filament distance between starburst and MS galaxies. These results show that the imprint of large-scale environmental effects on the star formation activity of galaxies, predicted by simulations, is detectable from z=2 down to z=0.5.

We answer a question of Biran and Cornea about the density of iterated cones of fibers in the Fukaya category of a cotangent bundle. We prove that indeed if we take a dense set of basepoints, the iterated cones of the cotangent fibres are dense in the Filtered Fukaya category. In an appendix we prove that the space of exact Lagrangians in a symplectic manifold is never totally bounded for the spectral distance (unless it is empty). This was implicit in \cite{MCA-VH-CV} for $n=1$ and proved for cotangent bundles of negatively curved manifolds in \cite{A-B-C}.

We study AT2024kmq and AT2024lhc, two tidal disruption events (TDEs) with blue featureless spectra associated with high-mass black holes ($M_{\rm BH}\sim 10^8\,M_\odot$). Both events show optical precursors consistent with shock dissipation from stream self-intersection. Their X-ray emission is luminous ($L_{\rm X}\sim 10^{44}\,{\rm erg\,s^{-1}}$), highly variable (with minimum observed variability timescales of 1.3\,hr and 4.8\,hr for factor of $\sim3$ flux changes), long-lasting ($>1\,\rm yr$), emerging no later than the optical peak, and well characterized by power-laws with $1.7<Γ<3$ (where $f_ν\propto ν^{1-Γ}$). The X-ray properties and radio non-detections support a compact corona ($\lesssim 10 r_{\rm g}$) producing Comptonized X-ray emission. Using all published featureless TDEs, we find statistically significant bimodality in the distribution of their peak UV/optical blackbody luminosities and radii. We assemble a comparison TDE sample with early-time X-ray observations with eROSITA, in which we find different $M_{\rm BH}$ distributions in TDEs with different X-ray spectral evolution properties: low-mass black holes ($M_{\rm BH} \sim 10^6 M_\odot$) remain soft ($Γ>4$) within $t\lesssim 2$\,yr, intermediate masses ($\sim 10^7 M_\odot$) transition from soft to hard at $\sim$1 yr, while high masses ($\sim 10^8 M_\odot$) are hard ($1.5<Γ\lesssim 3$) from the outset. We interpret this result as evidence that the soft-to-hard state transition in TDEs occurs at the critical threshold of $\dot{M}_{\rm acc} \sim 0.03 \dot M_{\rm Edd}$ (similar to X-ray binaries), using the fact that the transition timescale predicted by simple disk theory scales with black hole mass as $t_{\rm tr}\propto M_{\rm BH}^{-3/4}$.

We investigate within the framework of linear theory the behaviour of the total (hydrodynamic) pressure and of the dynamic pressure in a regular wave train which propagates at the surface of water with a flat bed in a flow with constant vorticity. We show that nonzero vorticity, the hallmark of a non-uniform underlying current, may strongly alter the behaviour with respect to the case of irrotational flows, for which the maximum and minimum of the dynamic pressure always occur at the wave crest and at the wave trough, respectively (the extrema of the dynamic pressure may occur along the flat bed or along the critical level, depending on the vorticity strength). While vorticity does not modify the increase of the hydrodynamic pressure with depth, it can significantly alter the location of the extrema of the hydrodynamic pressure at a fixed depth level.

This paper studies whether interruptions to organized breast cancer screening lead to greater later use of emergency hospital care. It focuses on the first wave of COVID-19, when routine mammography was widely reduced across Europe, disrupting the usual screening pathway of early detection, follow-up testing, referral, and planned treatment. Using SHARE data from eight countries, the authors examine women aged 50 to 69, the main target group for organized screening programs. They estimate how mammography uptake affects all-cause overnight emergency hospitalization, interpreted as a broad measure of downstream strain on the health system after preventive care disruption. To address selection into screening, they use an instrumental variables strategy based on interview timing in Wave 9 interacted with cross-country differences in first-wave restrictions. The results suggest that pandemic-related declines in mammography increased later emergency hospitalization for screening-eligible women, while no such effect appears for women aged 70 and older.

Magic State Distillation is considered to be one of the promising methods for supplying the non-Clifford resources required to achieve universal fault tolerance. Conventional MSD protocols implemented in surface codes often require multiple code blocks and lattice surgery rounds, resulting in substantial qubit overhead, especially at low target error rates. In this work, we present practical magic state distillation factories on Bivariate Bicycle (BB) codes that execute Pauli-measurement-based Clifford circuits inside a single BB code block. We formulate distillation circuit design as a joint optimization of logical qubit mapping, gate scheduling, measurement nativization, and protocol compression via qubit recycling. Based on detailed resource analysis and simulations, our BB factories have space-time volume comparable to that of leading distillation factories while delivering lower target error at a smaller qubit footprint, and are particularly compelling as second-round distillers following magic state cultivations.

The Nekrasov instanton partition function of the 4d $\mathcal{N}=2^*$ $U(N)$ gauge theory (a mass deformation of 4d $\mathcal{N}=4$ super-Yang-Mills theory), which is a generating series of equivariant integrals over instanton moduli spaces, is given by a sum over colored partitions weighted by a counting parameter $\mathfrak{q}$. This note proves convergence of the series in the unit disk $|\mathfrak{q}|<1$ for generic parameters. Specifically, the absolute convergence radius of this sum is determined, assuming that mass and Coulomb branch parameters avoid some lattice. If the ratio $b^2=ε_1/ε_2$ of equivariant parameters is in $\mathbb{C}\setminus[0,+\infty)$, the radius is $1$, as expected. If $b^2$ is non-negative, three cases arise: the radius is finite if $b^2$ has finite exponential type (a generalization of Brjuno numbers), namely there exists $C>0$ such that $|b^2-p/q|>\exp(-Cq)$ for all integers $p,q\neq 0$; the series diverges if $b^2$ is super-exponentially well approximable by rationals; and if $b^2$ is rational some terms are singular. The AGT correspondence translates these results to convergence of torus one-point conformal blocks of the Virasoro and $W_N$ algebras with non-real $b$, within the unit disk. For the Virasoro algebra this corresponds to a central charge in $\mathbb{C}\setminus[25,+\infty)$.

We introduce a nearly parameter-free algorithm for minimizing piecewise smooth (PWS) convex functions under the quadratic-growth (QG) condition, where the locations and structure of the smooth regions are entirely unknown. Our algorithm, APEX (Accelerated Prox-Level method for Exploring Piecewise Smoothness), is an accelerated bundle-level method designed to adaptively exploit the underlying PWS structure. For this setting, APEX achieves the best-known oracle-complexity result among existing first-order methods, improving the dependence on the condition number relative to prior bundle-level guarantees. Furthermore, APEX generates a verifiable and accurate termination certificate, enabling a robust, nearly parameter-free implementation. To the best of our knowledge, APEX is the first algorithm to simultaneously achieve the best-known first-order oracle complexity for PWS optimization and provide certificate guarantees.

The Berry connection encodes the momentum-space geometry of occupied Bloch states in gapped insulators and plays a central role in topological materials. While gauge-invariant quantities can be evaluated from overlap matrices between neighboring $k$ points, accessing the Berry connection itself as a smooth field requires specifying a continuous gauge over the Brillouin zone. Wannier-based workflows achieve this through projection onto localized orbitals, enabling stable evaluation of geometric quantities and response functions. In this setting, the Berry connection enters directly in Wannier-interpolated calculations of polarization, Berry curvature, and related response functions. In practical implementations, however, the projection-gauge Berry connection is typically constructed from finite-difference overlaps between neighboring $k$ points, discretizing momentum derivatives and introducing errors tied to $k$-mesh spacing and gauge alignment. These effects can become numerically delicate in systems with small band gaps or when evaluating higher-order responses such as the Chern-Simons axion angle. Here, we derive an exact expression for the non-Abelian Berry connection in the projection gauge that is local in crystal momentum. Starting from projected and orthonormalized Bloch-like states, we obtain a closed-form equation expressed entirely in terms of $k$-local quantities. We validate the formulation in one and three dimensions by computing the Berry phase and Chern-Simons axion angle in tight-binding models. The resulting framework provides a stable route to evaluating geometric properties within Wannier interpolation schemes and future first-principles implementations.

The issue of separating Schrödinger-type quantum time evolution into a product of holonomic and dynamical parts in the non-adiabatic non-Abelian case is examined. We identify all special cases in which this kind of separation is possible, and we prove that separability is a gauge invariant property of quantum time evolution. The general analysis is implemented in a three-level system with $Λ$-type coupling structures. The typical case where the holonomic and dynamical parts do not separate is illustrated by means of two non-commuting $Λ$-type Hamiltonians.

A single geometric invariant fixes the relative normalization and structure of gravity, Yang--Mills theory, and fermion kinetic terms. The restricted invariant basis contains known linearized ghost-free quadratic gravitational sectors with propagating torsion. Our results establish a minimal geometric route to unification that does not rely on extra dimensions or symmetry breaking by hand. Unlike previous gauge--gravity constructions, the relative normalizations and ghost freedom emerge from a single Clifford--algebraic invariant.

A levitated ferromagnet provides an exceptionally sensitive probe of ultralight dark matter (ULDM) through measuring weak magnetic-like field signals. We propose a ferromagnet lattice magnetometer that coherently combines multiple levitated ferromagnets to enhance effective sensitivity. By replacing a single ferromagnet with a lattice, we increase the total polarized spin while preserving the intrinsic dynamical response of each constituent ferromagnet. We show that magnetic dipole-dipole interactions within the lattice can be dynamically suppressed through a high-frequency magnetic field, rendering the system effectively noninteracting, at the cost of only a moderate reduction in signal amplitude due to the distinct renormalization of linear and quadratic spin responses. We analyze the noise properties of the lattice and demonstrate that collective readout leads to favorable scaling with the number of ferromagnets. Interpreted in terms of axion-electron, dark photon, and axion-photon couplings, our results yield projected sensitivities that significantly exceed existing single-ferromagnet implementations. In particular, for axion-photon interactions, we find a nontrivial lattice-induced enhancement of the signal itself, leading to sensitivities that surpass existing constraints over a broad mass range.

We prove a new rigidity criterion for families of polarized Calabi--Yau manifolds. Motivated by known non-rigid examples, we conjecture that a family over a quasi-projective curve is rigid if, near a boundary point, the total space is smooth, the relative canonical bundle is trivial, and the boundary fiber contains an isolated singular point. We verify this conjecture when one such isolated singularity has a concentrated mixed Hodge spectrum, a class including ordinary double points and cusps. The proof combines a local vanishing-cycle analysis with a global tensor-product decomposition of the associated variation of Hodge structures.

Recent advances in photonic inverse design have demonstrated the ability to automatically synthesize compact, high-performance photonic components that surpass conventional, hand-designed structures, offering a promising path toward scalable and functionality-rich photonic hardware. However, the practical deployment of inverse-designed PICs is bottlenecked by manufacturability: their irregular, subwavelength geometries are highly sensitive to fabrication variations, leading to large performance degradation, low yield, and a persistent gap between simulated optimality and fabricated performance. Unlike electronics, photonics lacks a systematic, flexible mask optimization flow. Fabrication deviations in photonic components cause large optical response drift and compounding error in cascaded circuits, while calibrating fabrication models remains costly and expertise-heavy, often requiring repeated fabrication cycles that are inaccessible to most designers. To bridge this gap, we introduce PRISM, a photonics-informed inverse lithography workflow that makes photonic mask optimization data-efficient, reliable, and optics-informed. PRISM (i) synthesizes compact, informative calibration patterns to minimize required fabrication data, (ii) trains a physics-grounded differentiable fabrication model, enabling gradient-based optimization, and (iii) performs photonics-informed inverse mask optimization that prioritizes performance-critical features beyond geometry matching. Across multiple inverse-designed components with both electron-beam lithography and deep ultra-violet photolithography processes, PRISM significantly boosts post-fabrication performance and yield while reducing calibration area and turnaround time, enabling and democratizing manufacturable and high-yield inverse-designed photonic hardware at scale.

We first present a reduction of properties of compact sets of real numbers to properties of countable orders. Then discuss a variant of homogeneity of compact subsets of real numbers, focusing on the family of $t$-sets. Finally, we prove that there are exactly $ω_1$ many non-homeomorphic $t$-sets.

The angular, harmonic cross-correlation between gravitational wave (GW) events and galaxy catalogues contains rich information on the large-scale structure and the origin of compact binary mergers. In this work, we study how uncertainties in the binary formation channel affect the predicted cross-correlation signal for both current-generation and next-generation networks of detectors. We generate five mock GW catalogues for which we vary the progenitor-to-remnant mass-transfer function and the time-delay probability distribution between progenitor and remnant. We then cross-correlate these catalogues with galaxy samples modelled on the 2MASS Photometric Redshift catalogue (2MPZ) and the Gaia-unWISE quasar catalogue (Quaia). We find that the mass-transfer function has negligible effect on the cross-correlation signal, with differences remaining within redshift uncertainties. In contrast, the time-delay distribution dramatically affects the redshift distribution of the GW events and, with it, the cross-correlation signal, particularly for shallow galaxy catalogues. In particular, current-generation facilities can achieve significant detections only for the longest time delays when cross-correlated with 2MPZ, whilst all cross-correlations with the deeper Quaia catalogue are marginally detectable or consistent with zero. Our exploratory results thus demonstrate that forecasts on cosmological or astrophysical parameters derived from GW-galaxy cross-correlations are, as expected, strongly sensitive to the assumed binary formation history.