We construct a 2-parameter family of new triaxial $SU(2)$-invariant complete negative Einstein metrics on the complex line bundle $\mathcal{O}(-4)$ over $\mathbb{C}P^1$. The metrics are conformally compact and neither Kähler nor self-dual. The proof involves using rigorous numerics to produce an approximate Einstein metric to high precision in a bounded region containing the singular orbit or "bolt", which is then perturbed to a genuine Einstein metric using fixed-point methods. At the boundary of this region, the latter metric is sufficiently close to hyperbolic space for us to show that it indeed extends to a complete, asymptotically hyperbolic Einstein metric.

We construct a new family of distance-biregular graphs related to hyperovals and a new sporadic example of a distance-biregular graph related to Mathon's perp system. The infinite family can be explained using 2-$\bipartB$-homogeneity, while the sporadic example belongs to a generalization of a construction by Delorme. Additionally, we establish a new non-existence condition for distance-biregular graphs which, for instance, rules out the existence of a distance-biregular graph on $225+60$ vertices.

We revisit the problem of fault-tolerant (FT) distance preservers, when failure events in the network admit a form of correlation modeled as color faults. FT distance preservers are sparse subgraphs that preserve distances between specified pairs of vertices, even after some edge or vertex failures occur. In the classical fault model, any set of at most $k$ edges or vertices might fail (where $k \geq 1$ is a given parameter). Despite extensive research, the classical model admits significant and tantalizing gaps, both in terms of sparsity bounds and of algorithmic efficiency. In this work, we study the problem in the recently introduced color fault-tolerant (CFT) model: the given graph $G=(V,E)$ has arbitrary colors on its edges/vertices where each color appears at most $k$ times, and is susceptible to color faults, where the failure of color $c$ causes all the $c$-colored elements to crash. Our main contribution is in the multi-source setting, where $G$ has a source-set $S \subseteq V$, and the CFT preserver should preserve $S \times V$ distances under any single color fault. We show the following results (where $n = |V|$, $m = |E|$): - There exists a CFT distance preserver $H$ of $G$ with $\tilde{O}(n^{2 - \frac{1}{k+1}} \cdot |S|^{\frac{1}{k+1}} )$ edges. - The above sparsity bound is worst-case optimal up to polylogarithmic terms. - There is a combinatorial randomized algorithm that produces a preserver $H$ whose size meets the above optimal sparsity bound, with running time of $\tilde{O}(m \cdot n^{1 - \frac{1}{k+1}} \cdot |S|^{\frac{1}{k+1}})$. - The above running time is conditionally optimal: a polynomial improvement would refute the combinatorial Boolean Matrix Multiplication (BMM) conjecture. Furthermore, the running time remains optimal even if we only require mild sparsification to $m^{1-ε}$ edges.

This study documents a three-week workshop with architecture students, where we designed and 3D printed various minimal surfaces using wood-based filaments, and used them as molds in which to grow mycelium. We detail the design process and the growth of the mycelium in different shapes, together with participants' experiences of working with a living material. After exhibiting the results of the work in a public-facing exhibition, we conducted interviews with members of the general public about their perceptions on interacting with a material such as mycelium in design. Our findings show that 3D-printed minimal surfaces with wood-based filaments can function as structural cores for mycelium-based composites and mycelium binds to the filament. Participants in the workshop exhibited stronger feelings for living materials compared to non-living ones, displaying both biophilia and, to a lesser extent, biophobia when interacting with the mycelium. Members of the general public discuss pragmatic aspects including mold, fragility, or production costs, and speculate on the future of bio-technology and its impact on everyday life. While all are positive about the impact on bio-technologies on the future, they have diverging opinions on how much ethical considerations should influence research directions.

Accurate knowledge of scrap composition can increase the usage of recycled material to produce steel, reducing the need for raw ore extraction and minimizing environmental impact by conserving natural resources and lowering carbon emissions. First, we introduce two state-space models for the elemental composition of scrap in Electric Arc Furnaces (EAF) and Basic Oxygen Furnaces (BOF): a linear model for elements that transfer entirely into steel, and a non-linear model for elements that partition between steel and slag. The models are fitted with the Kalman filter and the unscented Kalman filter, respectively, using only data already collected in the standard steel production process. Crucially, the resulting scrap composition estimates can in turn be used to predict the elemental composition of future steel production. Second, we analyze how key hyperparameters affect estimation accuracy and stability, and we provide practical guidelines for tuning them from expert knowledge and historical data. Third, we validate the models on real BOF data from ArcelorMittal, using Cu and Cr as representative elements. Both filters outperform windowed non-negative least squares regression, a strong baseline method for scrap composition estimation, yielding reliable real-time estimates of scrap composition.

In the spirit of [M. Biskup & O. Louidor, Adv. Math. 330 (2018)], we study the local structure of $\star$-scale invariant fields -- a class of log-correlated Gaussian fields -- around their extremal points by characterising the law of the "shape" of the field's configuration near such points. As a consequence, we obtain a refined understanding of the freezing phenomenon in supercritical Gaussian multiplicative chaos.

Measurements of $t\bar{t}\ell^{+}\ell^{-}$ production in the region of high dilepton invariant mass with effective field theory (EFT) interpretations are presented. They are performed using final states with three isolated leptons (electrons or muons) and are based on $\sqrt{s} = 13$ TeV proton-proton collision data with an integrated luminosity of $140\,\mathrm{fb}^{-1}$, recorded from 2015 to 2018 with the ATLAS detector at the Large Hadron Collider. Measurements of the $t\bar{t}\ell^{+}\ell^{-}$ signal strength and cross-section upper-limits are performed inclusively in lepton flavour and separately for electrons and muons. The study also aims to probe anomalous four-fermion interactions including to test for possible lepton flavor universality violation. No significant deviations from the Standard Model predictions are observed and the measurements are interpreted through the EFT formalism to provide new constraints on relevant operators.

Any function from a round $n$-dimensional sphere of radius $r$ into $n$-dimensional Euclidean space must distort the metric additively by at least $\displaystyle \frac{πr}{1 + \sqrt{1 - \frac{2}{n+2}}}$ if $n$ is even and $\displaystyle \frac{πr}{1 + \sqrt{1 - \frac{2(n+2)}{(n+1)(n+3)}}}$ if $n$ is odd. This is proved using a fixed-point theorem of Granas that generalizes the classical theorem of Borsuk-Ulam to set-valued functions.

Cosmic voids are low-mass-density regions on intergalactic scales. They are where cosmic expansion and acceleration are most dominant, important places to understand and analyze for cosmology. This entry summarises theoretical underpinnings of cosmic voids, and explores several observational aspects, statistics and applications of voids. The density profiles, velocity profiles, evolution history and the abundances of voids are shown to encode information about cosmology, including the sum of neutrino masses and the law of gravity. These properties manifest themselves into a wide range of observables, including the void distribution function, redshift-space distortions, gravitational lensing and their imprints on the cosmic-microwave background. We explain how each of these observables work, and summarise their applications in observations. We also comment on the possible impact of a local void on the interpretations of the expansion of the Universe, and discuss opportunities and challenges for the research subject of cosmic voids.

Biological evolution depends on the passing down to subsequent generations of genetic information encoding beneficial traits, and on the removal of unfit individuals by a selection mechanism. However, selection acts on phenotypes, and is affected by random contingencies. Thus, a combination of fitness and luck determines which individuals will successfully reproduce and give rise to the next generation. To understand how randomness in the selection mechanism affects the long-term patterns of evolution, we studied an idealized evolution model. We show through simulations and mathematical analysis, that the speed of adaptation increases with increasing selection pressure only up to a threshold. Beyond the threshold, any increase of the selection pressure results in more weight given to random effects rather than on genetic fitness in determining which individuals will successfully reproduce. This severely reduces the speed of adaptation and the diversity in the gene pool. Our findings may be considered as a biological instance of Goodhart's law: "When a measure becomes a target, it ceases to be a good measure". Finally, we show that this intricate response of evolution to natural selection can be mathematically explained by a novel phase transition for pulled traveling waves.

With the advancement of AI models, more software systems are adopting AI as a component to facilitate automation. Pre-trained models (PTMs) have become a cornerstone of AI-based software, allowing for rapid integration and development with lower training cost. However, their adoption also introduces failure modes such as data leakage and biased outputs, that may require careful handling by downstream developers. While previous research has proposed taxonomies of these technical concerns and various mitigation strategies, how downstream developers address these issues during the development of general AI-based software when reusing PTMs remains unexplored. Understanding downstream developers' perspectives is essential because they directly influence how these potential failures concerns translate into practice, such as determining whether immediate risks like data leakage or model bias are recognised, mitigated, or inadvertently overlooked in real-world deployments. This study investigates downstream developers' concerns, practices and perceived challenges regarding practical AI failures during the development of AI-based software. To achieve this, we conducted a mixed-method study, including interviews with 16 participants, a survey of 86 practitioners,

In the field of scientific computing, one often finds several alternative software packages (with open or closed source code) for solving a specific problem. These packages sometimes even use alternative methodological approaches, e.g., different numerical discretizations. If one decides to use one of these packages, it is often not clear which one is the best choice. To make an informed decision, it is necessary to measure the performance of the alternative software packages for a suitable set of test problems, i.e. to set up a benchmark. However, setting up benchmarks ad-hoc can become overwhelming as the parameter space expands rapidly. Very often, the design of the benchmark is also not fully set at the start of some project. For instance, adding new libraries, adapting metrics, or introducing new benchmark cases during the project can significantly increase complexity and necessitate laborious re-evaluation of previous results. This paper presents a proven approach that utilizes established Continuous Integration tools and practices to achieve high automation of benchmark execution and reporting. Our use case is the numerical integration (quadrature) on arbitrary domains, which are bounded by implicitly or parametrically defined curves or surfaces in 2D or 3D.

Black hole solutions in general scalar-tensor theories are known to permit hair, i.e. non-trivial scalar profiles and/or metric solutions different from the ones of General Relativity (GR). Imposing that some such solutions$\unicode{x2013}$e.g. Schwarzschild or de Sitter solutions motivated in the context of black hole physics or cosmology$\unicode{x2013}$should exist, the space of scalar-tensor theories is strongly restricted. Here we investigate precisely what these restrictions are within general quadratic/cubic higher-order scalar-tensor theories for stealth solutions, whose metric is given by that in GR, supporting time-dependent scalar hair with a constant kinetic term. We derive, in a fully covariant approach, the conditions under which the Euler-Lagrange equations admit all (or a specific set of) exact GR solutions, as the first step toward our understanding of a wider class of theories that admit approximately stealth solutions. Focusing on static and spherically symmetric black hole spacetimes, we study the dynamics of linear odd-parity perturbations and discuss possible deviations from GR. Importantly, we find that requiring the existence of all stealth solutions prevents any deviations from GR in the odd-parity sector. In less restrictive scenarios, in particular for theories only requiring the existence of Schwarzschild(-de Sitter) black holes, we identify allowed deviations from GR, derive the stability conditions for the odd modes, and investigate the generic deviation of a non-trivial speed of gravitational waves. All calculations performed in this paper are reproducible via companion $\texttt {Mathematica}$ notebooks.

We consider the problem of meta-analyzing outcome measures based on median survival times. Primary studies with time-to-event outcomes often report estimates of median survival times and confidence intervals based on the Kaplan-Meier estimator. However, outcome measures based on median survival are rarely meta-analyzed, as standard inverse-variance weighted methods require within-study standard errors that are typically not reported. In this article, we consider an inverse-variance weighted approach to meta-analyze median survival times that estimates the within-study standard errors from the reported confidence intervals. We show that this method consistently estimates the standard error of median survival when applied to confidence intervals constructed by the Brookmeyer-Crowley method. We conduct a series of simulation studies evaluating the performance of this approach at the study level (i.e., for estimating the standard error of median survival) and the meta-analytic level (i.e., for estimating the pooled median, difference of medians, and ratio of medians) for commonly used confidence intervals for median survival, including the Brookmeyer-Crowley method and nonparametric bootstrap. We find that this approach often performs comparably to a benchmark approach that uses the true within-study standard errors for meta-analyzing median-based outcome measures when within-study sample sizes are moderately large (e.g., above 50). However, when the effective sample sizes are small, the method can yield biased estimates of within-study standard errors. We illustrate an application of this approach in a meta-analysis evaluating survival benefits of being assigned to experimental arms versus comparator arms in randomized trials for non-small cell lung cancer therapies.

Encoding quantum information in a quantum error correction (QEC) code offers protection against decoherence and enhances the fidelity of qubits and gate operations. One of the fundamental challenges of QEC is to construct codes with asymptotically good parameters, i.e. a non-vanishing rate and relative minimum distance. Such codes provide compact quantum memory with low overhead and enhanced error correcting capabilities, compared to state-of-the-art topological error correction codes such as the surface or colour codes. Recently, bivariate bicycle (BB) codes have emerged as a promising candidate for such compact memory, though the exact tradeoff of the code parameters $[[n,k,d]]$ remained unknown. In this Article, we explore these codes by leveraging their ring structure, and predict their dimension as well as conditions on their existence. Finally, we highlight asymptotic badness. Though this excludes this subclass of codes from the search towards practical good low-density parity check (LDPC) codes, it does not affect the utility of the moderately long codes that are known, which can already be used to experimentally demonstrate better QEC beyond the surface code.

The development of turbulent mixing layers can be altered by the application of anisotropic strain rates, potentially arising from radial motion in convergent geometry or movement through non-uniform geometry. Previous closure models and calibrations of compressible turbulence models tend to focus on incompressible flows or isotropic strain cases, which is in contrast to many real flow conditions. The treatment of bulk compression under anisotropic strain is investigated using the K-L turbulence model, a two-equation Reynolds-Averaged Navier-Stokes (RANS) model that is commonly used for simulating interfacial instabilities. One-dimensional simulations of shock-induced turbulent mixing layers under applied axial or transverse strain rates are performed using three different closures for the bulk compression of the turbulent length scale. The default closure method using the mean isotropic strain rate is able to reasonably predict the integral width and turbulent kinetic energy of the mixing layer under the applied strain rates. However, the K-L model's performance is improved with the transverse strain closure, while the axial strain closure worsens the model. The effects of this new closure are investigated for the buoyancy-drag model, showing that a three-equation model which evolves the integral width and turbulent length scale separately is most effective for modelling anisotropic strain. Through the equivalence of two-equation RANS models, the modification of the bulk compression closure for the turbulent length scale also suggests an alteration to the K-$ε$ and K-$ω$ models.

The growth of interfacial instabilities such as the Rayleigh-Taylor (RTI) and Richtmyer-Meshkov instability (RMI) are modified when developing in convergent geometries. Whilst these modifications are usually quantified by the compression rate and convergence rate of the mixing layer, an alternative framework is proposed, describing the evolution of the mixing layer through the effects of the mean strain rates experienced by the mixing layer. An investigation into the effect of the transverse strain rate on the mixing layer development is conducted through application of transverse strain rates in planar geometry. A model for the linear regime in planar geometry with transverse strain rate is derived, with equivalent solutions to convergent geometry, and validated with two-dimensional simulations demonstrating the amplification of the instability growth under transverse compression. The effect of the transverse strain rate on the transitional-to-turbulent mixing layer is investigated with implicit large eddy simulation based on the multi-mode quarter-scale $θ$-group case by Thornber et al. (Phys. Fluids, vol. 29, 2017, 105107). The mixing layer's growth exhibits the opposite trend to the linear regime model, with reduced growth under transverse compression. The effect of shear-production under transverse compression causes the mixing layer to become more mixed and the turbulent kinetic energy is increasingly dominated by the transverse directions, deviating from the unstrained self-similar state. The mixing layer width is able to be predicted by adjusting the buoyancy-drag model by Youngs & Thornber (Physica D, vol. 410, 2020, 132517) to utilise a drag length scale that scales with the transverse expansion.

Let $A$ be a $W$-algebra over a field $F$ of characteristic zero, where $W$ is any $F$-algebra. We first develop a comprehensive theory of generalized identities independent of the algebraic structure of $W$, using the multiplier algebra of $A.$ Then, we investigate the generalized variety generated by the $k\times k$ matrix algebra with a suitable action, proving that it exhibits almost polynomial growth of the generalized codimensions. Furthermore, we characterize the generalized varieties of almost polynomial growth generated by finite dimensional $W$-algebras. Finally, we provide a counterexample to the Specht property of generalized $T_W$-ideals in characteristic zero.

Real-time mechanical fault diagnosis in high-speed railway (HSR) networks requires ultra-reliable and low-latency upload of ultra-high-definition (UHD) video streams. However, energy constraints of trackside cameras and severe transmission latency pose critical challenges. This paper proposes a novel 6G infrastructure-to-vehicle (I2V) architecture employing double intelligent reflecting surfaces (IRSs) to enhance wireless powered communication network (WPCN) and hybrid-frequency data transmission. Crucially, to guarantee the quality of experience (QoE) for in-cabin passengers using Mobile Multimedia Broadcasting Services (MBMS), a strict zero-forcing spatial interference isolation constraint is imposed via the window-mounted IRS. We formulate a weighted latency minimization problem and develop a block coordinate descent (BCD) algorithm. Downlink energy beamforming and uplink information transmission are alternately optimized utilizing difference of convex (DCA) and semi-definite relaxation (SDR) techniques. Additionally, a low-complexity heuristic algorithm is proposed to mitigate the severe Doppler spread induced by train mobility. Simulation results demonstrate that the proposed scheme significantly reduces upload latency to meet stringent URLLC thresholds while ensuring interference isolation within the carriage.

The quantum anomalous Hall effect in magnetic kagome materials has emerged as a versatile platform for dissipationless electronic and spintronic devices. In this work, we demonstrate that the orientation of magnetic moments $\hat{m}(θ,ϕ)$ at lattice sites provides a practical tuning mechanism for engineering nontrivial topological phases in monolayer kagome ferromagnets. To elucidate the mechanism, we construct a symmetry-adapted minimal tight-binding model for kagome ferromagnets that includes intrinsic spin-orbit coupling (SOC) and the intrinsic Rashba SOC permitted by broken out-of-plane mirror symmetry between nearest-neighbor kagome sites and can capture the resulting topological phase diagram as a function of $\hat{m}(θ,ϕ)$. In particular, the restoration of in-plane mirror symmetry for specific values of $ϕ$ drives a topological phase transition upon varying the in-plane orientation of the moments $\hat{m}(θ= 90^{\circ}, ϕ)$. In contrast, for fixed $ϕ$, the transitions driven by varying $θ$ originate from the competition between Rashba SOC and intrinsic SOC. Density functional theory calculations for ferromagnetic kagome monolayers belonging to the Co$_3$X$_3$Y$_2$ family ($X=\mathrm{Sn},\mathrm{Pb}$; $Y=\mathrm{S},\mathrm{Se}$) support the predictions of the proposed minimal tight-binding model. These findings provide design guidelines for tunable topological phases in kagome materials.

In this paper, we consider people counting and localization systems exploiting channel state information (CSI) measured from commodity WiFi network interface cards (NICs). While CSI has useful information of amplitude and phase to describe signal propagation in a measurement environment of interest, CSI measurement suffers from offsets due to various uncertainties. Moreover, an uncontrollable external environment where other WiFi devices communicate each other induces interfering signals, resulting in erroneous CSI captured at a receiver. In this paper, preprocessing of CSI is first proposed for offset removal, and it guarantees low-latency operation without any filtering process. Afterwards, we design people counting and localization models based on pre-training. To be adaptive to different measurement environments, meta-learning-based people counting and localization models are also proposed. Numerical results show that the proposed meta-learning-based people counting and localization models can achieve high sensing accuracy, compared to other learning schemes that follow simple training and test procedures.

We consider the Dirichlet problem of the indefinite Helmholtz equation in 1D, $u''+k^2u=f$ in $(0,1)$, $u(0)=g_0$, $u(1)=g_1$, with a constant wavenumber $k\in(0,\infty)\backslashπ\mathbb{N}$ and a source term $f\in H^p_0(0,1)$, $p\ge 4$. We propose an approach based on Fourier analysis to derive wavenumber explicit sharp estimates of absolute and relative errors of \emph{finite difference} methods. Such results have been well known for \emph{finite element} methods (FEM). We use the approach to analyze the classical centered finite difference scheme. For the Fourier interpolants of the discrete solution with homogeneous (or inhomogeneous) Dirichlet conditions, we show rigorously, under the two assumptions $k>20$ and $k(kh)^2/σ_k\le4/(π-2)$ with $σ_k:=\operatorname{dist}(k,π\mathbb{N})$, that the worst case attainable convergence order of the absolute error with $\sum_{p=0}^4k^{-p}\|f^{(p)}\|_{L^2}=O(1)$ (or $|g_i|\asymp k^{-1}$) is $(kh)^2/σ_k^2$ in the $L^2$-norm and $k(kh)^2/σ_k^2$ in the $H^1$-semi-norm, and that of the relative error is $k(kh)^2/σ_k$ in both $L^2$- and $H^1$-semi-norms if $\|u^{(p)}\|_{L^2}/\|u^{(p-2)}\|_{L^2}\asymp k^2$ for $p=2,3$. In particular, the lower bounds of these error estimates are established rigorously in the same orders as the upper bounds, which is the main novelty of this work. We show also that the Fourier analysis approach can be used as a convenient visual tool for evaluating finite difference schemes in presence of source terms, which is beyond the scope of dispersion analysis. The results from the theory and visual analysis are corroborated by numerical experiments.

We study the succinct representations of vertex cuts by centralized oracles and labeling schemes. For an undirected $n$-vertex graph $G = (V,E)$ and integer parameter $f \geq 1$, the goal is supporting vertex cut queries: Given $F \subseteq V$ with $|F| \leq f$, determine if $F$ is a vertex cut in $G$. In the centralized data structure setting, it is required to preprocess $G$ into an $f$-vertex cut oracle that can answer such queries quickly, while occupying only small space. In the labeling setting, one should assign a short label to each vertex in $G$, so that a cut query $F$ can be answered by merely inspecting the labels assigned to the vertices in $F$. While the ``$st$ cut variants'' of the above problems have been extensively studied and are known to admit very efficient solutions, the basic (global) ``cut query'' setting is essentially open (particularly for $f > 3$). This work achieves the first significant progress on these problems: [$f$-Vertex Cut Labels:] Every $n$-vertex graph admits an $f$-vertex cut labeling scheme, where the labels have length of $\tilde{O}(n^{1-1/f})$ bits (when $f$ is polylogarithmic in $n$). This nearly matches the recent lower bound given by Long, Pettie and Saranurak (SODA 2025). [$f$-Vertex Cut Oracles:] For $f=O(\log n)$, every $n$-vertex graph $G$ admits $f$-vertex cut oracle with $\tilde{O}(n)$ space and $\tilde{O}(2^f)$ query time. We also show that our $f$-vertex cut oracles for every $1 \leq f \leq n$ are optimal up to $n^{o(1)}$ factors (conditioned on plausible fine-grained complexity conjectures). If $G$ is $f$-connected, i.e., when one is interested in \emph{minimum} vertex cut queries, the query time improves to $\tilde{O}(f^2)$, for any $1 \leq f \leq n$.

Using the algebraic approach to promise constraint satisfaction problems, we establish complexity classifications of three natural variants of hypergraph colourings: standard nonmonochromatic colourings, conflict-free colourings, and linearly-ordered colourings. Firstly, we show that finding an $\ell$-colouring of a $k$-colourable $r$-uniform hypergraph is NP-hard for all constant $2\leq k\leq \ell$ and $r\geq 3$. This provides a shorter proof of a celebrated result by Dinur et al. [FOCS'02/Combinatorica'05]. Secondly, we show that finding an $\ell$-conflict-free colouring of an $r$-uniform hypergraph that admits a $k$-conflict-free colouring is NP-hard for all constant $3\leq k\leq\ell$ and $r\geq 4$, except for $r=4$ and $k=2$ (and any $\ell$); this case is solvable in polynomial time. The case of $r=3$ is the standard nonmonochromatic colouring, and the case of $r=2$ is the notoriously difficult open problem of approximate graph colouring. Thirdly, we show that finding an $\ell$-linearly-ordered colouring of an $r$-uniform hypergraph that admits a $k$-linearly-ordered colouring is NP-hard for all constant $3\leq k\leq\ell$ and $r\geq 4$, thus improving on the results of Nakajima and Živný [ICALP'22/ACM TocT'23].

We give tightness criteria for random variables taking values in the space of all compact sets of cadlag real-valued paths, in terms of both the Skorohod J1 and M1 topologies. This extends earlier work motivated by the study of the Brownian web that was concerned only with continuous paths. In the M1 case, we give a natural extension of our tightness criteria which ensures that non-crossing systems of paths have weak limit points that are also non-crossing. This last result is exemplified through a rescaling of heavy tailed Poisson trees and a more general application to weaves.

We develop a general formalism of phonon magnetic moment by including the relaxation process. We then identify the skew-scattering and side-jump contributions to the phonon magnetic moment originating from the non-adiabaticity, both of which are related to the nonlocal phonon Berry curvature and are in close analogy to those in the electronic Hall effect. All contributions of the phonon magnetic moment are exemplified in a honeycomb lattice, showing that the extrinsic contribution can be as important as the intrinsic one and that the resulting phonon angular momentum varies significantly across the Brillouin zone. Our work offers a systematic framework of the phonon chirality and paves the way of tuning the phonon magnetic moment through the non-adiabaticity.

Early detection and localization of gravitational waves (GWs) are essential for identifying electromagnetic (EM) counterparts, playing a key role in multi-messenger astronomy. However, second-generation (2G) ground-based detectors are most sensitive to frequencies of tens to hundreds of hertz, limiting the in-band duration of GW signals to $\mathcal{O}(0.1)$ to several tens of seconds. This constraint hinders early-warning capabilities and early localization. We present the first theoretical study on how eccentricity-induced higher harmonic modes, which enters the detector band significantly earlier than the dominant mode, enhance early detection and localization in a 2G detector network. By decomposing each harmonic mode in the frequency domain and tracking their sequential entry into the detector band, we analyze the evolution of the average signal-to-noise ratios (SNRs) and localization accuracy as functions of time-to-merger. For a GW170817-like BNS, an eccentricity of $e_0=0.4$ at 10 Hz allows the signal to reach SNR 4 and the detection threshold of SNR 8 approximately 12 and 5 minutes before merger, respectively-gains of 4.5 and 1.5 minutes over the circular case. Localization within $1000 \, (100)\,\rm deg^2$ is achievable 5 (1) minutes before merger, improving by 2 minutes (15 seconds). Our results highlight the potential of eccentricity-induced higher harmonics in improving early warnings and localization, particularly for BNS mergers, enhancing the prospects for multi-messenger astronomy.

We consider the Vlasov--Poisson system in a $C^3$ convex domain $D$ with a perfectly conducting wall. We introduce the asymptotic domain $D_{\infty}$ for the domain $D$. Then under acceptable assumptions on $D$, we show that for localized initial data, the velocity of particles is asymptotically supported in the (closure of the) asymptotic domain $\overline{D_{\infty}}$ and the solutions exhibit the asymptotics of modified scattering.

To test scientific theories and develop individualized treatment rules, researchers often wish to learn heterogeneous treatment effects that can be consistently found across diverse populations and contexts. We consider the problem of generalizing heterogeneous treatment effects (HTE) based on data from multiple sites. A key challenge is that a target population may differ from the source sites in unknown and unobservable ways. This means that the estimates from site-specific models lack external validity, and a simple pooled analysis risks bias. We develop a robust CATE (conditional average treatment effect) estimation methodology with multisite data from heterogeneous populations. We propose a minimax-regret framework that learns a generalizable CATE model by minimizing the worst-case regret over a class of target populations whose CATE can be represented as convex combinations of site-specific CATEs. Using robust optimization, the proposed methodology accounts for distribution shifts in both individual covariates and treatment effect heterogeneity across sites. We show that the resulting CATE model has an interpretable closed-form solution, expressed as a weighted average of site-specific CATE models. Thus, researchers can utilize a flexible CATE estimation method within each site and aggregate site-specific estimates to produce the final model. Through simulations and a real-world application, we show that the proposed methodology improves the robustness and generalizability of existing approaches.

Fano profiles are observed across various fields of wave physics. They emerge from interference phenomena and are quantified by the asymmetry parameter q. In optics, q is usually considered as a phenomenological coefficient obtained by fitting experimental or numerical data. In this work, we introduce an ab initio Maxwellian approach using quasinormal modes to analytically describe line shapes in light scattering problems. We show that the response of each individual quasinormal mode inherently exhibits a Fano profile and derive an explicit analytical formula for the Fano parameter. Experimental and numerical validations confirm the formula's accuracy across a broad spectrum of electromagnetic systems. The general expression for q opens new possibilities for fine-tuning and optimizing spectral line shapes in electromagnetism.