Collisional gates in optical superlattices have recently achieved record fidelities, but their operation times are typically limited by tunneling. Here we propose and analyze an alternative route to a fast $\sqrt{\mathrm{SWAP}}$ gate for two fermionic atoms in an optical superlattice based on optimized, time-dependent control of the short and long lattice depths. The gate is implemented by transiently releasing the atoms into a quasi-harmonic confinement centered between the two sites. With an appropriately chosen contact interaction strength, a controlled collision accumulates the exchange phase required for $\sqrt{\mathrm{SWAP}}$ and generates entanglement. We employ a continuum, time-dependent Schrödinger-equation simulation that goes beyond a two-site Fermi--Hubbard description and benchmark it against experimentally implemented tunneling-based protocols, reproducing the observed single-particle tunneling and spin-exchange dynamics. For experimentally accessible lattice depths, we find that the proposed gate operates in $\sim 21\,μ\mathrm{s}$, more than an order of magnitude faster than tunneling-based implementations, while achieving fidelities $\gtrsim 99\%$. We further analyze sensitivity to lattice-depth variations and show that a composite sequence improves robustness. Our results establish fast, collision-mediated entangling gates in superlattices as a promising building block for scalable neutral-atom quantum computation.

Ni-W based medium heavy alloys offer a promising pathway to bridge the density-strength gap between tungsten heavy alloys and ultrahigh-strength steels. In this study, the effects of W concentration on chemical short-range order (CSRO), deformation behavior, and grain boundary chemistry of Ni-xW alloys in the range x = 0 to 38 wt% were systematically investigated using a suite of advanced characterization and modeling techniques, including synchrotron X-ray diffraction, transmission electron microscopy, atom probe tomography, and first-principles thermodynamic simulations. Our study reveals that strong CSRO emerges when W content exceeds about 30 wt%, producing distinct diffuse scattering and significantly enhancing strain-hardening capacity. During deformation, the presence of SRO promotes planar slip and twin formation, leading to strong dislocation interactions and elevated flow stress. Hall-Petch analysis demonstrates an exceptionally high grain boundary strengthening coefficient (ky about 1100 MPa micrometer^(1/2)) in Ni-38W, underscoring the intrinsic strengthening effect associated with CSRO. First-principles cluster expansion coupled with Monte Carlo simulations reveals that increasing W content enhances SRO tendency through the stabilization of Ni4W-type local configurations. These findings establish a mechanistic link between W concentration, CSRO evolution, and mechanical response, providing new insights for designing high-density, high-strength Ni-W based alloys with optimized performance.

Many statistical and econometric problems involve parameters defined by moments of a joint distribution when only marginal distributions are observed, leading naturally to partial identification. We develop a methodology for identification, estimation, and inference in the corresponding partially identified GMM model. We characterize the sharp identified set for the parameter of interest via a support-function/optimal-transport (OT) representation. To estimate the identified set, we employ entropic regularization, which yields a smooth approximation to the classical OT problem that can be computed efficiently using the Sinkhorn algorithm. We also propose a test statistic for hypothesis testing and the construction of confidence regions for the identified set. To derive its asymptotic distribution, we establish a novel central limit theorem for the entropic OT value under general smooth cost functions. We then obtain valid critical values using the bootstrap for directionally differentiable functionals of Fang and Santos (2019). The resulting testing procedure controls size locally uniformly, including at parameter values on the boundary of the identified set. We demonstrate good finite-sample performance of our methodology in Monte Carlo simulations. Finally, as an empirical illustration, we estimate a panel logit model of self-reported happiness with attrition and refreshment, using data from the Understanding America Study.

Laser manipulation plays a critical role in precisely tailoring relativistic electron beams through energy modulation, enabling the generation of coherent, intense, and ultrashort radiation in accelerator-based light sources such as synchrotron radiation facilities and free-electron lasers (FELs). However, laser-induced energy modulation inevitably degrades electron beam quality by increasing the energy spread, thereby limiting high-repetition-rate operation. Here, we investigate energy modulation and demodulation in a seeded FEL using two modulators separated by a tunable phase shifter. Analytical analysis and three-dimensional simulations show that a $π$ phase delay can nearly reverse the laser-beam interaction and substantially suppress the residual modulation. Diagnostics based on coherent undulator radiation and time-resolved measurements are established to characterize weak residual modulation, and a dedicated demodulation undulator is designed for controlled studies. Preliminary experiments performed at the Shanghai soft X-ray FEL facility using the existing seeding beamline demonstrate laser-induced energy-modulation suppression. Together with the analytical and numerical studies, these results establish a practical framework for investigating the transition from energy modulation to demodulation in seeded FELs, with potential applications in high-repetition-rate, fully coherent X-ray sources with improved preservation of electron beam quality.

Health care systems are increasingly considering large language model (LLM)-based chatbots for vaccine communication, but evidence that they improve durable, behaviorally relevant outcomes beyond existing health materials is limited. This randomized clinical trial tested whether brief, multiturn LLM chatbot interactions increased parental intention to vaccinate children against human papillomavirus (HPV) compared with no intervention and government public health materials, and whether effects persisted. Parents in the US, Canada, and UK were recruited online from March 3 to May 25, 2025, with follow-up at 15 and 45 days. Eligible participants were adults with at least one HPV vaccine-eligible child who was unvaccinated or whose vaccination status was unknown. Participants were randomized to no-message control, country-matched government materials with at least 3 minutes of exposure, or a 3-minute GPT-4o chatbot interaction using either a default persuasive style or a shorter conversational style. The primary outcome was self-reported likelihood of vaccinating the child against HPV within 12 months, measured immediately after intervention on a 0-100 scale. Follow-up outcomes included vaccination intent and self-reported vaccination at 15 and 45 days. In total, 1297 participants were randomized (mean age 42.84 years; 72.1% female). Compared with no intervention, public health materials increased immediate vaccination intent (Cohen d = 0.53; 95% CI, 0.36-0.70), as did the default chatbot (d = 0.48; 95% CI, 0.30-0.65) and conversational chatbot (d = 0.33; 95% CI, 0.17-0.49). At 45 days, neither chatbot increased intent relative to controls, whereas public health materials maintained modest effects. No intervention increased self-reported vaccination uptake. Findings suggest well-designed public health materials may match or exceed short LLM chatbot conversations for HPV vaccine promotion.

We investigate certain complexes that are associated to an operad $\mathscr{O}$ in $k$-vector spaces, where $k$ is a field of characteristic $0$. This exploits the study of modules over the $k$-linearization of the upward walled Brauer category, $k\mathsf{uwb}$ (respectively of the downward walled Brauer category, $k\mathsf{dwb}$). These are Koszul over $k(\mathbf{FB \times FB})$, where $\mathbf{FB}$ is the category of finite sets and bijections. We show that the Chevalley-Eilenberg complex for the Lie algebra of derivations $\mathrm{Der} (\mathscr{O} (V))$ of the free $\mathscr{O}$-algebra on a finite-dimensional vector space $V$ has a precursor given by the Koszul complex on an explicit module over $(k\mathsf{dwb})_-$ (a twisted $k$-linearization of $\mathsf{dwb}$); this module is constructed naturally from the operad $\mathscr{O}$. Following Dotsenko, we also consider the more general case where a {\em wheeled} term is included. This identification exploits functoriality with respect to the category of finite-dimensional $k$-vector spaces with morphisms taken to be split monomorphisms, together with the relationship with functors on the upward (and downward) walled Brauer category. We also exploit methods developed by Sam and Snowden for investigating the stabilization of the families of representations of the general linear groups associated to a functor on the category of split monomorphisms between $k$-vector spaces. We give a new perspective on the results of Dotsenko, who investigated the stable homology of Lie algebras of derivations and established a link with the wheeled bar construction for wheeled operads. In particular, we explain why one of the Koszul complexes that we consider should be considered as the appropriate form of hairy graph complex for operads, by analogy with the case of cyclic operads.

In this paper, we revisit the construction of the hairy graph complexes associated to a cyclic operad, by exploiting modules over the appropriate twisted linearization of the downward Brauer category (and working over a field of characteristic zero). The different flavours (even or odd) of complexes appear as forms of Koszul complexes; the Koszul property of the linear category provides an elegant homological interpretation of their homology. This approach allows a second form of Koszul complex to enter the picture. For the `even' flavour, this corresponds to a precursor of the Chevalley-Eilenberg complex of the Conant-Vogtmann Lie algebra associated to a cyclic operad and a symplectic vector space (generalizing Kontsevich's Lie algebras). Again, the cohomology of the Koszul complex has an elegant interpretation. This sheds light on the relationship between the unstable case and Kontsevich's identification (generalized by Conant and Vogtmann) of the homology in the infinite-dimensional case with a form of graph homology (in the even case). We observe that this is already of interest in the case of an algebra with involution, viewed as a cyclic operad.

We explore the quantisation of the tachyonic type 0B superstring and the non-tachyonic $\text{Spin}(16) \times \text{Spin}(16) \rtimes \mathbb{Z}_2$ heterotic string on AdS$_3 \times S^3 \times T^4$ and AdS$_3 \times S^3 \times S^3 \times S^1$ backgrounds. Adapting the analysis for the supersymmetric and bosonic string theories to these set-ups, we provide a world-sheet description for a generic level of the $\text{SL}(2,\mathbb{R})$ WZW model, and we read the spectrum through the associated partition functions. Focusing on the low-energy theory, we show that the $\text{Spin}(16) \times \text{Spin}(16) \rtimes \mathbb{Z}_2$ heterotic string on both backgrounds accommodates non-trivial Wilson lines that are responsible for the appearance of tachyonic regions in the classical moduli space, hence jeopardising the stability of the vacuum. We show this with a concrete example on the AdS$_3 \times S^3 \times S^3 \times S^1$ space and provide general formulas for a systematic analysis of the classical moduli space.

In this note, we first try to prove a uniform lower bound of nodal volume in elliptic homogenization setting. This lower bound is far from optimal. But, we can prove a constant lower bound in dimension two. Motivated by the proof, we extend this results to more general settings. To be more specific, we prove that the nodal volume has a constant lower bound for all continuous functions with strong maximum principle. Our result works for general functions beyond solutions to elliptic PDEs.

We analyse the size of quantum corrections in the Zee model using effective field theory techniques. We derive the relevant 1-loop matching conditions and use them together with the existing renormalisation group equations in the two Higgs doublet model to calculate quantum corrections to the neutrino mass squared differences, mixing angles, and phases. Using four benchmark scenarios, we demonstrate when quantum corrections have to be included in studies of neutrino mass parameters in the Zee model.

Digital twins of radio access networks require packet-level traffic generators that reproduce the size and timing of packets while remaining compact and easy to recalibrate as traffic changes. We address this need with a hybrid generator that combines a small hidden Markov model, which captures buffering, streaming, and idle states, with a mixture density network that models the joint distribution of payload length and inter-arrival time (IAT) in each state using Student-t mixtures. The state space and emission family are designed to handle heavy-tailed IAT by anchoring an explicit idle state in the tail and allowing each component to adapt its tail thickness. We evaluate the model on public traces of web, smart home, and encrypted media traffic and compare it with recent neural network and transformer based generators as well as hidden Markov baselines. Across most datasets and metrics, including average per-flow cumulative distribution functions, autocorrelation based measures of temporal structure, and Wasserstein distances between flow descriptors, the proposed generator matches the real traffic most closely in the majority of cases while using orders of magnitude fewer parameters. The full model occupies around 0.2 MB in our experiments, which makes it suitable for deployment inside digital twins where memory footprint and low-overhead adaptation are critical.

We consider a denoiser that reconstructs a stationary ergodic source by lossily compressing samples of the source observed through a memoryless noisy channel. Prior work on compression-based denoising has been limited to additive noise channels. We extend this framework to general discrete memoryless channels by deliberately choosing the distortion measure for the lossy compressor to match the channel conditional distribution. By bounding the deviation of the empirical joint distribution of the source, observation, and denoiser outputs from satisfying a Markov property, we give an exact characterization of the loss achieved by such a denoiser. Consequences of these results are explicitly demonstrated in special cases, including for MSE and Hamming loss. A comparison is made to an indirect rate-distortion perspective on the problem.

The anisotropic Rabi model (ARM), which features tunable Jaynes-Cummings (JC) and anti-Jaynes-Cummings (AJC) interactions, has remained challenging to realize fully. We present a circuit QED architecture featuring a qubit, a resonator, and a flux-tunable coupler that provides complete dynamic control over the ARM Hamiltonian. By leveraging simultaneous capacitive and inductive couplings, we can in-situ tune the interaction from the pure JC to the pure AJC regime without requiring external parametric modulation. This dynamic control enables useful quantum measurement and coherence capabilities, including dispersive shift cancellation for protection against photon shot-noise dephasing, and Purcell-suppressed readout. Our work establishes a versatile platform for exploring the ARM's full parameter space and its broader applications in quantum information processing.

Nowadays, Artificial Intelligence (AI), particularly Machine Learning (ML) and Large Language Models (LLMs), is widely applied across various contexts. However, the corresponding models often operate as black boxes, leading them to unintentionally act unfairly towards different demographic groups. This has led to a growing focus on fairness in AI software recently, alongside the traditional focus on the effectiveness of AI models. Through 26 semi-structured interviews with practitioners from different application domains and with varied backgrounds across 23 countries, we conducted research on fairness requirements in AI from software engineering perspective. Our study assesses the participants' awareness of fairness in AI / ML software and its application within the Software Development Life Cycle (SDLC), from translating fairness concerns into requirements to assessing their arising early in the SDLC. It also examines fairness through the key assessment dimensions of implementation, validation, evaluation, and how it is balanced with trade-offs involving other priorities, such as addressing all the software functionalities and meeting critical delivery deadlines. Findings of our thematic qualitative analysis show that while our participants recognize the aforementioned AI fairness dimensions, practices are inconsistent, and fairness is often deprioritized with noticeable knowledge gaps. This highlights the need for agreement with relevant stakeholders on well-defined, contextually appropriate fairness definitions, the corresponding evaluation metrics, and formalized processes to better integrate fairness into AI/ML projects.

We use the Dark Energy Spectroscopic Instrument Data Release 1 (DESI DR1) to identify stellar members of the Local Group dwarf galaxies. We cross-match DESI targets with candidate members that are based on Gaia proper motions, positions, and photometry. The addition of DESI radial velocities enables secure membership determination in 15 systems. Our results confirm that Gaia-based selection algorithms are effective in minimising foreground contamination. Two stars are found to be associated with DES~J0225$+$0304; if this is the case, then it leads to the first determination of the systemic radial velocity (RV$_{\rm{sys}}=-150.0\pm7.0$~km~s$^{-1}$). Draco and Sextans are the galaxies with the largest number of members. We focus on Sextans and, for the first time with DESI, trace its stellar kinematics to large radii (up to $\sim$10~half-light radii). We find that the metal-poor population exhibits a higher velocity dispersion and extends to larger radii, whereas the metal-rich population is kinematically colder and centrally concentrated. The metallicity gradient is steeper in the inner regions of Sextans ($\sim -12\times 10^{-3}$~dex~arcmin$^{-1}$ or $\sim -0.36$~dex~kpc$^{-1}$), while almost no gradient in the outskirts, hinting for an ex-situ halo or for an ``outside-in'' star formation. Although DESI [$α$/Fe] ratios for Sextans stars with $\FeH\gtrsim-2.0$ are in line with literature values, those for very metal-poor stars ($\FeH\lesssim-2.0$) present a large scatter and strong anti-correlation with metallicity, warranting a caution for using DESI abundances in this regime. With a less strict selection, we identify 8 ultra metal-poor ([Fe/H]~$< -4$) candidates that require higher signal-to-noise ratio spectroscopic observations to determine their metallicities.

The extended-domain method is a strategy for applying spectral methods to complex geometries. Its stability is complicated by the ill-conditioning of the Fourier extension frame. This paper provides an analysis of the method's pre-asymptotic behavior. We confirm that the spectral collocation system is asymptotically ill-conditioned for both the Poisson and convection-diffusion operators, driven by the redundancy of the underlying frame. However, we prove a fundamental structural dichotomy in their discrete Green's functions. We show that the inverse of the convection-diffusion operator is numerically quasi-sparse, exhibiting exponential off-diagonal decay, in contrast to the numerically dense inverse of the Poisson operator. This intrinsic sparsity explains why the convection-diffusion operator is significantly more robust to the underlying frame instability in practical computations.

Composite endpoints that combine recurrent non-fatal events with a terminal event are increasingly used in randomized clinical trials, yet conventional time-to-first event analyses may obscure clinically relevant information. We compared two statistical frameworks tailored to such endpoints: the joint frailty model (JFM) and the last-event assisted recurrent-event win ratio (LWR). The JFM specifies proportional hazards for the recurrent and terminal events linked through a shared frailty, yielding covariate-adjusted, component-specific hazard ratios that account for informative recurrences and dependence with death. The LWR is a nonparametric, prioritized pairwise comparison that incorporates all observed events over follow-up and summarizes a population-level benefit of treatment while respecting a pre-specified hierarchy between death and recurrences. We first assessed the performance of the methods using simulations that varied both the gamma-frailty variance and the event rates. We next illustrated both approaches using two clinical application examples in oncology and cardiology, highlighting how conclusions depend on whether treatment primarily affects recurrent events, mortality, or both. The JFM provided component-specific estimates, while the LWR led to a summary measure of treatment effect with direction. Power was systematically improved with JFM, which thus appeared as the most reliable approach for inference and sample size estimation. Methodological extensions of the LWR to appropriately handle censoring and to formalize causal estimands remain a promising direction for future research.

In [DP12], Delzant and Py showed that there exist continuous irreducible isometric actions of $\mathrm{PSL}_2(\mathbb{R})$ on the infinite-dimensional hyperbolic space $\mathbb{H}^\infty$. Such continuous irreducible actions do not exist on the hyperbolic spaces $\mathbb{H}^n$ when $n>2$ and their associated embeddings $\mathbb{H}^2 \to \mathbb{H}^\infty$ given by the orbit maps were later called \emph{exotic} by Monod and Py in [MP14]. In this article, we produce a continuous and irreducible representation of $\mathrm{PSL}_2(\mathbb{R})\to \mathrm{Isom}(\mathbb{H}^\infty)$ using the hyperbolic model for convex bodies introduced in [DF22]. This yields a convex cocompact $\mathrm{PSL}_2(\mathbb{R})$-action on the infinite-dimensional hyperbolic space $\mathbb{H}^\infty$, of which the compact quotient over the minimal $\mathrm{PSL}_2(\mathbb{R})$-invariant convex set is homeomorphic to the 2-dimensional oriented Banach--Mazur compactum. Moreover, we study the geometry of one of its orbit maps and compute the Hausdorff dimension of the limit set of this representation.

The Milky Way Galactic Center hosts a $\sim4\times10^{6}\,M_\odot$ supermassive black hole (SMBH), Sagittarius A* (Sgr A*). The dominant structures in its immediate vicinity are the nuclear star cluster (NSC), whose enclosed mass at 2 pc is approximately half that of the SMBH, and the circumnuclear disk (CND)/ring, which extends between $\sim0.5$ pc and $\sim3$ pc from Sgr A* and is the largest reservoir of molecular gas in this region. Existing models of the CND commonly use one circular orbit to describe the motion of its gas. Here, we explore a much broader range of models. In the combined potential of Sgr A* and the NSC, we consider non-Keplerian rosette orbits as well as a circular disk, which is formed using a finely spaced set of concentric rings. For both systems, we test various inner/outer radii, inclinations, and position angles, sampling a total of $\sim3.3 \times 10^{5}$ models. We then conduct mock observations of all models to construct velocity maps, which we compare with HCN ($J=1{-}0$) observations of the CND. We find that the best-fitting model is a circular disk with inner and outer radii of 1.0 pc and 2.9 pc, an inclination of $i=60^{\circ}$, and a position angle of $\text{PA} = 35^{\circ}.$

Grover's algorithm is a fundamental quantum algorithm that offers a quadratic speedup for the unstructured search problem by alternately applying physically implementable oracle and diffusion operators. In this paper, we reformulate the unstructured search as a maximization problem on the unitary manifold and solve it via the Riemannian gradient ascent (RGA) method. To overcome the difficulty that generic RGA updates do not, in general, correspond to physically implementable quantum operators, we introduce Grover-compatible retractions to restrict RGA updates to valid oracle and diffusion operators. Theoretically, we establish a local Riemannian $μ$-Polyak-Łojasiewicz (PL) inequality with $μ= \tfrac{1}{2}$, which yields a linear convergence rate of $1 - κ^{-1}$ toward the global solution. Here, the condition number $κ= L_{\mathrm{Rie}} / μ$, where $L_{\mathrm{Rie}}$ denotes the Riemannian Lipschitz constant of the gradient. Taking into account both the geometry of the unitary manifold and the special structure of the cost function, we show that $L_{\mathrm{Rie}} = O(\sqrt{N})$ for problem size $N = 2^n$. Consequently, the resulting iteration complexity is $O(\sqrt{N} \log(1/\varepsilon))$ for attaining an $\varepsilon$-accurate solution, which matches the quadratic speedup of $O(\sqrt{N})$ achieved by Grover's algorithm. These results demonstrate that an optimization-based viewpoint can offer fresh conceptual insights and lead to new advances in the design of quantum algorithms.

We characterise an efficient optically-heated neutral atom source for ion trapping. We observe loading rates of up to $24(3)\,\mathrm{s}^{-1}$ with heating powers below $85\,\mathrm{mW}$, and demonstrate loading of a single ion in under $30\,\mathrm{s}$ with $41.4(4)\,\mathrm{mW}$ of optical power in a room-temperature ion trap system with an ionisation probability of $1.50(5)\times10^{-5}$. We calibrate a thermal model for the source's internal temperature by imaging the fluorescence of a collimated flux of neutral calcium that effuses from the oven at various optical heating powers. We show that the thermal performance of this oven is mainly limited by radiative losses. We explore the effect of second-stage photo-ionisation laser power on the loading rate, and identify a path beyond the loading rates reported in this study. We predict that this source is also well-suited to a wide range of metals used in ion-trapping.

The Central Molecular Zone (CMZ) is an extreme star formation environment, characterized by higher density, higher turbulence, stronger orbital shear, and stronger magnetic field strength than the solar neighborhood. It is still debated whether classical theories of star formation hold within this extreme environment. In order to assess the impact of these different conditions on the interstellar medium (ISM) and on star formation, we present radiation magnetohydrodynamic {\sc arepo} simulations of a Milky Way-type galaxy. We set up a high-resolution ($M_{\rm cell}=20$~\Msun) region in a ring around the solar radius and in the barred region of the Galaxy to have a coherent comparison between the CMZ and the solar neighborhood. Although the high densities and strong levels of turbulence affect star formation and feedback, a key difference in the regulation of star formation between the two environments comes from the short orbital times and the strong shear in the CMZ. In particular, we highlight the role of the quick dynamical decoupling of stars and gas, which leads to periodic re-embedding events in the early lifetimes of radiating O stars. Young stellar associations are efficiently sheared apart, such that the ISM is deprived of the compounding effect of radiation and supernovae in disrupting molecular clouds. This dramatically changes the evolution of giant molecular clouds and how feedback can regulate star formation in the CMZ. Stellar feedback is no longer directly coupled to the molecular cloud from which they formed, and no strong and disruptive superbubbles can develop. The feedback instead rather acts as a background source of turbulence.

A Wishart kernel density estimator (KDE) is introduced for density estimation in the cone of positive definite matrices. The estimator is boundary-aware and mitigates the boundary bias suffered by conventional KDEs, while remaining simple to implement. Its mean squared error, uniform strong consistency on expanding compact sets, and asymptotic normality are established under the Lebesgue measure and suitable mixing conditions. This work represents the first study of density estimation for dependent data on this space under any metric. For independent observations, an asymptotic upper bound on the mean absolute error is also derived. A simulation study compares the performance of the Wishart KDE with that of the log-Gaussian KDE, another boundary-aware estimator based on the matrix-variate lognormal distribution proposed by Schwartzman [Int. Stat. Rev., 2016, 84(3), 456--486], and with the naive Gaussian KDE on the ambient Euclidean space. When estimating the stationary marginal density of a Wishart autoregressive process for several autoregressive coefficient matrices and innovation covariance matrices, the Wishart KDE exhibits the best overall accuracy and stability. The practical utility of the Wishart KDE is illustrated by estimating the marginal density of a one-year time series of realized covariance matrices computed from 5-minute intra-day returns on Amazon Corp. shares and on the Standard & Poor's 500 exchange-traded fund. All code is publicly available via the R package ksm to facilitate implementation of the method and reproducibility of the findings.

Urban Air Mobility (UAM) presents a transformative vision for metropolitan transportation, but its practical implementation is hindered by substantial infrastructure costs and operational complexities. We address these challenges by modeling a UAM network that leverages existing regional airports and operates with an optimized, heterogeneous fleet of aircraft. We introduce LPSim, a Large-Scale Parallel Simulation framework that utilizes multi-GPU computing to co-optimize UAM demand, fleet operations, and ground transportation interactions simultaneously. Our equilibrium search algorithm is extended to accurately forecast demand and determine the most efficient fleet composition. Applied to a case study of the San Francisco Bay Area, our results demonstrate that this UAM model can yield over 20 minutes' travel time savings for 230,000 selected trips. However, the analysis also reveals that system-wide success is critically dependent on seamless integration with ground access and dynamic scheduling.

We develop a microscopic theory of magnon-exciton drag effect in a bilayer van der Waals antiferromagnetic semiconductor CrSBr. Effective exciton-magnon coupling arises from an orbital mechanism: Magnons tilt the layer magnetizations, enabling charge carrier tunneling that mixes intra- and interlayer excitons and thereby modulate the exciton energy. We derive the effective Hamiltonian of exciton-magnon coupling, based on our calculation of the magnon spectrum taking into account short-range exchange interaction between Cr-ion spins, single-ion anisotropy, and long-range dipole-dipole interactions. The latter produces a negative group velocity of magnons at small wavevectors. We show that despite rather small renormalization of exciton's energy and effective mass by the exciton-magnon interaction, the three key two-magnon processes: exciton-magnon scattering, two-magnon absorption by exciton, and two-magnon emission are highly efficient. By solving the Boltzmann kinetic equation, we evaluate short exciton-magnon scattering time which is in the sub-ps range and strongly decreases with the increase of magnon population. Hence, exciton-magnon scattering is likely to be dominant over other scattering processes related to the exciton-phonon and exciton-disorder interactions. We demonstrate that magnons can efficiently drag excitons, resulting in a large and nearly isotropic exciton propagation that can significantly exceed the intrinsic anisotropic diffusion. Our results provide a theoretical basis for recent observations of anomalous exciton transport in CrSBr [F. Dirnberger, et al., Nat. Nano. (2025)] and establish magnon-exciton drag as a powerful mechanism for controlling exciton propagation in magnetic systems.

Tensor networks are a compressed format for multi-dimensional data. One dimensional tensor networks -- often referred to as tensor trains (TT) or matrix product states (MPS) -- are increasingly being used as a numerical ansatz for continuum functions by ``quantizing'' the inputs into discrete binary digits. Here we demonstrate the power of more general tree tensor networks (TTNs) for this purpose. We provide direct constructions of a number of elementary functions as generic tree tensor networks and interpolative constructions for more complicated functions via a generalization of the tensor cross interpolation algorithm. For a range of multi-dimensional functions we show how more structured tree tensor networks offer a significantly more efficient ansatz than the commonly used tensor train. Finally, we demonstrate how the methods introduced in this work can be used to realize a TTN-based solver for multi-dimensional, non-linear Fredholm equations.

Every dark matter halo forms with a $ρ\propto r^{-1.5}$ density cusp at its center. For warm dark matter (WDM), these prompt cusps can be massive enough to influence the kinematics of dwarf galaxies. By implementing prompt cusps in the Galacticus galaxy formation model, we show that the measured velocity dispersions of Tucana V and Triangulum II are serious outliers for dwarf galaxies arising in WDM models. For thermal-relic dark matter, the three faintest Milky Way satellites together constrain the particle mass to be $m_χ>5.8$ keV at 95 percent confidence or $m_χ>9.4$ keV at 90 percent confidence. Improved velocity dispersion measurements for these systems could greatly refine this constraint, as could identification and kinematic characterization of more such galaxies.

The Dalitz decay $π^0 \to e^+e^-γ$ has been measured with the highest statistical accuracy obtained so far in the $γp\to π^0 p$ reaction with the A2 tagged-photon facility at the Mainz Microtron, MAMI. The value of the slope parameter for the $π^0$ electromagnetic transition form factor, $a_π=0.0315\pm 0.0026_{\mathrm{stat}}\pm 0.0010_{\mathrm{syst}}$, is obtained from the analysis of $2.4\times10^6$ $π^0 \to e^+e^-γ$ observed decays. Within experimental uncertainties, it is in agreement with existing measurements and theoretical calculations, with its own uncertainty being smaller than previous results based on the analysis of $π^0\to e^+e^-γ$ decays.

Korn's inequalities show that the $L^2$-norm of $\nabla u$ can be controlled by the $L^2$-norm of $\mathrm{Sym}(\nabla u)$, which only has $d(d+1)/2$ components. In [J. Math. Pures Appl. 148 (2021), pp. 199-220] Chipot posed the question of \textit{how many scalar measurements are needed to have a Korn-type control on $\nabla u$} when $u$ is in $H_0^1(Ω)$ and $H^1(Ω)$, introducing the minimal numbers $N(d,Ω)$ and $N'(d,Ω)$ respectively. He proved general bounds and calculated several low-dimensional values of $N,N'$. We reframe Chipot's problem in the language of rank-one convexity and quasiconvexity and obtain a purely algebraic characterisation of when such inequalities hold, which yields the sharp bounds \begin{align*} N(d,Ω)&=2d(1-o(1))\\ N'(d,Ω)&=2d-1. \end{align*} As a consequence, we recover and streamline several of Chipot's results, we obtain a dimension-optimal Korn inequality and several sharp estimates for the best constant for various Korn-type inequalities. Generalisations to the rectangular case and to general $L^p$ estimates are also considered.\par The central new ingredient of our approach is a systematic connection between laminates and martingales which produces explicit families of laminates realising these bounds. This method is of independent interest in the calculus of variations: for instance, we use it to obtain a new quick and quantitative proof of Ornstein's non-inequality, valid for all first order homogeneous operators in $\mathbb{R}^{2\times 2}$ and for a large class of operators in general dimensions (including Korn's $\frac{\nabla u+\nabla u^t}2$ and $\frac{\nabla u+\nabla u^t}2-\mathrm{div}(u)\frac{\mathrm{Id}}d$).

Born effective charge, a fundamental quantity in lattice dynamics and ferroelectrics, provides a quantitative measure of linear polarization response to ionic displacements. However, it does not account for higher-order effects, which can play a significant role in certain materials, such as fluorite HfO$_2$. In this letter, we use the second-order mode effective charges defined with the second-order atomic dynamical charges as a measure of the dipole moments generated by nonpolar lattice distortions. Using first-principles calculations, we demonstrate that specific combinations of nonpolar phonons in many oxides can induce strongly aligned second-order polarizations, reaching magnitudes comparable to those of intrinsically polar modes even in the zero frequency limit, broadening the understanding of second-order effects, which have historically been emphasized for their dynamical effects at specific frequency ranges. Through a symmetry-based analysis of the charge density, we elucidate the microscopic origin of these effects, tracing them to variations in bond covalency and local electronic rearrangements. We also demonstrate large second-order mode effective charge in well-studied perovskites, highlighting the generality of these phenomena. Our results offer new insights into the design principles of next-generation ferroelectric, piezoelectric and multifunctional materials from the higher-order contribution to polarization in crystalline solids.