Papers

We use the proton spectrum resolved by LHAASO across the knee to test superheavy dark matter in the nucleon channel at PeV energies. Both the hardening at $0.34$ PeV and the knee at $3.3$ PeV are reproduced by nucleons from a relic of mass $5\cdot 10^{7}$ GeV decaying in the Galactic halo, with the mass as the only shape parameter of the spectrum and the background index profiled under an independent prior on the proton slope below $0.1$ PeV. It works equally well in all three hadronic-interaction-model reconstructions. On the other hand, the photons of the same cascade rule out this interpretation by about two orders of magnitude against the photon fraction of the cosmic radiation, and by about one order of magnitude against the LHAASO diffuse Galactic emission.

Quantum imaginarity, as a critical resource metric for quantifying intrinsic nonreal coherence encoded in quantum states, exhibits nontrivial evolutionary behaviors in curved spacetime backgrounds. This work focuses on bipartite Dirac field reduced states in the quantum atmosphere of a static Schwarzschild black hole, aiming to explore the modulation of three mainstream imaginarity measures by Hawking thermal radiation. We reveal that the relative-entropy imaginarity, the geometric imaginarity and robustness of imaginarity, the fully accessible state presents a valley-shaped radial profile with a local minimum inside the quantum atmosphere, while the cross-coupling and fully inaccessible states follow opposite peak-shaped trends. Further analysis demonstrates that the Hartle-Hawking constant significantly strengthens the redistribution effect of imaginarity across both regions, whereas an increase in the event horizon radius weakens such redistribution and flattens the extremum features. These findings offer a new perspective for decoding the information structure of black hole quantum atmospheres and the intrinsic quantum nature of Hawking radiation.

Exceptional points are topological defects of complex band structures that are stable against weak perturbations, yet in two-band systems with bounded non-Hermitian couplings they are ultimately removed by a sufficiently strong Hermitian field. Here we demonstrate a striking exception in a two-dimensional subwavelength atomic array. Along a continuous square-to-triangular deformation at fixed magnetic field, the bulk passes between line-gapped topological regions with \textcolor{black}{band Chern numbers \( (C_1,C_2)=(2,-2) \)} through a gapless exceptional region. Within a finite interval of lattice deformation, increasing the magnetic field merely drives the exceptional points toward the light cone because of the singular radiative dipolar couplings. We further show that skin localization toward open boundaries responds non-monotonically to the same field. An intermediate field drives a bipolar skin localization, with bulk modes from different spectral branches accumulating at opposite boundaries, whereas stronger fields suppress boundary localization. Our results establish the interplay of lattice geometry, light-cone singularity, and Hermitian magnetic field as a route to engineering Chern and exceptional topology beyond the conventional strong-field limit.

We establish the sharp CFL condition for the piecewise constant sparse grid discontinuous Galerkin (DG) method with forward Euler time stepping, applied to transport equations with constant coefficients on periodic domains in arbitrary dimensions. For the transport velocity $\boldsymbol c=(c_1,\ldots,c_d)$ and a uniform mesh of size $h$, we prove that the scheme is $L^2$ stable if and only if $\Delta t \leq {h}/{\max_{1\leq \ell\leq d}|c_\ell|}$, whereas the corresponding full grid upwind scheme is well-known to require $\Delta t\leq h/\sum_{\ell=1}^d |c_\ell|$. The sparse grid discretization therefore enlarges the admissible time step by a factor of ${(\sum_{\ell=1}^d |c_\ell|)}/{(\max_{1\leq \ell\leq d}|c_\ell|)}$, which lies between $1$ and $d$ and reaches $d$ for isotropic transport. The proof of sufficiency relies on projection leakage identities for the multilevel Haar decomposition, which allow the mixed directional terms in the energy estimate to be absorbed by the energy discarded by the sparse grid projection. The proof of sharpness follows from alternating modes in one dimension at the finest level. As a by-product, we obtain explicit formulas for the $L^2$ operator norm and the spectral radius of the amplification operator. For spaces over general downward closed index sets, we derive an explicit sufficient CFL condition and a geometric criterion for its sharpness. Numerical experiments in two and four dimensions confirm the theoretical results.

By consuming multiple copies of an unknown qubit state, one can modify its purity while preserving the direction of its Bloch vector. We determine the maximum linear rate at which qubit states of different purities can be interconverted, allowing a nonzero error, quantified, for instance, by the trace distance, provided that it vanishes in the limit of infinitely many copies. Interestingly, the optimal conversion rate is determined by the two eigenvalues of the complex right-logarithmic-derivative (RLD) Fisher information matrix associated with $\mathrm{SU}(2)$ rotations of the qubit state. When the output qubits have higher purity, corresponding to concentration, the optimal rate is given by the ratio of the maximum eigenvalues of the input and output RLD matrices. In contrast, when the output qubits have lower purity, corresponding to dilution, the optimal rate is given by the ratio of their minimum eigenvalues. Remarkably, both concentration and dilution can be implemented using SWAP tests as the only nontrivial two-qubit measurement primitive, together with ancillary qubits initially prepared in maximally mixed states, without requiring any additional two-qubit gates. Our work thus provides a novel operational interpretation of the full complex RLD Fisher information matrix. Crucially, its antisymmetric, purely imaginary part encodes geometric information beyond the statistical distance between density operators and plays an essential role in determining the optimal state-conversion rates.

This study investigates the zero-shot ability of large language models (LLMs) to identify and classify hidden narratives in social messages. Our research hypothesis is that LLMs' extensive contextual knowledge allows them to interpret messages on a deeper, pragmatic level, going beyond basic sentiment or topic analysis. Experiments on the Dipromats and SemEval datasets show that providing models with human-written narrative descriptions significantly improves performance, without the need of training examples. In contrast, automatically generated descriptions or the use of few examples (few-shot) often degrade accuracy due to subtle shifts in framing. The study also finds that ensemble methods, particularly majority voting, enhance robustness and that larger models perform best while also being less sensitive to prompt variations. The findings validate that LLMs can effectively detect strategic narratives in a zero-shot setting, and when combined with simple ensembling and human-written descriptions, they can rival supervised systems, offering a scalable solution for narrative detection, specially when there is no training data for the vast majority of domains.

The generalised quantum Stein's lemma is a key result in quantum hypothesis testing, and connects this fundamental primitive of quantum information processing with quantum resource manipulation, a task that is central for technological applications. Prior works have proved this statement in the idealised setting of independent and identically distributed (i.i.d.) sequences of quantum states, and recent extensions consider also sources that are 'close' to i.i.d., according to the strict notion put forth by Mazzola, Sutter, and Renner. For several applications, however, one would need to consider yet more general sources. We establish a version of the generalised quantum Stein's lemma that is conceptually much simpler and general, as it applies to any source that is asymptotically close to an i.i.d. state with respect to the normalised quantum Wasserstein distance of order 1. As an immediate consequence, we solve the Stein exponent of a scenario where the null hypothesis is arbitrarily varying, expressing it in terms of i.i.d. Stein exponents corresponding to arbitrary states in the convex hull of the null hypothesis base set.

Visual monitoring of flapping-wing vehicles requires distinguishing individual wingbeats from motion strength and average frequency. This paper presents a controlled MuJoCo evaluation of wingbeat counting from signed optical flow observed by virtual cameras mounted on Crazyflie vehicles. Three flapping-wing models were recorded at optical distances of 1.5 and 3.0 m, producing 1,440 clips from 240 paired scene configurations with a scene-level 3:1 training-test split. A common spatial convolutional encoder was combined with a causal temporal convolutional network, a recurrent leaky integrate-and-fire spiking network, or causal self-attention. Each model predicted phase and activity, followed by the same directed-crossing event counter. The six existing convolutional models were retained, and all twelve new models were frozen before their test predictions were generated. Exact-count accuracies at 1.5 m were 96.67%, 95.00%, and 96.67%, respectively; at 3.0 m they were 94.44%, 92.22%, and 95.00%. All paired scene-bootstrap intervals for differences in exact-count accuracy included zero. Seven far-distance spiking-model clips had correct totals despite event-timing mismatches, demonstrating why total-count and event-level measurements must be reported together. The results support the feasibility of causal optical-flow counting in the tested setting and identify boundary-sensitive errors. They do not establish an architecture ranking across repeated training, real-flight robustness, or hardware efficiency.

A system between a preparation and a post-selection has had no agreed state since 1964. With positivity as the criterion, a post-selection admits an interval of orderings around the symmetric one exactly when the subspace it forbids is spanned by eigenvectors of a full-rank filtered state. Otherwise it certifies contextuality, testable on a qubit. The averaged filtered state carries the entanglement spectrum of the record, so the smallest forbidden subspaces a symmetry allows are even-dimensional in the Haldane class and odd in the trivial one. That parity is the record's topological class.

Multi-agent Systems (MAS) combine multiple model outputs to solve complex reasoning tasks. However, despite rapid growth of available open-source models, there is limited research on how to select optimal model candidates out of this massive pool. We systematically evaluate 8 model selection strategies (including model size, accuracy and answer diversity) across before-generation (routing) and after-generation (majority-voting, LLM-as-a-judge) MAS architectures on challenging scientific benchmarks. Our findings show a significant gap between theoretical oracle potential and actual performance: Expanding candidate pool sizes often degrades performance below that of the top performing base-model. We find that candidate selection within a single model family is the strategy that yields the best relative performance over a standalone model. These results demonstrate that adding arbitrary models to a heterogeneous MAS can introduce system instability, highlighting model selection as a critical design choice for multi-agent systems.

Graphene nanoribbons (GNRs) obtained by on-surface synthesis combine a width-controlled band gap with atomic precision, making chemical decoration of their edges and interiors a practical route to designed electronic and optical behavior. Ullmann coupling of a phenazine-bearing precursor yields a nine-atom-wide armchair ribbon that is periodically perforated and carries two two-coordinated nitrogen atoms at every pore rim. Here we characterize this ribbon across the properties relevant to device operation, alongside the pristine and undoped porous ribbon, disentangling the roles of pore formation and nitrogen incorporation. Perforation primarily governs mechanical and thermal response, whereas nitrogen substitution predominantly controls electronic and optical properties. Perforation removes the atomic row carrying frontier states, opening the gap into the range measured by tunneling spectroscopy while substantially reducing stiffness and thermal conductivity. Substitution leaves the mechanical response essentially unchanged and contributes a secondary conductivity reduction through phonon spectrum reweighting. Its primary effect is electronic: it selectively narrows the conduction band, binds the lowest exciton by 414 meV, and displaces the absorption edge into the red. The effective phonon mean free path we obtain, 9.9 nm, matches the length to which the synthesis presently limits these ribbons, placing reported samples at the ballistic-to-diffusive crossover. Adsorption on Au(111), Ag(111), and Cu(111) is energetically nearly indistinguishable and remains van der Waals in character, accounting for the substrate tolerance observed experimentally. Finally, graphitic rather than pyrazinic nitrogen would make the ribbon metallic, except when two atoms occupy pore-rim sites, yielding a ferromagnetic semiconducting state having a magnetic moment of 2 mu_B per unit cell.

In 1989, Roth and Lempel constructed a well-known family of non-Reed-Solomon maximum distance separable (MDS) codes. For decades, this family of codes has attracted extensive research attention due to its algebraic structure, low-complexity decoding, and broad applications in cryptography and data storage. In this paper, we present a class of twisted Roth-Lempel codes. We investigate their minimum distance, MDS and NMDS properties. Specifically, we determine the necessary and sufficient conditions for the TRL codes to have minimum distance n-k or n-k+1. Furthermore, we determine the necessary and sufficient conditions for the TRL code to be an MDS or NMDS code. Moreover, we show that the dimension of the Schur square of the TRL code is at least 2k+1, and thus the TRL code is a non-RS code inequivalent to the corresponding RL code.

We give a variational comparison proof of the sharp logarithmic Sobolev inequality with constant $2$ for the word-length Poisson semigroup on free group von Neumann algebras. Our approach extends the Lagrange method for cyclic groups in [Yao26] to a framework in finite tracial von Neumann algebras. The inequality was recently established by Xie and Zhang in [XZ26] using a completely different approach.

Autonomous robots are increasingly deployed on long duration single- and multi-session missions in dynamic environments, where the ability to identify environmental changes such as fallen trees or opened doors provides important contextual information for online planning. We propose a framework called Change Detection via Scene Decomposition (CDSD) for accurate online geometric change detection using LiDAR or RGB-D sensors. Recent advances in geometric SLAM have made it possible to generate dense, tightly aligned maps without post processing, but comparing global maps across entire sessions is computationally expensive and does not allow for single-session online change detection. CDSD instead spatially decomposes mapped environments into unique scenes where changes can be found efficiently by comparing dense, local subsets of the global map called submaps. As the first submap-based approach for geometric change detection, we identify and address the following core challenges: 1) identifying appropriate scenes for change detection that require minimal redundant information; 2) generating dense and representative submaps for each scene; 3) detecting changes between submaps with differing fields of view; and 4) processing detected changes for real-time map reconstruction. Results demonstrate our algorithm on custom datasets collected at the Army Research Laboratory facility in Graces Quarters, Maryland, and on open-source multi-session change detection datasets.

Generative AI increasingly supports complex financial and health decisions, yet we know little about when its responses become difficult to process in real-world dialogue. We analyse more than 84,000 ChatGPT and Gemini conversations, using repeated prompting and clarification following misunderstanding as behavioural indicators of cognitive difficulty. We find that response characteristics such as length, readability and lexical diversity do not have fixed relationships with conversational difficulty; instead, their relationships depend on how they combine. Most notably, greater lexical diversity was associated with less repeated prompting in shorter responses, but this association weakened as response length increased, a pattern that replicated across financial and health conversations. We propose a conversational complexity budget to conceptualise these interdependencies: the demands associated with one response characteristic may depend on those accompanying it. The resulting design challenge is how to configure response complexity for the particular user, task and interaction.

Artificial ontogeny, developmental encodings, robot reproduction, and inherited controllers are established research directions, yet a narrower question remains: can a newborn artificial agent exhibit measurable biparental heredity before learning, and can that dependence be isolated causally rather than inferred only from parent-offspring resemblance? We introduce Machine Zygote, a computational germline-soma architecture designed to test this question. Two parental germlines are independently mutated and recombined into a zygote that parameterizes development of an initially generic eight-module soma, which is then frozen and evaluated without learning. A preregistered 4 x 4 diallel of 640 offspring shows significant dam and sire dependence for five of six behavioral traits after Holm correction, with parental and interaction components accounting for 36-53 percent of modeled variance across five principal traits. In matched-background interventions (n=60), substituting one parental germline while holding recombination and stochastic background fixed causes phenotype shifts exceeding a same-parent re-mutation control for five of six traits for both parental channels. Recombination also yields excess transgressive offspring for speed and gait frequency. A preregistered developmental-dependence hypothesis is not supported: a quasistatic no-dynamics ablation preserves the mean phenotype distribution while altering parental variance structure. Thus the study supports causal biparental pre-learning heredity in this simulation, but not the stronger claim that recurrent developmental dynamics are necessary. It does not establish physical heredity, biological genetics, or autonomous evolution. The contribution is an intervention-centered framework and reproducible benchmark for separating heredity, development, stochastic variation, and post-birth learning.

In spatially resolved X-ray diffraction experiments using narrow beams, diffraction patterns from polycrystalline materials often fall between two well-served regimes. Fine-grained, weakly textured microstructures produce smooth Debye-Scherrer rings suited to powder- and tensor-tomography methods, whereas coarse, weakly deformed grains produce isolated spots that can be indexed grain by grain. Many important polycrystalline materials, including plastically deformed metals, martensitic and ferroelastic materials containing complex twin microstructures, and geological aggregates with strong texture or heterogeneous grain size, produce spotty diffraction rings with broadened and overlapping peaks between these limits. Texture tomography addresses this regime by reconstructing spatial orientation distributions from diffraction data. Here, conventional texture tomography lacks the angular resolution needed for sharp distributions, while grain-by-grain indexing can introduce boundary artifacts and underestimate intragranular misorientation. This work introduces basis-adaptive texture tomography. Candidate orientations obtained from peak indexing replace the uniform orientation grid, achieving higher angular resolution. Like conventional texture tomography, it benefits from reconstructing a full orientation distribution function in each voxel, allowing voxels to retain contributions from multiple grains, subgrains or domains rather than being forced into a single orientation. Simulated aluminum polycrystals show improved delineation of grain and sub-grain boundaries accompanied by lower intragranular orientation errors compared with uniform-basis texture tomography and point-by-point scanning 3DXRD. An experimental demonstration on tensile-deformed aluminum shows that bulk grain and subgrain structures with orientation spreads of several degrees can be mapped.

This work introduces quantum-inspired tensor-network circuits as trainable transforms for image inpainting. Among the proposed architectures, the diagonal quantum Fourier transform (QFT) relaxation is invertible with $O(N^2 \log N)$ computational cost for $N\times N$ images, inherently preserving minimum coherence throughout training via its circuit structure and eliminating the need for explicit coherence penalties. Unconstrained gradient-based phase optimization (Riemannian-optimization free) enables efficient learning from randomly sampled training data, allowing the learned transform to generalize to test images observed through fixed sampling masks. Numerical tests show that the learned models outperform fixed transforms and per-image optimization while matching the performance of much larger unitary architectures, yet with far fewer parameters.

Efficient physical resource block (PRB) allocation in 5G networks requires accurate demand forecasting. Conventional methods minimize symmetric error metrics (MAE, RMSE), ignoring the operational cost asymmetry where under-provisioning (service degradation) is far costlier than over-provisioning (wasted capacity). We propose a goal-oriented probabilistic forecasting framework that aligns model training with the operator's decision-making objectives. Specifically, we train DeepAR and Temporal Fusion Transformer (TFT) models using the Pinball Loss function and derive the optimal allocation quantile from the operator's cost matrix. Evaluation on a real beam-level 5G traffic dataset shows that the proposed approach reduces operational cost compared to MSE-trained baselines while maintaining calibrated uncertainty estimates. The framework enables dynamic PRB allocation that explicitly balances service reliability against resource efficiency.

Policy learning aims to determine who should be treated based on individual characteristics. In high-stakes settings such as medicine and public policy where safety is a central concern, improving the average outcomes alone may not be sufficient: decision makers may also seek to protect individuals from harm, in line with the Hippocratic principle of “do no harm.” In this paper, we propose conformal policy learning (CPL), a policy learning procedure with a new distribution-free safety guarantee that controls the probability of assigning treatment to an individual who would be harmed relative to control. CPL views each treatment decision as testing a hypothesis of counterfactual harm and assigns treatment by thresholding conformal p-values. These p-values use observable proxies and selective calibration to address the challenge that the potential outcomes under comparison are never simultaneously observed. For randomized experiments, under standard exchangeability conditions, CPL provides finite-sample safety guarantee at a user-specified level, without imposing any outcome modeling assumptions. Moreover, when the outcome model is consistently estimated, CPL achieves asymptotically optimal welfare subject to the safety constraint. In observational studies, CPL with learn-then-balance weights achieves doubly robust safety guarantees. We evaluate CPL through extensive simulations and apply it to an empirical study of AI-powered interventions designed to reduce conspiracy beliefs.

Wall shear stress (WSS) is implicated in carotid atherosclerosis, and 4D flow MRI offers a non-invasive route to its estimation, but the agreement of MRI-derived plaque-surface WSS with computational fluid dynamics (CFD) has not been quantified in a large cohort. We compared peak-systolic velocity and WSS from 4D flow MRI and patient-specific CFD in 240 carotid arteries of 120 patients, with CFD geometries and boundary conditions derived from MRI. Velocity and circumferential WSS were compared at three standardized cross-sections, and plaque-surface WSS in 63 of 149 stenosed arteries with a reliably segmented plaque. Agreement was assessed with Bland-Altman analysis, Spearman correlation with stenosis degree, and exploratory multivariable regression of the plaque-surface discrepancy on hemodynamic and geometric variables. MRI reproduced the broad flow features but underestimated peak velocity, increasingly toward the distal internal carotid artery. WSS disagreement was location dependent: mean circumferential WSS showed little average bias in the common carotid artery, whereas MRI missed the high WSS at the bifurcation apex and underestimated plaque-surface mean and maximum WSS by $40.9 \pm 28.8\%$ and $44.5 \pm 26.8\%$; the difference in Pa increased with stenosis degree ($\rho = 0.47$ and $0.50$). In exploratory regression, the CFD-derived pressure drop across the plaque was the only significant correlate of the mean WSS discrepancy, whereas stenosis degree and geometric variables were associated with the maximum WSS discrepancy. Under the present protocol, MRI-derived plaque-surface WSS showed magnitude- and location-dependent disagreement with CFD, greater in more severely stenosed arteries and, in exploratory analyses, associated with factors beyond stenosis degree.

We present an open source Python package, ConteXtuAlity, for computing various quantities related to contextuality. This package features an interface to the sheaf-theoretic framework for contextuality, providing an implementation of measurement scenarios and empirical models as well as linear programs to compute the contextual fraction and the signalling fraction. In this work, we demonstrate the package's features and give examples of its use. We also provide benchmarks, demonstrating how performances scale with the size of measurement scenarios. The package is designed for both experienced theorists and newcomers to the field of contextuality alike, with an emphasis on flexibility and extensibility.

Recently, dynamic state feedback controllers that are based on dynamic extensions have been presented for heterodirectional hyperbolic systems. In this paper, a similar concept for the control of coupled diffusion-reaction systems is suggested. The introduction of a specific controller dynamics leads to homogenized diffusion coefficients for the extended system. Then, a backstepping-based static state feedback for the dynamically extended system is designed, which, overall, results in a dynamic state feedback. Such a design allows stabilizing a more general class of parabolic systems as well as assigning arbitrary closed-loop dynamics. This can be used, e.g., to achieve a decoupled input-output behavior, which is, in general, not possible with a static state feedback. A simulation example illustrates the results.

Control barrier functions for input-constrained systems place the admissible input set inside the definition of the safe set, yet the resulting barrier is almost always a function of the state alone; On a quadrotor this is not cosmetic: because the thrust vector must be reoriented before it can decelerate an approach, and reorientation is limited by the attainable body rate, a state-only barrier certifies states from which no escape is reachable in time; We characterize the certification gap in closed form and show its width is proportional to closing speed and inversely proportional to the body-rate limit; We then define an escape barrier on the augmented pair of state and previously applied input, with escape authority measured over the one-step reachable thrust cap; It admits a closed form and an analytic inverse for the maximum certifiable closing speed, and embeds in a predictive controller at no additional state cost; Across 550 paired closed-loop episodes on a 13-state quadrotor, the proposed controller completes every tested scenario, whereas the stopping-distance barrier enforced over the same horizon fails 15% and 25% of episodes in exactly the two scenarios that enter the predicted gap; Against an online backup-CBF baseline enforcing the same escape condition at the reached state, it holds a 29-74 degree larger directional margin and 3-18 times the clearance, and an independent conservative rollout referee finds no certified state from which escape fails.

The quest for new materials increasingly relies on predictive models and comprehensive simulations that span scales from atomic to macroscopic levels. However, essential data necessary for these models and simulations are often embedded in scientific literature as unstructured text, limiting reusability and posing challenges for researchers seeking to leverage existing knowledge effectively. While extracting structured data from unstructured text using large language models is gaining popularity, traditional methods typically generate key-value pairs data with straightforward schemas. In contrast, we introduce eolas, a modular pipeline that uses large language models to automatically transform scientific documents into knowledge graphs aligned with a specified ontology. We demonstrate eolas effectiveness in extracting useful information for scientists studying materials designed to endure the extreme temperatures and radiation levels found in fusion reactors. While a human expert might spend between thirty to ninety minutes extracting relevant data from an article, eolas can generate high-quality knowledge graphs in just a few minutes. These are presented in a tabular format with faceted navigation for easy human validation. Additionally, we introduce the first benchmark dataset designed to assess large language models capabilities in constructing knowledge graphs within the domain of irradiated materials. The analysis of 168 experiments using our dataset, various large language models and prompting techniques provides key insights that we summarize into practical guidelines for effectively extracting knowledge graphs aligned with an input ontology.

Several alkali chlorides and alkaline-earth oxides adopt the B1 structure at ambient conditions and transform to B2 under compression, allowing to change coordination number and cation-anion distance independently across chemically distinct hosts. The change in anion polarizability under high pressure dominates the optical response of these prototypical ionic solids, yet its dependence on local structure and cation chemistry remains experimentally unconstrained at high pressure. Here we report refractive indices of NaCl, KCl, CaO, and SrO to ~100, ~100, ~120, and ~60 GPa, each in both the B1 and B2 structures, complemented by published MgO-B1 indices to 140 GPa and DFT calculations. Lorentz-Lorenz analysis yields pressure-independent strain polarizability parameters $\Lambda$ ranging from 0.34$\pm$0.05 for KCl-B1 to 1.57$\pm$0.02 for MgO-B2. Our results establish coordination number and cation-anion distance as separable predictors of anion polarizability in both B1 and B2 structures. Increasing anion coordination from six to eight at fixed cation-anion distance lowers the polarizability of both $Cl^{-}$ and $O^{2-}$ by ~0.34-0.40 $\mathring{A}^3$ and ~0.38-0.47 $\mathring{A}^3$ respectively. Our results suggest that the polarizability of $O^{2-}$ is transferable to within ~0.06 $\mathring{A}^3$ between MgO-B1 and CaO-B1 at fixed cation-anion distance, and that this transferability possibly extends to SrO-B1 and the B2 oxides. In contrast, the polarizability of $Cl^{-}$ is not transferable between NaCl-B2 and KCl-B2: the difference between them varies with cation-anion distance, from ~0.2 $\mathring{A}^3$ at 2.65 $\mathring{A}$ to 0 at ~2.5 $\mathring{A}$. The results show that the change of the strain polarizability parameters across the B1-B2 transition is governed by the decreasing and increasing sensitivities of $O^{2-}$ and $Cl^{-}$ polarizabilities to densification, respectively.

Two-dimensional tungsten-based transition metal dichalcogenides exhibit a rich emission spectrum with distinct lines of exciton and biexciton states, neutral and charged, which are typically considered as independent entities. Here, we present a study of the emission kinetics of a WS$_2$ monolayer, demonstrating that these states together form a single interacting ensemble, with their population and depletion mutually coordinated with temperature. Dark trions make a long-lived contribution to the bright trion on a time scale of 200-300 picoseconds, and replenishment from dark states promotes intense luminescence of charged biexcitons. The developed self-consistent rate equation model reproduces the temperature dependence of the kinetics well, opening the way to controlling exciton states in such materials.

Two features intrinsic to survey sampling complicate semiparametric efficiency analysis: design-induced dependence among sampling indicators and the randomness of finite-population targets under the superpopulation law. For general semiparametric full-data models, we show that the observed-data experiment under a broad class of dependent designs is locally asymptotically normal with the tangent-space structure of a reference Poisson experiment. Under the joint superpopulation-design law, first-order efficiency depends on the design only through the limiting inclusion-probability function. Standard missing-at-random projection in the reference experiment characterizes the observed-data efficient influence function. Finite-population targets are treated through first-order asymptotic expansions, extending the analysis beyond exact random sums to nonlinear census characteristics. Superpopulation and finite-population centerings yield equivalent notions of local regularity and efficiency, with their bounds linked by a Pythagorean decomposition that gives a generalized finite-population correction. We then give general and design-specific conditions under which cross-fitted estimators with estimated nuisance functions attain both efficiency bounds. For the finite-population mean, the bound equals the large-sample limit of the Godambe-Joshi anticipated-variance lower bound. For scalar targets, we characterize optimal limiting inclusion probabilities. Simulations and California Academic Performance Index data illustrate the theory.

In flow matching (FM), a velocity model $v_{\theta}$ is trained using a predefined path $g_t$ that connects data and noise samples (e.g., $g_t(x_0, x_1) = (1 - t) x_0 + t x_1$). In this work, we study the choice of this path from an optimization perspective by analyzing the variance of stochastic gradients. We consider the class $G(p_t,v^\star_t)$ of paths that induce the same marginal distributions $p_t$ and marginal velocity field $v^\star_t$, and therefore the same FM objective. Our main finding is that the choice of path $g_t$ can fundamentally change the convergence rate of SGD, even when the FM objective remains exactly the same. (i) For a linear velocity model and one-dimensional Gaussian data, we derive a tight bound on the SGD iteration complexity up to logarithmic factors and find an analytically optimal path that minimizes this bound among linear paths inducing the same FM problem. (ii) We then extend the variance analysis to general FM problems and formulate path selection at a fixed $\theta$ as the variance-minimization problem PathOpt$_\theta$, constrained to $g_t\in G(p_t,v^\star_t)$. We show that this constraint is essential: reducing variance without it can lead to slower convergence. (iii) Since the constraint $g_t \in G(p_t,v^\star_t)$ cannot generally be verified directly, we derive an equivalent formulation with constraints that can be estimated from samples, allowing paths to be found numerically. Our theoretical results are supported by experiments with Gaussian data, Gaussian mixture models, and real datasets.

Estimating the second frequency moment ($F_2$) of an underlying frequency vector is a fundamental problem in the streaming model. While recent work by Braverman and Zamir [STOC 2025] resolved the space complexity for constant failure probability in the insertion-only model, the optimal dependence on the failure parameter $\delta$ remained open. We close this gap by proving a tight high-probability lower bound of $\Omega\left(\frac{1}{\varepsilon^2}\log\frac{1}{\delta}\,\log\frac{\varepsilon\sqrt{n}}{\log(1/\delta)}\right)$ for $(1\pm\varepsilon)$-approximate $F_2$ estimation. The key challenge is the failure of prior multi-scale direct sum arguments under noise sensitivity. We introduce a noise-robust communication primitive, Exam Mostly Set Disjointness, and prove an $\Omega\left(\frac{m}{t}\log\frac{1}{\delta}\right)$ one-way lower bound. Embedding this into a multi-scale reduction yields the correct $\log(1/\delta)$ dependence. We also give two complementary algorithms under natural structure assumptions. For streams with frequency bound $B$, we design a subsampling method using continuous $F_0$ tracking that replaces a $\log(n)$ factor with $\text{polylog}(B)$. For $k$-sparse streams, we develop a two-stage sketch using approximate Morris counters, replacing $\log n$ with $\log k$ and achieving a further $\log\log m$ dependence on stream length.