Papers

Let $n\geq3$, $2\leq k\leq n-1$, and $m=n-k-1$. We prove that a complete, connected, noncompact, oriented manifold $(M^n,g)$ with scalar curvature $R_M\geq k(k-1)$ is isometric to $\mathbb{S}^k\times\mathbb{T}^m_\Lambda\times\mathbb{R}$ if it admits a smooth proper map of non-zero degree to $\mathbb{S}^k\times\mathbb{T}^m\times\mathbb{R}$ whose spherical component is 1-Lipschitz. We also establish a weighted scalar curvature obstruction at infinity for sphere-torus targets with a higher dimensional Euclidean factor under suitable control of the Euclidean component. These results hold in all dimensions without a spin assumption.

We introduce Adaptive Score-based Routing Balancer (ASRB), a dynamic, score-based request routing mechanism for Kubernetes-based service deployments over the computing continuum. ASRB jointly considers infrastructure-level information, response time measurements, and application-level quality indicators, with a particular focus on serving Machine Learning (ML) workloads. For these workloads, ASRB balances requests over service instances deployed in the continuum, following service provider-defined policies encoded as weighted combinations of QoS criteria to flexibly address latency-accuracy trade-offs. To drive routing decisions and swiftly adapt to changes in the operating environment, ASRB monitors a range of runtime metrics across multiple system layers. To deal with the associated monitoring overhead, particularly important for large-scale deployments, it selectively and adaptively controls monitoring intensity without sacrificing on routing quality. ASRB is implemented without requiring any modifications to Kubernetes, making it straightforward to deploy and operate in existing cluster environments. Our testbed experiments demonstrate the versatility of ASRB: When tuned for latency reduction, it achieves at least 10 ms lower mean response time compared with latency-oriented state-of-the-art routing mechanisms, while it achieves higher accuracy when this is prioritized through specific configurations, thus enabling flexible and operator-controllable trade-offs. At the same time, it attains reduced failure rates, higher responsiveness to changes in the operating environment, and up to ~70% less monitoring cost than relevant state-of-the-art solutions, at the potential expense of only a modest latency penalty in some configurations.

Classical confidence intervals, when repeatedly obtained on accumulating data at different sample sizes, produce contradictory inferences with high probability. We propose a simple and efficient strategy for computing, instead, mixture confidence sequences for regression coefficients in generalized linear models under this sequential framework. Simulations demonstrate the computational convenience of our approach and the importance of drawing inferential conclusions based on these anytime-valid tools when observations become available in batches over time. The usefulness of the proposed procedure is also shown in the analysis of streaming data from the American National Automotive Sampling System.

A direction of the affine plane $\mathbb{F}_p^2$ is special for a set if the lines in that direction do not all meet the set in the same number of points. We classify, for every prime $p\ge5$, the subsets of $\mathbb{F}_p^2$ with exactly four special directions. There are $54$ affine-equivalence classes, occurring only for $p=5,7,11,13,17$, and we give explicit representatives. In particular, $17$ is the largest prime admitting such a set, which answers a question of Ghidelli, Kiss and Somlai, and over $\mathbb{F}_{13}$ the minimum size is $65$, attained by exactly two classes. The key structural fact is that the projection polynomials of such a set share a vertex: the set is either centrally symmetric about this point or differs from its reflection by exchanging one full line with one empty line. We also show that, over an odd prime field, a Boolean function on $\mathbb{F}_p^d$ with exactly four active projective Fourier lines is pulled back from a plane, so the classification extends to every dimension. The classification and the exclusion of the primes $19\le p<2048$ are computer-assisted; the structural results and the exclusion of larger primes are proved directly.

We construct a class of positive cones that make $\mathbb{C}$ into a directed partially ordered ring. The positive cones are defined using integral closures of local rings, associated with a transcendence basis and a chosen real generator. A localization criterion also yields such orders on every transcendental extension of $\mathbb{Q}$. For a fixed coefficient field, we prove that two real generators define the same cone if and only if they differ by an affine map with positive real-algebraic slope and translation algebraic over that field. The nonzero positive elements are closed under inversion.

We review Raju's all-line recursion relations for Yang-Mills theory in AdS${}_4$ and evaluate four-point correlators for the All-plus, Single-minus, and MHV helicity configurations. We point out the relevant deformation for the legs needed to obtain the correlators. In particular, we explicitly derive the expressions for all the residues contributing to all three correlators. We also perform an explicit numerical check with the results computed by Witten diagram computations and find perfect agreement with our results. Finally, we conclude by discussing some applications of these recursions for obtaining higher-point functions.

A Leech tree of order $n$ is a tree with positive integral edge weights whose $n(n-1)/2$ pairwise weighted distances are precisely $1,2,\ldots,n(n-1)/2$. This paper gives a computer-assisted proof that no Leech tree of order $18$ exists. The argument has three layers. First, a development in Lean 4 verifies the structural facts used in the paper. These facts reduce every putative example to one of eight local configurations and justify several necessary conditions. Second, conventional mathematical arguments prove a component-pair whole-block exact-cover condition and the completeness of a recursive search. Third, exhaustive computations close all eight configurations. The computation records exact coverage, source and input hashes, terminal receipts, and checked exact-zero results. The structural layer is kernel-checked, but the search program, its execution, and the certificate checker have not been formalized in Lean. The result is therefore a computer-assisted proof, not an end-to-end Lean proof.

Let $B$ be a standard Brownian motion, $x\ge 0,\, \nu<1$, and $b:[0,\infty)\to\mathbb R$ is a continuous function locally of finite variation starting from 0. We define the perturbed Brownian motion reflected at the boundary $b$ by establishing strong existence and pathwise uniqueness of a solution to the equation \[ W_t=(1-\nu)x+B_t+\nu M_t(W)+\frac12 L_t^0(W-b), \qquad W_t\ge b(t), \] where $M_t(W):=\sup_{0\le s\le t} W_s$ and the process $L^0(W-b)$ is the semimartingale local time at 0 of the process $W-b$. We give a positive result under condition (PB) on the boundary $b$ : for every $T>0$, the upward increment $\sup_{0\le s<t\le T,\,t-s\le h}(b(t)-b(s))^+ = o(\sqrt{h})$ as $h\downarrow 0$. The proof splits into two regimes: the case $\nu<1/2$ is a consequence of the Skorokhod problem in an orthant proved by [Williams 1995], while the case $\nu\ge 1/2$ combines a deterministic comparison estimate and a logarithmic upper bound on the number of completed round-trips, following the strategy of [Chaumont and Doney 1999]. For $\alpha\in(0,1/2)$, we also construct an increasing $\alpha$-Hölder boundary for which no continuous adapted solution starting from zero exists for any $\nu<1$.

In this article, we present TeamCAMS (Cabin Air Management System), a collaborative work environment for simulating human-AI (artificial intelligence) interaction for scientific research. The article outlines how several psychological theories guided the development of this multiple-task simulation. Modelling a process control environment, previous versions of TeamCAMS have already been used in empirical studies to address a wide range of research questions (e.g., comparing different forms of automation, evaluating impact of automation reliability, effects of stress on multiple-task performance). Outlining the technical possibilities offered by TeamCAMS, the article points out how its latest version offers researchers the possibility of addressing a set of new research questions including problems associated with teamwork (e.g., within-team conflict, distributed teamwork) and human-AI interaction. Finally, we will outline how this simulation environment can be enhanced further still to address research questions in new fields (e.g., automation of leadership). To promote transparency, reproducibility, and further development, TeamCAMS is made available to the research community under an open-source license.

One hospital runs bloods and imaging at the same time. Another runs them one after the other, in either order, equally often. Knowing which actually happened, and how it is recorded in data, is critical for all operational managers. In process mining, the standard approach is to construct an event log, and attempt to discover concurrent and sequential processes in a data-driven way. We show this standard approach, built on the stochastic language of an event log, reports only the assumptions of its discovery algorithm, because every such log is explained equally well by a model with no concurrency at all. Further, before any data is acquired, we characterise when data can and cannot distinguish concurrent behaviour. Where it cannot, the distinction is recoverable from evidence the stochastic language discards, such as the times at which activities start and end, or object-centric records that fix an order within an execution. The remedy is therefore a choice of what is recorded, rather than a larger sample. This impacts decision making, as planning resource for truly concurrent services is very different from sequential services.

Let $F$ be a field of characteristic zero, $G$ be a finite abelian group and $M_2(F)$ be the algebra of $2\times 2$ matrices over $F$. In this paper, we consider all $G$-graded involutions on $M_2(F)$ and determine the generators of the $T_{(G,*)}$-ideal of identities and of the $T_{(G,*)}$-space of central polynomials of $M_2(F)$. Moreover, we explicitly compute the $\langle n\rangle$-cocharacter and the $n$-th $(G, *)$-codimensions for most of the gradings. For the case of gradings by the Klein group, the $(G, *)$-central codimensions and proper central $(G, *)$-codimensions are also explicitly computed.

Two-component supersolids can exhibit in-phase or out-of-phase component density modulations, corresponding to density and spin supersolids, respectively. We formulate a general hydrodynamic theory for the collective dynamics of multicomponent supersolids, guided by their broken symmetries and conservation laws. We benchmark it against microscopic calculations for a binary dipolar condensate confined to an infinite tube, finding quantitative agreement for the sound speeds of all three Goldstone branches throughout the density- and spin-supersolid regions. The resulting relations link collective-mode measurements to elastic coefficients and superfluid fractions.

Antiferromagnetic (AF) metals are rare, yet they combine properties attractive for spintronic devices like robustness against stray fields and electrical readout. Among AF metal oxide candidates, SrCrO$_3$ remains largely unexplored due to its notoriously difficult synthesis. In this paper, we demonstrate the growth of high-quality SrCrO$_3$ thin films by magnetron sputtering on substrates that impose a wide range of tensile and compressive strains. Muon spin relaxation experiments, supported by x-ray magnetic dichroism, unveil the emergence of an AF phase with dilute magnetic disorder at low temperatures, while resistivity measurements confirm the simultaneous metallic ground state of SrCrO$_3$ under low strain. As both compressive and tensile strain increase, a metal-to-insulator transition is induced in the films, while the onset of the magnetic transition temperature remains unchanged. Moreover, an intriguing resistivity upturn, accompanied by a change in the dominant charge-carrier type, occurs at a temperature that correlates with strain. These observations suggest a complex strain-dependent band structure, with strain-induced Jahn-Teller distortions or tilting of the CrO$_6$ octahedra that emerge depending on the sign of the strain, as inferred from density functional theory calculations.

High-performance racing shoes rely on ultra-low-density elastomeric foams that undergo large, repeated deformations during running. Yet little is known about how their mechanical properties vary throughout the shoe or change with repeated use. Here, we characterize the midsole foam in an elite-level racing shoe from the heel, midfoot, and toe of a new shoe and a shoe worn for 300 miles. Microscopy reveals a characteristic pore length scale of 128+/-18 um and supports an approximately isotropic continuum description. We then quantify the mechanical response under tension, compression, and shear. Remarkably, despite 300 miles of real-world use, the foam retains its mechanical response across all three loading modes and shoe regions. Energy return remains largely unchanged, with values of 85-93% in tension and compression and 64-71% in shear. At the same time, we observe strong regional variations, with tensile and compressive stiffnesses 38-51% lower in the toe than in the heel. The foam also exhibits a pronounced tension-compression asymmetry in Poisson's ratio. Together, these findings reveal a spatially structured and mode-dependent mechanical response that remains largely preserved after 300 miles of use. This mechanical resilience may extend the functional lifetime of racing shoes, with implications for runners, replacement recommendations, and sustainability.

Despite the widely recognized potential of AI in education, most prior work has focused on individualized student assistance. In contrast, the majority of educational practice worldwide still takes place in collective classroom settings. To enable researchers to study AI assistance in collective teaching, we introduce Edustories, a dataset of 1,492 teacher-written case studies describing real elementary and high-school classroom situations involving challenging student behavior, pedagogical interventions, and their outcomes. Among many other applications, Edustories enables evaluating LLMs' ability to predict the success of teacher interventions, crucial for providing practicing teachers with useful feedback. Comparing the latest models from four language-model families against expert assessments, we find that current models fall short of human expertise in predicting classroom outcomes; the strongest models reach 58% accuracy compared to 64% of human experts. This gap highlights both the limitations and the emerging potential of AI as assistants for practicing teachers.

Sparse computations are important workloads in applications such as scientific computing, graph neural networks (GNNs), and machine learning. While many sparse operations can benefit from modern GPUs, the sparsity pattern remains important to performance because it affects memory coalescing, block organization, and load balancing. Previous studies show that spectral signatures can help analyze the global structure of sparse matrices. The fast Fourier transform (FFT) is commonly used to extract spectral signatures, and efficient GPU FFT libraries are available. However, sparse matrices, especially adjacency matrices for large graphs, tend to be very large and sparse. Existing dense-matrix-based FFT implementations are difficult to scale up, making the spectral patterns of these matrices difficult to obtain. We therefore propose a three-fold research approach comprising a lossless Binary-Sparse FFT (BS-FFT) and two compression methods: Elastic BS-FFT, which reuses the BS-FFT pipeline on a sampled frequency grid, and density-map-based spatial compression. Experiments show that BS-FFT reduces GPU memory use by 2.9–11.6 times relative to dense cuFFT and completes all 15 GNN adjacency matrices where dense cuFFT completes 6 on a 40 GB A100. Elastic BS-FFT and Density Map compression reduce GPU computation time by 2.0–1466.4 times relative to BS-FFT with spectral feature error of only 0.16% to 11.56% across the sampling rates from 6.25% to 0.0061%.

Interleaving dielectric layers into ferroelectric Hf0.5Zr0.5O2 (HZO) films increases the memory window (MW) beyond what is accounted for by the dielectric constants. Determining the physical mechanisms behind these MW improvements is critical to reaching the full potential of HZO FeNAND. Here, we show that MW improvements stem from the interfacial charge dynamics enabled by oxygen vacancies at the interlayer interface. X-ray photoelectron spectroscopy(XPS) etching experiments demonstrate increased off-stoichiometry at the interface, with a 2.3x increase in oxygen vacancies. Polarization-dependent XPS and first-order reversal curves(FORC) show that tunneling between interfacial defect states causes a bidirectional internal bias of 0.56MV/cm. The impact of defects is further corroborated through phase-field modeling(PFM), which only recreates the coercive fields, FORC, and internal bias for defect densities and tunneling barrier heights that are consistent with experiment, quantitatively capturing an internal electric field of 0.55 MV/cm. The phase field models are then used to simulate 36 devices with varied charge densities and dielectric thickness to provide a predictive framework for further improvements in the MW of interlayer HZO. These findings redefine the role of defects in ferroelectric HZO from deleterious to engineerable and provide critical insights into how to tune ferroelectric device architectures for improved memory.

Conferences, journals, funders, schools, and universities are struggling with a surge of potentially AI-generated submissions from ostensibly human authors, who may not have exercised sufficient human oversight for their manuscripts. In turn, institutions evaluating submissions can no longer reliably credit expertise based solely on authors' names on submitted work. To address this problem, we propose greCAPTCHA, a proctored assessment approach that measures authors' understanding of research manuscripts via the construct of capacity to verify, which we define as the knowledge and reasoning required to critically assess the contents underlying one's contributions to a manuscript. greCAPTCHA generates questions assessing multiple levels of understanding and provides an evaluative report based on authors' responses. Using a prototype implementation, we conduct a user study and semi-structured interviews with $31$ researchers to evaluate greCAPTCHA. Its automated scores predict which papers were or were not authored by study participants with an AUC of $0.90$. Participants reported positive overall experiences with the system and remarked on the appropriate construct validity for author understanding, while also suggesting important changes to be made before deployment. Our results provide initial evidence that greCAPTCHA can assess manuscript-specific understanding under proctored conditions.

Occlusion creates fundamental uncertainty in autonomous driving. Existing methods often propagate frame-wise hypotheses or optimize ego behavior against prescribed hidden-agent predictions, leaving the worst history-consistent interaction unexplored. We introduce History-Conditioned Minimax Trajectory Search (HC-MTS), which combines temporal occlusion reasoning with response-aware search. First, HC-MTS constructs finite hidden-state modes, each certified by a backward witness satisfying multi-frame visibility, occupancy, semantic-map support, and class-specific kinematic constraints. It then solves a bilevel minimax problem: an inner finite oracle maximizes the ego driving score over destination attainment and ride comfort, while the outer search selects the legal hidden-vehicle trajectory that minimizes this best-response value. Across eight Waymo Open Motion Dataset scenarios, increasing the visibility-memory horizon from K=1 to K=20 reduces the mean per-scenario vehicle, pedestrian, and total retained hidden-seed counts by 18.12%, 21.67%, and 18.45%, respectively. HC-MTS identifies six avoidable counterexamples, while no legal collision-producing attacker is found in the remaining two scenes within the finite search budget.

Aims. In this paper we present the software and first seeing measurements from a SHAdow Band Ranger (SHABAR) system that is coupled with the recently comissioned PoET solar telescope, installed at ESO's VLT platform in the Paranal Observatory. The seeing measurements that are collected by this system play a pivotal role in the observational strategy of PoET, as it employs apertures ranging between 1 and 55 arcseconds to observe resolved solar regions. As such, the usage of the smaller apertures hinges upon good observational conditions, which are assessed through real-time measurements from the instrument. Methods. We employ a SHABAR system, consisting of a series of scintillometers that are non-uniformly spaced in a bar, measuring the scintillation of the incoming light. The scintillation is measured in individual detectors, which are then used to characterize the atmospheric turbulence at a given range of heights. We use previously derived formulations, following Kolmogorov turbulence models, to model the collected data and transform it into a seeing measurement. Results. We find that the Paranal daytime seeing can reach values close to 1 arcsecond in the early morning, before the ground temperature increases and creates turbulence in the lower layers of the atmosphere. Over the day, the seeing gradually worsens, with the median seeing reaching values larger than 4 arcseconds in the afternoon. We also find that these variations appears to be stable over the first weeks of observations, yielding compatible results when comparing 37 independent days of operations, with a median seeing of 2.37 arcseconds.

Run two process-discovery algorithms on the same event log and they return two different pictures of the same process. Petri nets, causal nets, process trees and BPMN each rely on routing machinery of their own, and their only common ground is the traces they generate. A trace lists activities one after another, so it discards the concurrency the notations exist to express, and two models with identical trace languages can describe genuinely different processes. Whether two discovered models mean the same thing therefore has no notation-independent answer. We show that all four notations admit one canonical presentation, a signature recording a model's activities and the typed interfaces along which they compose, and nothing of the routing machinery. Four construction theorems establish this presentation notation by notation, so two models are compared in a form that each notation determines on its own. Signature equality implies trace equivalence and is strictly finer, separating genuine concurrency from interleaved choice, which a trace comparison cannot, and signature inclusion implies trace inclusion. In a recovery study on one object-centric log, the discovered causal net has exactly the ground-truth signature, while the discovered Petri net's signature strictly contains it and locates every behaviour the Petri net adds in its silent structure. The gain is largest for object-centric data, where a single log supports several notations at once. The four notations become one calculus, in which a translation between them is a claim that can be checked.

Rebar insertion is among the most repetitive and physically demanding tasks on construction sites, and a contact-rich problem at 1.4 mm clearance. The parts, however, vary at two levels: a nominal design per structural member, and fabrication tolerance around each nominal design. Real-world data therefore has to be re-collected as designs and batches change. We present RebarSim, a visual sim-to-real system trained entirely in simulation. A privileged state-based teacher is trained with reinforcement learning over procedurally generated rebar geometries, then distilled into a multi-view student that maps raw RGB and proprioception directly to actions under extensive domain randomization. The student transfers to the real world zero-shot, seating rebars taken from a real factory production run in 91.3% of real-robot rollouts. Underlying that result, geometry diversity and pretraining both bring benefits. Training across a diverse set of nominal designs rather than one lifts the zero-shot success of both the teacher and the student on unseen designs, and the student policy outperforms a single-design specialist on that specialist's own design. A pretrained student then adapts to a new design with 4–6x fewer distillation samples than one trained from scratch. Visual sim-to-real transfer depends on appearance randomization and the DAgger mixture: removing either one sharply lowers success. Videos, code, and task assets are available at https://rebarsim.github.io.

We study the master equation $ (\partial_t -\Delta)^{s} u(x,t) = R(|x|)f(u(x,t))\quad\mbox{in}\ \mathbb{R}^n\times\mathbb{R}, $ where $s\in(0,1)$, $R$ is positive and strictly decreasing in the radial variable, and $f$ is positive, locally Lipschitz, and satisfies $f'(0)<0$. Existing symmetry results for this operator require $f(0)=0$ with $f'(0)\ge 0$ (or, more generally, that $f$ be non-decreasing near the origin), because the sign of the moving-plane comparison inequality is then controlled by the nonlocal diffusion term. When $f'(0)<0$, the linear term in the comparison inequality appears at the same order as the nonlocal diffusion but with the opposite sign, destroying the comparison principle underlying the standard cut-off perturbation argument. We prove that, despite this obstruction, every positive bounded classical solution with uniform spatial decay is radially symmetric and strictly radially decreasing in $x$ for each $t$. The proof reconciles the direct method of moving planes with this adverse sign by exploiting the interplay between the spatial decay of $u$ and the strict radial monotonicity of $R$. This appears to be the first symmetry result for the master operator that accommodates a local damping mechanism at the origin.

Open-vocabulary scene understanding is fundamental for robotics, laying the groundwork for spatial reasoning and object manipulation. While closed-vocabulary 3D instance segmentation heavily leverages 3D shape information, state-of-the-art open-vocabulary methods remain predominantly restricted to 2D image features or image-distilled representations during mask labeling. In this paper, we propose SenseFuse, a label-free fusion method that balances 2D image and 3D shape encoders for robust open-vocabulary 3D instance segmentation, refining only the mask-labeling stage of existing pipelines. We reveal that 2D image and 3D shape encoders exhibit largely disjoint failure patterns and rarely share identical wrong labels, whereas two 2D image encoders frequently repeat the same errors. This distinct behavior makes the 2D and 3D pair inherently complementary. We introduce an adaptive mechanism that selects a scene-level fusion weight to maximize a label-free sensitivity measure, estimated directly from a single scene's unlabeled proposals in milliseconds. SenseFuse improves labeling accuracy in every evaluated setting across ScanNet200, Replica, and ScanNet++, recovering 67-100% (median 93%) of the gain achievable with an oracle weight, and it raises instance AP in 21 of 22 reported settings. Code is available at https://github.com/hanes1207/SenseFuse.

Agent harnesses supply planning guidance, organize execution, and check completion. We study how these components affect success, erroneous acceptance, and cost in two Retail experiments and an Airline pilot in $\tau^2$-bench. The primary comparison pairs prewritten task-specific plans (Fixed) with shuffled policy text matched in word count (Sham), isolating the contribution of guidance content. Across 265 matched cells, Fixed improves oracle-verified success by 7.17 percentage points (90% task-clustered bootstrap interval, 1.15–13.36 points), with gains concentrated in higher-complexity tasks. A read-only terminal verifier rejects 61% of Retail oracle-invalid episodes while withholding 17% of correct ones, at less than one cent of additional cost per episode. Which component matters more depends on the loss assigned to erroneous acceptance: at low liability the planning gain dominates; at high liability the verifier's avoided false passes dominate—and a standalone verifier captures nearly all the false-pass benefit of the full planning-plus-verification stack at a fraction of its cost.

We examine semiparametric solutions to contamination bias for nonbinary treatments. Deepening the discussion by Goldsmith-Pinkham et al. (2024), we detail how spline functions approximate conditional expectation and propensity score functions under weak functional-form assumptions. Reanalyzing 18 regressions across 11 studies, we compare standard linear regressions against parametric and semiparametric versions of three contamination-robust estimators. We document large point-estimate discrepancies between parametric and semiparametric approaches and find that adopting flexible semiparametric solutions may not increase statistical uncertainty substantially. We recommend that researchers verify the robustness of their conclusions to the use of semiparametric tools that address contamination bias.

Charge order is conventionally characterized by a static modulation of the electronic density, while its collective excitations remain less developed from a quasiparticle perspective than those of spin-ordered systems. Here, we formulate the collective excititations of charge order within an effective charge-pseudospin model, in which the charge-ordered ground state is represented by staggered pseudospin order. Quantizing fluctuations around this ordered state via a Holstein–Primakoff transformation, we reveal two branches of bosonic quasiparticles with degenerate, gapped dispersions that carry opposite quantized electric charges $\pm 2e$. We therefore term these charge-$2e$ bosons “bichargons,” closely paralleling the two magnon branches of a bipartite antiferromagnet that carry opposite spin angular momenta. We show that a temperature gradient drives the diffusion of thermally excited bichargons, generating a charge Seebeck response when the degeneracy between the oppositely charged branches is lifted by tuning the chemical potential away from the charge-neutrality point. In contrast, despite carrying finite electric charges, a thermal bichargon gas remains electrically insulating under a static electric field because bichargon quasiparticle number is not conserved. An ac electric field, however, can parametrically generate coherent pairs of oppositely charged bichargons that support a finite dc drift current in the presence of a bias electric field, offering a bosonic analogue of photoconductivity mediated by photoexcited electron–hole pairs in semiconductors. Our results establish bichargons as a new class of collective bosonic charge carriers in charge-ordered systems and extend the quasiparticle paradigm of magnons in spin-ordered systems to the charge sector, with electric charge replacing spin angular momentum as the transported quantity.

We study the effects of impurity scattering on the nonlinear Hall response of Weyl semimetals within the semiclassical Boltzmann approach. We derive the rectified and second-harmonic conductivity tensors for a general momentum-dependent transport relaxation time and evaluate this quantity microscopically for short-range, Gaussian, screened Coulomb, and magnetic impurities. For scalar disorder, the relaxation time is isotropic and chirality independent. The nonlinear Hall response is then determined by the anomalous velocity associated with the Berry curvature, and a finite net response requires energetically inequivalent Weyl nodes to avoid cancellation between opposite chiralities. Polarized magnetic impurities lead to a qualitatively different behavior. We find that interference between the first- and second-order Born amplitudes generates a helicity-dependent anisotropic correction to the relaxation time. This anisotropy changes the tensor structure of the nonlinear Hall conductivity and gives rise to a finite second-harmonic current for suitable orientations of the electric field relative to the impurity polarization. For representative parameters, however, the anisotropic contribution is several orders of magnitude smaller than the dominant isotropic response. These results establish how the microscopic form of impurity scattering enters the nonlinear Hall response of Weyl semimetals through the transport relaxation time.

We prove representation stability for rational cohomology of spaces of string links and manifold links in Euclidean space as the number of links grows. For string links we consider the component of the standard embedding of disjoint copies of $\mathbb{R}^{m}$ into $\mathbb{R}^{d}$, where $m \geq 1$ and $d \geq m+3$. For manifold links we consider the component determined by disjoint copies of a fixed embedding of a closed smooth $m$-manifold into $\mathbb{R}^{d-2}$, where $d \geq 3$. In both cases, the rational cohomology groups form finitely generated $\mathrm{FI}^{\#}$-modules in each degree with generation arity at most $n\frac{d-2}{d-m-2}$ in degree $n$. We also obtain explicit generation bounds for the rational homotopy groups. The proofs combine geometric constructions of structure maps, hairy graph complex models for embeddings modulo immersions and a functorial framework that allows generation bounds to be established after forgetting the symmetric group actions.

The classical Whittle formula provides a closed-form expression for the asymptotic Fisher information matrix (FIM) rate of multidimensional, real-valued, zero-mean, purely nondeterministic stationary Gaussian processes (GPs), expressed in terms of their parameterized spectra within a maximum-likelihood framework. However, the Gaussian assumption underlying this result restricts its applicability to many real-world signals exhibiting heavy-tailed or non-Gaussian behavior. In this paper, we extend Whittle's result to multidimensional, real-valued stationary compound Gaussian processes (CGPs) with arbitrary mean, under a unified framework encompassing fully known, parameterized, and completely unknown density generators. Building upon the Slepian-Bangs formula for $n$ consecutive observations and extending it to the semiparametric setting, we leverage the asymptotic properties of block Toeplitz matrices to obtain a closed-form spectral-domain expression for the asymptotic FIM rate. The resulting expression, common to all density generator families, generalizes the standard zero-mean Gaussian formula by incorporating a distribution-dependent contribution associated with the nonzero mean, and an additional covariance term that is invariant to the choice of non-Gaussian distribution. This extension enables efficient and theoretically grounded performance analysis for heavy-tailed signal processing applications.