Papers

Advanced, orbital-dependent exchange–correlation (XC) functionals can significantly improve the description of electronic structural properties, but they substantially worsen spectral properties that are computed within standard linear-response time-dependent density functional theory frameworks. This is not a failure of the underlying Kohn-Sham states, but due to a formal inconsistency in the treatment of the dynamic density response when the non-locality of the XC potential is not taken into account consistently on the level of the full off-diagonal density matrix. To avoid these complexities, we present a non-empirical additive correction $\Delta f_\textnormal{xc}(\mathbf{q},\omega)$ to the dynamic XC kernel that re-enforces the exact f-sum rule of the non-local KS Hamiltonian within TDDFT. Comparing our new results against a representative set of accurate experimental measurements (ambient aluminum, silicon and carbon, as well as heated and compressed aluminum) reveals a dramatic improvement in all cases without any additional computational cost. The corresponding extension to the open-source GPAW code is made freely available online. We further investigate the implications of non-local pseudopotentials and show that the non-locality has an important, physically motivated effect that is indispensable to capture the correct plasmon dispersion in lieu of full all-electron simulations. In addition to being important for the estimation of a plethora of dynamic and spectral properties, our work constitutes an important step towards a universal XC functional that can be used to estimate all kinds of observables with high accuracy. Finally, we outline the potential utility of our framework for the development of advanced non-local XC functionals, and suggest a new way to rigorously verify non-local pseudopotentials against experimental measurements of collective excitations.

The scientific literature contains decades of experimental measurements that remain difficult to access as structured data for modern AI and data-driven research. Much of this information is distributed across figures, captions, text, and tables, requiring experimental data and their context to be identified, connected, and verified before they can be reused. Here we introduce ERAF4XRD (Experiment Reader Agentic Framework for X-Ray Diffraction), a fully automated multimodal (i.e., image and text), multi-agent framework that reconstructs validated X-ray diffraction (XRD) records from scientific publications. ERAF4XRD downloads and screens documents, identifies XRD figures, extracts and links metadata to the corresponding experimental data, and validates outputs against source evidence using an independent validation agent. On a manually curated benchmark of 273 scientific publications containing 3,150 candidate figures, ERAF4XRD achieved up to 98.7% accuracy for XRD figure identification and generated 1,400 metadata values across 22 fields. Independent manual assessment of the final validated records yielded 98.5% precision and 90.7% recall, with no unsupported metadata observed among 443 evaluated fields. By moving beyond information extraction to the reconstruction and validation of linked experimental records, ERAF4XRD establishes an automated approach for transforming published scientific information into machine-readable experimental datasets for AI and data-driven science.

Precise multi-camera tracking traditionally relies on rigorous 3D site calibration, yet this requirement is often operationally impossible in large-scale deployments. Privacy regulations frequently prohibit recording video for offline calibration; limited bandwidth precludes synchronizing high-resolution streams from hundreds of cameras; and covering immense physical sites with calibration targets is logistically infeasible. We present a multi-camera homography calibration system designed to overcome these barriers through "on-the-fly" geometric refinement. Starting from coarse manual homographies, we introduce a centroid-based projection optimization (PO) that continuously aligns the ground-plane geometry using live detection streams. Because PO operates asynchronously on already-transmitted, lightweight metadata, it adds zero computational latency to the real-time tracker. This allows the system to adapt automatically to camera movements or environmental changes without human intervention. This optimized geometry feeds a multi-camera bird's-eye-view (BEV) tracker that fuses detections and unifies trajectories across zones. Crucially, by operating strictly on live anonymous metadata, our solution ensures a privacy-safe, zero-overhead, and resilient tracking pipeline that maintains global consistency in dynamic environments where static, recorded-video calibration is impossible.

Although vision-language models (VLMs) possess strong visual understanding and reasoning capabilities, existing vision-and-language navigation (VLN) agents struggle to connect semantic reasoning with spatial execution. Two coupled gaps remain in this connection, as intermediate reasoning is not explicitly anchored to visual evidence and high-level decisions lack precise spatial goals to guide low-level motion. Cognitive science suggests that human navigation bridges these levels hierarchically by anchoring cognition to relevant landmarks and guiding locomotion toward spatial goals. Motivated by this principle, we propose GroundingVLN, which uses visual grounding as a shared interface between reasoning and action. GroundingVLN first reasons with grounding by anchoring task-relevant visual evidence to precise image locations throughout structured reasoning. It then acts through grounding by predicting a progress-aligned pixel goal that a geometric planner translates into primitive actions. To learn these capabilities, we construct GroundingCOTVLN-188K, a dataset of temporally aligned grounded reasoning traces, and introduce Grounded and Execution-Aware Reinforcement Learning (GEAR), which aligns grounded reasoning and spatial decisions with downstream execution. Experiments demonstrate that GroundingVLN achieves state-of-the-art performance (69.9% SR on R2R-CE and 75.1% SR on RxR-CE) with high sample efficiency, using just 0.9% as much training data as the strongest baseline. It also generalizes strongly across datasets, attaining 59.9% SR on RxR-CE when trained solely on R2R, a gain of 20.1% over the strongest baseline. Code and models will be released after review. Code is available at [https://github.com/Teacher-Tom/GroundingVLN](https://github.com/Teacher-Tom/GroundingVLN).

Quantum computers can potentially solve large-scale combinatorial problems very efficiently when the problems are first converted into the quadratic unconstrained binary optimization (QUBO) format. Scheduling in fifth generation (5G) base stations is a practical combinatorial problem that cannot be solved optimally in real-time using classical computing. We formulate the downlink (DL) multiple-input multiple-output (MIMO) scheduling at 5G base stations as QUBO and analyze the QUBO formulation scalability with respect to the key system parameters. The single-user MIMO (SU-MIMO) QUBO formulation looks promising because the number of QUBO variables grows linearly while the problem search space grows exponentially with increasing number of users. Based on the simulation results, the suboptimal greedy algorithm for the SU-MIMO performs well with a high number of users and low bandwidth. A hybrid approach, where either a quantum solver or a suboptimal low-complexity classical algorithm is selected based on the system parameters, seems sensible in practice. This work paves the way for future quantum and quantum-inspired implementations of scheduling in cellular systems.

Let $S$ be a Kato surface and $D$ its maximal reduced divisor of rational curves. On $S\setminus D$ we construct Hermitian metrics which are flat along the leaves of the canonical foliation and study their evolution under the Chern-Ricci flow. For Enoki surfaces, we construct an immortal normalised solution which, on every compact sublevel of the natural exhaustion, converges in the Gromov-Hausdorff sense to the elliptic base endowed with an explicit flat metric. For Kato surfaces of intermediate type, the affine Green model and its finite-index extension give, under the assumption $0<\mu<2$, an explicit normalised solution which, on every compact Green block, collapses in the Gromov-Hausdorff sense to a circle. In the Enoki case the limiting area is $2\pi b_2(S)$; in the intermediate case the length of the limiting circle is determined by the Green and leafwise monodromies.

Pathologists diagnose diseases by first locating suspicious tissue and then examining it at higher magnification, whereas self-supervised vision transformers (ViTs) allocate the same spatial resolution to every image region despite diagnostic evidence being sparse and spanning multiple biological scales. Recent pathology foundation models have substantially improved representation quality by scaling training data and model capacity, but largely retain uniform tokenization. We instead investigate whether pathology representations can be improved by learning where to allocate spatial resolution during self-supervised learning. To this end, we propose CRAFT (Coarse-to-fine Region-Adaptive Feature Tokenization), a DINO-based framework that learns image-dependent mixed-scale representations by using self-supervised attention to selectively refine informative regions while preserving coarse context, together with a symmetric cross-scale regularization objective that encourages complementary coarse and fine representations. Across CAMELYON16, TCGA-Lung subtype classification, and TCGA-LUAD survival prediction, CRAFT consistently outperforms comparable-scale self-supervised methods while requiring lower inference computation. Despite using only a compact 22M parameter backbone trained on comparatively small pathology datasets, CRAFT remains competitive with, and often surpasses, substantially larger pathology foundation models.

We consider the problem of estimating the trace of an implicit matrix $\mathbf{A} \in \mathbb{R}^{d^p\times d^p}$ that can only be accessed through matrix-vector products queries. The Hutchinson trace estimator% ~\cite{Girard1987algorithme, article-hutchinson} is a classical sketching method for this problem. Their estimator, $H_{m}(\mathbf{A}) = \frac{1}{m} \sum_{i=1}^{m} {\mathbf{z}^{(i)}}^T \mathbf{A} \mathbf{z}^{(i)}, \quad \text{where } \ {\mathbf{z}^{(i)}}\in \mathbb{R}^{d^p}$, and $z^{(i)}_j \in {N}(0, 1), j\in [d^p]$, satisfies the following guarantees: (i) $\mathbb{E}[H_{m}(\mathbf{A})]=\operatorname{tr}(\mathbf{A})$, and (ii) $\mathrm{Var}[H_{m}(\mathbf{A})]=\frac{2}{m}||\mathbf{A}||_F^2$. Generating one query vector $\mathbf{z}^{(i)}$ requires $O(d^p)$ random bits; thus, $m$ queries require $O(md^p)$ random bits, which can be prohibitive in large-scale applications. Recent work by Meyer et al.~\cite{meyer2025hutchinsonsestimatorbadkroneckertraceestimation} proposes a variant of the Hutchinson trace estimator in which each query vector in $\mathbb{R}^{d^p}$ is constructed as the Kronecker product of $p$ random vectors in $\mathbb{R}^d$, requiring $O(mpd)$ random bits for $m$ query vectors. The estimator of~\cite{meyer2025hutchinsonsestimatorbadkroneckertraceestimation} is unbiased; however, its variance grows exponentially with $p$. In this work, we address this limitation by proposing a sketching-based estimator that requires $O\!\big(p (d + m)\log m\big)$ random bits, yields an unbiased estimate of the trace, and simultaneously achieves a variance bound that grows polynomially with $p$.

Model updating under hybrid uncertainty is challenging because aleatory input variability makes the simulator output a probability distribution rather than a scalar, rendering the likelihood analytically intractable. Existing Approximate Bayesian Computation (ABC) methods typically employ nested Monte Carlo sampling, where aleatory samples are redrawn for each epistemic parameter evaluation, introducing sampling noise into the discrepancy and consequently affecting posterior inference and model evidence. This paper eliminates this resampling noise by construction. The probability integral transform (PIT) converts the stochastic simulator into a deterministic map of distribution-free latent variables and epistemic parameters. By freezing a set of stratified quantile particles, the resulting discrepancy becomes a deterministic, sampling-noise-free function of the unknown parameters. Transitional Markov Chain Monte Carlo (TMCMC) is then employed for posterior inference and model evidence estimation. The framework is validated on a two-dimensional benchmark, a high-dimensional transient oscillator, and Subproblem A of the NASA Langley Multidisciplinary Uncertainty Quantification Challenge. The complete Bayesian analysis is achieved in approximately half a minute on a standard desktop workstation.

Quantum networks require scalable photon sources combining narrow linewidth, high efficiency, and high indistinguishability. Microresonator photon-pair sources are promising candidates, yet a source-only description based on the joint spectral amplitude (JSA) predicts near-zero Hong-Ou-Mandel (HOM) interference visibility between photons generated by independent, CW-driven microresonators. In this work, we show that the observed HOM interference is not determined by the JSA alone. By combining finite-time detection with cavity-enhanced spontaneous four-wave mixing, we characterize a detector-conditioned heralded state governed by the idler-photon detection window. We further demonstrate that independently optimizing the idler and signal detection windows allows both heralded-photon indistinguishability and intrinsic heralding efficiency to approach unity, without spectral filtering or complex source engineering. Utilizing integrated high-$Q$ silicon nitride microresonators, we achieve HOM visibilities of 0.992(8) and 0.942(12), without background subtraction, at fourfold count rates of 4.5(3) and 12.2(6) Hz, respectively. Our work establishes CW-driven high-$Q$ microresonators as a robust and scalable platform for quantum-network primitives.

Common randomness (CR) is a valuable resource for enhancing the trustworthiness of 6G communication systems. This article highlights the role of CR in improving scalability, security, and resilience in distributed 6G architectures. It provides an overview of information-theoretic two-source models for CR generation and summarizes known capacity results, together with their implications for practical systems under different communication settings, including one-way, two-way, helper-assisted, and interactive scenarios. Furthermore, the article explores CR-assisted secure identification over Gaussian channels as an application and highlights selected open research problems in CR generation for next-generation wireless systems. The article targets researchers and practitioners interested in bridging information-theoretic tools with emerging 6G communication systems.

Group III-nitride thin films are essential for optoelectronic and power devices, where surface and interface quality critically influence performance. It is often necessary to transfer these films through atmosphere for processing or characterization steps, which can introduce significant surface contamination. Here we demonstrate a technique to protect the surface of III-N films during atmospheric exposure by capping with sacrificial InN layers. Using molecular beam epitaxy grown AlGaN films as our representative protected material, we take advantage of the lower decomposition and desorption temperatures of InN and metallic In to remove the protective cap layer in situ via thermal desorption without damaging the AlGaN film beneath. Angle-resolved photoemission spectroscopy (ARPES) measurements of the valence band dispersion in Al0.4Ga0.6N demonstrate that the film surface is recovered after InN decapping, highlighting the versatility of this process in allowing further surface-sensitive characterization of films that had been exposed to air.

Semiconducting Mo$_x$W$_{1-x}$Se$_2$ alloys provide a versatile platform for tailoring the optical properties of two-dimensional materials through both composition and layer thickness. Here, we systematically investigate mechanically exfoliated Mo$_{0.58}$W$_{0.42}$Se$_2$ flakes ranging from monolayer (1L) to nine layers by combining Raman scattering (RS), photoluminescence (PL), reflectance contrast (RC) spectroscopy, and first-principles phonon calculations. Thirteen RS peaks are identified, including the low-frequency interlayer shear mode, whose thickness dependence is well described by a linear-chain model, yielding an interlayer force constant of $K_s=(2.996\pm0.015)\times10^{19}$ N m$^{-3}$. PL measurements reveal a crossover from the direct-bandgap 1L to indirect-bandgap multilayers. The thickness evolution of the indirect optical transition is quantitatively reproduced using a quantum-confinement model, yielding an out-of-plane reduced effective mass of $\mu_\perp=0.75 m_0$. RC spectroscopy reveals four excitonic resonances. While the A and B excitons associated with the $K^\pm$ valleys remain nearly independent of layer thickness, the higher-energy C and D resonances originating from the band-nesting regions exhibit pronounced redshifts, reflecting substantial thickness-induced modifications of the electronic band structure. These results establish comprehensive spectroscopic fingerprints of flake thickness, interlayer coupling, and electronic structure in Mo$_x$W$_{1-x}$Se$_2$ alloys and provide a reliable, non-destructive framework for their optical characterization.

This study examines how the 2014 Donbas-war breakpoint was associated with changes in the semantic composition of research funding recorded in Estonia, a geopolitically exposed country outside the belligerent states. It combines 17,952 research-funding records from the Estonian Research Information System (ETIS) for 2000 to 2019 with a field-by-year matched OpenAlex reference corpus and geocoded Donbas conflict records. Contrastive text projections distinguish explicit-war language from dual-use technological orientation and eight crisis-relevant capability channels, allowing shifts to be detected beyond projects that directly mention war or security. Segmented annual models show positive post-2014 slope changes in dual-use and maximum-capability measures, whereas explicit-war language follows a different trajectory. Financing-weighted estimates identify positive post-2014 level differences among larger recorded projects. Capability-channel comparisons indicate the strongest positive period differences in computer science, energy, and engineering, together with a temporary narrowing of the capability profile. The results suggest that a neighboring research system can register geopolitical pressure through changes in the technical and preparedness-oriented language of funded projects. More broadly, the study demonstrates how project-level semantic evidence can reveal shifts in public science-funding priorities that remain difficult to observe through disciplinary classifications or explicit conflict terminology alone.

We demonstrate the possibility to activate genuine multipartite entanglement (GME), the strongest form of entanglement for multipartite states, within the framework of quantum catalysis. Specifically, we show that any biseparable state (i.e. not GME) that is not partition separable can be deterministically transformed into a GME state via the help of a catalyst and local operations, without any classical communication. In turn, we construct a catalytic protocol tailored to the multipartite case. The protocol is termed "sum-to-product", as it transforms a mixture of states into their tensor product in a heralded manner. We apply this protocol to random network entangled states, which are biseparable by construction, and demonstrate catalytic activation of both GME and genuine multipartite Bell nonlocality.

Euler-Kronecker constants are analogues of the Euler-Mascheroni constant for number fields. Assuming the Generalized Riemann Hypothesis for Hecke $L$-functions, we obtain extreme values of Euler-Kronecker constants of abelian cubic fields. We also prove a similar result for quadratic fields.

We study maximum purity and minimum von Neumann entropy of absolutely positive partial transpose (APPT) states, together with the relative volume of their spectral sets. A consequence of Hildebrand's criterion gives an explicit outer spectral polytope, whose vertices we classify. Optimizing purity over this polytope, together with the Song–Chen result for the $2\otimes3$ system, yields, for every $mn\ge6$, an explicit upper bound on the purity of APPT states that is asymptotic to $4/(3mn)$. This improves the previous $2/(mn)$ upper bound for absolutely separable states. The new bound applies to every APPT state, a class containing all absolutely separable states, and is sharp for every $2\otimes n$ system with $n\ge3$. For every $3\otimes n$ system with $n\ge3$, however, the unique outer-polytope maximizer is not APPT, so the bound is strict and disproves the Dũng–Khôi qutrit–qudit conjecture. The polytope also gives an explicit entropy lower bound in arbitrary bipartite dimensions and, together with the Song–Chen extreme-point classification, the exact minimum entropy for every $2\otimes n$ system. Finally, exact formulas for the relative volumes of an inner polytope and the outer spectral polytope give explicit two-sided bounds on the qubit–qudit relative spectral volume $a_n$ whose ratio is less than $4$ and tends to $3$. Consequently, $a_n=\Theta\!\left(\sqrt n(4/27)^n\right)$, and the relative volume of the qubit–qudit APPT spectral set (equivalently, the absolutely separable spectral set) has exact exponential decay rate $\ln(27/4)$.

A stable inversion method is developed to reconstruct millimeter-scale solids-concentration profiles in particulate suspensions from monostatic sub-terahertz frequency-modulated continuous-wave (FMCW) radar measurements. In industrial particulate flows, cumulative attenuation renders the direct inversion of the path-integrated volume-scattering radar equation ill-conditioned. The method resolves this by an ensemble-averaged Mie-scattering closure coupled to a stable backward-integration scheme, yielding an analytical solution for the range-resolved solids concentration without case-specific parameter fitting against reference concentration measurements. The required range-dependent system response is determined by absolute near- and far-field calibration via external substitution with an electrically large metallic sphere. The method was evaluated against solids-volume-fraction estimates derived from differential-pressure measurements in a 3.1 m-tall circulating fluidized-bed riser operated with ambient air and copper powder (median diameter 32.6 $\mu$m, density 8920 kg m$^{-3}$). The radar-derived and pressure-derived profiles agreed well across three superficial gas velocities producing distinct axial solids distributions, and the radar indicates sensitivity down to solids volume fractions of order $10^{-6}$.

We present a physics-informed machine learning framework based on Neural Ordinary Differential Equations that solves the holographic inverse problem: reconstructing the bulk spacetime and gauge field of a charged AdS black hole directly from boundary fermionic spectral functions. Encoding the UV asymptotics, horizon regularity, and zero temperature extremality as hard constraints in the neural network architecture, our framework reliably reconstructs the extremal Reissner-Nordström AdS geometry across three quantum critical regimes set by the $U(1)$ probe charge—non-Fermi liquid, marginal Fermi liquid (strange metal), and Fermi-liquid-like states—and can jointly infer the probe charge itself to sub-percent accuracy. Relaxing the near-AdS boundary constraint uncovers a geometrical degeneracy: bulk profiles that differ throughout the radial direction but share the same near-horizon $AdS_2 \times \mathbb{R}^2$ data reproduce identical spectral functions near the Fermi surface. This isospectral non-uniqueness is precisely the bulk degeneracy expected on general holographic grounds at zero temperature, and its spontaneous emergence across independent training runs shows that the network isolates the IR CFT universality rather than overfitting a single UV completion.

We propose a compact NISQ-compatible quantum transformer architecture for synthetic QNLP sequence modelling. The model preserves the autoregressive next-token interface of a classical transformer, but replaces attention and feed-forward sublayers with variational quantum encoder blocks, connector circuits, decoder blocks and a direct two-qubit measurement readout. Token contexts are angle-encoded into small quantum registers, processed by parallel variational heads and encoder integration circuits and conditioned through decoder ancillae to produce a distribution over a four-token vocabulary. We evaluate several architecture variants on deterministic and lexicographic grammar-generation tasks against a compact classical transformer baseline. The quantum models are trainable end-to-end and learn nontrivial grammar structure, including perfect deterministic generation in individual runs and high lexicographic validity in the strongest variant. The classical baseline remains more accurate and stable and the quantum models are sensitive to initialization. The contribution is therefore not a claim of quantum advantage, but a concrete architecture and evaluation of transformer-inspired QNLP sequence modelling under near-term quantum constraints.

The recent LUX-ZEPLIN (LZ) search at high nuclear-recoil energies reported an intriguing candidate event near 250 keV, motivating interpretations in terms of inelastic dark matter. A simple realization with Higgsino dark matter, however, is strongly constrained by capture and subsequent annihilation in the Sun, which would produce a high-energy neutrino flux excluded by IceCube. We propose an asymmetric inelastic dark-matter scenario that naturally avoids this tension. The dark matter is a predominantly Standard-Model-singlet Dirac fermion that mixes weakly with a nearly degenerate electroweak doublet. Its primordial asymmetry is generated by CP-violating out-of-equilibrium decays of heavy Majorana fermions produced nonthermally from inflaton decays, while the symmetric component is efficiently depleted through dark-sector interactions. The absence of an appreciable antiparticle abundance then suppresses dark-matter annihilation in the Sun and eliminates the associated IceCube constraint. The singlet-doublet structure simultaneously yields an off-diagonal Z-boson coupling proportional to the mixing angle, whereas the diagonal coupling is suppressed by its square. Consequently, an observable inelastic scattering rate can coexist with stringent limits on elastic scattering. We find that the LZ event can be accommodated for dark-matter masses of a few hundred GeV to 1 TeV, with mass splittings of a few hundred keV and mixing angles below O$(10^{-2})$. Since the relic abundance is set by the primordial asymmetry rather than thermal freeze-out, lighter dark matter is also viable and can alleviate the potential tension with the absence of events in the LZ high-energy sideband. This framework predicts correlated elastic and inelastic direct-detection signals, together with complementary signatures at collider and precision experiments.

Peer sampling is a crucial primitive in distributed systems, used to manage overlays and disseminate information in large-scale scenarios such as permissionless blockchain systems. Its purpose is to maintain and regularly update a local and partial snapshot, or view, of the complete system's membership. These protocols are often targeted by malicious actors who aim to disrupt higher-level protocols. Typically, an adversary who controls a set of byzantine nodes attempts to manipulate how legitimate nodes perceive the presence of byzantine ones by increasing their representation in the view of honest nodes. While state-of-the-art byzantine-tolerant peer sampling protocols mitigate this bias, their effectiveness decreases significantly as the number of malicious nodes increases. This paper introduces AUPE, the first collaborative Byzantine-tolerant peer sampling protocol that leverages the presence of trusted nodes, such as Intel's SGX capable devices, to collaboratively track the spread of identifiers in the system and locally debias the representation of byzantine nodes. Simulations with 10,000 nodes demonstrate that AUPE outperforms state-of-the-art solutions, achieving nearperfect resilience even when faced with an adversary controlling 26% of the nodes. Overall, by including as few as 10% of trusted nodes, AUPE increases the tolerance of BRAHMS by up to 60% while limiting the impact of the adversary's attack, even when possessing up to 40% of the nodes.

Track 2 of the AI City Challenge 2026 requires both visual question answering (VQA) and traffic event description generation under a challenging synthetic-to real domain shift. Existing vision-language approaches often entangle semantic understanding with language generation, making them susceptible to hallucination and inconsistent reasoning across event phases. In this work, we propose a decoupled semantic understanding framework that first resolves predefined traffic questions into structured semantic facts and subsequently uses these facts to guide caption generation. A frozen V-JEPA encoder extracts predictive scene representations, while a lightweight Llama-based predictor produces answers for VQA queries. To improve reliability, we introduce a training-free structured refinement mechanism that exploits statistical priors, inter-question relationships, and temporal event consistency to correct prediction errors. The refined semantic facts are then provided to Qwen3-VL-8B to generate pedestrian and vehicle descriptions for each traffic event. Experimental results on the official 2026 AI City Challenge Track 2 benchmark show that the proposed method achieves 87.09% VQA accuracy and an overall S2 score of 60.0853, ranking first among all participating teams. These results demonstrate that predictive world representations combined with structured semantic refinement enable more accurate and reliable traffic understanding, leading to higher-quality lan guage generation.

We study limit cycles produced by Sotomayor-Teixeira regularizations of piecewise linear vector fields with generic two-fold singularities. We focus on the visible-visible and visible-invisible cases where sliding cycles occur, treating cycles from both sides of the switching manifold in a unified way. In further details, by relating the cyclicity of sliding cycles and zeros of the slow divergence integral, we prove that the cyclicity of compact families of sliding cycles is bounded by two when such integral does not vanish identically. In contrast to previous works, we do not perform a case-by-base study, but instead relate zeros of slow divergence integrals to crossing limit cycles of a suitably defined auxiliary piecewise linear system. For visible folds, we provide necessary and sufficient conditions that assure the existence of a unique simple zero of the slow divergence integral, which implies the existence of two limit cycles. We also show that, when a hyperbolic singularity of the sliding vector field lies at the boundary of the sliding segment, then the cyclicity is bounded by one.

Some aspects of AI development resemble a population process in which models are specialised, retrained on the output of peers, or combined by averaging weights. These practices lead to generations of models, in the biological sense studied by population genetics. Here, I develop this parallelism and interpret multigenerational model populations in terms of sexual and asexual reproduction, formally recombining the two fields. I test these analogies in an exact inheritance model, in trained networks (recurrent, feedforward and variational autoencoder generators) and in large language models, and show that they hold generally, with some measurable architecture-specific biases. Training recursively on model output is known to lead to model collapse, a process previously described as akin to genetic drift; I develop all that follows. A minimal model of a learner retrained on its parent's output reproduces the Wright-Fisher process exactly; verified real data added to each generation play the role of immigration, with the surprising finding that the absolute number of real data samples matters, not their share, exactly as in population genetics. Training a child on the average of its parents' outputs cancels the benefit of having several parents, matching blending inheritance (and reviving Jenkin's objection to Darwin), whereas combining parents so that each keeps its strongest contribution preserves it; merged language-model specialists exceeded every parent across seeds (the Fisher-Muller effect); and lineages become reproductively isolated, losing the ability to merge at all, when they have learned conflicting conventions and not when they have merely drifted apart. As AI societies become societies in time as well as in space, a mathematical framework for their inheritance acquires predictive power. Remarkably, that framework can be adapted almost wholesale from biology.

Indefinite causal order extends the conventional circuit paradigm by allowing local quantum operations to be connected without a predetermined global order. Within the process-matrix framework, it is characterized by causal nonseparability, whereas extensible causal separability (ECS) requires that, under arbitrary input-ancilla extensions, a process admit a recursive decomposition into components, each compatible with a particular operation acting first. Quantum circuits with classical control of causal order (QC-CC), in which previous outcomes dynamically determine which operation acts next, are known to generate ECS processes, but whether every ECS process admits such a realization has remained a longstanding open problem. We settle it through a generalized teleportation construction that realizes every multipartite ECS process as a QC-CC. We further establish consistency between ECS definitions for trivial and nontrivial global past and future systems. These results provide ECS with an exact operational interpretation and identify QC-CC as the complete circuit structure underlying this class of processes.

The gap between the classical and quantum Fisher information matrices (CFIM and QFIM) separates what is operationally accessible through measurements from what is intrinsic to a quantum state. In the multiparameter setting, this quantum obstruction is generically not saturable. Motivated by the recently introduced semiclassical geometric tensor (SCGT), we perform an explicit information-geometric study for a class of pure four-parameter single-qutrit states (FPSQSs). These states are probed by a one-parameter family of measurements that interpolates between an uninformative POVM and a sharp projective measurement. We derive closed-form expressions for the CFIM, the quantum geometric tensor (QGT), and the SCGT. We show that the SCGT reproduces the QGT in the projective limit and vanishes in the trivial limit. The real part of the SCGT splits into two terms: the CFIM and an additional nonnegative measurement-transmitted metric in the phase sector. Its imaginary part provides a semiclassical Berry curvature. Its loss relative to the QGT is quantified by a measurement-dependent gap. Our results provide an exactly solvable four-parameter platform for the semiclassical geometric framework. They also clarify how realistic measurements read out the geometric content of quantum states, and how they partially degrade it.

We present a uniform method for proving meromorphic function identities by comparing complete zero and pole multisets. A fixed annular Weierstrass normalization represents every nonzero meromorphic function uniquely as \[ q_t=e^{h_t}\frac{p_{Z_t}}{p_{P_t}},\qquad t=([h_t],Z_t,P_t),\qquad [h_t]\in\mathcal O(\mathbb C)/(2\pi i\mathbb Z). \] Thirteen principal comparisons, together with their specializations and consequences, use the same four steps: represent the two sides, compare their divisors, apply a divisor-comparison theorem (DCT), and normalize $h_s-h_t$. A small library packages classical finite-order, parity, recurrence, and lattice-rigidity arguments for repeated use. The examples span sine, Gamma, Barnes $G$, Bessel, completed zeta, theta, and elliptic functions. Their breadth demonstrates reuse of one proof structure across these families; the family-specific hypotheses and scalar calculations remain explicit. The contribution is a methodological synthesis: shorter proofs where available, and otherwise a modular organization of classical arguments. The fixed factors supply common coordinates, rather than a new uniqueness hypothesis. Historically, the viewpoint is motivated by the nineteenth-century contrast between Riemann's global geometric approach to complex function theory and Weierstrass's analytic construction of functions; the present method deliberately combines global divisor data with fixed Weierstrass factors. An appendix develops the associated ring and field presentations, separately from the ordinary operations used in the proofs.

Early wildfire detection is critical to prevent small ignitions from escalating into large-scale disasters, yet current monitoring systems lack a quantitative framework for allocating detection infrastructure at scale. We jointly optimize the placement of monitoring infrastructure and the routing of autonomous drones under realistic operational constraints to quantify the investment required for rapid, large-scale wildfire detection. Evaluated out-of-sample on 3,693 California ignitions from 2021-2024, an optimized drone network operating at a $100 million five-year budget detects 97.3% of fires, including 74% within the first hour. Amortized over five years, that budget is about $20 million per year, roughly 5% of California's annual wildfire-prevention expenditure. Under current technology costs, drone-based monitoring is substantially more cost-effective than static ground sensors. Detection is governed primarily by spatial coverage, while routing strategy mainly determines detection speed.

Wildfire spread is traditionally predicted using physics-based simulators, which are physically interpretable but whose cost increases with each additional ensemble member. We ask how well deep learning surrogates can reproduce these simulations at a fraction of this cost, training them on 10,584 fire spread simulations at 2m resolution for the Rectoret region in Catalonia, Spain. Four architectures are compared: a patch-based U-Net, a transfer-learned ResNet-50, a physics-informed network constrained by the wind-driven advection equation and a Swin-Unet transformer. Among the terrain and vegetation variables, only surface fuel load predicts burn probability with any strength (r = 0.27) and including it lowers prediction error by 21%. The remaining variables correlate weakly and are highly duplicative. Next, an experiment with saliency, occlusion and rotation demonstrates the models' learning. Convolutional models rely primarily on distance from the current fire front, while Swin-Unet assigns more weight to fuel and terrain, a finding also noted in an unrelated wildfire dataset. When applied without retraining to the second region, Pedriza, all three convolutional models still predict fire spread, losing accuracy by a small but systematic margin.