The fused multiply-add (FMA) instruction enables the radix-2 FFT butterfly to be computed in 6~FMA operations -- the proven minimum. The classical factorization by Linzer and Feig~\cite{linzer1993} precomputes the ratio $\cotθ= \cosθ/\sinθ$, which is singular when the twiddle factor is $W^0 = 1$ (i.e., $\sinθ= 0$). Standard practice clamps $\sinθ$ to a small epsilon, degrading numerical precision. We observe that an alternative factorization using $\cosθ$ as the outer multiplier (precomputing $\tanθ$) avoids this particular singularity but introduces a new one at $W^{N/4}$. We then propose a \emph{dual-select} strategy that chooses, per twiddle factor, whichever factorization yields $|\text{ratio}| \leq 1$. This eliminates all singularities, requires no epsilon clamping, and bounds the precomputed ratio to unity for all twiddle factors. For $N = 1024$, the worst-case ratio drops from 163 (Linzer-Feig) to exactly~1.0 (dual-select), yielding a $235\times$ tighter error bound in FP16 arithmetic over 10~FFT passes. The strategy adds zero computational overhead -- only the precomputed twiddle table changes.

Digital twins (DTs) are envisioned as a key enabler of the cyber-physical continuum in future wireless networks. However, efficient deployment and synchronization of DTs in dynamic multi-access edge computing (MEC) environments remains challenging due to time-varying communication and computational resources. This paper investigates the joint optimization of DT deployment and synchronization in dynamic MEC environments. A deep reinforcement learning (DRL) framework is proposed for adaptive DT placement and association to minimize interaction latency between physical and digital entities. To ensure semantic freshness, an update scheduling policy is further designed to minimize the long-term weighted sum of the Age of Changed Information (AoCI) and the update cost. A relative policy iteration algorithm with a threshold-based structure is developed to derive the optimal policy. Simulation results show that the proposed methods achieve lower latency, enhanced information freshness, and reduced system cost compared with benchmark schemes

This paper proposes a method for generating typical scenarios based on system-level macroscopic characteristics of power system and considering its stability properties. First, considering uncertainties such as renewable energy generation in power-electronics-dominated power systems, multidimensional scaling is used to construct an electrical coordinate system. Based on this, system-level characteristics of the distribution of physical quantities, such as power generation and load, are characterized. Furthermore, a method for generating typical scenarios based on the system's system-level characteristics and stability properties is proposed. For the obtained joint probability distribution of system-level characteristics, weighted Mahalanobis distance can be used to predict the stability properties of random scenarios. Finally, the typicality and representativeness of the scenarios generated by the proposed method with respect to stability properties are verified on the CSEE benchmark case, and stability prediction for random scenarios is achieved using a probabilistic testing method.

Output regulation is the problem of finding a control input to asymptotically track reference trajectories and reject disturbances. This can be addressed by using the internal model principle to embed a model of the disturbance in the controller. In this work, we present a Model Predictive Control scheme to achieve offset-free control. To do so, we extend Internal Model MPC to general bounded disturbances that must not be generated by the disturbance model. We show recursive feasibility, constraint satisfaction, and provide convergence conditions for the optimal reachable output. The proposed controller is validated on a four-tank system.

The paper is devoted to a categorical study of the category of probabilistic metric spaces. The study is based on an isomorphic description of the category of probabilistic metric spaces. The isomorphic description was obtained in [3] and is in terms of objects that are sets endowed with a collection of distances, where the distances involved do not satisfy the triangle inequality but fulfil a mixed triangle condition instead. The morphisms are levelwise non-expansive maps. We show that the category of probabilistic metric spaces is a monotopological category over the category of sets. We describe the regular closure on a probabilistic space and prove that it coincides with the closure in the underlying strong topology. This enables us to characterize the class of all epimorphisms as the dense maps and the class of all regular monomorphisms as the closed embeddings in terms of the closure operator. We prove that the category of extended metric spaces with non-expansive maps is both coreflectively and reflectively embedded in the category of probabilistic metric spaces.

This paper presents a specialized methodology for digitizing and segmenting mathematical documents from zbMATH Open, a comprehensive database of mathematical literature, to enhance machine processing capabilities. Currently, approximately 831,000 documents exist only in scanned volumes, which makes them not machine-processable. Furthermore, these scans often span multiple pages or share pages with other documents and incorporate diverse typesetting techniques, posing challenges for automated processing. To address these issues, we evaluate various Optical Character Recognition (OCR) tools and document separation techniques, proposing an optimized pipeline that outperforms existing approaches. Our study identifies Mathpix as the most effective OCR tool for LaTeX conversion, demonstrating superior performance based on BLEU and Edit Distance metrics. For document separation, we fine-tune generative Large Language Models (LLMs) and integrate them into a Majority Voting framework, achieving 97.5% accuracy when providing the text of the document. Additionally, our method identifies the start and end indexes for 90.6% of the test dataset, with an accuracy of 98.4% on applicable cases, resulting in an overall accuracy of 89.1% on the entire dataset. This approach surpasses traditional baselines, including regular expressions, ChatGPT-4o, and computer vision-based techniques. As a practical outcome, we process 810,977 mathematical documents into machine-readable text and extract precise document boundaries for 721,288 documents in LaTeX format. These contributions significantly improve accessibility for mathematical information retrieval systems, machine learning models, and related applications.

Nonreciprocity is known to generate a wide range of exotic phenomena in multi-species many-body systems, where different species influence one another through couplings that violate Newton's third law. In contrast, in the absence of explicitly imposed macroscopic nonreciprocal processes, single-species nonreciprocity -- another distinct form of nonreciprocity -- typically plays only a limited role in shaping macroscopic physics. Here, using a single-species Vicsek model with a vision cone and extrinsic noise, we show that spontaneous symmetry breaking (SSB) can dramatically enhance the macroscopic consequences of microscopic single-species nonreciprocity. In the ordered phase, this enhancement gives rise to an emergent macroscopic nonreciprocity that induces the system of identical active particles to admit an effective description with a "two-species" non-Hermitian structure. The resulting SSB-enhanced nonreciprocity substantially promotes traveling-band formation and, more strikingly, drives a novel real-space condensation of identical active particles, characterized by a "traveling line" with vanishing longitudinal width. Our findings uncover a fundamental mechanism by which microscopic single-species nonreciprocity can exert strong macroscopic influences in complex systems.

Modern medical research demands specialized causal inference methods evaluating complex continuous-time dynamic treatment regimens using observational data. For instance, obtaining the causal effects of intravenous administration, a continuous process involving dynamic adjustments of the treatment dose, can guide clinicians on drug use. However, the existing causal inference frameworks in longitudinal studies typically assume that time advances in discrete time steps. Therefore, this paper proposes a new methodology to estimate the causal effects of continuous-time dynamic treatments in the presence of unmeasured confounding. Unmeasured confounding is incorporated into estimating continuous-time Marginal Structural Models from a Bayesian perspective. Simulation demonstrates that compared to existing methods, the proposed approach can provide approximately unbiased estimates for target causal parameters across three degrees of confounding. The proposed method is applied to analyze the causal relationship between the intravenous oxytocin administration process and postpartum hemorrhage, leading to meaningful results that may guide clinicians in using oxytocin.

This paper presents an online linear model predictive control (MPC) framework for slew maneuvers that maintains star-tracker availability during ground-target tracking. The nonlinear rigid-body dynamics and geometric exclusion constraints are analytically linearized about the current state estimate at each control step, yielding a time-varying linear MPC formulation cast as a standard quadratic program (QP). This structure is compatible with established aerospace flight-software practices and offers a computational profile with lower online complexity than comparable nonlinear MPC schemes. The controller incorporates angular-rate, actuator, and star-tracker exclusion constraints over a receding horizon. Performance is assessed in high-fidelity nonlinear model-in-the-loop simulations using NASA's "42" spacecraft dynamics simulator, including a Monte Carlo campaign over varying target geometries and inertia perturbations.

For indefinite (Pontryagin space) canonical systems that contain an inner singularity we prove the existence of generalised boundary values at the singularity, which are used to formulate interface conditions. With the help of such interface conditions we construct the monodromy matrix of the canonical system and write it as a product of matrices, which separates the contributions of the Hamiltonian function and the finitely many discrete parameters that are associated with the singularity.

Resilience is emerging as a key requirement for next-generation wireless communication systems, requiring the ability to assess and control rare, path-dependent failure events arising from sequential degradation and delayed recovery. In this work, we develop a sequential Monte Carlo (SMC) framework for resilience assessment and control in networked systems. Resilience failures are formulated as staged, path-dependent events and represented through a reaction-coordinate-based decomposition that captures the progression toward non-recovery. Building on this structure, we propose a multilevel splitting approach with fixed, semantically interpretable levels and a budget-adaptive population control mechanism that dynamically allocates computational effort under a fixed total simulation cost. The framework is further extended to incorporate mitigation policies by leveraging SMC checkpoints for policy evaluation, comparison, and state-contingent selection via simulation-based lookahead. A delay-critical wireless network use case is considered to demonstrate the approach. Numerical results show that the proposed SMC method significantly outperforms standard Monte Carlo in estimating rare non-recovery probabilities and enables effective policy-driven recovery under varying system conditions. The results highlight the potential of SMC as a practical tool for resilience-oriented analysis and control in future communication systems.

Tidally locked lava planets are hot, rocky worlds on close-in orbits with a permanent molten dayside. With JWST, their surfaces and atmospheres are beginning to be revealed. This work investigates 3D magma-ocean dynamics, derives scaling laws for the resulting ocean heat transport (OHT), and predicts its detectability. For the first time, the ocean circulation driven by the intense momentum and mass exchanges with the supersonic atmosphere is considered in addition to that by thermal forcing. The wind forcing turns out to overwhelmingly dominate the other two mechanisms, driving ocean currents reaching $\sim$100 m s$^{-1}$ and greatly expanding the latitudinal extent of the Matsuno-Gill response. Despite these extreme flow speeds, scaling analysis and 3D simulations consistently demonstrate that magma-ocean circulation alone does not produce an observable hotspot offset. This inefficiency arises because basin geometry and circulation structure fundamentally constrain zonal heat redistribution, suppressing large-scale longitudinal transport even under vigorous flow.

We define a Fréchet topology on the space $C^\infty(X)[[\hbar]]$ of formal smooth functions on a symplectic manifold $X$, by constructing a sequence of semi-norms on it. For any star product $\star$ on $C^\infty(X)[[\hbar]]$ making it a formal deformation quantization of $X$, we will show that the quantum product $\star$ is jointly continuous, and making it a Fréchet algebra. We will show a quantum Weierstrass theorem which says quantum polynomials are locally dense in all formal smooth functions. We will also show that the canonical trace of any formal deformation quantization is continuous under this Fréchet topology.

Ferroic multipole orders break some symmetry and often activate unique physical properties, such as nonreciprocal directional dichroism and linear magnetoelectric effects. Here, we demonstrate the control of magnetic toroidal orientation in PbMn$_{2}$Ni$_{6}$Te$_{3}$O$_{18}$ through the application of electric and magnetic fields in two distinct configurations. Through directional dichroism, we successfully visualize magnetic ferrotoroidic domains, establishing the intrinsic coupling among magnetic toroidal moment, crystallographic ferroaxial moment, and magnetoelectric monopoles. Our findings not only present an effective pathway for controlling magnetic toroidal moment but also provide a novel approach for investigating ferroaxial ordering.

Data-driven predictive control methods can provide the constraint handling and optimization of model predictive control (MPC) without first-principles models. Two such methods differ in how they replace the model: Data-enabled predictive control (DeePC) uses behavioral systems theory to predict directly from input--output trajectories via Hankel matrices, while Koopman-based MPC (KMPC) learns a lifted linear state-space representation from data. Both methods are well studied on their own, but head-to-head comparisons on multivariable process control problems are few. This paper compares them on a pasteurization unit with three manipulated inputs and three measured outputs, using a neural-network-based digital twin as the plant simulator. Both controllers share identical prediction horizons, cost weights, and constraints, so that differences in closed-loop behavior reflect the choice of predictive representation. Results show that both methods achieve feasible constrained control with comparable tracking error, but with a clear trade-off: KMPC tracks more tightly under the chosen cost, while DeePC produces substantially smoother input trajectories. These results help practitioners choose between the two approaches for thermal processing applications.

We introduce stochastic GW with the orthogonalized projector augmented-wave method (OPAW-sGW). This implementation enables accurate quasiparticle band gaps on significantly coarser real-space grids than norm-conserving pseudopotential sGW (NCPP-sGW). The orthogonalized PAW representation preserves the formal all-electron character and enables stochastic sampling of the Green's function and screened Coulomb interaction.

We study the stability of general weakly coupled systems subject to a reduced number of local or boundary controls. We show that, under Kalman's rank condition, the exponential stability of the underlying scalar equation implies polynomial stability of the full coupled system. Moreover, the decay rate remains unchanged regardless of the number of equations in the system. The proof relies on resolvent estimates and a clever exploitation of Kalman's rank condition to ensure effective transmission of damping across the coupled equations. The abstract result is applied to several concrete models, including systems of wave equations with local viscous, local viscoelastic, or boundary damping; systems of plate equations with internal damping; and thermoelastic systems of type III. Moreover, the optimality of the decay rate is established via spectral analysis.

Linear system identification and sparse dictionary learning can both be seen as structured matrix factorization problems. However, these two problems have historically been studied in isolation by the systems theory and machine learning communities. Although linear system identification enjoys a mature theory when inputs are known, blind linear system identification remains poorly understood beyond restrictive settings. In contrast, complete sparse dictionary learning has recently benefited from strong global identifiability results and scalable nonconvex algorithms. In this work, we bridge these two areas by showing that under a sparse input assumption, fully observed blind system identification becomes a generalization of complete dictionary learning. This connection allows us to develop global identifiability guarantees for blind system identification, by leveraging techniques from the complete dictionary learning literature. We further show empirically that a principled application of the alternating direction method of multipliers can globally recover the ground-truth system from a single trajectory, provided sufficient samples and input sparsity.

Convection and rotation are both key processes in stellar evolution modelling. While standard mixing-length theory (MLT) provides a widely used modelling of convection, it neglects the effects of rotation on convective transport. We investigate how rotating mixing-length theory (R-MLT), which accounts for the influence of rotation on convection, affects the internal structure, convective mixing, and angular momentum transport in stellar models in comparison to the standard non-rotating MLT. Using the MESA stellar structure and evolution software, we model the main-sequence evolution of a 5 M$_{\odot}$ star, for three cases: non-rotating, rotating with standard MLT for modelling convection, and rotating with R-MLT in convection zones, with the initial rotation rate set to 20 percent of the critical (Keplerian) value at the surface for the rotating models. We find that R-MLT reduces both the convective velocity and mixing length in the stellar core, leading to a smaller convective diffusion coefficient and about 20 percent reduction in the extent of the convective overshooting region. While the overall size of the convective core remains nearly unchanged, R-MLT changes the resulting chemical gradient at the core-envelope boundary, shifting the peak of the Brunt-Väisälä frequency and modifying the angular momentum transport in that region. Including the effects of rotation in the treatment of convection through R-MLT introduces measurable structural and transport differences, underscoring the importance of incorporating rotation-convection coupling in models of stars.

Primordial black holes (PBHs) are widely considered as candidates for dark matter in many recent studies, and they are often modeled as Schwarzschild or Kerr black holes (BHs), which have curvature singularities. Nevertheless, resolving the classical singularity may require quantum gravity motivated corrections, thereby yielding an effective quantum corrected BH spacetime geometry different from the Schwarzschild or Kerr cases. Therefore, it is well motivated to consider BHs beyond the Schwarzschild or Kerr as viable PBH candidates. Based on these considerations, we investigate quantum Oppenheimer Snyder BHs as PBHs which could account for all the dark matter. Our results show that these BHs have temperatures and greybody factors markedly different from the Schwarzschild case, suppressing Hawking emission and thereby relaxing the $γ$-ray constraints from HEAO-1, COMPTEL, and EGRET, which, relative to the Schwarzschild case, broadens the allowed PBH mass window in the asteroid-mass range where PBHs can constitute all of the dark matter.

For a graph $G$ of order $n$, the spectral sum of $G$ is defined to be the sum $λ_1(G) + λ_2(G)$, where $λ_1(G)$ (resp. $λ_2(G)$) is the largest (resp. second largest) adjacency eigenvalue of $G$. Ebrahimi, Mohar, Nikiforov and Ahmady (2008) conjectured that the spectral sum \[ λ_1(G) + λ_2(G)\le \frac{8}{7}n \] for any graph $G$. We prove this conjecture by combining tools from the theory of graph limits, convex geometry, exterior algebra and convex optimization. The techniques developed are of independent interest.

We generalize the classical semiregularity theorem of Buchweitz and Flenner to the setting of noncommutative algebraic geometry, with group actions. This applies in particular to twisted derived categories, in which case it answers a question of Markman and streamlines part of his proof of the Hodge conjecture for abelian fourfolds. Along the way, we prove that for many finite group actions on derived categories of varieties, the invariant category is of geometric origin.

The heavy-tailed mutation operator, proposed by Doerr, Le, Makhmara, and Nguyen (2017) for evolutionary algorithms, is based on the power-law assumption of mutation rate distribution. Here we generalize the power-law assumption using a regularly varying constraint on the distribution function of mutation rate. In this setting, we generalize the upper bounds on the expected optimization time of the $(1+(λ,λ))$ genetic algorithm obtained by Antipov, Buzdalov and Doerr (2022) for the OneMax function class parametrized by the problem dimension $n$. In particular, it is shown that, on this function class, the sufficient conditions of Antipov, Buzdalov and Doerr (2022) on the heavy-tailed mutation, ensuring the $O(n)$ optimization time in expectation, may be generalized as well. This optimization time is known to be asymptotically smaller than what can be achieved by the $(1+(λ,λ))$ genetic algorithm with any static mutation rate. A new version of the heavy-tailed mutation operator is proposed, satisfying the generalized conditions, and promising results of computational experiments are presented.

We report a method for producing an array of fifty two ion-sensitive PEDOT:PSS organic electrochemical transistors on a glass coverslip, each featuring an integrated fluoropolymer microwell sealed with lipid bilayer into which membrane proteins can be inserted for simultaneous electrical and fluorescence microscopy studies. To demonstrate capability, we fill the microwells with an `inner' phosphate assay buffer solution containing 20 $μ$M Alexa-488 dye and 50 mM KCl, seal the microwells with lipid bilayer using an aqueous-organic-aqueous liquid exchange technique, and then fill the common flow-cell volume above the sealed microwells with a dye-free `outer' phosphate assay buffer containing 100 mM KCl. We insert $α$-hemolysin, which embeds into the lipid bilayer forming a heptameric pore with diameter ~ 2.6 nm. The pore allows K$^{+}$ ions to diffuse into the microwell and Alexa-488 dye molecules to diffuse out of the microwell producing a corresponding drop in transistor conductance and microwell fluorescence intensity, respectively. These two signals occur at different timescales, consistent with the known size difference between K$^{+}$ ions and Alexa-488 molecules. Our approach to fabricating microwell arrays with PEDOT:PSS OECTs incorporated into the bottom of selected microwells distributed in the array is both scalable and versatile, opening a path to studies using larger arrays and with other membrane proteins embedded in the lipid bilayer sealing the microwells.

Structured documents--tables paired with captions, figures with explanations, equations with the paragraphs that interpret them--are routinely fragmented when indexed for retrieval. Element-level indexing treats every parsed element as an independent chunk, scattering semantically cohesive units across separate retrieval candidates. This paper presents a parser-independent pipeline that constructs Evidence Units (EUs): semantically complete document chunks that group visual assets with their contextual text. We introduce four contributions: (1) ontology-grounded role normalization extending DoCO that maps heterogeneous parser outputs to a unified semantic schema; (2) a semantic global assignment algorithm that optimally assigns paragraphs to EUs via a full similarity matrix; (3) a graph-based decision layer in Neo4j that formalizes EU construction rules and validates completeness through two invariants; and (4) cross-parser validation showing EU spatial footprints converge across MinerU and Docling, with gains preserved under parser-induced bbox variance. Experiments on OmniDocBench v1.0 (1,340 pages; 1,551 QA pairs) show EU-based chunking improves retrieval LCS by +0.31 (0.50 to 0.81). Recall@1 increases from 0.15 to 0.51 (3.4x) and MinK decreases from 2.58 to 1.72. Cross-parser results confirm the gain (LCS +0.23 to +0.31) is preserved across parsers. Text queries show the most dramatic gain: Recall@1 rises from 0.08 to 0.47.

We derive an explicit representation of the fundamental solution to the heat equation in a half-space of ${\mathbb R}^N$ with a diffusive dynamical boundary condition, and establish sharp pointwise upper and lower bounds. We also investigate qualitative properties of the associated solutions, including precise decay estimates. Furthermore, we analyze the diffusion limits of solutions to the initial--boundary value problem, and reveal the role of the diffusive dynamical boundary condition in the behavior of solutions.

This paper presents QuadSoft, a novel fully actuated quadrotor equipped with continuous-curvature, tendon-driven soft robotic arms. The design combines a semi-rigid central frame with flexible arms, enabling controlled structural reconfiguration during flight without altering the propeller layout. Unlike existing soft aerial platforms that rely on discrete bending joints, QuadSoft utilizes a continuum deformation approach to modulate arm curvature, actively adjusting its thrust vector and aerodynamic characteristics. We characterize the geometric mapping between servomotor input and the resulting constant curvature, validating it experimentally. Outdoor flight tests demonstrate stable take-off, hover, directional maneuvers, and landing, confirming that controlled arm bending can generate horizontal displacement while preserving altitude. Measurements of pitch, roll, and curvature angles show that the platform follows intended actuation patterns with minimal attitude deviations. These results demonstrate that QuadSoft preserves the baseline stability of rigid quadrotors while enabling morphology-driven maneuverability, all under the standard PX4 autopilot without retuning. Beyond a proof of concept, this work establishes a distinctive outdoor validation of a tendon-driven continuum morphing quadrotor, opening a new research avenue toward adaptive aerial systems that combine the safety and versatility of soft robotics with the performance of conventional UAVs.

Liquid crystalline defects in 3D can be viewed as geometric spinors, whose emergent properties are reminiscent of those of topological excitations in quantum condensed matter, such as Majorana quasiparticles. However, it is unclear how deep this analogy is, and whether this is a purely mathematical mapping, or it extends to key physical features, such as the exchange statistics or braiding behaviour. To address this question, here we consider a simple pattern made up of four nematic Majorana-like defect profiles, and ask how the defect profiles change as we braid them repeatedly around each other. Surprisingly, we find that in a large range of parameter space the defect profiles behave as classical analogues of non-Abelian anyons, which can be described in our case by defect bivectors moving on a Bloch-like hemisphere. Elastic interactions and dynamical effects enhance the complexity of the gates which can be performed by braiding these quasiparticles, making these liquid crystalline spinors promising candidates as components of topological computers.

All Lipschitz dynamics with the weak infinitesimal contraction (WIC) property can be expressed as a Lipschitz nonlinear system in proportional negative feedback -- this statement, a ``structure theorem,'' is true in the $p=1$ and $p=\infty$ norms. Equivalently, a Lipschitz vector field is WIC if and only if it can be written as a scalar decay plus a Lipschitz-bounded residual. We put this theorem to use using neural networks to approximate Lipschitz functions. This results in a map from unconstrained parameters to the set of WIC vector fields, enabling standard gradient-based training with no projections or penalty terms. Because the induced $1$- and $\infty$-norms of a matrix reduce to row or column sums, Lipschitz certification costs only $O(d^2)$ operations -- the same order as a forward pass and appreciably cheaper than eigenvalue or semidefinite methods for the $2$-norm. Numerical experiments on a planar flow-fitting task and a four-node opinion network demonstrate that the parameterization (re-)constructs contracting dynamics from trajectory data. In a discussion of the expressiveness of non-Euclidean contraction, we prove that the set of $2\times 2$ systems that contract in a weighted $1$- or $\infty$-norm is characterized by an eigenvalue cone, a strict subset of the Hurwitz region that quantifies the cost of moving away from the Euclidean norm.

We show that a simple scoring-based tie-breaking can help improve lower bounds for the expansion (aka isoperimetric number) of random regular graphs with small even degrees. Specifically, for degrees 4, 6 and 8, we show that, with high probability, the expansions are at least 0.489, 1.120 and 1.813 respectively.