This paper considers the existence of short synchronizing words in deterministic finite automata (DFAs). We define two general strategies for generating synchronizing words, and we show that each of these strategies can be applied if and only if a DFA is synchronizable. Furthermore, we show that if a synchronizable DFA is well-structured, then our strategies generate short synchronizing words. The first of our strategies, called the cornering strategy , takes advantage of states in a DFA with properties similar to those of a polytope vertex. The second of our strategies, similar to the cornering strategy and called the f-ordered strategy , takes advantage of a partial order defined on the states of a DFA. We apply our cornering strategy to the class of difference DFAs , whose states form subsets of R d and whose input symbols correspond to translation vectors between states. We show that difference DFAs share many similarities with aperiodic DFAs, and in particular, a difference DFA M has a synchronizing word if and only if it has a universally reachable state. Using the cornering strategy, we also show that under certain conditions, such an n -state DFA M has a synchronizing word of length at most ( n − 1 ) 2 and thereby satisfies Černý’s conjecture. Using the f -ordered strategy, we also show that a synchronizable DFA whose states have a certain partial order that is preserved by a set of short words also has a short synchronizing word, and we consider several consequences of this result. Finally, we consider how the cornering strategy can be applied to the problem of synchronizing the product of two DFAs M 1 , M 2 that share a common alphabet, and we show that the product M 1 × M 2 often has a synchronizing word that is subquadratic in the number of states of M 1 × M 2 .

Abstract Accurate forecasts of near‐landfall TC characteristics (direction, translation speed, and intensity) are essential for timely disaster preparedness. Using best‐track data (1951–2023), this study reveals a significant pre‐landfall acceleration of TCs along the South China coast, with translation speed increasing by 35.5% and 16.4% during the 24 hr prior to landfall for eastbound and westbound cases, respectively. This acceleration is primarily contributed by the normal component of the translation vector. For westbound TCs, translation speed and its normal component increase with intensity, particularly at typhoon strength and above. Numerical simulations and diagnostic analyses attribute the acceleration to horizontal advection and diabatic heating, primarily driven by land‐induced asymmetric flow and convection. These findings strengthen the current understanding of TC motion dynamics and support more effective disaster prevention and mitigation strategies as TCs approach coastal regions.

In robotic assembly, precise pose estimation of assembly components or tools via vision is critical to task success. To enhance the accuracy of the classical Perspective-n-Point (PnP) algorithm based on circular features, this paper proposes a high-precision monocular pose estimation method that accounts for circular eccentricity. First, based on monocular projection geometry, we derive an eccentricity parameterization model for single circular contours and an image-processing-based eccentricity error estimation model. Furthermore, by introducing an error weighting factor to explicitly incorporate eccentricity errors into the reprojection error of the PnP problem, we establish a new pose estimation optimization model and solution strategy, to the best of our knowledge. Experimental results demonstrate that compared to traditional PnP methods that rely solely on feature center points, the proposed method further leverages the rich geometric information of circular features. It effectively enhances pose estimation accuracy and numerical stability in the translation vector while reducing processing time. In assembly application experiments, the proposed algorithm enables smoother convergence of end-effector pose errors compared to traditional methods, significantly improving assembly stability during the process.

The subject of the article is the methodology for building an integrated neuro-symbolic architecture of mental models for users with different levels of technical competence to generate personalized explanations of intelligent information systems decisions. The goal is to develop an architecture that provides automated detection of individual mental models from user behavioral data and the creation of interpretable symbolic representations of causal relationships with the adaptation of the level to detail to the user's skill level. The tasks addressed include: performing a comparative analysis of existing approaches to building mental models according to personalization criteria; developing an integrated neuro-symbolic architecture with functional distribution between neural network and symbolic components; conducting experimental verification of the proposed architecture; determining the scope of application for the developed architecture. The methods used include variational autoencoders with multi-channel attention mechanisms, neuro-symbolic translation with multi-level abstraction, and the generation of directed acyclic graphs. The following results were obtained: an integrated neuro-symbolic architecture was developed featuring a neural network component for the automated detection of individual cognitive structures through variational encoding and attention mechanisms with dynamic channel prioritization by user category, and a symbolic component for transforming latent descriptors into interpretable causal graphs with adaptive detailing and temporal validation to eliminate spurious dependencies. Conclusions. The results of the study confirmed the effectiveness of the integrated neuro-symbolic approach to building personalized mental models with the automated detection of latent cognitive structures from behavioral data without the need for expert knowledge. The scientific novelty of the results obtained lies in the development of an integrated neuro-symbolic architecture model that provides interaction between a neural network layer, designed for projecting behavioral trajectories into latent space and selecting significant features through multi-channel attention, and a symbolic layer for the neuro-symbolic translation of latent vectors into multi-level symbolic representation. This involves the generation of directed acyclic graphs and temporal validation, which improves the comprehensibility of intelligent systems' decisions through the construction of personalized, interpretable mental models. This, in turn, increases user trust in intelligent systems' decisions by tailoring explanations according to their level of technical competence.

This paper proposes a rigid body relative pose estimation method based on binocular vision and perpendicular skew Plücker lines. By acquiring the Plücker coordinates of two perpendicular skew lines on the tracked rigid body through a binocular vision system and combining dual quaternion theory, high-precision 6-DOF relative pose estimation between the target and tracking rigid bodies is achieved. First, feature lines are extracted from binocular images using stereo matching techniques, and their 3D Plücker coordinates are calculated; next, an orthogonal coordinate system is constructed based on the perpendicularity constraint of the direction vectors to solve the rotational component; then a linear equation system incorporating moment vector variations is established, and the translation vector is optimized via least-squares estimation. Simulation results demonstrate that the method maintains high accuracy and strong stability under noise, distance, and attitude variations.

Due to the loss of 3D information, accurate and robust 2D image feature matching remains challenging for many computer vision applications. This paper introduces a 2.5D feature that uses the disparity value from the light field Fourier disparity layer (FDL) as a rough proxy of scene depth. Without explicit depth estimation, a parameterized depth-degraded projection is proposed to construct the geometric transformation of paired features between two light fields. Then, we propose a parameterized learning solution to calculate the depth-degraded projection. This solution estimates a global constant fundamental matrix, a variable disparity-guided translation vector, and a depth compensation term using a very simple network. Although the 0.5D relative disparity provided by the FDL does not represent precise depth, it can also significantly reduce the depth ambiguity in feature matching. Therefore, the proposed solution achieves accurate feature-matching results by minimizing the sum of reprojection errors across all matching candidates. On the public light field feature-matching dataset, the proposed solution outperforms existing 2D image feature-matching solutions and light field feature-matching algorithms in terms of matching accuracy and robustness. The code is available online.

Given 2D point correspondences between an image pair, inferring the camera motion is a fundamental issue in the computer vision community. The existing works generally set out from the epipolar constraint and estimate the essential matrix, which is not optimal in the maximum likelihood (ML) sense. In this paper, we dive into the original measurement model with respect to the rotation matrix and normalized translation vector and formulate the ML problem. We then propose an optimal two-step algorithm to solve it: In the first step, we estimate the variance of measurement noises and devise a consistent estimator based on bias elimination; In the second step, we execute a one-step Gauss-Newton iteration on manifold to refine the consistent estimator. We prove that the proposed estimator achieves the same asymptotic statistical properties as the ML estimator: The first is consistency, i.e., the estimator converges to the ground truth as the point number increases; The second is asymptotic efficiency, i.e., the mean squared error of the estimator converges to the theoretical lower bound - Cramer-Rao bound. In addition, we show that our algorithm has linear time complexity. These appealing characteristics endow our estimator with a great advantage in the case of dense point correspondences. Experiments on both synthetic data and real images demonstrate that when the point number reaches the order of hundreds, our estimator outperforms the state-of-the-art ones in terms of estimation accuracy and CPU time.

Abstract To address the challenge of real-time detection and correction of assembly deviations during automated assembly processes, this study proposes an online assembly correction system based on a fiber Bragg grating (FBG) sensor array. The system utilizes an FBG array to continuously monitor changes in the strain field of the assembly structure, converting the measured wavelength shift Δλ into a spatial displacement vector for the fingers. Based on a rigid body kinematic model, the least-squares optimization algorithm was employed to solve the finger displacement into translation vector T and rotation angle θ of the misaligned assembly components. Real-time joint angle adjustment values were determined using inverse kinematic calculations of the robotic arm to achieve online position correction during the assembly process. The simulation validation confirmed the strain response under offset conditions. The experimental results demonstrate that the system can effectively detect assembly deviations in multiple directions. The correction algorithm had a high accuracy, with a displacement prediction error of ≤0.1 mm. The angle prediction deviation was small (standard deviation σ=0.30°, mean μ=0.02°), and there was no significant systematic deviation. This system achieves real-time monitoring and closed-loop correction of assembly deviations, thereby providing an effective solution for automated assembly tasks.

Scalable purification enables high-quality virus-like particles for therapeutic translation

We investigate the dynamics of the Ikeda map in the conservative limit, where it is represented as a two-dimensional area-preserving map governed by two control parameters, θ and ϕ. We demonstrate that the map can be interpreted as a composition of a rotation and a translation of the state vector. In the integrable case (ϕ=0), the map reduces to a uniform rotation by angle θ about a fixed point, independent of initial conditions. For ϕ≠0, the system becomes nonintegrable, and the rotation angle acquires a coordinate dependence. The resulting rotation number profile exhibits extrema as a function of position, indicating the formation of shearless barriers. We analyze the emergence, persistence, and breakup of these barriers as the control parameters vary.

BackgroundThe utility of surface‐guided radiation therapy (SGRT) with continuous positive airway pressure (CPAP) remains underexplored compared to its application with deep inspiratory breath hold (DIBH). This study investigates the integration of CPAP and SGRT, focusing on positional reproducibility and treatment efficiency.PurposeThis study evaluated the impact of patient surface displacement during breast cancer radiation therapy using optical and thermal SGRT monitoring and compared treatment time characteristics between patients undergoing SGRT, either with or without CPAP, and a cohort of patients undergoing treatment without SGRT.MethodsThe SGRT cohort comprised thirty patients: 15 with CPAP (CPAP + SGRT) and 15 without CPAP (SGRT‐only). The surface displacement was monitored using an advanced optical and thermal SGRT system with thresholds of 3 mm for translational and 2.5° for rotational displacement. Treatment workflow metrics and positional deviations were assessed across 16 fractions. A comparative analysis included a cohort of 27 free‐breathing (FB) patients who did not receive SGRT.ResultsPositional reproducibility was similar in both SGRT groups, with translation vectors of 1.46 ± 0.98 mm (CPAP + SGRT) and 1.37 ± 0.80 mm (SGRT‐only) and rotation vectors of 0.57 ± 0.40° and 0.57 ± 0.39°, respectively. Despite comparable displacement control, treatment delivery time variability was highest in the CPAP + SGRT group (normalized standard deviation: 0.16), followed by the SGRT‐only (0.11) and FB groups (0.03). The broader time distributions in the SGRT group were attributed to beam‐hold activations exceeding the displacement thresholds, whereas total treatment time did not differ significantly between groups.ConclusionsSGRT effectively minimized displacement‐related uncertainties during breast cancer radiation therapy with and without CPAP. Although CPAP provides additional internal stabilization and its integration with SGRT increased treatment delivery time variability, the total treatment time remained comparable across all groups. These findings underscore the potential of SGRT and CPAP as complementary tools to enhance precision and safety, particularly for techniques requiring high positional accuracy.

Tay-Sachs disease (TSD) and Sandhoff disease are fatal neurodegenerative diseases without an effective therapy that are caused by mutations in the HEXA and HEXB genes, respectively. Together they encode the heterodimeric isozyme of hexosaminidase, hexosaminidase A (HexA), that degrades GM2 ganglioside. This report describes a 5-year-long study using a bidirectional adeno-associated virus 9 (AAV9) vector (AAV9-Bic_HexA/HexB) encoding both HEXA and HEXB in the TSD sheep model. Bidirectional AAV9 was delivered i.v. or through various cerebrospinal fluid (CSF) delivery routes: intracerebroventricular (ICV), cisterna magna (CM), and lumbar intrathecal space (LIT). The longest survival and best distribution were achieved by multipoint CSF delivery (combined CM, ICV, and LIT) with treated animals that survived up to 5 years of age (untreated animals with TSD die after ~9 months). Extension in survival was accompanied by lasting improvement in neurological examination and maze testing. Improvement in biomarkers of efficacy, including MRI, magnetic resonance spectroscopy, diffusion tensor imaging, and CSF levels of GM2 ganglioside and HexA activity, was evident. Postmortem assessments showed broad HexA distribution, GM2 ganglioside clearance, and vector genome distribution, especially in deep brain structures. Therapeutic efficacy documented in this study supports translation of bidirectional vector and multipoint CSF delivery to a clinical trial in patients with TSD and Sandhoff disease.

Gene therapy holds immense potential for treating genetic disorders, malignancies, and infectious diseases through the targeted introduction, silencing, or precise editing of therapeutic genes. Although viral vectors exhibit exceptionally high gene transfection efficiency, their clinical application faces significant challenges, including robust immunogenicity, the insertional mutagenesis risks, complex and costly manufacturing processes hindering large-scale manufacturing, limited gene cargo capacity, and poor packaging efficiency for large genes. In contrast, nonviral vectors-such as lipid nanoparticles (LNPs), cationic polymers, and inorganic nanoparticles, offer numerous advantages, including superior safety profiles, the scalability for manufacturing, structural and functional reconfigurability in accommodating various sizes cargo. Consequently, these nonviral delivery platforms have emerged as promising alternatives in DNA/mRNA/siRNA delivery. This review systematically summarizes recent progress in nonviral gene delivery systems, highlighting their therapeutic potential and current challenges. We systematically investigate the cellular internalization mechanisms and intracellular trafficking pathways of gene-loaded nanoparticles, and explore their diverse applications in gene therapy. Furthermore, this review systematically summarizes recent examples of clinically approved nonviral vector-based gene therapies including vaccine development, genetic disease treatment, and cancer therapy. Finally, we highlight the current challenges and future perspectives for the clinical translation of the nonviral delivery vectors.

For the problem of rigid-body relative pose estimation, this paper proposes a binocular vision-based relative pose measurement algorithm using Plücker lines. The method utilizes two spatial perpendicular skew lines and solves the rotation and translation components separately through dual-quaternion algebra. The algorithm proceeds as follows: first, it establishes a line feature representation model based on Plücker coordinates and derives the rigid-body transformation relationships for direction vectors and moment vectors. Second, it constructs a direction vector alignment constraint and solves for the optimal rotation quaternion using an eigenvalue decomposition. Then, it formulates a system of linear equations based on the moment vector transformation and computes the translation vector via least-squares estimation. Simulation results demonstrate that the proposed algorithm not only achieves a unified representation of relative position and attitude, but also satisfies the measurement accuracy requirements for rigid-body relative pose estimation.

We report an approach to treat polarization effects in a two-dimensional (2D) environment using frozen-density embedding (FDE), suitable for computing response to electron loss or attachment as occurring in organic semiconductors during charge migration. FDE enables us to avoid an infinite repetition of the occurring charge. The procedure is carried out in two subsequent steps. First, the density of an unperturbed 2D molecular slab is relaxed self-consistently using FDE. Supermolecular quantities are avoided by translating the subsystem density along two translation vectors to compute long-range Coulomb potentials. The resulting large summation is tackled using the Van Wijngaarden transformation. Second, long-range contributions are frozen, and a local perturbation is introduced in the center subsystem. Freeze-thaw iterations are used to relax the electronic wave function of both the center subsystem and the subsystems in an active region around it. The proposed scheme can be applied to purely electronic perturbations as well as perturbations of the geometry. Application to systems with a molecule size of dozens of atoms leads quickly to systems consisting of thousands of atoms due to the 2D slab, which can be treated with the reported approach. As a sample application with regard to organic semiconductors, we report FDE calculations on a charged bay-CF3-TAPP-H4Cl4 dimer (84 atoms) polarizing 20 dimers (1680 atoms) in its surrounding, altogether enclosed by 24 dimers (2016 atoms) with frozen density, resulting in total 3780 atoms, all embedded in a long-range 2D Coulomb field.

To overcome the limitations in the perception performance of individual robots and homogeneous robot teams, this paper presents a distributed multi-robot collaborative SLAM method based on air–ground cross-domain cooperation. By integrating environmental perception data from UAV and UGV teams across air and ground domains, this method enables more efficient, robust, and globally consistent autonomous positioning and mapping. First, to address the challenge of significant differences in the field of view between UAVs and UGVs, which complicates achieving a unified environmental understanding, this paper proposes an iterative registration method based on semantic and geometric features assistance. This method calculates the correspondence probability of the air–ground loop closure keyframes using these features and iteratively computes the rotation angle and translation vector to determine the coordinate transformation matrix. The resulting matrix provides strong initialization for back-end optimization, which helps to significantly reduce global pose estimation errors. Next, to overcome the convergence difficulties and high computational complexity of large-scale distributed back-end nonlinear pose graph optimization, this paper introduces a multi-level partitioning majorization–minimization DPGO method incorporating loss kernel optimization. This method constructs a multi-level, balanced pose subgraph based on the coupling degree of robot nodes. Then, it uses the minimization substitution function of non-trivial loss kernel optimization to gradually converge the distributed pose graph optimization problem to a first-order critical point, thereby significantly improving global pose estimation accuracy. Finally, experimental results on benchmark SLAM datasets and the GRACO dataset demonstrate that the proposed method effectively integrates environmental feature information from air–ground cross-domain UAV and UGV teams, achieving high-precision global pose estimation and map construction.

In an experiment, two types of hexagonal structures, the primitive translation vector of which was parallel to that of substrate or rotated by 30°, were generated during colloidal heteroepitaxy. When colloidal particles smaller than the epitaxial particles were included as additives, the formation ratio of the two hexagonal structures changed depending on the size of the additive particles. To examine the dependence of the formation ratio of the two hexagonal structures on the size of the small colloidal particles, Brownian dynamics simulations were performed. Under a high particle density and strong interaction conditions, the hexagonal structure with a lower formation ratio without additives became the major product when additives much smaller than the epitaxial particles were included. Conversely, the hexagonal structure with a higher formation ratio without additives became difficult to form in the presence of additive particles. The effect of additive particles on the formation rates of hexagonal structures depended on whether the additive particles could intrude into the space between the substrate and epitaxial layer. Both hexagonal structures became more difficult to form as the additive particle size increased. At a specific ratio of the additive particle size to the substrate particle size, the formation ratio of the structure present in a lower content without additive increased because of the generation of a precursor structure.

Retinal gene therapy using dual adeno-associated viral (AAV) intein vectors can be applied to genetic forms of blindness caused by mutations in genes with coding sequences that exceed single AAV cargo capacity, such as Stargardt disease (STGD1), the most common inherited macular dystrophy. In view of clinical translation of dual AAV intein vectors, here we set to evaluate both the efficiency and safety of their subretinal administration in relevant large animal models. Accordingly, we have developed the first pig model of STGD1, which we found to accumulate lipofuscin similarly to patients. This accumulation is significantly reduced upon subretinal administration of dual AAV intein vectors whose safety and pharmacodynamics we then tested in nonhuman primates, which showed modest and reversible inflammation as well as high levels of photoreceptor transduction. This bodes well for further clinical translation of dual AAV intein vectors in patients with STGD1 as well as for other blinding diseases that require the delivery of large genes.

mRNA is an important molecule in vaccine development and treatment of genetic disorders. Its capability to hybridize with DNA oligonucleotides in a programmable manner facilitates the formation of RNA-DNA origami structures, which can possess a well-defined morphology and serve as rigid supports for mRNA delivery. However, to date, comprehensive studies on the requirements for efficient folding of mRNA into distinct mRNA-DNA structures while preserving its translation functionality remain elusive. Here, the impact of design parameters on the folding of protein-encoding mRNA into mRNA-DNA origami structures is systematically investigated and the importance of the availability of ribosome-binding sequences on the translation efficiency is demonstrated. Furthermore, these hybrid structures are encapsulated inside virus capsids resulting in protecting them against nuclease degradation and also in enhancement of their cellular uptake. This multicomponent system therefore showcases a modular and versatile nanocarrier. The work provides valuable insight into the design of mRNA-DNA origami structures contributing to the development of mRNA-based gene delivery platforms.

Abstract This article follows our recent work on the computation of kinematic confidence regions from a given set of uncertain spatial displacements with specified confidence levels. Dual quaternion algebra is used to compute the mean displacement as well as relative displacements from the mean. In constructing a 6D confidence ellipsoid, however, we use dual Rodrigues parameters resulting from dual quaternions. The advantages of using dual quaternions and dual Rodrigues parameters are discussed in comparison with those of three translation parameters and three Euler angles, which were used for the development of the so-called rotational and translational confidence limit (RTCL) method. The set of six dual Rodrigues parameters are used to define a parametric space in which a 6×6 covariance matrix and a 6D confidence ellipsoid are obtained. An inverse operation is then applied to first obtain dual quaternions and then to recover the rotation matrix and translation vector for each point on the 6D ellipsoid. Through examples, we demonstrate the efficacy of our approach by comparing it with the RTCL method known in literature. Our findings indicate that our method, based on the dual Rodrigues formulation, yields more compact and effective swept volumes than the RTCL method, particularly in cases involving screw displacements.