Mapping transcriptomic vector fields of single cells.

Single-cell (sc)RNA-seq, together with RNA velocity and metabolic labeling, reveals cellular states and transitions at unprecedented resolution. Fully exploiting these data, however, requires kinetic models capable of unveiling governing regulatory functions. Here, we introduce an analytical framework dynamo (https://github.com/aristoteleo/dynamo-release), which infers absolute RNA velocity, reconstructs continuous vector fields that predict cell fates, employs differential geometry to extract underlying regulations, and ultimately predicts optimal reprogramming paths and perturbation outcomes. We highlight dynamo's power to overcome fundamental limitations of conventional splicing-based RNA velocity analyses to enable accurate velocity estimations on a metabolically labeled human hematopoiesis scRNA-seq dataset. Furthermore, differential geometry analyses reveal mechanisms driving early megakaryocyte appearance and elucidate asymmetrical regulation within the PU.1-GATA1 circuit. Leveraging the least-action-path method, dynamo accurately predicts drivers of numerous hematopoietic transitions. Finally, in silico perturbations predict cell-fate diversions induced by gene perturbations. Dynamo, thus, represents an important step in advancing quantitative and predictive theories of cell-state transitions.

Optical vector field rotation and switching with near-unity transmission by fully developed chiral photonic crystals.

State-of-the-art nanostructured chiral photonic crystals (CPCs), metamaterials, and metasurfaces have shown giant optical rotatory power but are generally passive and beset with large optical losses and with inadequate performance due to limited size/interaction length and narrow operation bandwidth. In this work, we demonstrate by detailed theoretical modeling and experiments that a fully developed CPC, one for which the number of unit cells N is high enough that it acquires the full potentials of an ideal (N → ∞) crystal, will overcome the aforementioned limitations, leading to a new generation of versatile high-performance polarization manipulation optics. Such high-N CPCs are realized by field-assisted self-assembly of cholesteric liquid crystals to unprecedented thicknesses not possible with any other means. Characterization studies show that high-N CPCs exhibit broad transmission maxima accompanied by giant rotatory power, thereby enabling large (>π) polarization rotation with near-unity transmission over a large operation bandwidth. Polarization rotation is demonstrated to be independent of input polarization orientation and applies equally well on continuous-wave or ultrafast (picosecond to femtosecond) pulsed lasers of simple or complex (radial, azimuthal) vector fields. Liquid crystal-based CPCs also allow very wide tuning of the operation spectral range and dynamic polarization switching and control possibilities by virtue of several stimuli-induced index or birefringence changing mechanisms.

Highly Robust Adaptive Sliding Mode Trajectory Tracking Control of Autonomous Vehicles.

Autonomous driving technology has not yet been widely adopted, in part due to the challenge of achieving high-accuracy trajectory tracking in complex and hazardous driving scenarios. To this end, we proposed an adaptive sliding mode controller optimized by an improved particle swarm optimization (PSO) algorithm. Based on the improved PSO, we also proposed an enhanced grey wolf optimization (GWO) algorithm to optimize the controller. Taking the expected trajectory and vehicle speed as inputs, the proposed control scheme calculates the tracking error based on an expanded vector field guidance law and obtains the control values, including the vehicle's orientation angle and velocity on the basis of sliding mode control (SMC). To improve PSO, we proposed a three-stage update function for the inertial weight and a dynamic update law for the learning rates to avoid the local optimum dilemma. For the improvement in GWO, we were inspired by PSO and added speed and memory mechanisms to the GWO algorithm. Using the improved optimization algorithm, the control performance was successfully optimized. Moreover, Lyapunov's approach is adopted to prove the stability of the proposed control schemes. Finally, the simulation shows that the proposed control scheme is able to provide more precise response, faster convergence, and better robustness in comparison with the other widely used controllers.

Real-Space Observations of Three-Dimensional Antiskyrmions and Skyrmion Strings.

Nanometric topological spin textures, such as skyrmions (Sks) and antiskyrmions (antiSks), have attracted much attention recently. However, most studies have focused on two-dimensional spin textures in films with inherent or synthetic antisymmetric spin-exchange interaction, termed Dzyaloshinskii-Moriya interaction, although three-dimensional (3D) topological spin textures, such as antiSks composed of alternating Bloch- and Néel-type spin spirals, chiral bobbers carrying emergent magnetic monopoles, and deformed Sk strings, are ubiquitous. To elucidate these textures, we have developed a 3D nanometric magnetic imaging technique, tomographic Lorentz transmission electron microscopy (TEM). The approach enables the visualization of the 3D shape of magnetic objects and their 3D vector field mapping. Here we report 3D vector field maps of deformed Sk-strings and antiSk using the technique. This research approach will lead to discoveries and understanding of fertile 3D magnetic structures in a broad class of magnets, providing insight into 3D topological magnetism.

Novel measures of Morris water maze performance that use vector field maps to assess accuracy, uncertainty, and intention of navigational searches.

Most commonly used behavioral measures for testing learning and memory in the Morris water maze (MWM) involve comparisons of an animal's residence time in different quadrants of the pool. Such measures are limited in their ability to test different aspects of the animal's performance. Here, we describe novel measures of performance in the MWM that use vector fields to capture the motion of mice as well as their search pattern in the maze. Using these vector fields, we develop quantitative measures of performance that are intuitive and more sensitive than classical measures. First, we describe search patterns in terms of vector field properties and use these properties to define three metrics of spatial memory namely Spatial Accuracy, Uncertainty and, Intensity of Search. We demonstrate the usefulness of these measures using four different data sets including comparisons between different strains of mice, an analysis of two mouse models of Noonan syndrome (NS; Ptpn11 D61G and Ptpn11 N308D/+), and a study of goal reversal training. Importantly, besides highlighting novel aspects of performance in this widely used spatial task, our measures were able to uncover previously undetected differences, including in an animal model of NS, which we rescued with the mitogen activated protein kinase kinase (MEK) inhibitor SL327. Thus, our results show that our approach breaks down performance in the MWM into sensitive measurable independent components that highlight differences in spatial learning and memory in the MWM that were undetected by conventional measures.

Optimal multiguidance integration in insect navigation.

In the last decades, desert ants have become model organisms for the study of insect navigation. In finding their way, they use two major navigational routines: path integration using a celestial compass and landmark guidance based on sets of panoramic views of the terrestrial environment. It has been claimed that this information would enable the insect to acquire and use a centralized cognitive map of its foraging terrain. Here, we present a decentralized architecture, in which the concurrently operating path integration and landmark guidance routines contribute optimally to the directions to be steered, with "optimal" meaning maximizing the certainty (reliability) of the combined information. At any one time during its journey, the animal computes a path integration (global) vector and landmark guidance (local) vector, in which the length of each vector is proportional to the certainty of the individual estimates. Hence, these vectors represent the limited knowledge that the navigator has at any one place about the direction of the goal. The sum of the global and local vectors indicates the navigator's optimal directional estimate. Wherever applied, this decentralized model architecture is sufficient to simulate the results of quite a number of diverse cue-conflict experiments, which have recently been performed in various behavioral contexts by different authors in both desert ants and honeybees. They include even those experiments that have deliberately been designed by former authors to strengthen the evidence for a metric cognitive map in bees.

Spatial Memory in a Spiking Neural Network with Robot Embodiment.

Cognitive maps and spatial memory are fundamental paradigms of brain functioning. Here, we present a spiking neural network (SNN) capable of generating an internal representation of the external environment and implementing spatial memory. The SNN initially has a non-specific architecture, which is then shaped by Hebbian-type synaptic plasticity. The network receives stimuli at specific loci, while the memory retrieval operates as a functional SNN response in the form of population bursts. The SNN function is explored through its embodiment in a robot moving in an arena with safe and dangerous zones. We propose a measure of the global network memory using the synaptic vector field approach to validate results and calculate information characteristics, including learning curves. We show that after training, the SNN can effectively control the robot's cognitive behavior, allowing it to avoid dangerous regions in the arena. However, the learning is not perfect. The robot eventually visits dangerous areas. Such behavior, also observed in animals, enables relearning in time-evolving environments. If a dangerous zone moves into another place, the SNN remaps positive and negative areas, allowing escaping the catastrophic interference phenomenon known for some AI architectures. Thus, the robot adapts to changing world.

Road Extraction from High Resolution Remote Sensing Images Based on Vector Field Learning.

Accurate and up-to-date road network information is very important for the Geographic Information System (GIS) database, traffic management and planning, automatic vehicle navigation, emergency response and urban pollution sources investigation. In this paper, we use vector field learning to extract roads from high resolution remote sensing imaging. This method is usually used for skeleton extraction in nature image, but seldom used in road extraction. In order to improve the accuracy of road extraction, three vector fields are constructed and combined respectively with the normal road mask learning by a two-task network. The results show that all the vector fields are able to significantly improve the accuracy of road extraction, no matter the field is constructed in the road area or completely outside the road. The highest F1 score is 0.7618, increased by 0.053 compared with using only mask learning.

[Interpolation Algorithm for Motion Vector Field of CTA Image and Accelerated Implementation Based on Uniform Grid and Multi-level B-spline].

In order to solve the problems of slow operation speed and low registration accuracy of thin plate spline (TPS) interpolation method for motion vector field in coronary computed tomography angiography (CTA), a multi-level B-spline interpolation method (MBS) with uniform grid is proposed. On the one hand, the interpolation method used local B-spline to refine the sparse mesh layer by layer in a multiscale way to improve the accuracy of registration. On the other hand, it used the splitting matrix method to interpolate the motion vector field, greatly reducing the operation time of interpolation. The experimental results show that the proposed method can be used for CTA image registration efficiently.

Real-Time Massive Vector Field Data Processing in Edge Computing.

The spread of the sensors and industrial systems has fostered widespread real-time data processing applications. Massive vector field data (MVFD) are generated by vast distributed sensors and are characterized by high distribution, high velocity, and high volume. As a result, computing such kind of data on centralized cloud faces unprecedented challenges, especially on the processing delay due to the distance between the data source and the cloud. Taking advantages of data source proximity and vast distribution, edge computing is ideal for timely computing on MVFD. Therefore, we are motivated to propose an edge computing based MVFD processing framework. In particular, we notice that the high volume feature of MVFD results in high data transmission delay. To solve this problem, we invent Data Fluidization Schedule (DFS) in our framework to reduce the data block volume and the latency on Input/Output (I/O). We evaluated the efficiency of our framework in a practical application on massive wind field data processing for cyclone recognition. The high efficiency our framework was verified by the fact that it significantly outperformed classical big data processing frameworks Spark and MapReduce.

Polarization Control with Plasmonic Antenna Tips: A Universal Approach to Optical Nanocrystallography and Vector-Field Imaging.

Controlling the propagation and polarization vectors in linear and nonlinear optical spectroscopy enables us to probe the anisotropy of optical responses providing structural symmetry selective contrast in optical imaging. Here, we present a novel tilted antenna-tip approach to control the optical vector-field by breaking the axial symmetry of the nanoprobe in tip-enhanced near-field microscopy. This gives rise to a localized plasmonic antenna effect with significantly enhanced optical field vectors with control of both in-plane and out-of-plane components. We use the resulting vector-field specificity in the symmetry selective nonlinear optical response of second-harmonic generation (SHG) for a generalized approach to optical nanocrystallography and imaging. In tip-enhanced SHG imaging of monolayer MoS2 films and single-crystalline ferroelectric YMnO3, we reveal nanocrystallographic details of domain boundaries and domain topology with enhanced sensitivity and nanoscale spatial resolution. The approach is applicable to any anisotropic linear and nonlinear optical response and enables the optical nanocrystallographic imaging of molecular or quantum materials.

3D reconstruction of magnetization from dichroic soft X-ray transmission tomography.

The development of magnetic nanostructures for applications in spintronics requires methods capable of visualizing their magnetization. Soft X-ray magnetic imaging combined with circular magnetic dichroism allows nanostructures up to 100-300 nm in thickness to be probed with resolutions of 20-40 nm. Here a new iterative tomographic reconstruction method to extract the three-dimensional magnetization configuration from tomographic projections is presented. The vector field is reconstructed by using a modified algebraic reconstruction approach based on solving a set of linear equations in an iterative manner. The application of this method is illustrated with two examples (magnetic nano-disc and micro-square heterostructure) along with comparison of error in reconstructions, and convergence of the algorithm.

Adaptive Discrete Vector Field in Sensor Networks.

Homology groups are a prime tool for measuring the connectivity of a network, and their computation in a distributed and adaptive way is mandatory for their use in sensor networks. In this paper, we propose a solution based on the construction of an adaptive discrete vector field from where, thanks to the discrete Morse theory, the generators of the homology groups are extracted. The efficiency and the adaptability of our approach are tested against two applications: the detection and the localization of the holes in the coverage, and the selection of active sensors ensuring complete coverage.

Semi-automated myocardial segmentation of bright blood multi-gradient echo images improves reproducibility of myocardial contours and T2* determination.

OBJECTIVES: Early detection of iron loading is affected by the reproducibility of myocardial contour assessment. A novel semi-automatic myocardial segmentation method is presented on contrast-optimized composite images and compared to the results of manual drawing. MATERIALS AND METHODS: Fifty-one short-axis slices at basal, mid-ventricular and apical locations from 17 patients were acquired by bright blood multi-gradient echo MRI. Four observers produced semi-automatic and manual myocardial contours on contrast-optimized composite images. The semi-automatic segmentation method relies on vector field convolution active contours to generate the endocardial contour. After creating radial pixel clusters on the myocardial wall, a combination of pixel-wise coefficient of variance (CoV) assessment and k-means clustering establishes the epicardial contour for each segment. RESULTS: Compared to manual drawing, semi-automatic myocardial segmentation lowers the variability of T2* quantification within and between observers (CoV of 12.05 vs. 13.86% and 14.43 vs. 16.01%) by improving contour reproducibility (P < 0.001). In the presence of iron loading, semi-automatic segmentation also lowers the T2* variability within and between observers (CoV of 13.14 vs. 15.19% and 15.91 vs. 17.28%). CONCLUSION: Application of semi-automatic myocardial segmentation on contrast-optimized composite images improves the reproducibility of T2* quantification.

Accelerating 4D flow MRI by exploiting vector field divergence regularization.

PURPOSE: To improve velocity vector field reconstruction from undersampled four-dimensional (4D) flow MRI by penalizing divergence of the measured flow field. THEORY AND METHODS: Iterative image reconstruction in which magnitude and phase are regularized separately in alternating iterations was implemented. The approach allows incorporating prior knowledge of the flow field being imaged. In the present work, velocity data were regularized to reduce divergence, using either divergence-free wavelets (DFW) or a finite difference (FD) method using the ℓ1-norm of divergence and curl. The reconstruction methods were tested on a numerical phantom and in vivo data. Results of the DFW and FD approaches were compared with data obtained with standard compressed sensing (CS) reconstruction. RESULTS: Relative to standard CS, directional errors of vector fields and divergence were reduced by 55-60% and 38-48% for three- and six-fold undersampled data with the DFW and FD methods. Velocity vector displays of the numerical phantom and in vivo data were found to be improved upon DFW or FD reconstruction. CONCLUSION: Regularization of vector field divergence in image reconstruction from undersampled 4D flow data is a valuable approach to improve reconstruction accuracy of velocity vector fields.

Thermal Image Sensing Model for Robotic Planning and Search.

This work presents a search planning system for a rolling robot to find a source of infra-red (IR) radiation at an unknown location. Heat emissions are observed by a low-cost home-made IR passive visual sensor. The sensor capability for detection of radiation spectra was experimentally characterized. The sensor data were modeled by an exponential model to estimate the distance as a function of the IR image's intensity, and, a polynomial model to estimate temperature as a function of IR intensities. Both theoretical models are combined to deduce a subtle nonlinear exact solution via distance-temperature. A planning system obtains feed back from the IR camera (position, intensity, and temperature) to lead the robot to find the heat source. The planner is a system of nonlinear equations recursively solved by a Newton-based approach to estimate the IR-source in global coordinates. The planning system assists an autonomous navigation control in order to reach the goal and avoid collisions. Trigonometric partial differential equations were established to control the robot's course towards the heat emission. A sine function produces attractive accelerations toward the IR source. A cosine function produces repulsive accelerations against the obstacles observed by an RGB-D sensor. Simulations and real experiments of complex indoor are presented to illustrate the convenience and efficacy of the proposed approach.

Three-dimensional observation of magnetic vortex cores in stacked ferromagnetic discs.

Electron holographic vector field electron tomography visualized three-dimensional (3D) magnetic vortices in stacked ferromagnetic discs in a nanoscale pillar. A special holder with two sample rotation axes, both without missing wedges, was used to reduce artifacts in the reconstructed 3D magnetic vectors. A 1 MV holography electron microscope was used to precisely measure the magnetic phase shifts. Comparison of the observed 3D magnetic field vector distributions in the magnetic vortex cores with the results of micromagnetic simulations based on the Landau-Lifshitz-Gilbert equation showed that the proposed technique is well suited for direct 3D visualization of the spin configurations in magnetic materials and spintronics devices.

A novel vector field analysis for quantitative structure changes after macular epiretinal membrane surgery.

The aim of this study was to introduce novel vector field analysis for the quantitative measurement of retinal displacement after epiretinal membrane (ERM) removal. We developed a novel framework to measure retinal displacement from retinal fundus images as follows: (1) rigid registration of preoperative retinal fundus images in reference to postoperative retinal fundus images, (2) extraction of retinal vessel segmentation masks from these retinal fundus images, (3) non-rigid registration of preoperative vessel masks in reference to postoperative vessel masks, and (4) calculation of the transformation matrix required for non-rigid registration for each pixel. These pixel-wise vector field results were summarized according to predefined 24 sectors after standardization. We applied this framework to 20 patients who underwent ERM removal to obtain their retinal displacement vector fields between retinal fundus images taken preoperatively and at postoperative 1, 4, 10, and 22 months. The mean direction of displacement vectors was in the nasal direction. The mean standardized magnitudes of retinal displacement between preoperative and postoperative 1 month, postoperative 1 and 4, 4 and 10, and 10 and 22 months were 38.6, 14.9, 7.6, and 5.4, respectively. In conclusion, the proposed method provides a computerized, reproducible, and scalable way to analyze structural changes in the retina with a powerful visualization tool. Retinal structural changes were mostly concentrated in the early postoperative period and tended to move nasally.

Improved algorithm for generating evenly-spaced streamlines from an orientation field on a triangulated surface.

BACKGROUND: Vector fields such as cardiac fiber orientation can be visualized on a surface using streamlines. The application of evenly-spaced streamline generation to the construction of interconnected cable structure for cardiac propagation models has more stringent requirements imperfectly fulfilled by current algorithms. METHOD: We developed an open-source C++/python package for the placement of evenly-spaced streamlines on a triangulated surface. The new algorithm improves upon previous works by more accurately handling streamline extremities, U-turns and limit cycles, by providing stronger geometrical guarantees on inter-streamline minimal distance, particularly when a high density of streamlines (up to 10µm spacing) is desired, and by making a more efficient parallel implementation available. The approach requires finding intersections between geometrical capsules and triangles to update an occupancy mask defined on the triangles. This enables fast streamline integration from thousands of seed points to identify optimal streamline placement. RESULTS: The algorithm was assessed qualitatively on different left atrial models of fiber orientation with varying mesh resolutions (up to 375k triangles) and quantitatively by measuring streamline lengths and distribution of inter-streamline minimal distance. The complexity and the computational performance of the algorithm were studied as a function of streamline spacing in relation to triangular mesh resolution. CONCLUSION: More accurate geometrical computations, attention to details and fine-tuning led to an algorithm more amenable to applications that require precise positioning of streamlines.

Domain generalization for retinal vessel segmentation via Hessian-based vector field.

Blessed by vast amounts of data, learning-based methods have achieved remarkable performance in countless tasks in computer vision and medical image analysis. Although these deep models can simulate highly nonlinear mapping functions, they are not robust with regard to the domain shift of input data. This is a significant concern that impedes the large-scale deployment of deep models in medical images since they have inherent variation in data distribution due to the lack of imaging standardization. Therefore, researchers have explored many domain generalization (DG) methods to alleviate this problem. In this work, we introduce a Hessian-based vector field that can effectively model the tubular shape of vessels, which is an invariant feature for data across various distributions. The vector field serves as a good embedding feature to take advantage of the self-attention mechanism in a vision transformer. We design paralleled transformer blocks that stress the local features with different scales. Furthermore, we present a novel data augmentation method that introduces perturbations in image style while the vessel structure remains unchanged. In experiments conducted on public datasets of different modalities, we show that our model achieves superior generalizability compared with the existing algorithms. Our code and trained model are publicly available at https://github.com/MedICL-VU/Vector-Field-Transformer.