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We present Perm, a learned parametric model of human 3D hair designed to facilitate various hair-related applications. Unlike previous work that jointly models the global hair shape and local strand details, we propose to disentangle them using a PCA-based strand representation in the frequency domain, thereby allowing more precise editing and output control. Specifically, we leverage our strand representation to fit and decompose hair geometry textures into low- to high-frequency hair structures. These decomposed textures are later parameterized with different generative models, emulating common stages in the hair modeling process. We conduct extensive experiments to validate the architecture design of \textsc{Perm}, and finally deploy the trained model as a generic prior to solve task-agnostic problems, further showcasing its flexibility and superiority in tasks such as 3D hair parameterization, hairstyle interpolation, single-view hair reconstruction, and hair-conditioned image generation. Our code, data, and supplemental can be found at our project page: https://cs.yale.edu/homes/che/projects/perm/, Comment: Project page: https://cs.yale.edu/homes/che/projects/perm/

Vision-language contrastive learning frameworks like CLIP enable learning representations from natural language supervision, and provide strong zero-shot classification capabilities. However, due to the nature of the supervisory signal in these paradigms, they lack the ability to learn localized features, leading to degraded performance on dense prediction tasks like segmentation and detection. On the other hand, self-supervised learning methods have shown the ability to learn granular representations, complementing the high-level features in vision-language training. In this work, we present Harmony, a framework that combines vision-language training with discriminative and generative self-supervision to learn visual features that can be generalized across vision downstream tasks. Our framework is specifically designed to work on web-scraped data by not relying on negative examples and addressing the one-to-one correspondence issue using soft CLIP targets generated by an EMA model. We comprehensively evaluate Harmony across various vision downstream tasks and find that it significantly outperforms the baseline CLIP and the previously leading joint self and weakly-supervised methods, MaskCLIP and SLIP. Specifically, when comparing against these methods, Harmony shows superior performance in fine-tuning and zero-shot classification on ImageNet-1k, semantic segmentation on ADE20K, and both object detection and instance segmentation on MS-COCO, when pre-training a ViT-S/16 on CC3M. We also show that Harmony outperforms other self-supervised learning methods like iBOT and MAE across all tasks evaluated. On https://github.com/MohammedSB/Harmony our code is publicly available., Comment: 20 pages, 2 figures

We investigate the problem of recovering coefficients in scalar nonlinear ordinary differential equations that can be exactly linearized. This contribution builds upon prior work by Lyakhov, Gerdt, and Michels, which focused on obtaining a linearizability certificate through point transformations. Our focus is on quasi-linear equations, specifically those solved for the highest derivative with a rational dependence on the variables involved. Our novel algorithm for coefficient recovery relies on basic operations on Lie algebras, such as computing the derived algebra and the dimension of the symmetry algebra. This algorithmic approach is efficient, although finding the linearization transformation necessitates computing at least one solution of the corresponding Bluman-Kumei equation system., Comment: 8 pages

We introduce LAESI, a Synthetic Leaf Dataset of 100,000 synthetic leaf images on millimeter paper, each with semantic masks and surface area labels. This dataset provides a resource for leaf morphology analysis primarily aimed at beech and oak leaves. We evaluate the applicability of the dataset by training machine learning models for leaf surface area prediction and semantic segmentation, using real images for validation. Our validation shows that these models can be trained to predict leaf surface area with a relative error not greater than an average human annotator. LAESI also provides an efficient framework based on 3D procedural models and generative AI for the large-scale, controllable generation of data with potential further applications in agriculture and biology. We evaluate the inclusion of generative AI in our procedural data generation pipeline and show how data filtering based on annotation consistency results in datasets which allow training the highest performing vision models., Comment: 10 pages, 12 figures, 1 table

We present a specialized procedural model for generating synthetic agricultural scenes, focusing on soybean crops, along with various weeds. This model is capable of simulating distinct growth stages of these plants, diverse soil conditions, and randomized field arrangements under varying lighting conditions. The integration of real-world textures and environmental factors into the procedural generation process enhances the photorealism and applicability of the synthetic data. Our dataset includes 12,000 images with semantic labels, offering a comprehensive resource for computer vision tasks in precision agriculture, such as semantic segmentation for autonomous weed control. We validate our model's effectiveness by comparing the synthetic data against real agricultural images, demonstrating its potential to significantly augment training data for machine learning models in agriculture. This approach not only provides a cost-effective solution for generating high-quality, diverse data but also addresses specific needs in agricultural vision tasks that are not fully covered by general-purpose models., Comment: 10 pages, 8 figures, 3 tables

We introduce the Lennard-Jones layer (LJL) for the equalization of the density of 2D and 3D point clouds through systematically rearranging points without destroying their overall structure (distribution normalization). LJL simulates a dissipative process of repulsive and weakly attractive interactions between individual points by considering the nearest neighbor of each point at a given moment in time. This pushes the particles into a potential valley, reaching a well-defined stable configuration that approximates an equidistant sampling after the stabilization process. We apply LJLs to redistribute randomly generated point clouds into a randomized uniform distribution. Moreover, LJLs are embedded in the generation process of point cloud networks by adding them at later stages of the inference process. The improvements in 3D point cloud generation utilizing LJLs are evaluated qualitatively and quantitatively. Finally, we apply LJLs to improve the point distribution of a score-based 3D point cloud denoising network. In general, we demonstrate that LJLs are effective for distribution normalization which can be applied at negligible cost without retraining the given neural network., Comment: Upon request, we are happy to share the source code to generate the results presented in this paper. Please contact the first or the last author of this manuscript

Robotic harvesting has the potential to positively impact agricultural productivity, reduce costs, improve food quality, enhance sustainability, and to address labor shortage. In the rapidly advancing field of agricultural robotics, the necessity of training robots in a virtual environment has become essential. Generating training data to automatize the underlying computer vision tasks such as image segmentation, object detection and classification, also heavily relies on such virtual environments as synthetic data is often required to overcome the shortage and lack of variety of real data sets. However, physics engines commonly employed within the robotics community, such as ODE, Simbody, Bullet, and DART, primarily support motion and collision interaction of rigid bodies. This inherent limitation hinders experimentation and progress in handling non-rigid objects such as plants and crops. In this contribution, we present a plugin for the Gazebo simulation platform based on Cosserat rods to model plant motion. It enables the simulation of plants and their interaction with the environment. We demonstrate that, using our plugin, users can conduct harvesting simulations in Gazebo by simulating a robotic arm picking fruits and achieve results comparable to real-world experiments., Comment: Upon request, we are happy to share our GazeboPlants plugin open-source (MPL 2.0)

This paper belongs to a group of work in the intersection of symbolic computation and group analysis aiming for the symbolic analysis of differential equations. The goal is to extract important properties without finding the explicit general solution. In this contribution, we introduce the algorithmic verification of nonlinear superposition properties and its implementation. More exactly, for a system of nonlinear ordinary differential equations of first order with a polynomial right-hand side, we check if the differential system admits a general solution by means of a superposition rule and a certain number of particular solutions. It is based on the theory of Newton polytopes and associated symbolic computation. The developed method provides the basis for the identification of nonlinear superpositions within a given system and for the construction of numerical methods which preserve important algebraic properties at the numerical level.

Across various scientific and engineering domains, a growing interest in flexible and deployable structures is becoming evident. These structures facilitate seamless transitions between distinct states of shape and find broad applicability ranging from robotics and solar cells to meta-materials and architecture. In this contribution, we study a class of mechanisms known as Kokotsakis polyhedra with a quadrangular base. These are $3\times3$ quadrilateral meshes whose faces are rigid bodies and joined by hinges at the common edges. Compared to prior work, the quadrilateral faces do not have to be planar. In general, such meshes are not flexible, and the problem of finding and classifying the flexible ones is old, but until now largely unsolved. It appears that the tangent values of the dihedral angles between different faces are algebraically related through polynomials. Specifically, by fixing one angle as a parameter, the others can be parameterized algebraically and hence belong to an extended rational function field of the parameter. We use this approach to characterize shape restrictions resulting in flexible polyhedra.

Epigraphy increasingly turns to modern artificial intelligence (AI) technologies such as machine learning (ML) for extracting insights from ancient inscriptions. However, scarce labeled data for training ML algorithms severely limits current techniques, especially for ancient scripts like Old Aramaic. Our research pioneers an innovative methodology for generating synthetic training data tailored to Old Aramaic letters. Our pipeline synthesizes photo-realistic Aramaic letter datasets, incorporating textural features, lighting, damage, and augmentations to mimic real-world inscription diversity. Despite minimal real examples, we engineer a dataset of 250,000 training and 25,000 validation images covering the 22 letter classes in the Aramaic alphabet. This comprehensive corpus provides a robust volume of data for training a residual neural network (ResNet) to classify highly degraded Aramaic letters. The ResNet model demonstrates high accuracy in classifying real images from the 8th century BCE Hadad statue inscription. Additional experiments validate performance on varying materials and styles, proving effective generalization. Our results validate the model's capabilities in handling diverse real-world scenarios, proving the viability of our synthetic data approach and avoiding the dependence on scarce training data that has constrained epigraphic analysis. Our innovative framework elevates interpretation accuracy on damaged inscriptions, thus enhancing knowledge extraction from these historical resources., Comment: 41 pages, 19 images

Neural shape representation generally refers to representing 3D geometry using neural networks, e.g., computing a signed distance or occupancy value at a specific spatial position. In this paper we present a neural-network architecture suitable for accurate encoding of 3D shapes in a single forward pass. Our architecture is based on a multi-scale hybrid system incorporating graph-based and voxel-based components, as well as a continuously differentiable decoder. The hybrid system includes a novel way of voxelizing point-based features in neural networks, which we show can be used in combination with oriented point-clouds to obtain smoother and more detailed reconstructions. Furthermore, our network is trained to solve the eikonal equation and only requires knowledge of the zero-level set for training and inference. This means that in contrast to most previous shape encoder architectures, our network is able to output valid signed distance fields without explicit prior knowledge of non-zero distance values or shape occupancy. It also requires only a single forward-pass, instead of the latent-code optimization used in auto-decoder methods. We further propose a modification to the loss function in case that surface normals are not well defined, e.g., in the context of non-watertight surfaces and non-manifold geometry, resulting in an unsigned distance field. Overall, our system can help to reduce the computational overhead of training and evaluating neural distance fields, as well as enabling the application to difficult geometry.

In this paper, we introduce and study a remarkable class of mechanisms formed by a $3 \times 3$ arrangement of rigid quadrilateral faces with revolute joints at the common edges. In contrast to the well-studied Kokotsakis meshes with a quadrangular base, we do not assume the planarity of the quadrilateral faces. Our mechanisms are a generalization of Izmestiev's orthodiagonal involutive type of Kokotsakis meshes formed by planar quadrilateral faces. The importance of this Izmestiev class is undisputed as it represents the first known flexible discrete surface -- T-nets -- which has been constructed by Graf and Sauer. Our algebraic approach yields a complete characterization of all flexible $3 \times 3$ quad meshes of the orthodiagonal involutive type up to some degenerated cases. It is shown that one has a maximum of 8 degrees of freedom to construct such mechanisms. This is illustrated by several examples, including cases which could not be realized using planar faces. We demonstrate the practical realization of the proposed mechanisms by building a physical prototype using stainless steel. In contrast to plastic prototype fabrication, we avoid large tolerances and inherent flexibility., Comment: 26 pages, 13 figures. arXiv admin note: text overlap with arXiv:1411.0289 by other authors

We present RLSS: a reinforcement learning algorithm for sequential scene generation. This is based on employing the proximal policy optimization (PPO) algorithm for generative problems. In particular, we consider how to effectively reduce the action space by including a greedy search algorithm in the learning process. Our experiments demonstrate that our method converges for a relatively large number of actions and learns to generate scenes with predefined design objectives. This approach is placing objects iteratively in the virtual scene. In each step, the network chooses which objects to place and selects positions which result in maximal reward. A high reward is assigned if the last action resulted in desired properties whereas the violation of constraints is penalized. We demonstrate the capability of our method to generate plausible and diverse scenes efficiently by solving indoor planning problems and generating Angry Birds levels., Comment: Accepted at the IEEE Winter Conference on Applications of Computer Vision, WACV 2022

We determine all helical surfaces in three-dimensional Euclidean space which possess a constant ratio $a:=\kappa_1/\kappa_2$ of principal curvatures (CRPC surfaces), thus providing the first explicit CRPC surfaces beyond the known rotational ones. A key ingredient in the successful determination of these surfaces is the proper choice of generating profiles. We employ the contours for parallel projection orthogonal to the helical axis. This has the advantage that the CRPC property can be nicely expressed with the help of the involution of conjugate surface tangents. The arising ordinary differential equation has an explicit parametric solution, which forms the basis for a further study and classification of the possible shapes and the singularities arising for $a>0$., Comment: 18 pages with 7 figures

Design decisions in urban planning have to be made with particular carefulness as the resulting constraints are binding for the whole architectural design that follows. In this context, investigating and optimizing the airflow in urban environments is critical to design comfortable outdoor areas as unwanted effects such as windy areas and the formation of heat pockets have to be avoided. Our UrbanFlow framework enables interactive architectural design allowing for decision making based on simulating urban flow. Compared to real-time fluid flow simulation, enabling interactive architecture design poses an even higher computational efficiency challenge as evaluating a design by simulation usually requires hundreds of time steps. This is addressed based on a highly efficient Eulerian fluid simulator in which we incorporate a unified porosity model which is devised to encode digital urban models containing objects such as buildings and trees. UrbanFlow is equipped with an optimization routine enabling the direct computation of design adaptations improving livability and comfort for given parameterized architectural designs. To ensure convergence of the optimization process, instead of the classical Navier-Stokes equations, the Reynolds-averaged Navier-Stokes equations are solved as this can be done on a relatively coarse grid and allows for the decoupling of the effects of turbulent eddies which are taken into account using a separate turbulence model. As we demonstrate on a real-world example taken from an ongoing architectural competition, this results in a fast convergence of the optimization process which computes a design adaptation avoiding heat pockets as well as uncomfortable windy areas., Comment: 17 pages, 9 figures

The simulation of large open water surface is challenging using a uniform volumetric discretization of the Navier-Stokes equations. Simulating water splashes near moving objects, which height field methods for water waves cannot capture, necessitates high resolutions. Such simulations can be carried out using the Fluid-Implicit-Particle (FLIP) method. However, the FLIP method is not efficient for the long-lasting water waves that propagate to long distances, which require sufficient depth for a correct dispersion relationship. This paper presents a new method to tackle this dilemma through an efficient hybridization of volumetric and surface-based advection-projection discretizations. We design a hybrid time-stepping algorithm that combines a FLIP domain and an adaptively remeshed Boundary Element Method (BEM) domain for the incompressible Euler equations. The resulting framework captures the detailed water splashes near moving objects with the FLIP method, and produces convincing water waves with correct dispersion relationships at modest additional costs.

With the growing interest in deep learning algorithms and computational design in the architectural field, the need for large, accessible and diverse architectural datasets increases. We decided to tackle this problem by constructing a field-specific synthetic data generation pipeline that generates an arbitrary amount of 3D data along with the associated 2D and 3D annotations. The variety of annotations, the flexibility to customize the generated building and dataset parameters make this framework suitable for multiple deep learning tasks, including geometric deep learning that requires direct 3D supervision. Creating our building data generation pipeline we leveraged architectural knowledge from experts in order to construct a framework that would be modular, extendable and would provide a sufficient amount of class-balanced data samples. Moreover, we purposefully involve the researcher in the dataset customization allowing the introduction of additional building components, material textures, building classes, number and type of annotations as well as the number of views per 3D model sample. In this way, the framework would satisfy different research requirements and would be adaptable to a large variety of tasks. All code and data are made publicly available., Comment: Project Page: https://cdinstitute.github.io/Building-Dataset-Generator/

Unique and flexible properties of non-Hermitian photonic systems attract ever-increasing attention via delivering a whole bunch of novel optical effects and allowing for efficient tuning light-matter interactions on nano- and microscales. Together with an increasing demand for the fast and spatially compact methods of light governing, this peculiar approach paves a broad avenue to novel optical applications. Here, unifying the approaches of disordered metamaterials and non-Hermitian photonics, we propose a conceptually new and simple architecture driven by disordered loss-gain multilayers and, therefore, providing a powerful tool to control both the passage time and the wave-front shape of incident light with different switching times. For the first time we show the possibility to switch on and off kink formation by changing the level of disorder in the case of adiabatically raising wave fronts. At the same time, we deliver flexible tuning of the output intensity by using the nonlinear effect of loss and gain saturation. Since the disorder strength in our system can be conveniently controlled with the power of the external pump, our approach can be considered as a basis for different active photonic devices., Comment: 8 pages, 7 figures

We consider the inverse spectral theory of vibrating string equations. In this regard, first eigenvalue Ambarzumyan-type uniqueness theorems are stated and proved subject to separated, self-adjoint boundary conditions. More precisely, it is shown that there is a curve in the boundary parameters' domain on which no analog of it is possible. Necessary conditions of the $n$-th eigenvalue are identified, which allows to state the theorems. In addition, several properties of the first eigenvalue are examined. Lower and upper bounds are identified, and the areas are described in the boundary parameters' domain on which the sign of the first eigenvalue remains unchanged. This paper contributes to inverse spectral theory as well as to direct spectral theory., Comment: 16

We present a novel domain adaptation framework that uses morphologic segmentation to translate images from arbitrary input domains (real and synthetic) into a uniform output domain. Our framework is based on an established image-to-image translation pipeline that allows us to first transform the input image into a generalized representation that encodes morphology and semantics - the edge-plus-segmentation map (EPS) - which is then transformed into an output domain. Images transformed into the output domain are photo-realistic and free of artifacts that are commonly present across different real (e.g. lens flare, motion blur, etc.) and synthetic (e.g. unrealistic textures, simplified geometry, etc.) data sets. Our goal is to establish a preprocessing step that unifies data from multiple sources into a common representation that facilitates training downstream tasks in computer vision. This way, neural networks for existing tasks can be trained on a larger variety of training data, while they are also less affected by overfitting to specific data sets. We showcase the effectiveness of our approach by qualitatively and quantitatively evaluating our method on four data sets of simulated and real data of urban scenes. Additional results can be found on the project website available at http://jonathank.de/research/eps/ ., Comment: This work has been supported by KAUST under individual baseline funding

Iterative solvers are widely used to accurately simulate physical systems. These solvers require initial guesses to generate a sequence of improving approximate solutions. In this contribution, we introduce a novel method to accelerate iterative solvers for physical systems with graph networks (GNs) by predicting the initial guesses to reduce the number of iterations. Unlike existing methods that aim to learn physical systems in an end-to-end manner, our approach guarantees long-term stability and therefore leads to more accurate solutions. Furthermore, our method improves the run time performance of traditional iterative solvers. To explore our method we make use of position-based dynamics (PBD) as a common solver for physical systems and evaluate it by simulating the dynamics of elastic rods. Our approach is able to generalize across different initial conditions, discretizations, and realistic material properties. Finally, we demonstrate that our method also performs well when taking discontinuous effects into account such as collisions between individual rods. Finally, to illustrate the scalability of our approach, we simulate complex 3D tree models composed of over a thousand individual branch segments swaying in wind fields. A video showing dynamic results of our graph learning assisted simulations of elastic rods can be found on the project website available at http://computationalsciences.org/publications/shao-2021-physical-systems-graph-learning.html ., Comment: This work has been supported by KAUST under individual baseline and center partnership funding

$\mathcal{PT}$ symmetry is a unique platform for light manipulation and versatile use in unidirectional invisibility, lasing, sensing, etc. Broken and unbroken $\mathcal{PT}$-symmetric states in non-Hermitian open systems are described by scattering matrices. A multilayer structure, as a simplest example of the open system, has no certain definition of the scattering matrix, since the output ports can be permuted. The uncertainty in definition of the exceptional points bordering $\mathcal{PT}$-symmetric and $\mathcal{PT}$-symmetry-broken states poses an important problem, because the exceptional points are indispensable in applications as sensing and mode discrimination. Here we derive the proper scattering matrix from the unambiguous relation between the $\mathcal{PT}$-symmetric Hamiltonian and scattering matrix. We reveal that the exceptional points of the scattering matrix with permuted output ports are not related to the $\mathcal{PT}$ symmetry breaking. Nevertheless, they can be employed for finding a lasing onset as demonstrated in our time-domain calculations and scattering-matrix pole analysis. Our results are important for various applications of the non-Hermitian systems including encircling exceptional points, coherent perfect absorption, $\mathcal{PT}$-symmetric plasmonics, etc., Comment: 7 pages, 5 figures

Autonomous UAV racing has recently emerged as an interesting research problem. The dream is to beat humans in this new fast-paced sport. A common approach is to learn an end-to-end policy that directly predicts controls from raw images by imitating an expert. However, such a policy is limited by the expert it imitates and scaling to other environments and vehicle dynamics is difficult. One approach to overcome the drawbacks of an end-to-end policy is to train a network only on the perception task and handle control with a PID or MPC controller. However, a single controller must be extensively tuned and cannot usually cover the whole state space. In this paper, we propose learning an optimized controller using a DNN that fuses multiple controllers. The network learns a robust controller with online trajectory filtering, which suppresses noisy trajectories and imperfections of individual controllers. The result is a network that is able to learn a good fusion of filtered trajectories from different controllers leading to significant improvements in overall performance. We compare our trained network to controllers it has learned from, end-to-end baselines and human pilots in a realistic simulation; our network beats all baselines in extensive experiments and approaches the performance of a professional human pilot. A video summarizing this work is available at https://youtu.be/hGKlE5X9Z5U, Comment: Accepted at CVPRW'19: UAVision 2019. First two authors contributed equally. Based on the initial work of arXiv:1803.01129 which was eventually split into two separate projects

We construct and analyze a strongly consistent second-order finite difference scheme for the steady two-dimensional Stokes flow. The pressure Poisson equation is explicitly incorporated into the scheme. Our approach suggested by the first two authors is based on a combination of the finite volume method, difference elimination, and numerical integration. We make use of the techniques of the differential and difference Janet/Groebner bases. In order to prove strong consistency of the generated scheme we correlate the differential ideal generated by the polynomials in the Stokes equations with the difference ideal generated by the polynomials in the constructed difference scheme. Additionally, we compute the modified differential system of the obtained scheme and analyze the scheme's accuracy and strong consistency by considering this system. An evaluation of our scheme against the established marker-and-cell method is carried out., Comment: 15 pages

We introduce a class of explicit exponential Rosenbrock methods for the time integration of large systems of stiff differential equations. Their application with respect to simulation tasks in the field of visual computing is discussed where these time integrators have shown to be very competitive compared to standard techniques. In particular, we address the simulation of elastic and nonelastic deformations as well as collision scenarios focusing on relevant aspects like stability and energy conservation, large stiffnesses, high fidelity and visual accuracy., Comment: 18 pages

Recent work has explored the problem of autonomous navigation by imitating a teacher and learning an end-to-end policy, which directly predicts controls from raw images. However, these approaches tend to be sensitive to mistakes by the teacher and do not scale well to other environments or vehicles. To this end, we propose Observational Imitation Learning (OIL), a novel imitation learning variant that supports online training and automatic selection of optimal behavior by observing multiple imperfect teachers. We apply our proposed methodology to the challenging problems of autonomous driving and UAV racing. For both tasks, we utilize the Sim4CV simulator that enables the generation of large amounts of synthetic training data and also allows for online learning and evaluation. We train a perception network to predict waypoints from raw image data and use OIL to train another network to predict controls from these waypoints. Extensive experiments demonstrate that our trained network outperforms its teachers, conventional imitation learning (IL) and reinforcement learning (RL) baselines and even humans in simulation. The project website is available at https://sites.google.com/kaust.edu.sa/oil/ and a video at https://youtu.be/_rhq8a0qgeg, Comment: Accepted at RSS'19. First two authors contributed equally

Automating the navigation of unmanned aerial vehicles (UAVs) in diverse scenarios has gained much attention in recent years. However, teaching UAVs to fly in challenging environments remains an unsolved problem, mainly due to the lack of training data. In this paper, we train a deep neural network to predict UAV controls from raw image data for the task of autonomous UAV racing in a photo-realistic simulation. Training is done through imitation learning with data augmentation to allow for the correction of navigation mistakes. Extensive experiments demonstrate that our trained network (when sufficient data augmentation is used) outperforms state-of-the-art methods and flies more consistently than many human pilots. Additionally, we show that our optimized network architecture can run in real-time on embedded hardware, allowing for efficient on-board processing critical for real-world deployment. From a broader perspective, our results underline the importance of extensive data augmentation techniques to improve robustness in end-to-end learning setups., Comment: Accepted at ECCVW'18

We devise a symbolic-numeric approach to the integration of the dynamical part of the Cosserat equations, a system of nonlinear partial differential equations describing the mechanical behavior of slender structures, like fibers and rods. This is based on our previous results on the construction of a closed form general solution to the kinematic part of the Cosserat system. Our approach combines methods of numerical exponential integration and symbolic integration of the intermediate system of nonlinear ordinary differential equations describing the dynamics of one of the arbitrary vector-functions in the general solution of the kinematic part in terms of the module of the twist vector-function. We present an experimental comparison with the well-established generalized alpha-method illustrating the computational efficiency of our approach for problems in structural mechanics., Comment: 12 pages, 2 figures. arXiv admin note: text overlap with arXiv:1610.03369

For a nonlinear ordinary differential equation solved with respect to the highest order derivative and rational in the other derivatives and in the independent variable, we devise two algorithms to check if the equation can be reduced to a linear one by a point transformation of the dependent and independent variables. The first algorithm is based on a construction of the Lie point symmetry algebra and on the computation of its derived algebra. The second algorithm exploits the differential Thomas decomposition and allows not only to test the linearizability, but also to generate a system of nonlinear partial differential equations that determines the point transformation and the coefficients of the linearized equation. Both algorithms have been implemented in Maple and their application is illustrated using several examples., Comment: 8 pages

Based on a Lie symmetry analysis, we construct a closed form solution to the kinematic part of the (partial differential) Cosserat equations describing the mechanical behavior of elastic rods. The solution depends on two arbitrary analytical vector functions and is analytical everywhere except a certain domain of the independent variables in which one of the arbitrary vector functions satisfies a simple explicitly given algebraic relation. As our main theoretical result, in addition to the construction of the solution, we proof its generality. Based on this observation, a hybrid semi-analytical solver for highly viscous two-way coupled fluid-rod problems is developed which allows for the interactive high-fidelity simulations of flagellated microswimmers as a result of a substantial reduction of the numerical stiffness., Comment: 14 pages, 3 figures

We analyze the performance of decoders for the 2D and 4D toric code which are local by construction. The 2D decoder is a cellular automaton decoder formulated by Harrington which explicitly has a finite speed of communication and computation. For a model of independent $X$ and $Z$ errors and faulty syndrome measurements with identical probability we report a threshold of $0.133\%$ for this Harrington decoder. We implement a decoder for the 4D toric code which is based on a decoder by Hastings arXiv:1312.2546 . Incorporating a method for handling faulty syndromes we estimate a threshold of $1.59\%$ for the same noise model as in the 2D case. We compare the performance of this decoder with a decoder based on a 4D version of Toom's cellular automaton rule as well as the decoding method suggested by Dennis et al. arXiv:quant-ph/0110143 ., Comment: 22 pages, 21 figures; fixed typos, updated Figures 6,7,8,9

We derive a combined analytical and numerical scheme to solve the (1+1)-dimensional differential Kirchhoff system. Here the object is to obtain an accurate as well as an efficient solution process. Purely numerical algorithms typically have the disadvantage that the quality of solutions decreases enormously with increasing temporal step sizes, which results from the numerical stiffness of the underlying partial differential equations. To prevent that, we apply a differential Thomas decomposition and a Lie symmetry analysis to derive explicit analytical solutions to specific parts of the Kirchhoff system. These solutions are general and depend on arbitrary functions, which we set up according to the numerical solution of the remaining parts. In contrast to a purely numerical handling, this reduces the numerical solution space and prevents the system from becoming unstable. The differential Kirchhoff equation describes the dynamic equilibrium of one-dimensional continua, i.e. slender structures like fibers. We evaluate the advantage of our method by simulating a cilia carpet., Comment: 13 Pages, 1 Figure