A fourth order symplectic and conjugate-symplectic extension of the midpoint and trapezoidal methods

The paper presents fourth order Runge–Kutta methods derived from symmetric Hermite– Obreshkov schemes by suitably approximating the involved higher derivatives. In particular, starting from the multi-derivative extension of the midpoint method we have obtained a new symmetric implicit Runge–Kutta method of order four, for the numerical solution of first-order differential equations. The new method is symplectic and is suitable for the solution of both initial and bound-ary value Hamiltonian problems. Moreover, starting from the conjugate class of multi-derivative trapezoidal schemes, we have derived a new method that is conjugate to the new symplectic method

Bvps codes for solving optimal control problems

Optimal control problems arise in many applications and need suitable numerical methods to obtain a solution. The indirect methods are an interesting class of methods based on the Pontrya-gin’s minimum principle that generates Hamiltonian Boundary Value Problems (BVPs). In this paper, we review some general-purpose codes for the solution of BVPs and we show their efficiency in solving some challenging optimal control problems

Numerical methods for second order singular pertubation problems

AbstractBy using sufficient conditions which ensure the well conditioning of tridiagonal matrices, we derive numerical methods for second order singular pertubations boundary values problems. Under hypotheses similar to the ones usually used in the continuous theory, methods are derived which use constant step sizes h≈O(ϵ12). In the more general case methods with variable step sizes, are defined which solve the problem with n(⪡ϵ−1) steps. Examples on standard test problems are shown

A minimum-time obstacle-avoidance path planning algorithm for unmanned aerial vehicles

In this article, we present a new strategy to determine an unmanned aerial vehicle trajectory that minimizes its flight time in presence of avoidance areas and obstacles. The method combines classical results from optimal control theory, i.e. the Euler-Lagrange Theorem and the Pontryagin Minimum Principle, with a continuation technique that dynamically adapts the solution curve to the presence of obstacles. We initially consider the two-dimensional path planning problem and then move to the three-dimensional one, and include numerical illustrations for both cases to show the efficiency of our approach

On the use of the Infinity Computer architecture to set up a dynamic precision floating-point arithmetic

We devise a variable precision floating-point arithmetic by exploiting the framework provided by the Infinity Computer. This is a computational platform implementing the Infinity Arithmetic system, a positional numeral system which can handle both infinite and infinitesimal quantities expressed using the positive and negative finite or infinite powers of the radix 1. The computational features offered by the Infinity Computer allow us to dynamically change the accuracy of representation and floating-point operations during the flow of a computation. When suitably implemented, this possibility turns out to be particularly advantageous when solving ill-conditioned problems. In fact, compared with a standard multi-precision arithmetic, here the accuracy is improved only when needed, thus not affecting that much the overall computational effort. An illustrative example about the solution of a nonlinear equation is also presented

Splines Parameterization of Planar Domains by Physics-Informed Neural Networks

The generation of structured grids on bounded domains is a crucial issue in the development of numerical models for solving differential problems. In particular, the representation of the given computational domain through a regular parameterization allows us to define a univalent mapping, which can be computed as the solution of an elliptic problem, equipped with suitable Dirichlet boundary conditions. In recent years, Physics-Informed Neural Networks (PINNs) have been proved to be a powerful tool to compute the solution of Partial Differential Equations (PDEs) replacing standard numerical models, based on Finite Element Methods and Finite Differences, with deep neural networks; PINNs can be used for predicting the values on simulation grids of different resolutions without the need to be retrained. In this work, we exploit the PINN model in order to solve the PDE associated to the differential problem of the parameterization on both convex and non-convex planar domains, for which the describing PDE is known. The final continuous model is then provided by applying a Hermite type quasi-interpolation operator, which can guarantee the desired smoothness of the sought parameterization. Finally, some numerical examples are presented, which show that the PINNs-based approach is robust. Indeed, the produced mapping does not exhibit folding or self-intersection at the interior of the domain and, also, for highly non convex shapes, despite few faulty points near the boundaries, has better shape-measures, e.g., lower values of the Winslow functional

Leveraging colour-based pseudo-labels to supervise saliency detection in hyperspectral image datasets

Saliency detection mimics the natural visual attention mechanism that identifies an imagery region to be salient when it attracts visual attention more than the background. This image analysis task covers many important applications in several fields such as military science, ocean research, resources exploration, disaster and land-use monitoring tasks. Despite hundreds of models have been proposed for saliency detection in colour images, there is still a large room for improving saliency detection performances in hyperspectral imaging analysis. In the present study, an ensemble learning methodology for saliency detection in hyperspectral imagery datasets is presented. It enhances saliency assignments yielded through a robust colour-based technique with new saliency information extracted by taking advantage of the abundance of spectral information on multiple hyperspectral images. The experiments performed with the proposed methodology provide encouraging results, also compared to several competitors

Towards the edge intelligence: Robot assistant for the detection and classification of human emotions

[EN] Deep learning is being introduced more and more in our society. Nowadays, there are very few applications that do not use deep learning as a classification tool. One of the main application areas is focused on improving people¿s life quality, allowing to create personal assistants with canned benefits. More recently, with the proliferation of mobile computing and the emergence of the Internet of Things (IoT), billions of mobile and IoT devices are connected to the Internet. This allows the generation of millions of bytes of information about sensors, images, sounds, etc. Driven by this trend, there is an urgent need to push the IoT frontiers to the edge of the network, in order to decrease this massive sending of information to large exchanges for analysis. As a result of this trend, a new discipline has emerged: edge intelligence or edge AI, a widely recognised and promising solution that attracts with special interest to the community of researchers in artificial intelligence. We adapted edge AI to classify human emotions. Results show how edge AI-based emotion classification can greatly benefit in the field of cognitive assistants for the elderly or people living alone.This work was partly supported by the Generalitat Valenciana (PROMETEO/2018/002) and by the Spanish Government (RTI2018-095390-B-C31). Universitat Politecnica de Valencia Research Grant PAID-10-19.Rincón Arango, JA.; Julian Inglada, VJ.; Carrascosa Casamayor, C. (2020). Towards the edge intelligence: Robot assistant for the detection and classification of human emotions. Springer. 31-41. https://doi.org/10.1007/978-3-030-51999-5_3S3141Chang, A.: The role of artificial intelligence in digital health. In: Wulfovich, S., Meyers, A. (eds.) Digital Health Entrepreneurship. HI, pp. 71–81. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-12719-0_7Yang, L., Henthorne, T.L., George, B.: Artificial intelligence and robotics technology in the hospitality industry: current applications and future trends. In: George, B., Paul, J. (eds.) Digital Transformation in Business and Society, pp. 211–228. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-08277-2_13Khayyam, H., Javadi, B., Jalili, M., Jazar, R.N.: Artificial intelligence and Internet of Things for autonomous vehicles. In: Jazar, R.N., Dai, L. (eds.) Nonlinear Approaches in Engineering Applications, pp. 39–68. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-18963-1_2Liang, F., Yu, W., Liu, X., Griffith, D., Golmie, N.: Towards edge-based deep learning in industrial Internet of Things. IEEE Internet of Things J. 7, 4329–4341 (2020)Nagaraju, P.B., Oliner, A.J., Gilmore, B.M., Dean, E.A., Wang, J.: Data analytics in edge devices. US Patent App. 16/573,745, 9 January 2020Eskandari, M., Janjua, Z.H., Vecchio, M., Antonelli, F.: Passban IDS: an intelligent anomaly based intrusion detection system for IoT edge devices. IEEE Internet of Things J. (2020)Harish, A., Jhawar, S., Anisha, B.S., Ramakanth Kumar, P.: Implementing machine learning on edge devices with limited working memory. In: Ranganathan, G., Chen, J., Rocha, Á. (eds.) Inventive Communication and Computational Technologies. LNNS, vol. 89, pp. 1255–1261. Springer, Singapore (2020). https://doi.org/10.1007/978-981-15-0146-3_123Rincon, J.A., Martin, A., Costa, Â., Novais, P., Julián, V., Carrascosa, C.: EmIR: an emotional intelligent robot assistant. In: AfCAI (2018)Ke, R., Zhuang, Y., Pu, Z., Wang, Y.: A smart, efficient, and reliable parking surveillance system with edge artificial intelligence on IoT devices. arXiv preprint arXiv:2001.00269 (2020)Mazzia, V., Khaliq, A., Salvetti, F., Chiaberge, M.: Real-time apple detection system using embedded systems with hardware accelerators: an edge AI application. IEEE Access 8, 9102–9114 (2020)Chollet, F., et al.: Keras (2015). https://github.com/fchollet/kerasHoward, A.G., et al.: MobileNets: efficient convolutional neural networks for mobile vision applications. arXiv preprint arXiv:1704.04861 (2017

Novel Reconstruction Errors for Saliency Detection in Hyperspectral Images

When hyperspectral images are analyzed, a big amount of data, representing the reflectance at hundreds of wavelengths, needs to be processed. Hence, dimensionality reduction techniques are used to discard unnecessary information. In order to detect the so called “saliency”, i.e., the relevant pixels, we propose a bottom-up approach based on three main ingredients: sparse non negative matrix factorization (SNMF), spatial and spectral functions to measure the reconstruction error between the input image and the reconstructed one and a final clustering technique. We introduce novel error functions and show some useful mathematical properties. The method is validated on hyperspectral images and compared with state-of-the-art different approaches