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The flight instability of an uncrewed aerial vehicle (UAV) can be considered critical, and investigations of stability can be compared to the study of the stabilization of an inverted pendulum. This study investigated the stability of two dynamic systems, represented by an inverted pendulum and a simple approximation of an aircraft wing surface exposed to aerodynamic forces. This study illustrates the advantages of time-domain simulation for solving the differential equation of motion. The simulation used the Euler integration approach for various system parameters. Essentially, an aircraft in flight must constantly maintain pitch stability, which, in practical considerations, can be compared to the mechanism of a rotary motion represented by the up-swinging motion of an inverted pendulum. The pendulum may conserve the same concept as an aircraft's acceleration, as both are affected by the same gravity and acceleration forces, in which the longitudinal stability of the aircraft must be ensured immediately upon takeoff. An inverted pendulum and a UAV aircraft system simulation were developed with basic MATLAB software. The inverted pendulum simulation showed that as the value of the spring's stiffness at the limit of stability (klim) increased, the system became more convergent and, as a result, more stable. The stiffness of the spring at the limit of stability, klim = 32.69 N m-1 (i.e., equivalent to an initial angular rotation θ = 5°), and the system's stability were observed up to the value of klim = 179.79 N m-1, which resulted in an unstable short initial period. In addition, for the aircraft's wing, the damping coefficient (clim) value was in the range of clim ≥ 10,000 N s m-1. Therefore, with the damping ratio ζ being equal to zero, the system vibrated consistently at its natural frequency (wn), never deviating drastically to become unstable. [ABSTRACT FROM AUTHOR]

Diffeomorphic deformable image registration is one of the crucial tasks in medical image analysis, which aims to find a unique transformation while preserving the topology and invertibility of the transformation. Deep convolutional neural networks (CNNs) have yielded well-suited approaches for image registration by learning the transformation priors from a large dataset. The improvement in the performance of these methods is related to their ability to learn information from several sample medical images that are difficult to obtain and bias the framework to the specific domain of data. In this paper, we propose a novel diffeomorphic training-free approach; this is built upon the principle of an ordinary differential equation. Our formulation yields an Euler integration type recursive scheme to estimate the changes of spatial transformations between the fixed and the moving image pyramids at different resolutions. The proposed architecture is simple in design. The moving image is warped successively at each resolution and finally aligned to the fixed image; this procedure is recursive in a way that at each resolution, a fully convolutional network (FCN) models a progressive change of deformation for the current warped image. The entire system is end-to-end and optimized for each pair of images from scratch. In comparison to learning-based methods, the proposed method neither requires a dedicated training set nor suffers from any training bias. We evaluate our method on three cardiac image datasets. The evaluation results demonstrate that the proposed method achieves state-of-the-art registration accuracy while maintaining desirable diffeomorphic properties. [ABSTRACT FROM AUTHOR]

This paper provides the theory of integration with respect to Euler characteristics of finite categories. As an application, we use sensors to enumerate the targets lying on a poset. This is a discrete analogue to Baryshnikov and Ghrist's work on integral theory using topological Euler characteristics. [ABSTRACT FROM AUTHOR]

Hedgehogs are (possibly singular and self-intersecting) hypersurfaces that describe Minkowski differences of convex bodies in $$\mathbb {R}^{n+1}$$ . They are the natural geometrical objects when one seeks to extend parts of the Brunn-Minkowski theory to a vector space which contains convex bodies. In terms of characteristic functions, Minkowski addition of convex bodies correspond to convolution with respect to the Euler characteristic. In this paper, we extend this relationship to hedgehogs with an analytic support function. In this context, resorting only to the support functions and the Euler characteristic, we give various expressions for the index of a point with respect to a hedgehog. [ABSTRACT FROM AUTHOR]