Symmetry

We present two new models for dynamic beams deduced from three dimensional theory of linear elasticity. The first model is deduced from virtual work considered for small beam sections. For the second model, we suppose a Taylor-Young expansion of the displacement field up to the fourth order in transverse dimensions of the beam. We consider the Fourier series expansion for considering Neumann lateral boundary conditions together with dynamical equations, we obtain a system of fifteen vector equations with the fifteen coefficients vector unknown of the displacement field. For beams with two fold symmetric cross sections commonly used (for example circular, square, rectangular, elliptical…), a unique decomposition of any three-dimensional loads is proposed and the symmetries of these loads is introduced. For these two theories, we show that the initial problem decouples into four subproblems. For an orthotropic material, these four subproblems are completely independent. For a monoclinic material, two subproblems are coupled and independent of the two other coupled subproblems. For the first model, we also give the detailed expression of these four subproblems when we consider the approximation of the displacement field used in the second model. Full article

The feasibility of prediction of same-limb kinematics using a single inertial measurement unit attached to the same limb has been demonstrated using machine learning. This study was performed to see if a single inertial measurement unit attached to the tibia can predict the opposite leg’s kinematics (cross-leg prediction). It also investigated if there is a minimal or smaller data set in a convolutional neural network model to predict lower extremity running kinematics under other running conditions and with what accuracy for the intra- and inter-participant situations. Ten recreational runners completed running exercises under five conditions, including treadmill running at speeds of 2, 2.5, 3, and 3.5 m/s and level-ground running at their preferred speed. A one-predict-all scheme was adopted to determine which running condition could be used to best predict a participant’s overall running kinematics. Running kinematic predictions were performed for intra- and inter-participant scenarios. Among the tested running conditions, treadmill running at 3 m/s was found to be the optimal condition for accurately predicting running kinematics under other conditions, with R² values ranging from 0.880 to 0.958 and 0.784 to 0.936 for intra- and inter-participant scenarios, respectively. The feasibility of cross-leg prediction was demonstrated but with significantly lower accuracy than the same leg. The treadmill running condition at 3 m/s showed the highest intra-participant cross-leg prediction accuracy. This study proposes a novel, deep-learning method for predicting running kinematics under different conditions on a small training data set. Full article

In this paper, we develop an efficient spectral method for numerically solving the nonlinear Volterra integral equation with weak singularity and delays. Based on the symmetric collocation points, the spectral method is illustrated, and the convergence results are obtained. In the end, two numerical experiments are carried out to confirm the theoretical results. Full article

We consider a function $g\left(r,x,u\right)$ with $x,u\in ℂ$ and $r\in \mathbb{N}$, which, over a symmetric domain, equals the sum of an infinite series as noted in the 16th Entry of Chapter 3 in Ramanujan’s second notebook. The function attracted new attention since it was established to be closely connected to the theory of labelled trees. However, to the best of our knowledge, a closed-form solution allowing, e.g., the rapid computation of $g\left(r,x,u\right)$ in Mathematica without explicit use of recursions has been lacking until now. Our proposed formula transforms the part depending on the variable $u$ into a more symmetric form, which then appears inside a finite triple sum consisting of binomials and Stirling numbers of the second kind. Full article

Recently we started the development of Dendrographic Hologram Theory (DH-theory). It is based on the novel mathematical representation of the relational event universe (in the spirit of Smolin et al.). Elementary events are represented by branches of dendrograms, finite trees that are generated from data with clustering algorithms. In this context, we studied the dynamics of the event universe generated by the appearance of a new event. Generally, each new event can generate the complete reconstruction of the whole dendrogramic universe. However, we found (via numerical simulation) unexpected stability in this universe. Its events are coupled via the hierarchic relational structure, which is relatively stable even with respect to the random generation of new events. We also observed the regularity patterns in the location of new events on dendrograms. In the course of evolution, the dendrogram’s complexity increases and determines the arrow of time in the event universe. We used the complexity measure from particle shape dynamics, which was shown to increase in both directions away from a Janus point and thus determine the arrow of time in symmetrical manner away from a Janus point. The particle shape dynamics theory is a relational theory with close ideological resemblance to DH-theory, as both rely on Mach’s principle and Leibniz’s relationalism and principles. By using the complexity measure on dendrograms and its p-adic string representation, we demonstrate the emergence of a time arrow from the p-adic zero-dimensional field, where space and time are absent. Full article

The single-core alternating current (AC) submarine cable can be provided with an outer sheath that is firmly grounded on both ends of the cable. The circulating currents of the outer sheath are generated to be almost as large as the conductor current. The outer sheaths, which have different structures and properties, generate unwanted losses, asymmetric distribution of circulating current, and extra heat in the single-core AC submarine cables. The formation mechanism of the circulating currents in the submarine cable sheath and armoring is analyzed from the perspective of electromagnetic shielding using electromagnetic transient theoretical analysis, simulation calculation, and field experiments. Equations for calculating the circulating currents of the sheath and armoring are proposed, and influences of these relationships that include the different material characteristics of the sheath and armoring are analyzed. The influence factors, which include different levels of magnetic armoring permeability, resistivity, and ground resistance of the outer sheath, can affect the symmetrical distribution of the circulating current in the outer sheaths. We propose using the phase differences to determine the material properties of each metallic section in the submarine cable. Full article

In this paper we consider the ChaCha20 stream cipher in the related-key scenario and we study how to obtain rotational-XOR pairs with nonzero probability after the application of the first quarter round. The ChaCha20 input can be viewed as a $4\times 4$ matrix of 32-bit words, where the first row of the matrix is fixed to a constant value, the second two rows represent the key, and the fourth some initialization values. Under some reasonable independence assumptions and a suitable selection of the input, we show that the aforementioned probability is about $2^{-251.7857}$, a value greater than $2^{-256}$, which is the one expected from a random permutation. We also investigate the existence of constants, different from the ones used in the first row of the ChaCha20 input, for which the rotational-XOR probability increases, representing a potential weakness in variants of the ChaCha20 stream cipher. So far, to our knowledge, this is the first analysis of the ChaCha20 stream cipher from a rotational-XOR perspective. Full article

In the present work, we examine the following points in the context of curvature coupling helical magnetogenesis scenario where the electromagnetic field couples with the background Ricci scalar as well as with the background Gauss-Bonnet cuvature term: (1) whether the model is consistent with the predictions of perturbative quantum field theory (QFT) and (2) whether the curvature perturbation induced by the generated electromagnetic (EM) field during inflation is consistent with the Planck data. Such requirements are well motivated in order to argue for the viability of the magnetogenesis model under consideration. In fact, our recently proposed helical magnetogenesis scenario seems to predict sufficient magnetic strength over large scales and also leads to the correct baryon asymmetry of the universe for a suitable range of the model parameter. However in the realm of inflationary magnetogenesis, these requirements are not enough to argue for the viability of the model; in particular, one needs to examine some more important requirements in this regard. We may recall that the calculations generally used to determine the magnetic field’s power spectrum are based on the perturbative QFT; therefore, it is important to examine whether the predictions of such perturbative QFT are consistent with the observational bounds of the model parameter. On other hand, the generated gauge field acts as a source of the curvature perturbation which needs to be suppressed compared to that contributed from the inflaton field in order to be consistent with the Planck observation. For the perturbative requirement, we examine whether the condition $\left|\frac{S_{CB}}{S_{can}}\right|<1$ is satisfied, where $S_{CB}$ and $S_{can}$ are the non-minimal and the canonical action of the EM field, respectively. Moreover, we determine the power spectrum of the curvature perturbation sourced by the EM field during inflation and evaluate necessary constraints in order to be consistent with the Planck data. Interestingly, both the aforementioned requirements in the context of the curvature coupling helical magnetogenesis scenario are found to be simultaneously satisfied by that range of the model parameter which leads to the correct magnetic strength over the large scale modes. Full article

A hybrid energy-storage system (HESS), which fully utilizes the durability of energy-oriented storage devices and the rapidity of power-oriented storage devices, is an efficient solution to managing energy and power legitimately and symmetrically. Hence, research into these systems is drawing more attention with substantial findings. A battery–supercapacitor hybrid energy-storage system (BS-HESS) is widely adopted in the fields of renewable energy integration, smart- and micro-grids, energy integration systems, etc. Focusing on the BS-HESS, in this work we present a comprehensive survey including technologies of the battery management system (BMS), power conversion system (PCS), energy management system (EMS), predictive control techniques of the underlying system, application and cost-effective feasibility aspects, etc. This work reflects strong symmetry on different aspects of designing an HESS, and provides guidelines and design references for the research and application of an HESS. Full article

In this paper, we reconstruct the dynamic behavior of the ring-coupled Lorenz oscillators system by reservoir computing. Although the reconstruction of various complex chaotic attractors has been well studied by using various neural networks, little attention has been paid to whether the spatio-temporal structure of some special attractors can be maintained in long-term prediction. Reservoir computing has been shown to be effective for model-free prediction, so we want to investigate whether reservoir computing can restore the rotational symmetry of the original ring-coupled Lorenz system. We find that although the state prediction of the trained reservoir computer will gradually deviate from the actual trajectory of the original system, the associated spatio-temporal structure is maintained in the process of reconstruction. Specifically, we show that the rotational symmetric structure of periodic rotating waves, quasi-periodic torus, and chaotic rotating waves is well maintained. Full article

The non-axisymmetric problem of frictionless contact between an isotropic elastic half-space and a cylindrical punch with an arbitrarily shaped base is considered. The contact problem is formulated as a two-dimensional Fredholm integral equation of the first type in a fixed circular domain with the right-hand side being representable in the form of a Fourier series. A number of general solutions of the contact problem, which were published in the literature, are discussed. Based on the Galin–Mossakovskii general solution, new formulas are derived for the particular value of the contact pressure at the contact center and the contact stress-intensity factor at the contour of the contact area. Since the named general solution does not employ the operation of differentiation of a double integral with respect to the coordinates that enter it as parameters, the form of the general solution derived by Mossakovskii as a generalization of Galin’s solution for the special case, when the contact pressure beneath the indenter is bounded, is recommended for use as the most simple closed-form general solution of the non-axisymmetric Boussinesq contact problem. Full article

The marine economy has become a new growth point of the national economy, and many countries have started to implement the marine ranch project and made the project a new strategic industry to support vigorously. In fact, with the continuous improvement of people’s living standards, the market demand for precious seafood such as fish, sea cucumbers, and sea urchins increases. Shallow sea aquaculture has extensively promoted the vigorous development of marine fisheries. However, traditional diving monitoring and fishing are not only time consuming but also labor intensive; moreover, the personal injury is significant and the risk factor is high. In recent years, underwater robots’ development has matured and has been applied in other technologies. Marine aquaculture energy and chemical construction is a new opportunity for growth. The detection of marine organisms is an essential part of the intelligent strategy in marine ranch, which requires an underwater robot to detect the marine organism quickly and accurately in the complex ocean environment. This paper proposes a method called YOLOv4-embedding, based on one-stage deep learning arithmetic to detect marine organisms, construct a real-time target detection system for marine organisms, extract the in-depth features, and improve the backbone’s architecture and the neck connection. Compared with other object detection arithmetics, the YOLOv4-embedding object detection arithmetic was better at detection accuracy—with higher detection confidence and higher detection ratio than other one-stage object detection arithmetics, such as EfficientDet-D3. The results show that the suggested method could quickly detect different varieties in marine organisms. Furthermore, compared to the original YOLOv4, the mAP75 of the proposed YOLOv4-embedding improves 2.92% for the marine organism dataset at a real-time speed of 51 FPS on an RTX 3090. Full article

Most deep-learning-based multi-channel speech enhancement methods focus on designing a set of beamforming coefficients, to directly filter the low signal-to-noise ratio signals received by microphones, which hinders the performance of these approaches. To handle these problems, this paper designs a causal neural filter that fully exploits the spectro-temporal-spatial information in the beamspace domain. Specifically, multiple beams are designed to steer towards all directions, using a parameterized super-directive beamformer in the first stage. After that, a deep-learning-based filter is learned by, simultaneously, modeling the spectro-temporal-spatial discriminability of the speech and the interference, so as to extract the desired speech, coarsely, in the second stage. Finally, to further suppress the interference components, especially at low frequencies, a residual estimation module is adopted, to refine the output of the second stage. Experimental results demonstrate that the proposed approach outperforms many state-of-the-art (SOTA) multi-channel methods, on the generated multi-channel speech dataset based on the DNS-Challenge dataset. Full article

Unmanned aerial vehicles have large prospects for organizing territory monitoring. To integrate them into this sphere, it is necessary to improve their high functionality and safety. Computer vision is one of the vital monitoring aspects. In this paper, we developed and validated a methodology for terrain classification. The overall classification procedure consists of the following steps: (1) pre-processing, (2) feature extraction, and (3) classification. For the pre-processing stage, a clustering method based on particle swarm optimization was elaborated, which helps to extract object patterns from the image. Feature extraction is conducted via Gray-Level Co-Occurrence Matrix calculation, and the output of the matrix is turned into the input for a feed-forward neural network classification stage. The developed computer vision system showed 88.7% accuracy on the selected test set. These results can provide high quality territory monitoring; prospectively, we plan to establish a self-positioning system based on computer vision. Full article

The kernel ridge regression (KRR) and its updated version taking into account the odd-even effects (KRRoe) are employed to improve the mass predictions of the relativistic density functional theory. Both the KRR and KRRoe approaches can improve the mass predictions to a large extent. In particular, the KRRoe approach can significantly improve the predictions of the one-nucleon separation energies. The extrapolation performances of the KRR and KRRoe approaches to neutron-rich nuclei are examined, and the impacts of the KRRoe mass corrections on the r-process simulations are studied. It is found that the KRRoe mass corrections for the nuclei in the r-process path are remarkable in the light mass region, e.g., $A<150$, and this could influence the corresponding r-process abundances. Full article

Ultrasonic based inspection of thin-walled structures often requires prior knowledge of their mechanical properties. Their accurate estimation could be achieved in a non-destructive manner employing, e.g., elastic guided waves. Such procedures require efficient approaches for experimental data extraction and processing, which is still a challenging task. An advanced automated technique for material properties identification of an elastic waveguide is proposed in this investigation. It relies on the information on dispersion characteristics of guided waves, which are extracted by applying the matrix pencil method to the measurements obtained via laser Doppler vibrometry. Two objective functions have been successfully tested, and the advantages of both approaches are discussed (accuracy vs. computational costs). The numerical analysis employing the synthetic data generated via the mathematical model as well as experimental data shows that both approaches are stable and accurate. The influence of the presence of various modes in the extracted data is investigated. One can conclude that the influence of the corruptions related to the extraction of dispersion curves is not critical if the majority of guided waves propagating in the considered frequency range are presented. Possible extensions of the proposed technique for damaged and multi-layered structures are also discussed. Full article

The human eyes observe an image through perceptual units surrounded by symmetrical or asymmetrical object contours at a proper scale, which enables them to quickly extract the foreground of the image. Inspired by this characteristic, a model combined with multiscale perceptual grouping and unit-based segmentation is proposed in this paper. In the multiscale perceptual grouping part, a novel total variation regularization is proposed to smooth the image into different scales, which removes the inhomogeneity and preserves the edges. To simulate perceptual units surrounded by contours, the watershed method is utilized to cluster pixels into groups. The scale of smoothness is determined by the number of perceptual units. In the segmentation part, perceptual units are regarded as the basic element instead of discrete pixels in the graph cut. The appearance models of the foreground and background are constructed by combining the perceptual units. According to the relationship between perceptual units and the appearance model, the foreground can be segmented through a minimum-cut/maximum-flow algorithm. The experiment conducted on the CMU-Cornell iCoseg database shows that the proposed model has a promising performance. Full article

When focusing on changes in political party support, it is crucial to determine whether or not there has been a change in the aggregate. From this perspective, various types of marginal homogeneity models have been proposed. We propose local marginal homogeneity models, which indicate that there are symmetric structures of probabilities for only one pair of symmetric marginal probabilities or cumulative probabilities. In addition, we propose two measures, one for nominal categories and one for ordered categories, to express the degree of departure from local marginal homogeneity models. We also apply the measures to data and confirm that the measures help compare the degree of departure from the model in several tables. Full article