Symmetry, Volume 13, Issue 6 (June 2021) – 190 articles

We studied supramolecular chirality induced by circularly polarized light. Photoresponsive azopolymers form a helical intermolecular network. Furthermore, studies on photochemical materials using optical vortex light will also attract attention in the future. In contrast to circularly polarized light carrying spin angular momentum, an optical vortex with a spiral wave front and carrying orbital angular momentum may impart torque upon irradiated materials. In this review, we summarize a few examples, and then theoretically and computationally deduce the differences in spin angular momentum and orbital angular momentum depending on molecular orientation not on, but in, polymer films. UV-vis absorption and circular dichroism (CD) spectra are consequences of electric dipole transition and magnetic dipole transition, respectively. However, the basic effect of vortex light is postulated to originate from quadrupole transition. Therefore, we explored the simulated CD spectra of azo dyes with the aid of conventional density functional theory (DFT) calculations and preliminary theoretical discussions of the transition of CD. Either linearly or circularly polarized UV light causes the trans–cis photoisomerization of azo dyes, leading to anisotropic and/or helically organized methyl orange, respectively, which may be detectable by CD spectroscopy after some technical treatments. Our preliminary theoretical results may be useful for future experiments on the irradiation of UV light under vortex. Full article

This paper provides three classes of q-summation formulas in the form of general contiguous extensions of the first q-Kummer summation theorem. Their derivations are presented by using three methods, which are along the lines of the three types of well-known proofs of the q-Kummer summation theorem with a key role of the q-binomial theorem. In addition to the q-binomial theorem, the first proof makes use of Thomae’s q-integral representation and the second proof needs Heine’s transformation. Whereas the third proof utilizes only the q-binomial theorem. Subsequently, the applications of these summation formulas in obtaining the general contiguous extensions of the second and the third q-Kummer summation theorems are also presented. Furthermore, the investigated results are specialized to give many of the known as well as presumably new q-summation theorems, which are contiguous to the three q-Kummer summation theorems. This work is motivated by the observation that the basic (or q-) series and basic (or q-) polynomials, especially the basic (or q-) gamma and q-hypergeometric functions and basic (or q-) hypergeometric polynomials, are applicable particularly in several diverse areas including Number Theory, Theory of Partitions and Combinatorial Analysis as well as in the study of Combinatorial Generating Functions. Just as it is known in the theory of the Gauss, Kummer (or confluent), Clausen and the generalized hypergeometric functions, the parameters in the corresponding basic or quantum (or q-) hypergeometric functions are symmetric in the sense that they remain invariant when the order of the p numerator parameters or when the order of the q denominator parameters is arbitrarily changed. A case has therefore been made for the symmetry possessed not only by hypergeometric functions and basic or quantum (or q-) hypergeometric functions, which are studied in this paper, but also by the symmetric quantum calculus itself. Full article

In this article, we present a two-point boundary value problem with separated boundary conditions for a finite nabla fractional difference equation. First, we construct an associated Green’s function as a series of functions with the help of spectral theory, and obtain some of its properties. Under suitable conditions on the nonlinear part of the nabla fractional difference equation, we deduce two existence results of the considered nonlinear problem by means of two Leray–Schauder fixed point theorems. We provide a couple of examples to illustrate the applicability of the established results. Full article

Majorana bound states in topological superconductors have attracted intense research activity in view of applications in topological quantum computation. However, they are not the only example of topological bound states that can occur in such systems. Here, we study a model in which both Majorana and Tamm bound states compete. We show both numerically and analytically that, surprisingly, the Tamm state remains partially localized even when the spectrum becomes gapless. Despite this fact, we demonstrate that the Majorana polarization shows a clear transition between the two regimes. Full article

Using a small number of mathematical transformations, this article examines the nature of fractional models described by fractional differential equations or pseudo state space descriptions. Computation of the impulse response of a fractional model using the Cauchy method shows that they exhibit infinitely small and high time constants. This impulse response can be rewritten as a diffusive representation whose Fourier transform permits a representation of a fractional model by a diffusion equation in an infinite space domain. Fractional models can thus be viewed as doubly infinite dimensional models: infinite as distributed with a distribution in an infinite domain. This infinite domain or the infinitely large time constants of the impulse response reveal a property intrinsic to fractional models: their infinite memory. Solutions to generate fractional behaviors without infinite memory are finally proposed. Full article

The aim of this paper is to derive some common best proximity point results in partial metric spaces defining a new class of symmetric mappings, which is a generalization of cyclic ϕ-contraction mappings. With the help of these symmetric mappings, the characterization of completeness of metric spaces given by Cobzas (2016) is extended here for partial metric spaces. The existence of a solution to the Fredholm integral equation is also obtained here via a fixed-point formulation for such mappings. Full article

Recent advances in experimental biology studies have produced large amount of molecular activity data. In particular, individual patient data provide non-time series information for the molecular activities in disease conditions. The challenge is how to design effective algorithms to infer regulatory networks using the individual patient datasets and consequently address the issue of network symmetry. This work is aimed at developing an efficient pipeline to reverse-engineer regulatory networks based on the individual patient proteomic data. The first step uses the SCOUT algorithm to infer the pseudo-time trajectory of individual patients. Then the path-consistent method with part mutual information is used to construct a static network that contains the potential protein interactions. To address the issue of network symmetry in terms of undirected symmetric network, a dynamic model of ordinary differential equations is used to further remove false interactions to derive asymmetric networks. In this work a dataset from triple-negative breast cancer patients is used to develop a protein-protein interaction network with 15 proteins. Full article

This paper develops a novel soft fault diagnosis approach for analog circuits. The proposed method employs the backward difference strategy to process the data, and a novel variant of convolutional neural network, i.e., convolutional neural network with global average pooling (CNN-GAP) is taken for feature extraction and fault classification. Specifically, the measured raw domain response signals are firstly processed by the backward difference strategy and the first-order and the second-order backward difference sequences are generated, which contain the signal variation and the rate of variation characteristics. Then, based on the one-dimensional convolutional neural network, the CNN-GAP is developed by introducing the global average pooling technical. Since global average pooling calculates each input vector’s mean value, the designed CNN-GAP could deal with different lengths of input signals and be applied to diagnose different circuits. Additionally, the first-order and the second-order backward difference sequences along with the raw domain response signals are directly fed into the CNN-GAP, in which the convolutional layers automatically extract and fuse multi-scale features. Finally, fault classification is performed by the fully connected layer of the CNN-GAP. The effectiveness of our proposal is verified by two benchmark circuits under symmetric and asymmetric fault conditions. Experimental results prove that the proposed method outperforms the existing methods in terms of diagnosis accuracy and reliability. Full article

Differential equations with delay arguments are one of the branches of functional differential equations which take into account the system’s past, allowing for more accurate and efficient future prediction. The symmetry of the equations in terms of positive and negative solutions plays a fundamental and important role in the study of oscillation. In this paper, we study the oscillatory behavior of a class of odd-order neutral delay differential equations. We establish new sufficient conditions for all solutions of such equations to be oscillatory. The obtained results improve, simplify and complement many existing results. Full article

Forward error correction codes (FEC) are one of the vital sections of modern communication systems; therefore, recognition of the coding type is an important issue in non-cooperative communication. At present, the recognition of FEC codes is mainly concentrated in the field of semi-blind identification with known types of codes. However, based on information asymmetry, the receiver cannot know the types of channel coding previously used in non-cooperative systems such as cognitive radio and remote sensing of communication. Therefore, it is important to recognize the error-correcting encoding type with no prior information. Although the traditional algorithm can also recognize the type of codes, it is only applicable to the case without errors, and its practicability is poor. In the paper, we propose a new method to identify the types of FEC codes based on depth distribution in non-cooperative communication. The proposed algorithm can effectively recognize linear block codes, convolutional codes, and Turbo codes under a low error probability level, and has a higher robustness to noise transmission environment. In addition, an improved matrix estimation algorithm based on Gaussian elimination was adopted in this paper, which effectively improves the parameter identification in a noisy environment. Finally, we used a general framework to unify all the reconstruction algorithms to simplify the complexity of the algorithm. The simulation results show that, compared with the traditional algorithm based on matrix rank, the proposed algorithm has a better anti-interference performance. The method proposed is simple and convenient for engineering and practical applications. Full article

In this communication, using a generalized conformable differential operator, a simulation of the well-known Newton’s law of cooling is made. In particular, we use the conformable $t^{1-\alpha }$, $e^{(1-\alpha )t}$ and non-conformable $t^{-\alpha }$ kernels. The analytical solution for each kernel is given in terms of the conformable order derivative $0<\alpha \le 1$. Then, the method for inverse problem solving, using Bayesian estimation with real temperature data to calculate the parameters of interest, is applied. It is shown that these conformable approaches have an advantage with respect to ordinary derivatives. Full article

Swarm-based algorithm can successfully avoid the local optimal constraints, thus achieving a smooth balance between exploration and exploitation. Salp swarm algorithm (SSA), as a swarm-based algorithm on account of the predation behavior of the salp, can solve complex daily life optimization problems in nature. SSA also has the problems of local stagnation and slow convergence rate. This paper introduces an improved salp swarm algorithm, which improve the SSA by using the chaotic sequence initialization strategy and symmetric adaptive population division. Moreover, a simulated annealing mechanism based on symmetric perturbation is introduced to enhance the local jumping ability of the algorithm. The improved algorithm is referred to SASSA. The CEC standard benchmark functions are used to evaluate the efficiency of the SASSA and the results demonstrate that the SASSA has better global search capability. SASSA is also applied to solve engineering optimization problems. The experimental results demonstrate that the exploratory and exploitative proclivities of the proposed algorithm and its convergence patterns are vividly improved. Full article

As the COVID-19 pandemic rapidly spreads across the world, regrettably, misinformation and fake news related to COVID-19 have also spread remarkably. Such misinformation has confused people. To be able to detect such COVID-19 misinformation, an effective detection method should be applied to obtain more accurate information. This will help people and researchers easily differentiate between true and fake news. The objective of this research was to introduce an enhanced evolutionary detection approach to obtain better results compared with the previous approaches. The proposed approach aimed to reduce the number of symmetrical features and obtain a high accuracy after implementing three wrapper feature selections for evolutionary classifications using particle swarm optimization (PSO), the genetic algorithm (GA), and the salp swarm algorithm (SSA). The experiments were conducted on one of the popular datasets called the Koirala dataset. Based on the obtained prediction results, the proposed model revealed an optimistic and superior predictability performance with a high accuracy (75.4%) and reduced the number of features to 303. In addition, by comparison with other state-of-the-art classifiers, our results showed that the proposed detection method with the genetic algorithm model outperformed other classifiers in the accuracy. Full article

Reversible data hiding in the encrypted domain (RDH-ED) is a technique that protects the privacy of multimedia in the cloud service. In order to manage three-dimensional (3D) models, a novel RDH-ED based on prediction error expansion (PEE) is proposed. First, the homomorphic Paillier cryptosystem is utilized to encrypt the 3D model for transmission to the cloud. In the data hiding, a greedy algorithm is employed to classify vertices of 3D models into reference and embedded sets in order to increase the embedding capacity. The prediction value of the embedded vertex is computed by using the reference vertex, and then the module length of the prediction error is expanded to embed data. In the receiving side, the data extraction is symmetric to the data embedding, and the range of the module length is compared to extract the secret data. Meanwhile, the original 3D model can be recovered with the help of the reference vertex. The experimental results show that the proposed method can achieve greater embedding capacity compared with the existing RDH-ED methods. Full article

While walking on split-belt treadmills (two belts running at different speeds), the slower limb shows longer anterior steps than the limb dragged by the faster belt. After returning to basal conditions, the step length asymmetry is transiently reversed (after-effect). The lower limb joint dynamics, however, were not thoroughly investigated. In this study, 12 healthy adults walked on a force-sensorised split-belt treadmill for 15 min. Belts rotated at 0.4 m s⁻¹ on both sides, or 0.4 and 1.2 m s⁻¹ under the non-dominant and dominant legs, respectively. Spatiotemporal step parameters, ankle power and work, and the actual mean velocity of the body’s centre of mass (CoM) were computed. On the faster side, ankle power and work increased, while step length and stance time decreased. The mean velocity of the CoM slightly decreased. As an after-effect, modest converse asymmetries developed, fading within 2–5 min. These results may help to decide which belt should be assigned to the paretic and the unaffected lower limb when split-belt walking is applied for rehabilitation research in hemiparesis. Full article

DEM parameters calibration is the most important step in preparing a DEM model. At the same time, the lack of a universal approach to DEM parameters calibration complicates this process. The paper presents the author’s approach to creating a universal calibration approach based on the physical meaning of the friction coefficients and conducting symmetrical experiments at full scale and in a simulation, as well as the implementation of the approach in the form of a physical test rig. Several experiments were carried out to determine the DEM parameters of six material–boundary pairs. The resulting parameters were adjusted using a refinement experiment. The results confirmed the adequacy of the developed approach, as well as its applicability in various conditions. The limitations of both the approach itself and its specific implementation in the form of a test rig were identified. Full article

There are some classes of methods for solving integral equations of the variable boundaries. It is known that each method has its own advantages and disadvantages. By taking into account the disadvantages of known methods, here was constructed a new method free from them. For this, we have used multistep methods of advanced and hybrid types for the construction methods, with the best properties of the intersection of them. We also show some connection of the methods constructed here with the methods which are using solving of the initial-value problem for ODEs of the first order. Some of the constructed methods have been applied to solve model problems. A formula is proposed to determine the maximal values of the order of accuracy for the stable and unstable methods, constructed here. Note that to construct the new methods, here we propose to use the system of algebraic equations which allows us to construct methods with the best properties by using the minimal volume of the computational works at each step. For the construction of more exact methods, here we have proposed to use the multistep second derivative method, which has comparisons with the known methods. We have constructed some formulas to determine the maximal order of accuracy, and also determined the necessary and sufficient conditions for the convergence of the methods constructed here. One can proved by multistep methods, which are usually applied to solve the initial-value problem for ODE, demonstrating the applications of these methods to solve Volterra integro-differential equations. For the illustration of the results, we have constructed some concrete methods, and one of them has been applied to solve a model equation. Full article

Under the low voltage ride through (LVRT) control strategy, the inverter interfaced distributed generation (IIDG) needs to change the output mode of the inverter according to the voltage of the connected nodes. The short-circuit current is related to the system rated capacity, network short-circuit impedance, and distributed power output. So, based on the deep learning algorithm, a predicting method of the voltage drop is proposed. By predicting the voltage of connected nodes, the output mode of IIDG can be determined based on the LVRT control. Thus, the fault calculation model of IIDG is accurately established. Compared with the three-phase asymmetric Gaussian fault calculation method, the proposed method can achieve fault calculation accurately. Finally, a case study is built to verify the effectiveness of the proposed method. The results indicate that the proposed method can make accurate voltage prediction and improve the computation speed of the fault calculation. Full article

In this article, plenty of wave solutions of the (2 + 1)-dimensional Kadomtsev–Petviashvili–Benjamin–Bona–Mahony ((2 + 1)-D KP-BBM) model are constructed by employing two recent analytical schemes (a modified direct algebraic (MDA) method and modified Kudryashov (MK) method). From the point of view of group theory, the proposed analytical methods in our article are based on symmetry, and effectively solve those problems which actually possess explicit or implicit symmetry. This model is a vital model in shallow water phenomena where it demonstrates the wave surface propagating in both directions. The obtained analytical solutions are explained by plotting them through 3D, 2D, and contour sketches. These solutions’ accuracy is also tested by calculating the absolute error between them and evaluated numerical results by the Adomian decomposition (AD) method and variational iteration (VI) method. The considered numerical schemes were applied based on constructed initial and boundary conditions through the obtained analytical solutions via the MDA, and MK methods which show the synchronization between computational and numerical obtained solutions. This coincidence between the obtained solutions is explained through two-dimensional and distribution plots. The applied methods’ symmetry is shown through comparing their obtained results and showing the matching between both obtained solutions (analytical and numerical). Full article

In this study, we present the notion of the quasi-ordinarization transform of a numerical semigroup. The set of all semigroups of a fixed genus can be organized in a forest whose roots are all the quasi-ordinary semigroups of the same genus. This way, we approach the conjecture on the increasingness of the cardinalities of the sets of numerical semigroups of each given genus. We analyze the number of nodes at each depth in the forest and propose new conjectures. Some properties of the quasi-ordinarization transform are presented, as well as some relations between the ordinarization and quasi-ordinarization transforms. Full article

In this paper we propose a novel learning-based wavelet transform and demonstrate its utility as a representation in solving a number of linear inverse problems—these are asymmetric problems, where the forward problem is easy to solve, but the inverse is difficult and often ill-posed. The wavelet decomposition is comprised of the application of an invertible 2D wavelet filter-bank comprising symmetric and anti-symmetric filters, in combination with a set of $1\times 1$ convolution filters learnt from Principal Component Analysis (PCA). The $1\times 1$ filters are needed to control the size of the decomposition. We show that the application of PCA across wavelet subbands in this way produces an architecture equivalent to a separable Convolutional Neural Network (CNN), with the principal components forming the $1\times 1$ filters and the subtraction of the mean forming the bias terms. The use of an invertible filter bank and (approximately) invertible PCA allows us to create a deep autoencoder very simply, and avoids issues of overfitting. We investigate the construction and learning of such networks, and their application to linear inverse problems via the Alternating Direction of Multipliers Method (ADMM). We use our network as a drop-in replacement for traditional discrete wavelet transform, using wavelet shrinkage as the projection operator. The results show good potential on a number of inverse problems such as compressive sensing, in-painting, denoising and super-resolution, and significantly close the performance gap with Generative Adversarial Network (GAN)-based methods. Full article

Risk and security are two symmetric descriptions of the uncertainty of the same system. If the risk early warning is carried out in time, the security capability of the system can be improved. A safety early warning model based on fuzzy c-means clustering (FCM) and back-propagation neural network was established, and a genetic algorithm was introduced to optimize the connection weight and other properties of the neural network, so as to construct the safety early warning system of coal mining face. The system was applied in a coal face in Shandong, China, with 46 groups of data as samples. Firstly, the original data were clustered by FCM, the input space was fuzzy divided, and the samples were clustered into three categories. Then, the clustered data was used as the input of the neural network for training and prediction. The back-propagation neural network and genetic algorithm optimization neural network were trained and verified many times. The results show that the early warning model can realize the prediction and early warning of the safety condition of the working face, and the performance of the neural network model optimized by genetic algorithm is better than the traditional back-propagation artificial neural network model, with higher prediction accuracy and convergence speed. The established early warning model and method can provide reference and basis for the prediction, early warning and risk management of coal mine production safety, so as to discover the hidden danger of working face accident as soon as possible, eliminate the hidden danger in time and reduce the accident probability to the maximum extent. Full article

In recent years, Android malware has continued to evolve against detection technologies, becoming more concealed and harmful, making it difficult for existing models to resist adversarial sample attacks. At the current stage, the detection result is no longer the only criterion for evaluating the pros and cons of the model with its algorithms, it is also vital to take the model’s defensive ability against adversarial samples into consideration. In this study, we propose a general framework named AdvAndMal, which consists of a two-layer network for adversarial training to generate adversarial samples and improve the effectiveness of the classifiers in Android malware detection and family classification. The adversarial sample generation layer is composed of a conditional generative adversarial network called pix2pix, which can generate malware variants to extend the classifiers’ training set, and the malware classification layer is trained by RGB image visualized from the sequence of system calls. To evaluate the adversarial training effect of the framework, we propose the robustness coefficient, a symmetric interval i = [−1, 1], and conduct controlled experiments on the dataset to measure the robustness of the overall framework for the adversarial training. Experimental results on 12 families with the largest number of samples in the Drebin dataset show that the accuracy of the overall framework is increased from 0.976 to 0.989, and its robustness coefficient is increased from 0.857 to 0.917, which proves the effectiveness of the adversarial training method. Full article

The wide application of encryption technology has made traffic classification gradually become a major challenge in the field of network security. Traditional methods such as machine learning, which rely heavily on feature engineering and others, can no longer fully meet the needs of encrypted traffic classification. Therefore, we propose an Inception-LSTM(ICLSTM) traffic classification method in this paper to achieve encrypted traffic service identification. This method converts traffic data into common gray images, and then uses the constructed ICLSTM neural network to extract key features and perform effective traffic classification. To alleviate the problem of category imbalance, different weight parameters are set for each category separately in the training phase to make it more symmetrical for different categories of encrypted traffic, and the identification effect is more balanced and reasonable. The method is validated on the public ISCX 2016 dataset, and the results of five classification experiments show that the accuracy of the method exceeds 98% for both regular encrypted traffic service identification and VPN encrypted traffic service identification. At the same time, this deep learning-based classification method also greatly simplifies the difficulty of traffic feature extraction work. Full article

Neuroevolutionary models are used to predict magnetic hysteresis for barium hexaferrites (to predict magnetic hysteresis for barium hexaferrites). Magnetic hysteresis for a specific set of samples of barium hexaferrite doped with titanium were measured experimentally at room temperature and reported before. Neural networks are trained using these experimental data in order to generate magnetization and predict magnetic hysteresis for various concentrations of titanum. We present the prediction for various methods of neural calculations and the deviations from actual data results were negligible. Finally, the predictions of magnetic hysteresis are summerized for the titanume concentration between 0.0 and 1.0. Full article

We consider the optimal order quantity problem for exponentially deteriorating items where the opportunity cost is based on compound interest and backorders are allowed. Our objectives in this research are to develop a model that accurately models deterioration, compound interest and backordering, and determine a near-optimal and intuitive closed-form solution for the proposed model. Deteriorating items include various chemicals, gasoline and petroleum products, fresh produce, bulk and liquid food products, batteries, and some electronic components. These items incur losses over time due to spoilage, evaporation, chemical decomposition, breakdown, or deterioration in general. Exponential deterioration is commonly used to model this phenomenon, which results in a negative exponential inventory level function, which is asymmetric in the sense that the rate of depletion is highest at the beginning of an ordering cycle, and lowest at the end. On the other hand, the rate of deterioration for individual items is the same at both ends of the cycle, which means it is symmetric. Compounding also leads to exponential terms in the opportunity cost function. Both of these factors result in a total cost function that does not have a closed-form optimal solution. We therefore approximate the total cost function using a Taylor series expansion approximation of the exponential function and derive a closed-form solution that is simple and logical, and very close to the exact optimum, which makes it attractive to the practitioners as a quick and accurate calculation. Our closed form solutions for both the basic and the planned backorders models are very close to the exact optimum, as shown by extensive numerical experiments. Full article

Dubrovin’s work on the classification of perturbed KdV-type equations is reanalyzed in detail via the gradient-holonomic integrability scheme, which was devised and developed jointly with Maxim Pavlov and collaborators some time ago. As a consequence of the reanalysis, one can show that Dubrovin’s criterion inherits important parts of the gradient-holonomic scheme properties, especially the necessary condition of suitably ordered reduction expansions with certain types of polynomial coefficients. In addition, we also analyze a special case of a new infinite hierarchy of Riemann-type hydrodynamical systems using a gradient-holonomic approach that was suggested jointly with M. Pavlov and collaborators. An infinite hierarchy of conservation laws, bi-Hamiltonian structure and the corresponding Lax-type representation are constructed for these systems. Full article

Let G be a simple graph of order n with vertex set $V\left(G\right)$ and edge set $E\left(G\right)$, and let k be an integer such that $1\le k\le n-1$. The k-token graph $G^{\left\{k\right\}}$ of G is the graph whose vertices are the k-subsets of $V\left(G\right)$, where two vertices A and B are adjacent in $G^{\left\{k\right\}}$ whenever their symmetric difference $A▵B$, defined as $(A\setminus B)\cup (B\setminus A)$, is a pair $\{a,b\}$ of adjacent vertices in G. In this paper we study the Hamiltonicity of the k-token graphs of some join graphs. We provide an infinite family of graphs, containing Hamiltonian and non-Hamiltonian graphs, for which their k-token graphs are Hamiltonian. Our result provides, to our knowledge, the first family of non-Hamiltonian graphs for which it is proven the Hamiltonicity of their k-token graphs, for any $2<k<n-2$. Full article

Patellofemoral pain (PFP) is often associated with impaired muscle strength, flexibility, and stability. It has been suggested that inter-leg asymmetries have an important role in increasing the risk of musculoskeletal injuries, including PFP. Thus, the aim of this study was to identify significant asymmetries and determine the effects of a symmetry targeted exercise program in patients with PFP. Eighteen patients aged 13 to 54 years (24.17 ± 12.52 years) with PFP participated in this study. Strength, flexibility and stability outcomes of the trunk, hip, knee and ankle muscles were assessed. A single-group pretest–posttest design was used to assess changes in inter-leg and agonist–antagonist asymmetries resulting from the 8-week period of the supervised exercise program. Results indicated a significant improvement in inter-leg symmetry regarding bilateral stance in a semi-squat position (p = 0.020, d = 0.61, df = 17) and ankle plantarflexion (p = 0.003, d = 0.32, df = 17) and ankle dorsiflexion strength (p < 0.001, d = 0.46, df = 17). In addition, the ratio of ankle dorsiflexion/plantarflexion (p = 0.036, d = 1.14, df = 17) and hip extension/flexion (p = 0.031, d = 0.94, df = 16) changed significantly during the intervention period. To our knowledge, this was the first study to evaluate inter-leg asymmetries resulting from a period of a supervised exercise program. The results indicate that an exercise program focusing on individual asymmetries may influence specific deficits and contribute to better rehabilitation outcomes. Full article

This work is devoted to the research of new asymmetry effects in symmetric protective structures with triple modal reservation. We analyzed the structures with different cross-sectional locations of the reference conductor: in the center (unshielded structure), around (shielded structure), at the top and bottom (multilayer printed circuit board), and in the form of side polygons (double-sided printed circuit board). First, a preliminary quasi-static simulation was performed in the range of parameters. It was revealed that in all structures, except for the shielded one (in the form of a cable), the deviations of the output voltage amplitude, bandwidth, and frequency of the first resonance were insignificant, whereas in the shielded structure there were significant deviations in the time and frequency responses. The attenuation of the output voltage in relation to the input for each structure was also estimated. In addition, we performed a parametric optimization of the structures under consideration using a heuristic search, which made it possible to improve their characteristics. Finally, the switching order between the conductors in these structures with the original and optimized parameter sets was investigated in detail. The optimal conductor switching order in the case of a component failure was determined, and the best (according to protective characteristics) parameter configuration for each structure was found. Full article