Symmetry

A computational methodology using Density-Functional Theory (DFT) calculations was developed to determine the partition coefficient of a compound in a solution of Sodium Dodecyl Sulfate (SDS) micelles. Different sets of DFT calculations were used to predict the free energy of a set of 63 molecules in 15 different solvents with the purpose of identifying the solvents with similar physicochemical characteristics to the studied micelles. Experimental partition coefficients were obtained from Micellar Electrokinetic Chromatography (MEKC) measurements. The experimental partition coefficient of these molecules was compared with the predicted partition coefficient in heptane/water, cyclohexane/water, N-dodecane/water, pyridine/water, acetic acid/water, decan-1-ol/water, octanol/water, propan-2-ol/water, acetone/water, propan-1-ol/water, methanol/water, 1,2-ethane diol/water, dimethyl sulfoxide/water, formic acid/water, and diethyl sulphide/water systems. It is observed that the combination of pronan-1-ol/water solvent was the most appropriated to estimate the partition coefficient for SDS micelles. This approach allowed us to estimate the partition coefficient orders of magnitude faster than the classical molecular dynamics simulations. The DFT calculations were carried out with the well-known exchange correlation functional B3LYP and with the global hybrid functional M06-2X from the Minnesota functionals with 6-31++G ** basis set. The effect of solvation was considered by the continuum model based on density (SMD). The proposed workflow for the prediction rate of the participation coefficient unveiled the symmetric balance between the experimental data and the computational methods. Full article

Considering the Poincaré group $ISO(d-1,1)$ in any dimension $d>3$, we characterise the coadjoint orbits that are associated with massive and massless particles of discrete spin. We also comment on how our analysis extends to the case of continuous spin. Full article

The presence of binaural low-level background noise has been shown to enhance the transient evoked N1 response at about 100 ms after sound onset. This increase in N1 amplitude is thought to reflect noise-mediated efferent feedback facilitation from the auditory cortex to lower auditory centers. To test this hypothesis, we recorded auditory-evoked fields using magnetoencephalography while participants were presented with binaural harmonic complex tones embedded in binaural or monaural background noise at signal-to-noise ratios of 25 dB (low noise) or 5 dB (higher noise). Half of the stimuli contained a gap in the middle of the sound. The source activities were measured in bilateral auditory cortices. The onset and gap N1 response increased with low binaural noise, but high binaural and low monaural noise did not affect the N1 amplitudes. P1 and P2 onset and gap responses were consistently attenuated by background noise, and noise level and binaural/monaural presentation showed distinct effects. Moreover, the evoked gamma synchronization was also reduced by background noise, and it showed a lateralized reduction for monaural noise. The effects of noise on the N1 amplitude follow a bell-shaped characteristic that could reflect an optimal representation of acoustic information for transient events embedded in noise. Full article

In the present paper, we propose a Baskakov operator of integral type using a function $\phi$ on $[0,\infty )$ with the properties: $\phi \left(0\right)=0,$${\phi }^{\prime }>0$ on $[0,\infty )$ and ${lim}_{x\to \infty }\phi \left(x\right)=\infty$. The proposed operators reproduce the function $\phi$ and constant functions. For the constructed operator, some approximation properties are studied. Voronovskaja asymptotic type formulas for the proposed operator and its derivative are also considered. In the last section, the interest is focused on weighted approximation properties, and a weighted convergence theorem of Korovkin’s type on unbounded intervals is obtained. The results can be extended on the interval $(-\infty ,0]$ (the symmetric of the interval $[0,\infty )$ from the origin). Full article

Brain–Computer Interfaces (BCI) are systems that allow external devices to be controlled by means of brain activity. There are different such technologies, and electroencephalography (EEG) is an example. One of the most common EEG control methods is based on detecting changes in sensorimotor rhythms (SMRs) during motor imagery (MI). The aim of this study was to assess the laterality of cortical function when performing MI of the lower limb. Brain signals from five subjects were analyzed in two conditions, during exoskeleton-assisted gait and while static. Three different EEG electrode configurations were evaluated: covering both hemispheres, covering the non-dominant hemisphere and covering the dominant hemisphere. In addition, the evolution of performance and laterality with practice was assessed. Although sightly superior results were achieved with information from all electrodes, differences between electrode configurations were not statistically significant. Regarding the evolution during the experimental sessions, the performance of the BCI generally evolved positively the higher the experience was. Full article

We evaluate a coupled oscillator solver by applying it to square lattice (N × N) Ising spin problems for N values up to 50. The Ising problems are converted to a classical coupled oscillator model that includes both positive (ferromagnetic-like) and negative (antiferromagnetic-like) coupling between neighboring oscillators (i.e., they are reduced to eigenmode problems). A map of the oscillation amplitudes of lower-frequency eigenmodes enables us to visualize oscillator clusters with a low frustration density (unfrustrated clusters). We found that frustration tends to localize at the boundary between unfrustrated clusters due to the symmetric and asymmetric nature of the eigenmodes. This allows us to reduce frustration simply by flipping the sign of the amplitude of oscillators around which frustrated couplings are highly localized. For problems with N = 20 to 50, the best solutions with an accuracy of 96% (with respect to the exact ground state) can be obtained by simply checking the lowest ~N/2 candidate eigenmodes. Full article

Metal/lipase-combo catalyzed dynamic kinetic resolution (DKR) of racemic chiral alcohols is a general and practical process to obtain the corresponding enantiopure esters R with quantitative conversion. The use of known Ru-catalysts as well as newly developed homogeneous and heterogeneous metal catalysts (Fe, V) contributed to make the DKR process more sustainable and to expand the substrate scope of the reaction. In addition to classical substrates, challenging allylic alcohols, tertiary alcohols, C1-and C2-symmetric biaryl diols turned out to be competent substrates. Synthetic utility further emerged from the integration of this methodology into cascade reactions leading to linear/cyclic chiral molecules with high ee through the formation of multiple bonds, in a one-pot procedure. Full article

With the development of the Industrial Internet in recent years, security issues have been a hot topic of the industrial control system (ICS) network management. Identifying the protocol traffic in the communication process of the ICS is an important prerequisite to avoid security problems, especially in ICSs that use many private protocols. The private protocols cannot be analyzed due to the unknown internal structure of the protocols, which makes the ICS protocol identification work more difficult. However, the Internet-oriented protocol identification method is not applicable to the scenario of the private ICS protocols network environment. With this problem in mind, this paper proposes a method of ICS protocol identification based on the raw traffic payload. The method firstly performs data preprocessing such as data selection, interception, cleaning conversion, and labeling on the raw traffic of the protocol based on the characteristics of the industrial control protocol. Then it uses an AM-1DCNN+LSTM deep learning model to extract temporal and spatial features of the ICS raw traffic, and performs protocol identification. This method can effectively extract ICS protocol features in scenarios where protocol parsing is impossible compared with existing methods. We constructed a dataset for ICS protocol identification based on open-source data and tested the proposed method for experiments, and the identification accuracy rate reached 93%. Full article

A great deal of operational information exists in the form of text. Therefore, extracting operational information from unstructured military text is of great significance for assisting command decision making and operations. Military relation extraction is one of the main tasks of military information extraction, which aims at identifying the relation between two named entities from unstructured military texts. However, the traditional methods of extracting military relations cannot easily resolve problems such as inadequate manual features and inaccurate Chinese word segmentation in military fields, failing to make full use of symmetrical entity relations in military texts. With our approach, based on the pre-trained language model, we present a Chinese military relation extraction method, which combines the bi-directional gate recurrent unit (BiGRU) and multi-head attention mechanism (MHATT). More specifically, the conceptual foundation of our method lies in constructing an embedding layer and combining word embedding with position embedding, based on the pre-trained language model; the output vectors of BiGRU neural networks are symmetrically spliced to learn the semantic features of context, and they fuse the multi-head attention mechanism to improve the ability of expressing semantic information. On the military text corpus that we have built, we conduct extensive experiments. We demonstrate the superiority of our method over the traditional non-attention model, attention model, and improved attention model, and the comprehensive evaluation value F1-score of the model is improved by about 4%. Full article

Animal bodies in general and faces in particular show mirror symmetry with respect to the median-sagittal plane, with exceptions rarely occurring. Bilateral symmetry to the median sagittal plane of the body also evolved very early. From an evolutionary point of view, it should therefore have fundamental advantages, e.g., more effective locomotion and chewing abilities. On the other hand, the recognition of bilaterally symmetric patterns is an important module in our visual perception. In particular, the recognition of faces with different spatial orientations and their identification is strongly related to the recognition of bilateral symmetry. Maxillofacial surgery and Dentistry affect effective masticatory function and perceived symmetry of the lower third of the face. Both disciplines have the ability to eliminate or mitigate asymmetries with respect to form and function. In our review, we will demonstrate symmetric structures from single teeth to the whole face. We will further describe different approaches to quantify cranial, facial and dental asymmetries by using either landmarks or 3D surface models. Severe facial asymmetries are usually caused by malformations such as hemifacial hyperplasia, injury or other diseases such as Noma or head and neck cancer. This could be an important sociobiological reason for a correlation between asymmetry and perceived disfigurement. The aim of our review is to show how facial symmetry and attractiveness are related and in what way dental and facial structures and the symmetry of their shape and color influence aesthetic perception. We will further demonstrate how modern technology can be used to improve symmetry in facial prostheses and maxillofacial surgery. Full article

Burglary resistance expresses the time required to overcome the barriers to cause the damage in order to unlawfully enter a place for the purposes of stealing property or committing a felony (i.e., disruption of important assets, e.g., critical infrastructure). Damage to the object protection system means damage to the symmetry of the system—the balance between protection measures and security threats. Barriers are considered to be the walls of buildings or secure storage units (safe, safe, etc.), i.e., passive barriers that separate asset (protected value) from the security threat. The role of barriers in the security system is also to slow down the attack and create a time reserve for the intervention of a security service. There is no uniform approach to express the burglary resistance of such barriers using explosives; however, burglary by explosion are present. Explosives in the article are a tool that can be used by the offenders. The article uses mainly Delphi method and Saaty method. These methods have made it possible to identify and expertly evaluate scenarios for the use of explosives to break a barrier. Logical methods and interviews were also used. The result of the article is the identification and evaluation of the possibilities of using explosives to overcome barriers and expressing the blast burglary resistance of barriers. The universal assessment approach allows the inclusion of explosives to the burglary resistance protection system assessment schemes. Full article

Substructure shake table testing (SSTT) is an advanced experimental technique that is suitable for investigating the vibration control of secondary structure-type dampers such as tuned mass dampers (TMDs). The primary structure and damper are considered as analytical and experimental substructures, respectively. The analytical substructures of existing SSTTs have mostly been simplified as SDOF structures or shear-type structures, which is not realistic. A common trend is to simulate the analytical substructure via the finite element (FE) method. In this study, the control effects of four dampers, i.e., TMD, tuned liquid damper (TLD), particle damper (PD) and particle-tuned mass damper (PTMD), on a frame were examined by conducting virtual SSTTs. The frame was modeled through stiffness-based beam-column elements with fiber sections and was solved by a family of model-based integration algorithms. The influences of the auxiliary mass ratio, integration parameters, time step, and time delay on SSTT were investigated. The results indicate that the TLD had the best performance. In addition, SSTT using model-based integration algorithms can provide satisfactory results, even when the time step is relatively large. The effects of integration parameters and time delay are not significant. Full article

This work is motivated by the work of Josip Pečarić in 2013 and 1982 and the work of Srivastava in 2017. By the utilization of the diamond-$\alpha$ dynamic inequalities, which are defined as a linear mixture of the delta and nabla integrals, we present and prove very important generalized results of diamond-$\alpha$ Steffensen-type inequalities on a general time scale. Symmetry plays an essential role in determining the correct methods to solve dynamic inequalities. Full article

For symmetric non-orthogonal multiple access (NOMA)/multiple-input multiple-output (MIMO) systems, radio resource allocation is an important research problem. The optimal solution is of high computational complexity. Thus, one existing solution Kim et al. proposed is a suboptimal user selection and optimal power assignment for total data rate maximization. Another existing solution Tseng et al. proposed is different suboptimal user grouping and optimal power assignment for sum video distortion minimization. However, the performance of sub-optimal schemes by Kim et al. and Tseng et al. is still much lower than the optimal user grouping scheme. To approach the optimal scheme and outperform the existing sub-optimal schemes, a deep neural network (DNN) based approach, using the results from the optimal user selection (exhaustive search) as the training data, and a loss function modification specific for NOMA user selection to meet the constraint that a user cannot be in both the strong and weak set, and avoid the post processing online computational complexity, are proposed. The simulation results show that the theoretical peak signal-to-noise ratio (PSNR) of the proposed scheme is higher than the state-of-the-art suboptimal schemes Kim et al. and Tseng et al. by 0.7~2.3 dB and is only 0.4 dB less than the optimal scheme at lower online computational complexity. The online computational complexity (testing stage) of the proposed DNN user selection scheme is 60 times less than the optimal user selection scheme. The proposed DNN-based scheme outperforms the existing suboptimal solution, and slightly underperforms the optimal scheme (exhaustive search) at a much lower computation complexity. Full article

In many problems appearing in applied mathematics in the nonlinear ordinary differential systems, as in physics, chemist, economics, etc., if we have a differential system on a manifold of dimension, two of them having a first integral, then its phase portrait is completely determined. While the existence of first integrals for differential systems on manifolds of a dimension higher than two allows to reduce the dimension of the space in as many dimensions as independent first integrals we have. Hence, to know first integrals is important, but the following question appears: Given a differential system, how to know if it has a first integral? The symmetries of many differential systems force the existence of first integrals. This paper has two main objectives. First, we study how to compute first integrals for polynomial differential systems using the so-called Darboux theory of integrability. Furthermore, second, we show how to use the existence of first integrals for finding limit cycles in piecewise differential systems. Full article

We investigated the dynamic processes in a superconducting neuron based on Josephson contacts without resistive shunting (S_C-neuron). Such a cell is a key element of perceptron-type neural networks that operate in both classical and quantum modes. The analysis of the obtained results allowed us to find the mode when the transfer characteristic of the element implements the “sigmoid” activation function. The numerical approach to the analysis of the equations of motion and the Monte Carlo method revealed the influence of inertia (capacitances), dissipation, and temperature on the dynamic characteristics of the neuron. Full article

Orthodontic treatment carries the risk of major complications such as enamel demineralization, tooth decay, gingivitis, and periodontal damage. A large number of elements of fixed orthodontic appliance results in the creation of additional plaque retention sites which increase the risk of biofilm creation. Modification of the surface of orthodontic elements may prevent the formation of bacterial biofilm. In this paper, surface modification of stainless steel orthodontic wires with TiO₂: Ag was carried out by the sol-gel thin film dip-coating method. To obtain the anatase crystal structure, substrates were calcined for 2 h at 500 °C. The properties of the obtained coatings were investigated using scanning electron microscopy, X-ray diffraction, and electrochemical tests. Corrosion studies were performed in a Ringer’s solution, which simulated physiological solution. SEM and XRD analyses of the coated surface confirmed the presence of Ag nanoparticles which may have antimicrobial potential. Full article

The emissivity is an important surface property parameter in many fields, including infrared temperature measurement. In this research, a symmetry theoretical model of directional spectral emissivity prediction is proposed based on Gaussian random rough surface theory. A numerical solution based on a matrix method is determined based on its symmetrical characteristics. Influences of the index of refraction n and the root mean square (RMS) roughness σ_rms on the directional spectrum emissivity ε are analyzed and discussed. The results indicate that surfaces with higher n and lower σ_rms tend to have a peak in high viewing angles. On the contrary, surfaces with lower n and higher σ_rms tend to have a peak in low viewing angles. Experimental verifications based on infrared (IR) temperature measurement of Inconel 718 sandblasted surfaces were carried out. This model would contribute to understand random rough surfaces and their emitting properties in fields including machining, process controlling, remote sensing, etc. Full article

The symmetry SU(2) and its geometric Bloch Sphere rendering have been successfully applied to the study of a single qubit (spin-1/2); however, the extension of such symmetries and geometries to multiple qubits—even just two—has been investigated far less, despite the centrality of such systems for quantum information processes. In the last two decades, two different approaches, with independent starting points and motivations, have been combined for this purpose. One approach has been to develop the unitary time evolution of two or more qubits in order to study quantum correlations; by exploiting the relevant Lie algebras and, especially, sub-algebras of the Hamiltonians involved, researchers have arrived at connections to finite projective geometries and combinatorial designs. Independently, geometers, by studying projective ring lines and associated finite geometries, have come to parallel conclusions. This review brings together the Lie-algebraic/group-representation perspective of quantum physics and the geometric–algebraic one, as well as their connections to complex quaternions. Altogether, this may be seen as further development of Felix Klein’s Erlangen Program for symmetries and geometries. In particular, the fifteen generators of the continuous SU(4) Lie group for two qubits can be placed in one-to-one correspondence with finite projective geometries, combinatorial Steiner designs, and finite quaternionic groups. The very different perspectives that we consider may provide further insight into quantum information problems. Extensions are considered for multiple qubits, as well as higher-spin or higher-dimensional qudits. Full article