Symmetry, Volume 12, Issue 5 (May 2020) – 188 articles

This article introduces a new probability distribution capable of modeling positive data that present different levels of asymmetry and high levels of kurtosis. A slashed quasi-gamma random variable is defined as the quotient of independent random variables, a generalized gamma is the numerator, and a power of a standard uniform variable is the denominator. The result is a new three-parameter distribution (scale, shape, and kurtosis) that does not present the identifiability problem presented by the generalized gamma distribution. Maximum likelihood (ML) estimation is implemented for parameter estimation. The results of two real data applications revealed a good performance in real settings. Full article

In this study, a new way of criteria selection and a weighting system will be presented in a multi-disciplinary framework. Weighting criteria in Multi-Attribute Decision Making (MADM) has been developing as the most attractive section in the field. Although many ideas have been developed during the last decades, there is no such great diversity that can be mentioned in the literature. This study is looking from outside the box and is presenting something totally new by using big data and text mining in a Prospective MADM outline. PMADM is a hybrid interconnected concept between the Futures Studies and MADM fields. Text mining, which is known as a useful tool in Futures Studies, is applied to create a widespread pilot system for weighting and criteria selection in the PMADM outline. Latent Semantic Analysis (LSA), as an influential method inside the general concept of text mining, is applied to show how a data warehouse’s output, which in this case is Scopus, can reach the final criteria selection and weighting of the criteria. Full article

Various defects are formed on the workpiece surface during the production process. Workpiece surface defects are classified according to various characteristics, which includes a bumped surface, scratched surface and pit surface. Suppliers analyze the cause of workpiece surface defects through the defect types and thus determines the subsequent processing. Therefore, the correct classification is essential regarding workpiece surface defects. In this paper, a multi-classifier decision-level fusion classification model for workpiece surface defects based on a convolutional neural network (CNN) was proposed. In the proposed model, the histogram of oriented gradient (HOG) was used to extract the features of the second fully connected layer of the CNN, and the features of the HOG were further extracted by using the local binary patterns (LBP), which was called the HOG–LBP feature extraction. Finally, this paper designed a symmetry ensemble classifier, which was used to classify the features of the last fully connected layer of the CNN and the features of the HOG–LBP. The comprehensive decision was made by fusing the classification results of the symmetry structure channels. The experiments were carried out, and the results showed that the proposed model could improve the accuracy of the workpiece surface defect classification. Full article

The daily commute represents a source of chronic stress that is positively correlated with physiological consequences, including increased blood pressure, heart rate, fatigue, and other negative mental and physical health effects. The purpose of this research is to investigate and predict the physiological effects of commuting in Greater London on the human body based on machine-learning approaches. For each participant, the data were collected for five consecutive working days, before and after the commute, using non-invasive wearable biosensor technology. Multimodal behaviour, analysis and synthesis are the subjects of major efforts in computing field to realise the successful human–human and human–agent interactions, especially for developing future intuitive technologies. Current analysis approaches still focus on individuals, while we are considering methodologies addressing groups as a whole. This research paper employs a pool of machine-learning approaches to predict and analyse the effect of commuting objectively. Comprehensive experimentation has been carried out to choose the best algorithmic structure that suit the problem in question. The results from this study suggest that whether the commuting period was short or long, all objective bio-signals (heat rate and blood pressure) were higher post-commute than pre-commute. In addition, the results match both the subjective evaluation obtained from the Positive and Negative Affect Schedule and the proposed objective evaluation of this study in relation to the correlation between the effect of commuting on bio-signals. Our findings provide further support for shorter commutes and using the healthier or active modes of transportation. Full article

Chaotic systems have attracted considerable attention and been applied in various applications. Investigating simple systems and counterexamples with chaotic behaviors is still an important topic. The purpose of this work was to study a simple symmetrical system including only five nonlinear terms. We discovered the system’s rich behavior such as chaos through phase portraits, bifurcation diagrams, Lyapunov exponents, and entropy. Interestingly, multi-stability was observed when changing system’s initial conditions. Chaos of such a system was predicted by applying a machine learning approach based on a neural network. Full article

In this work, new approaches are proposed for the 3D decomposition of a cubical tensor of size N × N × N for N = 2ⁿ through hierarchical deterministic orthogonal transforms with low computational complexity, whose kernels are based on the Walsh-Hadamard Transform (WHT) and the Complex Hadamard Transform (CHT). On the basis of the symmetrical properties of the real and complex Walsh-Hadamard matrices are developed fast computational algorithms whose computational complexity is compared with that of the famous deterministic transforms: the 3D Fast Fourier Transform, the 3D Discrete Wavelet Transform and the statistical Hierarchical Tucker decomposition. The comparison results show the lower computational complexity of the offered algorithms. Additionally, they ensure the high energy concentration of the original tensor into a small number of coefficients of the so calculated transformed spectrum tensor. The main advantage of the proposed algorithms is the reduction of the needed calculations due to the low number of hierarchical levels compared to the significant number of iterations needed to achieve the required decomposition accuracy based on the statistical methods. The choice of the 3D hierarchical decomposition is defined by the requirements and limitations related to the corresponding application area. Full article

High dimensionality continues to be a challenge in computational systems biology. The kinetic models of many phenomena of interest are high-dimensional and complex, resulting in large computational effort in the simulation. Model order reduction (MOR) is a mathematical technique that is used to reduce the computational complexity of high-dimensional systems by approximation with lower dimensional systems, while retaining the important information and properties of the full order system. Proper orthogonal decomposition (POD) is a method based on Galerkin projection that can be used for reducing the model order. POD is considered an optimal linear approach since it obtains the minimum squared distance between the original model and its reduced representation. However, POD may represent a restriction for nonlinear systems. By applying the POD method for nonlinear systems, the complexity to solve the nonlinear term still remains that of the full order model. To overcome the complexity for nonlinear terms in the dynamical system, an approach called the discrete empirical interpolation method (DEIM) can be used. In this paper, we discuss model reduction by POD and DEIM to reduce the order of kinetic models of biological systems and illustrate the approaches on some examples. Additional computational costs for setting up the reduced order system pay off for large-scale systems. In general, a reduced model should not be expected to yield good approximations if different initial conditions are used from that used to produce the reduced order model. We used the POD method of a kinetic model with different initial conditions to compute the reduced model. This reduced order model is able to predict the full order model for a variety of different initial conditions. Full article

As a type of distributed computing, volunteer computing (VC) has provided unlimited computing capacity at a low cost in recent decades. The architecture of most volunteer computing platforms (VCPs) is a master–worker model, which defines a master–slave relationship. Therefore, VCPs can be considered asymmetric multiprocessing systems (AMSs). As AMSs, VCPs are very promising for providing computing services for users. Users can submit tasks with deadline constraints to the VCPs. If the tasks are completed within their deadlines, VCPs will obtain the benefits. For this application scenario, this paper proposes a new task assignment problem with the maximum benefits in VCPs for the first time. To address the problem, we first proposed a list-based task assignment (LTA) strategy, and we proved that the LTA strategy could complete the task with a deadline constraint as soon as possible. Then, based on the LTA strategy, we proposed a maximum benefit scheduling (MBS) algorithm, which aimed at maximizing the benefits of VCPs. The MBS algorithm determined the acceptable tasks using a pruning strategy. Finally, the experiment results show that our proposed algorithm is more effective than current algorithms in the aspects of benefits, task acceptance rate and task completion rate. Full article

Accurately forecasting the daily production of coalbed methane (CBM) is important forformulating associated drainage parameters and evaluating the economic benefit of CBM mining. Daily production of CBM depends on many factors, making it difficult to predict using conventional mathematical models. Because traditional methods do not reflect the long-term time series characteristics of CBM production, this study first used a long short-term memory neural network (LSTM) and transfer learning (TL) method for time series forecasting of CBM daily production. Based on the LSTM model, we introduced the idea of transfer learning and proposed a Transfer-LSTM (T-LSTM) CBM production forecasting model. This approach first uses a large amount of data similar to the target to pretrain the weights of the LSTM network, then uses transfer learning to fine-tune LSTM network parameters a second time, so as to obtain the final T-LSTM model. Experiments were carried out using daily CBM production data for the Panhe Demonstration Zone at southern Qinshui basin in China. Based on the results, the idea of transfer learning can solve the problem of insufficient samples during LSTM training. Prediction results for wells that entered the stable period earlier were more accurate, whereas results for types with unstable production in the early stage require further exploration. Because CBM wells daily production data have symmetrical similarities, which can provide a reference for the prediction of other wells, so our proposed T-LSTM network can achieve good results for the production forecast and can provide guidance for forecasting production of CBM wells. Full article

A Shannon cipher can be used as a building block for the block cipher construction if it is considered as one data block cipher. It has been proved that a Shannon cipher based on a matrix power function (MPF) is perfectly secure. This property was obtained by the special selection of algebraic structures to define the MPF. In an earlier paper we demonstrated, that certain MPF can be treated as a conjectured one-way function. This property is important since finding the inverse of a one-way function is related to an $NP$ -complete problem. The obtained results of perfect security on a theoretical level coincide with the $NP$ -completeness notion due to the well known Yao theorem. The proposed cipher does not need multiple rounds for the encryption of one data block and hence can be effectively parallelized since operations with matrices allow this effective parallelization. Full article

One can question the relationship between the symmetries of the exterior and interior of black holes with an isotropic and static exterior. This question is justified by the variety of recent findings indicating substantial or even dramatic differences in the properties of the exterior and interior of isotropic, static black holes. By invoking some of these findings related to a variety of the thought experiments with freely falling or uniformly accelerated test particles, one can establish the dynamic properties of the interior, which turn out to be equivalent to anisotropic cosmology, simultaneously expanding and contracting, albeit in different directions. In order to illustrate the comparison between the symmetry of the exterior vs. the interior, we apply conventional t, r, θ, φ coordinates to both of these ranges, although on the horizon(s) they display singular behavior. Using a simple approach based on co-moving and freely falling observers, the dynamics of the cylindrically shaped interior are explored. That enables us to present schematic snapshots of the interior of a Schwarzschild black hole, expanding along its cylindrical axis and contracting along its spherical base, as well as the interior of a Reissner–Nordström black hole, expanding first and then contracting along the cylindrical axis up to the terminal instant r =r₋. Full article

Smartphones and mobile tablets play significant roles in daily life and have led to an increase in the number of users of this technology. The rising number of mobile device end-users has resulted in the generation of malware by hackers. Thus, mobile devices are becoming vulnerable to malware. Machine learning plays an important role in the detection of mobile malware applications. In this study, we focus on static analysis for Android malware detection. The ultimate goal of this research is to find out the symmetric features across the malware Android application to easily detect them. Many state-of-the-art methods focus on extracting asymmetric patterns of the category of features, e.g., application permissions to distinguish the malware application from the benign application. In this work, we propose a compromise by considering different types of static features and select the most important features that affect the detection process. These features represent the symmetric pattern to be used for the classification task. Inspired by TF-IDF, we propose a novel method of feature selection. Moreover, we propose a new method for merging the Android application URLs into a single feature called the URL_score. Several linear machine learning classifiers are utilized to evaluate the proposed method. The proposed methods significantly reduce the feature space, i.e., the symmetric pattern, of the Android application dataset and the memory size of the final model. In addition, the proposed model achieves the highest reported accuracy for the Drebin dataset to date. Based on the evaluation results, the linear support vector machine achieves an accuracy of 99%. Full article

Each business faces large competition in the market, and it is necessary to adopt the most effective methodology as possible in order to obtain the best solution. Six Sigma (6σ) is a set of techniques and tools for process improvement. The tools of Six Sigma apply within a simple improvement model known as Define–Measure–Analyze–Improve–Control (DMAIC). This paper shows that implementing Six Sigma can be more effective in managing the vehicle fleet. The combination of mathematical, i.e., statistical basis and practice makes Six Sigma so successful. The Six Sigma project, implemented to reduce costs and increase the availability of a vehicle fleet in a selected company, can be widely applied in other similar enterprises. Full article

The aim of this paper is to give some fixed point results in generalized metric spaces in Perov’s sense. The generalized metric considered here is the w-distance with a symmetry condition. The operators satisfy a contractive weakly condition of Hardy–Rogers type. The second part of the paper is devoted to the study of the data dependence, the well-posedness, and the Ulam–Hyers stability of the fixed point problem. An example is also given to sustain the presented results. Full article

As a common method applied in the construction of tunnels with Grade IV and Grade V surrounding rock, the center diaphragm (CD) method has the advantage of resisting the inward horizontal convergence of the tunnel. However, due to the small lateral earth pressure of the shallow tunnel, the curved center diaphragm would have an unstable stress state and cannot provide sufficient support to the surrounding rock. Based on the CD method, this study presents a vertical center diaphragm (VCD) method with an axisymmetric structure. The application condition of the VCD method relies on the comparison of the surface settlement and tunnel deformation with the two methods in different surrounding rock grades and buried depths by using a three-dimensional finite-difference code. Based on the Shenzhen Eastern Transit Expressway Connection Line Tunnel, which has six lanes of double lines, the deformation regularities and mechanical characteristics of the VCD method, including the surface settlement, tunnel deformation, internal force of the center diaphragm, surrounding rock pressure, and steel arch stress, are investigated by numerical calculations and a field comparative test. The results obtained in this study provide several suggestions for constructing shallow tunnels. Furthermore, the construction efficiency and economy of the VCD method are evaluated. Full article

Sports activities engagement is a sustainable lifestyle that can signal that individuals have the potential to become successful. The lifetime wellbeing that comes from participating in sports activities results in a general and global policy agenda encouraging populations to be part of it. However, prior studies have seldom tested how individuals’ characteristics influence their wellbeing through sports activities engagement from a lifetime perspective. In the current study, based on the conservation of resources and signaling theories, we suggest that with a high level of personal control and self-esteem, individuals will proactively maintain a good lifestyle by engaging in more sports activities. Moreover, this engagement is not only good for these individuals’ physical and mental health, but will also bring them much more life satisfaction than others. A large and representative sample with 12,686 participants collected from over 35-year surveys across different social classes in the United States is used to test our hypotheses. The results indicate that individuals’ characteristics will indeed influence their wellbeing, even after 40 years of age, by changing their sports activities engagement, which includes both light activities such as walking and vigorous activities such as running and swimming. Potential theoretical contributions and policy implications are also proposed. Full article

This paper proposes neutrosophic vague N-soft sets which is composed of neutrosophic vague sets and N-soft sets for the first time. The new hybrid model includes a pair of asymmetric functions: truth-membership and false-membership, and an indeterminacy-membership function. Some useful operations and propositions are given and illustrated by examples. Moreover, a method of priority relation ranking based on neutrosophic vague N-soft sets is presented. The validity of the method is verified by comparison. It is more flexible and reasonable to use this method in our daily life. Finally, a potential application of multi-attribute decision making is presented. Full article

Benefiting from the rapid development of big data and high-performance computing, more data is available and more tasks could be solved by machine learning now. Even so, it is still difficult to maximum the power of big data due to each dataset is isolated with others. Although open source datasets are available, algorithms’ performance is asymmetric with the data volume. Hence, the AI community wishes to raise a symmetric continuous learning architecture which can automatically learn and adapt to different tasks. Such a learning architecture also is commonly called as lifelong machine learning (LML). This learning paradigm could manage the learning process and accumulate meta-knowledge by itself during learning different tasks. The meta-knowledge is shared among all tasks symmetrically to help them to improve performance. With the growth of meta-knowledge, the performance of each task is expected to be better and better. In order to demonstrate the application of lifelong machine learning, this paper proposed a novel and symmetric lifelong learning approach for sentiment classification as an example to show how it adapts different domains and keeps efficiency meanwhile. Full article

The Marshall-Olkin extended family of distributions is an alternative for modeling lifetimes, and considers more or less asymmetry than its parent model, achieved by incorporating just one extra parameter. We investigate the bias of maximum likelihood estimators and use it to develop an estimator with less bias than traditional estimators, by a modification of the score function. Unlike other proposals, in this paper, we consider a bias reduction methodology that can be applied to any member of the family and not necessarily to any particular distribution. We conduct a Monte Carlo simulation in order to study the performance of the corrected estimators in finite samples. This simulation shows that the maximum likelihood estimator is quite biased and the proposed estimator is much less biased; in small sample sizes, the bias is reduced by around 50 percent. Two applications, related to the air conditioning system of an airplane and precipitations, are presented to illustrate the results. In those applications, the bias reduction for the shape parameters is close to 25% and the bias reduction also reduces, among others things, the width of the 95% confidence intervals for quantiles lower than 0.594. Full article

It is a very important but difficult task to seek explicit variational formulations for nonlinear and complex models because variational principles are theoretical bases for many methods to solve or analyze the nonlinear problem. By designing skillfully the trial-Lagrange functional, different groups of variational principles are successfully constructed for two kinds of coupled nonlinear equations in shallow water, i.e., the Broer-Kaup equations and the (2+1)-dimensional dispersive long-wave equations, respectively. Both of them contain many kinds of soliton solutions, which are always symmetric or anti-symmetric in space. Subsequently, the obtained variational principles are proved to be correct by minimizing the functionals with the calculus of variations. The established variational principles are firstly discovered, which can help to study the symmetries and find conserved quantities for the equations considered, and might find lots of applications in numerical simulation. Full article

Venlafaxine (VFX) is a modern antidepressant from the serotonin and norepinephrine reuptake inhibitor (SNRI) class. It is a chiral substance used in therapy as a racemate, but differences between the pharmacological properties of the two enantiomers have been reported. The current article presents the development of a simple capillary electrophoresis (CE) method for the rapid chiral separation of VFX enantiomers. A complex cyclodextrin (CD) screening at four different pH levels was carried out to establish the optimum chiral selector; carboxymethyl-β-CD (CM-β-CD) at pH 2.5 was selected for further method development. An initial “one factor at time” (OFAT) screening strategy was used to establish the influence of analytical parameters on the separation, followed by a face centered central composite design (FCCD) for the optimization process. The analytical performances of the newly developed method were verified in terms of accuracy, linearity, precision, repeatability, and sensitivity. The method was used for the determination of VFX enantiomer ratio in pharmaceutical forms. Finally, computer modelling of VFX-CD complexes was undertaken to characterize host–guest chiral recognition. Full article

This work is devoted to the investigation of a two-dimensional porous material under weak, strong and normal conductivity, using the eigenvalues method. By using Laplace–Fourier transformations with the eigenvalues technique, the variables are analytically obtained. The derived technique is assessed with numerical results that are obtained from the porous mediums using simplified symmetric geometry. The results, including the displacements, temperature, stresses and the change in the volume fraction field, are offered graphically. Comparisons are made among the outcomes obtained under weak, normal and strong conductivity. Full article

The development of the regional economy cannot be separated from the support of regional logistics, as the scientific decisions of regional logistics are helpful to promote the healthy development of the regional economy. The comprehensive evaluation of regional logistics competitiveness is the premise and foundation of regional logistics scientific decision-making; the evaluation index system, evaluation data, and index weight are the key links affecting a comprehensive evaluation. In order to improve the quality of a comprehensive evaluation, the study aims at addressing problems such as the evaluation index system of regional logistics competitiveness being complex and scattered, the normalized distribution of the evaluation data being extremely asymmetric and seriously deviating from the normal distribution, and the logic of calculating index weights by the analytic hierarchy process (AHP) not being accurate. To do this, a triangle model of regional logistics competitiveness is constructed based on Porter’s diamond model, and the evaluation index system of regional logistics competitiveness is refined from the three dimensions of resource supply, logistics service, and market demand. Based on the concept of symmetry theory, a normalization method of segmental mapping with quartiles as multiple reference points is proposed, which improves the distribution rationality, symmetry, and distance discrimination of normalized data. The dynamic index scale is used to determine the scale of the analytic hierarchy process, and the evaluation matrix is constructed based on the importance level grading table; the index weights are directly solved without a consistency check, which improves the logical accuracy of a subjective evaluation. Based on the data of segment mapping, the comprehensive evaluation value of the evaluation object is calculated, and the competitiveness of regional logistics is compared and ranked, which improves the differentiation and consistency of the results. Through the comparative analysis of the calculation results, it was proven that the improvement of the data standardization method is necessary when the range is too large. The method in this paper can make the distribution of data standardization with a range too large closer to the normal distribution. It was found that the ranking of regional logistics competitiveness is highly consistent with the total social logistics, and that the total amount of regional logistics has an important reference value for the competitiveness of regional logistics. The ranking calculated by the indicators and methods in this paper has a certain reference value for regional logistics decision-making. Full article

Although the turbulent intensity is suppressed in the drag-reducing channel flow by viscoelastic additives, the mean velocity distribution in the channel flow is symmetrical and tends to be similar to the laminar flow. In the study of near-wall modulation of the drag-reducing flow with an injected ultrathin water layer, an asymmetrical mean velocity distribution was found. To further investigate this phenomenon and the underlying cause, an experiment was carried out with the water injected from a porous channel wall at a small velocity (~10⁻⁴ m/s) into the drag-reducing flow of surfactant solution. The instantaneous concentration and flow fields were measured by using planar laser-induced fluorescence (PLIF) and particle imaging velocimetry (PIV) techniques, respectively. Moreover, analyses on turbulent statistical characteristics and spatial distribution of viscoelastic structures were carried out on the basis of comparison among various flow cases. The results showed that the injected ultrathin water layer under present experimental conditions affected the anisotropy of the drag-reducing flow. The characteristics, such as turbulence intensity, showed the zonal feature in the wall-normal direction. The Reynolds shear stress was enhanced in the near-wall region, and the viscoelastic structure was modified severely due to the redistributed stress. These results may provide experimental supports for the near-wall modulation of turbulence and the exploration of the drag-reducing mechanism by viscoelastic additives. Full article

Because Herglotz’s variational problem achieves the variational representation of non-conservative dynamic processes, its research has attracted wide attention. The aim of this paper is to explore Herglotz’s variational problem for a non-conservative system with delayed arguments under Lagrangian framework and its Noether’s theorem. Firstly, we derive the non-isochronous variation formulas of Hamilton–Herglotz action containing delayed arguments. Secondly, for the Hamilton–Herglotz action case, we define the Noether symmetry and give the criterion of symmetry. Thirdly, we prove Herglotz type Noether’s theorem for non-conservative system with delayed arguments. As a generalization, Birkhoff’s version and Hamilton’s version for Herglotz type Noether’s theorems are presented. To illustrate the application of our Noether’s theorems, we give two examples of damped oscillators. Full article

The conditional Lie–Bäcklund symmetry method is applied to investigate the functionally generalized separation of variables for quasi-linear diffusion equations with a source. The equations and the admitted conditional Lie–Bäcklund symmetries related to invariant subspaces are identified. The exact solutions possessing the form of the functionally generalized separation of variables are constructed for the resulting equations due to the corresponding symmetry reductions. Full article

As online social networks play a more and more important role in public opinion, the large-scale simulation of social networks has been focused on by many scientists from sociology, communication, informatics, and so on. It is a good way to study real information diffusion in a symmetrical simulation world by agent-based modeling and simulation (ABMS), which is considered an effective solution by scholars from computational sociology. However, on the one hand, classical ABMS tools such as NetLogo cannot support the simulation of more than thousands of agents. On the other hand, big data platforms such as Hadoop and Spark used to study big datasets do not provide optimization for the simulation of large-scale social networks. A two-tier partition algorithm for the optimization of large-scale simulation of social networks is proposed in this paper. First, the simulation kernel of ABMS for information diffusion is implemented based on the Spark platform. Both the data structure and the scheduling mechanism are implemented by Resilient Distributed Data (RDD) to simulate the millions of agents. Second, a two-tier partition algorithm is implemented by community detection and graph cut. Community detection is used to find the partition of high interactions in the social network. A graph cut is used to achieve the goal of load balance. Finally, with the support of the dataset recorded from Twitter, a series of experiments are used to testify the performance of the two-tier partition algorithm in both the communication cost and load balance. Full article

Our work is based on the multiple inequalities illustrated in 1967 by E. K. Godunova and V. I. Levin, in 1990 by Hwang and Yang and in 1993 by B. G. Pachpatte. With the help of the dynamic Jensen and Hölder inequality, we generalize a number of those inequalities to a general time scale. In addition to these generalizations, some integral and discrete inequalities will be obtained as special cases of our results. Full article

Surface Plasma resonance (SPR) sensors combined with biological receptors are widely used in biosensors. Due to limitations of measurement techniques, small-scale, low accuracy, and sensitivity to the refractive index of solution in traditional SPR prism sensor arise. As a consequence, it is difficult to launch commercial production of SPR sensors. The theory of localized surface plasmon resonance (LSPR) developed based on SPR theory has stronger coupling ability to near-field photons. Based on the LSPR sensing theory, we propose a submicron-sized golden-disk and graphene composite structure. By varying the thickness and diameter of the array disk, the performance of the LSPR sensor can be optimized. A graphene layer sandwiched between the golden-disk and the silver film can prevent the latter from oxidizing. Symmetrical design enables high-low concentration of dual-channel distributed sensing. As the fixed light source, we use a 632.8-nm laser. A golden nano-disk with 45 nm thickness and 70 nm radius is designed, using a finite difference time domain (FDTD) simulation system. When the incident angle is 42°, the figure of merit (FOM) reaches 8826, and the measurable refractive index range reaches 0.2317. Full article