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Researchers in cognitive science have long been interested in modeling human perception using statistical methods. This requires maneuvers because these multiple dimensional data are always intertwined with complex inner structures. The previous studies in cognitive sciences commonly applied principal component analysis (PCA) to truncate data dimensions when dealing with data with multiple dimensions. This is not necessarily because of its merit in terms of mathematical algorithm, but partly because it is easy to conduct with commonly accessible statistical software. On the other hand, dimension reduction might not be the best analysis when modeling data with no more than 20 dimensions. Using state-of-the-art techniques, researchers in various research disciplines (e.g., computer vision) classified data with more than hundreds of dimensions with neural networks and revealed the inner structure of the data. Therefore, it might be more sophisticated to process human perception data directly with neural networks. In this paper, we introduce the multi-dimensional data analysis platform (MuDAP), a powerful toolbox for data analysis in cognitive science. It utilizes artificial intelligence as well as network analysis, an analysis method that takes advantage of data symmetry. With the graphic user interface, a researcher, with or without previous experience, could analyze multiple dimensional data with great ease. [ABSTRACT FROM AUTHOR]

In computer science, and especially in computer vision, the contour of an object is used to describe its features; thus, the shape descriptor plays an indispensable role in target detection and recognition. Further, Fourier is an important mathematical description method, and the Fourier transform of a shape contour has symmetry. This paper will demonstrate the symmetry of shape contour in the frequency domain. In recent years, increasing numbers of shape descriptors have come to the fore, but many descriptors ignore the details of shape. It is found that the most fundamental reason affecting the performance of shape descriptors is structural restraints, especially feature structure restraint. Therefore, in this paper, the restraint of feature structure that intrinsically deteriorates recognition performance is shown, and a fast shape recognition method via the Bone Point Segment (BPS) restraint reduction is proposed. An approach using the inner distance to find bone shapes and segment the shape contour by these bones is proposed. Then, Fourier transform is performed on each segment to form the shape feature. Finally, the restraints of the shape feature are reduced in order to build a more effective shape feature. What is commendable is that its discriminability and robustness is strong, the process is simple, and matching speed is fast. More importantly, the experiment results show that the shape descriptor has higher recognition accuracy and the matching speed runs up to more than 1000 times faster than the existing description methods like CBW and TCD. More importantly, it is worth noting that the recognition accuracy approaches 100% in the self-build dataset. [ABSTRACT FROM AUTHOR]

The characterisation of geometric shapes produces their concise description and is, therefore, important for subsequent analyses, for example in Computer Vision, Machine Learning, or shape matching. A new method for extracting characterisation vectors of 2D geometric shapes is proposed in this paper. The shape of interest, embedded into a raster space, is swept several times by sweep-lines having different slopes. The interior shape's points, being in the middle of its boundary and laying on the actual sweep-line, are identified at each stage of the sweeping process. The midpoints are then connected iteratively into chains. The chains are filtered, vectorised, and normalised. The obtained polylines from the vectorisation step are used to design the shape's characterisation vector for further application-specific analyses. The proposed method was verified on numerous shapes, where single- and multi-threaded implementations were compared. Finally, characterisation vectors, among which some were rotated and scaled, were determined for these shapes. The proposed method demonstrated a good rotation- and scaling-invariant identification of equal shapes. [ABSTRACT FROM AUTHOR]

The notion of fuzzy graph (FG) is widely used in many problems arising from partial or incomplete descriptions of the real world and in particular from fields such as engineering, economics, computer science, social disciplines, or medical diagnostics, and has been used in many fields of pure mathematics as well as in several areas of applied sciences such as decision making, statistics and networking. In this paper we will deal with the graph of the picture fuzzy(symmetric) set using the notion of domination in picture fuzzy graph (PFG) as a generalization of both the concept of fuzzy graph domination and intuitionistic fuzzy graph (IFG) domination. The concepts of domination theory (DT) and double domination theory (DDT) of a PFG are introduced, studied and concretely applied to the real case of an election competition to determine the minimum number of citizens a politician should meet in person in order to win the election. The choice of fuzzification (symmetric) and defuzzification (anti-symmetric) methods depends on the specific application and the type of fuzzy sets being used, whether they are symmetric or anti-symmetric. There are various methods for each process, such as centroid, max-min, and weighted average methods for defuzzification. Finally, in the last section, drawing from the application example, the features and benefits of PFGs with respect to fuzzy graphs and intuitionistic fuzzy graphs are compared and discussed. [ABSTRACT FROM AUTHOR]

Graphs are useful for analysing the structure models in computer science, operations research, and sociology. The word metric dimension is the basis of the distance function, which has a symmetric property. Moreover, finding the resolving set of a graph is NP-complete, and the possibilities of finding the resolving set are reduced due to the symmetric behaviour of the graph. In this paper, we introduce the idea of the edge-multiset dimension of graphs. A representation of an edge is defined as the multiset of distances between it and the vertices of a set, B ⊆ V (Γ) . If the representation of two different edges is unequal, then B is an edge-multiset resolving a set of Γ. The least possible cardinality of the edge-multiset resolving a set is referred to as the edge-multiset dimension of Γ. This article presents preliminary results, special conditions, and bounds on the edge-multiset dimension of certain graphs. This research provides new insights into structure models in computer science, operations research, and sociology. They could have implications for developing computer algorithms, aircraft scheduling, and species movement between regions. [ABSTRACT FROM AUTHOR]

The metric dimension has various applications in several fields, such as computer science, image processing, pattern recognition, integer programming problems, drug discovery, and the production of various chemical compounds. The lowest number of vertices in a set with the condition that any vertex can be uniquely identified by the list of distances from other vertices in the set is the metric dimension of a graph. A resolving function of the graph G is a map ϑ : V (G) → [ 0 , 1 ] such that ∑ u ∈ R { v , w } ϑ (u) ≥ 1 , for every pair of adjacent distinct vertices v , w ∈ V (G) . The local fractional metric dimension of the graph G is defined as ldim f (G) = min { ∑ v ∈ V (G) ϑ (v) , where ϑ is a local resolving function of G } . This paper presents a new family of planar networks namely, rotationally heptagonal symmetrical graphs by means of up to four cords in the heptagonal structure, and then find their upper-bound sequences for the local fractional metric dimension. Moreover, the comparison of the upper-bound sequence for the local fractional metric dimension is elaborated both numerically and graphically. Furthermore, the asymptotic behavior of the investigated sequences for the local fractional metric dimension is addressed. [ABSTRACT FROM AUTHOR]

The International Institute of Knowledge Innovation and Invention (IIKII) is an institute that promotes the exchange of innovations and inventions, and establishes a communication platform for international innovations and researches. In 2019, IIKII cooperated with the Institute of Electrical and Electronics Engineers (IEEE) Tainan Section Sensors Council to hold IEEE conferences such as IEEE ICIASE 2019, IEEE ECBIOS 2019, IEEE ICKII 2019, ICUSA-GAME 2019, and IEEE ECICE 2019. This Special Issue entitled "Selected Papers from IIKII 2019 conferences" aims to select excellent papers from IIKII 2019 conferences, including symmetry in physics, chemistry, biology, mathematics, and computer science, etc. It selected 21 excellent papers from 750 papers presented in IIKII 2019 conferences on the topic of symmetry. The main goals of this Special Issue are to encourage scientists to publish their experimental and theoretical results in as much detail as possible, and to discover new scientific knowledge relevant to the topic of symmetry. [ABSTRACT FROM AUTHOR]

Local fractional calculus (fractal calculus) plays a crucial role in applications, especially in computer sciences and engineering. One of these applications appears in the theory of chaos. Therefore, this paper studies the dynamics of a fractal complex logistic map and then employs this map to generate chaotic sequences for a new symmetric image encryption algorithm. Firstly, we derive the fractional complex logistic map and investigate its dynamics by determining its equilibria, geometric properties, and chaotic behavior. Secondly, the fractional chaotic sequences of the proposed map are employed to scramble and alter image pixels to increase resistance to decryption attacks. The output findings indicate that the proposed algorithm based on fractional complex logistic maps could effectively encrypt various kinds of images. Furthermore, it has better security performance than several existing algorithms. [ABSTRACT FROM AUTHOR]

A new algorithm is presented for detecting the global reflection symmetry of geometric objects. The algorithm works for 2D and 3D objects which may be open or closed and may or may not contain holes. The algorithm accepts a point cloud obtained by sampling the object's surface at the input. The points are inserted into a uniform grid and so-called boundary cells are identified. The centroid of the boundary cells is determined, and a testing symmetry axis/plane is set through it. In this way, the boundary cells are split into two parts and they are faced with the symmetry estimation function. If the function estimates the symmetric case, the boundary cells are further split until a given threshold is reached or a non-symmetric result is obtained. The new testing axis/plane is then derived and tested by rotation around the centroid. This paper introduces three techniques to accelerate the computation. Competitive results were obtained when the algorithm was compared against the state of the art. [ABSTRACT FROM AUTHOR]

This paper presents research focusing on visualization and pattern recognition based on computer science. Although deep neural networks demonstrate satisfactory performance regarding image and voice recognition, as well as pattern analysis and intrusion detection, they exhibit inferior performance towards adversarial examples. Noise introduction, to some degree, to the original data could lead adversarial examples to be misclassified by deep neural networks, even though they can still be deemed as normal by humans. In this paper, a robust diversity adversarial training method against adversarial attacks was demonstrated. In this approach, the target model is more robust to unknown adversarial examples, as it trains various adversarial samples. During the experiment, Tensorflow was employed as our deep learning framework, while MNIST and Fashion-MNIST were used as experimental datasets. Results revealed that the diversity training method has lowered the attack success rate by an average of 27.2 and 24.3% for various adversarial examples, while maintaining the 98.7 and 91.5% accuracy rates regarding the original data of MNIST and Fashion-MNIST. [ABSTRACT FROM AUTHOR]

Automatic speech recognition, especially large vocabulary continuous speech recognition, is an important issue in the field of machine learning. For a long time, the hidden Markov model (HMM)-Gaussian mixed model (GMM) has been the mainstream speech recognition framework. But recently, HMM-deep neural network (DNN) model and the end-to-end model using deep learning has achieved performance beyond HMM-GMM. Both using deep learning techniques, these two models have comparable performances. However, the HMM-DNN model itself is limited by various unfavorable factors such as data forced segmentation alignment, independent hypothesis, and multi-module individual training inherited from HMM, while the end-to-end model has a simplified model, joint training, direct output, no need to force data alignment and other advantages. Therefore, the end-to-end model is an important research direction of speech recognition. In this paper we review the development of end-to-end model. This paper first introduces the basic ideas, advantages and disadvantages of HMM-based model and end-to-end models, and points out that end-to-end model is the development direction of speech recognition. Then the article focuses on the principles, progress and research hotspots of three different end-to-end models, which are connectionist temporal classification (CTC)-based, recurrent neural network (RNN)-transducer and attention-based, and makes theoretically and experimentally detailed comparisons. Their respective advantages and disadvantages and the possible future development of the end-to-end model are finally pointed out. Automatic speech recognition is a pattern recognition task in the field of computer science, which is a subject area of Symmetry. [ABSTRACT FROM AUTHOR]

Prediction of visual attention is a new and challenging subject, and to the best of our knowledge, there are not many pieces of research devoted to the anticipation of students' cognition when solving tests. The aim of this paper is to propose, implement, and evaluate a machine learning method that is capable of predicting saliency maps of students who participate in a learning task in the form of quizzes based on quiz questionnaire images. Our proposal utilizes several deep encoder–decoder symmetric schemas which are trained on a large set of saliency maps generated with eye tracking technology. Eye tracking data were acquired from students, who solved various tasks in the sciences and natural sciences (computer science, mathematics, physics, and biology). The proposed deep convolutional encoder–decoder network is capable of producing accurate predictions of students' visual attention when solving quizzes. Our evaluation showed that predictions are moderately positively correlated with actual data with a coefficient of 0.547 ± 0.109. It achieved better results in terms of correlation with real saliency maps than state-of-the-art methods. Visual analyses of the saliency maps obtained also correspond with our experience and expectations in this field. Both source codes and data from our research can be downloaded in order to reproduce our results. [ABSTRACT FROM AUTHOR]

The intelligent production of sheet metal is a comprehensive technology involving control science, computer science, and sheet metal production. Intelligent rolling is an important development in the production process of sheet metal. In this paper, a new symmetrical four-roller bending (SFRB) process is introduced, which consists of feeding, pre-bending, reverse roll bending, second bending, and forward roll bending and unloading. A control strategy is proposed for the process, including on-line monitoring of curvature, on-line identification of the springback law, on-line prediction of final reduction, and control strategy. A convenient and reliable on-line curvature monitoring method is proposed. The quantitative relationship between the reduction and the curvature, in the form of a quadratic function, was established by physical experiments and numerical simulation, and the online identification of the springback law was realized. An on-line prediction method of the final reduction is proposed, and the determination principle of the reduction of three pre-bending processes is given. Finally, the control strategy of the SFRB process was verified by physical experiments. The relative error of the curvature radius of the final formed parts can be controlled within 0.8%. This research provides new insights into intelligent rolling. [ABSTRACT FROM AUTHOR]

Graphs are often used as models to solve problems in computer science, mathematics, and biology. A pancake sorting problem is modeled using a pancake graph whose classes include burnt pancake graphs, signed permutation graphs, and restricted pancake graphs. The network cost is degree × diameter. Finding a graph with a small network cost is like finding a good sorting algorithm. We propose a novel recursively divided pancake (RDP) graph that has a smaller network cost than other pancake-like graphs. In the pancake graph Pn, the number of nodes is n!, the degree is n − 1, and the network cost is O(n2). In an RDPn, the number of nodes is n!, the degree is 2log2n − 1, and the network cost is O(n(log2n)3). Because O(n(log2n)3) < O(n2), the RDP is superior to other pancake-like graphs. In this paper, we propose an RDPn and analyze its basic topological properties. Second, we show that the RDPn is recursive and symmetric. Third, a sorting algorithm is proposed, and the degree and diameter are derived. Finally, the network cost is compared between the RDP graph and other classes of pancake graphs. [ABSTRACT FROM AUTHOR]

The concepts of terms and tree languages are significant tools for the development of research works in both universal algebra and theoretical computer science. In this paper, we establish a strong connection between semigroups of terms and tree languages, which provides the tools for studying monomorphisms between terms and generalized hypersubstitutions. A novel concept of a seminearring of non-deterministic generalized hypersubstitutions is introduced and some interesting properties among subsets of its are provided. Furthermore, we prove that there are monomorphisms from the power diagonal semigroup of tree languages and the monoid of generalized hypersubstitutions to the power diagonal semigroup of non-deterministic generalized hypersubstitutions and the monoid of non-deterministic generalized hypersubstitutions, respectively. Finally, the representation of terms using the theory of n-ary functions is defined. We then present the Cayley's theorem for Menger algebra of terms, which allows us to provide a concrete example via full transformation semigroups. [ABSTRACT FROM AUTHOR]

Axiomatically, symmetry is a fundamental property of mathematical functions defining similarity measures, where similarity measures are important tools in many areas of computer science, including machine learning and image processing. In this paper, we investigate a new technique to measure the similarity between two images, a fixed image and a moving image, in multi-modal image registration (MIR). MIR in medical image processing is essential and useful in diagnosis and therapy guidance, but still a very challenging task due to the lack of robustness against the rotational variance in the image transformation process. Our investigation leads to a novel, local self-similarity descriptor, called the modality-independent and rotation-invariant descriptor (miRID). By relying on the mean of the intensity values, an miRID is simply computable and can effectively handle the complicated intensity relationship between multi-modal images. Moreover, it can also overcome the problem of rotational variance by sorting the numerical values, each of which is the absolute difference between each pixel's intensity and the mean of all pixel intensities within a patch of the image. The experimental result shows that our method outperforms others in both multi-modal rigid and non-rigid image registrations. [ABSTRACT FROM AUTHOR]

Electronic Learning (e-learning) has made a great success and recently been estimated as a billion-dollar industry. The users of e-learning acquire knowledge of diversified content available in an application using innovative means. There is much e-learning software available—for example, LMS (Learning Management System) and Moodle. The functionalities of this software were reviewed and we recognized that learners have particular problems in getting relevant recommendations. For example, there might be essential discussions about a particular topic on social networks, such as Twitter, but that discussion is not linked up and recommended to the learners for getting the latest updates on technology-updated news related to their learning context. This has been set as the focus of the current project based on symmetry between user project specification. The developed project recommends relevant symmetric articles to e-learners from the social network of Twitter and the academic platform of DBLP. For recommendations, a Reinforcement learning model with optimization is employed, which utilizes the learners' local context, learners' profile available in the e-learning system, and the learners' historical views. The recommendations by the system are relevant tweets, popular relevant Twitter users, and research papers from DBLP. For matching the local context, profile, and history with the tweet text, we recognized that terms in the e-learning system need to be expanded to cover a wide range of concepts. However, this diversification should not include such terms which are irrelevant. To expand terms of the local context, profile and history, the software used the dataset of Grow-bag, which builds concept graphs of large-scale Computer Science topics based on the co-occurrence scores of Computer Science terms. This application demonstrated the need and success of e-learning software that is linked with social media and sends recommendations for the content being learned by the e-Learners in the e-learning environment. However, the current application only focuses on the Computer Science domain. There is a need for generalizing such applications to other domains in the future. [ABSTRACT FROM AUTHOR]

Network traffic classification based on machine learning is an important branch of pattern recognition in computer science. It is a key technology for dynamic intelligent network management and enhanced network controllability. However, the traffic classification methods still facing severe challenges: The optimal set of features is difficult to determine. The classification method is highly dependent on the effective characteristic combination. Meanwhile, it is also important to balance the experience risk and generalization ability of the classifier. In this paper, an improved network traffic classification model based on a support vector machine is proposed. First, a filter-wrapper hybrid feature selection method is proposed to solve the false deletion of combined features caused by a traditional feature selection method. Second, to balance the empirical risk and generalization ability of support vector machine (SVM) traffic classification model, an improved parameter optimization algorithm is proposed. The algorithm can dynamically adjust the quadratic search area, reduce the density of quadratic mesh generation, improve the search efficiency of the algorithm, and prevent the over-fitting while optimizing the parameters. The experiments show that the improved traffic classification model achieves higher classification accuracy, lower dimension and shorter elapsed time and performs significantly better than traditional SVM and the other three typical supervised ML algorithms. [ABSTRACT FROM AUTHOR]

In many real world problems, science fields such as biology, computer science, data mining, electrical and mechanical engineering, and signal processing, researchers aim to compare and classify several regression models. In this paper, a computational approach, based on the non-parametric methods, is used to investigate the similarities, and to classify several linear and non-linear regression models with symmetric errors. The ability of each given approach is then evaluated using simulated and real world practical datasets. [ABSTRACT FROM AUTHOR]

A single qubit may be represented on the Bloch sphere or similarly on the 3-sphere S 3 . Our goal is to dress this correspondence by converting the language of universal quantum computing (UQC) to that of 3-manifolds. A magic state and the Pauli group acting on it define a model of UQC as a positive operator-valued measure (POVM) that one recognizes to be a 3-manifold M 3 . More precisely, the d-dimensional POVMs defined from subgroups of finite index of the modular group P S L (2 , Z) correspond to d-fold M 3 - coverings over the trefoil knot. In this paper, we also investigate quantum information on a few 'universal' knots and links such as the figure-of-eight knot, the Whitehead link and Borromean rings, making use of the catalog of platonic manifolds available on the software SnapPy. Further connections between POVMs based UQC and M 3 's obtained from Dehn fillings are explored. [ABSTRACT FROM AUTHOR]