Open AccessArticle
A Fault Feature Extraction Method for Motor Bearing and Transmission Analysis
Symmetry 2017, 9(5), 60; doi:10.3390/sym9050060 -
Abstract
Roller bearings are the most widely used and easily damaged mechanical parts in rotating machinery. Their running state directly affects rotating machinery performance. Empirical mode decomposition (EMD) easily occurs illusive component and mode mixing problem. From the view of feature extraction, a new
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Roller bearings are the most widely used and easily damaged mechanical parts in rotating machinery. Their running state directly affects rotating machinery performance. Empirical mode decomposition (EMD) easily occurs illusive component and mode mixing problem. From the view of feature extraction, a new feature extraction method based on integrating ensemble empirical mode decomposition (EEMD), the correlation coefficient method, and Hilbert transform is proposed to extract fault features and identify fault states for motor bearings in this paper. In the proposed feature extraction method, the EEMD is used to decompose the vibration signal into a series of intrinsic mode functions (IMFs) with different frequency components. Then the correlation coefficient method is used to select the IMF components with the largest correlation coefficient, which are carried out with the Hilbert transform. The obtained corresponding envelope spectra are analyzed to extract the fault feature frequency and identify the fault state by comparing with the theoretical value. Finally, the fault signal transmission performance of vibration signals of the bearing inner ring and outer ring at the drive end and fan end are deeply studied. The experimental results show that the proposed feature extraction method can effectively eliminate the influence of the mode mixing and extract the fault feature frequency, and the energy of the vibration signal in the bearing outer ring at the fan end is lost during the transmission of the vibration signal. It is an effective method to extract the fault feature of the bearing from the noise with interference. Full article
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Open AccessArticle
Reversible Data-Hiding Systems with Modified Fluctuation Functions and Reed-Solomon Codes for Encrypted Image Recovery
Symmetry 2017, 9(5), 61; doi:10.3390/sym9050061 -
Abstract
In this paper, reversible data-hiding (RDH) systems with modified fluctuation functions and rate-matched Reed–Solomon (RS) codes are proposed to enhance the data recovery from encrypted images. The modified fluctuation functions are used for estimating embedded codeword bits from the correlation of pixels. Instead
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In this paper, reversible data-hiding (RDH) systems with modified fluctuation functions and rate-matched Reed–Solomon (RS) codes are proposed to enhance the data recovery from encrypted images. The modified fluctuation functions are used for estimating embedded codeword bits from the correlation of pixels. Instead of direct data-bit embedding, codeword bits of RS codes are embedded by a data-hider. With the help of the error-correcting capability of RS codes, the encrypted message can be recovered from the weak correlation of adjacent pixels in the image. In the experimental results, bit error rate (BER) and peak signal to noise ratio (PSNR) performances of the proposed system are better than those of referenced data-hiding systems for three images. The proposed schemes based on the modified fluctuation function or rate-matched codes can be applied to various RDH systems with better data transmission and image recovery performance. Full article
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Open AccessArticle
Analysis of Clustering Evaluation Considering Features of Item Response Data Using Data Mining Technique for Setting Cut-Off Scores
Symmetry 2017, 9(5), 62; doi:10.3390/sym9050062 -
Abstract
The setting of standards is a critical process in educational evaluation, but it is time-consuming and expensive because it is generally conducted by an education experts group. The purpose of this paper is to find a suitable cluster validity index that considers the
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The setting of standards is a critical process in educational evaluation, but it is time-consuming and expensive because it is generally conducted by an education experts group. The purpose of this paper is to find a suitable cluster validity index that considers the futures of item response data for setting cut-off scores. In this study, nine representative cluster validity indexes were used to evaluate the clustering results. Cohen’s kappa coefficient is used to check the conformity between a set cut-off score using four clustering techniques and a cut-off score set by experts. We compared the cut-off scores by each cluster validity index and by a group of experts. The experimental results show that the entropy-based method considers the features of item response data, so it has a realistic possibility of applying a clustering evaluation method to the setting of standards in criterion referenced evaluation. Full article
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Open AccessArticle
Collaborative CAD Synchronization Based on a Symmetric and Consistent Modeling Procedure
Symmetry 2017, 9(4), 59; doi:10.3390/sym9040059 -
Abstract
One basic issue with collaborative computer aided design (Co-CAD) is how to maintain valid and consistent modeling results across all design sites. Moreover, modeling history is important in parametric CAD modeling. Therefore, different from a typical co-editing approach, this paper proposes a novel
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One basic issue with collaborative computer aided design (Co-CAD) is how to maintain valid and consistent modeling results across all design sites. Moreover, modeling history is important in parametric CAD modeling. Therefore, different from a typical co-editing approach, this paper proposes a novel method for Co-CAD synchronization, in which all Co-CAD sites maintain symmetric and consistent operating procedures. Consequently, the consistency of both modeling results and history can be achieved. In order to generate a valid, unique, and symmetric queue among collaborative sites, a set of correlated mechanisms is presented in this paper. Firstly, the causal relationship of operations is maintained. Secondly, the operation queue is reconstructed for partial concurrency operation, and the concurrent operation can be retrieved. Thirdly, a symmetric, concurrent operation control strategy is proposed to determine the order of operations and resolve possible conflicts. Compared with existing Co-CAD consistency methods, the proposed method is convenient and flexible in supporting collaborative design. The experiment performed based on the collaborative modeling procedure demonstrates the correctness and applicability of this work. Full article
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Open AccessArticle
A Fast K-prototypes Algorithm Using Partial Distance Computation
Symmetry 2017, 9(4), 58; doi:10.3390/sym9040058 -
Abstract
The k-means is one of the most popular and widely used clustering algorithm; however, it is limited to numerical data only. The k-prototypes algorithm is an algorithm famous for dealing with both numerical and categorical data. However, there have been no studies to
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The k-means is one of the most popular and widely used clustering algorithm; however, it is limited to numerical data only. The k-prototypes algorithm is an algorithm famous for dealing with both numerical and categorical data. However, there have been no studies to accelerate it. In this paper, we propose a new, fast k-prototypes algorithm that provides the same answers as those of the original k-prototypes algorithm. The proposed algorithm avoids distance computations using partial distance computation. Our k-prototypes algorithm finds minimum distance without distance computations of all attributes between an object and a cluster center, which allows it to reduce time complexity. A partial distance computation uses a fact that a value of the maximum difference between two categorical attributes is 1 during distance computations. If data objects have m categorical attributes, the maximum difference of categorical attributes between an object and a cluster center is m. Our algorithm first computes distance with numerical attributes only. If a difference of the minimum distance and the second smallest with numerical attributes is higher than m, we can find the minimum distance between an object and a cluster center without distance computations of categorical attributes. The experimental results show that the computational performance of the proposed k-prototypes algorithm is superior to the original k-prototypes algorithm in our dataset. Full article
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Open AccessReview
A Matter of Degree: Strength of Brain Asymmetry and Behaviour
Symmetry 2017, 9(4), 57; doi:10.3390/sym9040057 -
Abstract
Research on a growing number of vertebrate species has shown that the left and right sides of the brain process information in different ways and that lateralized brain function is expressed in both specific and broad aspects of behaviour. This paper reviews the
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Research on a growing number of vertebrate species has shown that the left and right sides of the brain process information in different ways and that lateralized brain function is expressed in both specific and broad aspects of behaviour. This paper reviews the available evidence relating strength of lateralization to behavioural/cognitive performance. It begins by considering the relationship between limb preference and behaviour in humans and primates from the perspectives of direction and strength of lateralization. In birds, eye preference is used as a reflection of brain asymmetry and the strength of this asymmetry is associated with behaviour important for survival (e.g., visual discrimination of food from non-food and performance of two tasks in parallel). The same applies to studies on aquatic species, mainly fish but also tadpoles, in which strength of lateralization has been assessed as eye preferences or turning biases. Overall, the empirical evidence across vertebrate species points to the conclusion that stronger lateralization is advantageous in a wide range of contexts. Brief discussion of interhemispheric communication follows together with discussion of experiments that examined the effects of sectioning pathways connecting the left and right sides of the brain, or of preventing the development of these left-right connections. The conclusion reached is that degree of functional lateralization affects behaviour in quite similar ways across vertebrate species. Although the direction of lateralization is also important, in many situations strength of lateralization matters more. Finally, possible interactions between asymmetry in different sensory modalities is considered. Full article
Open AccessArticle
Interactive Blow and Burst of Giant Soap Bubbles
Symmetry 2017, 9(4), 56; doi:10.3390/sym9040056 -
Abstract
Previous studies on virtual soap bubbles mainly focused on methods for visualizing the physical and geometrical properties of soap bubbles and paid little attention to the possible ways to enhance the interaction between the simulation and the user. In this paper, a user
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Previous studies on virtual soap bubbles mainly focused on methods for visualizing the physical and geometrical properties of soap bubbles and paid little attention to the possible ways to enhance the interaction between the simulation and the user. In this paper, a user interaction-based giant soap bubble simulation system is proposed in which the free-form shape, size, and position of giant soap bubbles are determined by the user’s hand motions. Our method improves the controllability of soap bubble simulation by correcting the jerky hand trajectory and hand velocity to a smooth and gradual path. Our air flow transfer algorithm can produce detailed deformation and standing wave for soap film in real time. Our novel soap film bursting algorithm represents the process of the bursting phenomenon of soap-film and giant soap bubbles in a unified framework. The results of our experiment demonstrate that the system allows the user to experience the giant soap bubble blowing and bursting process in a virtual environment. Full article
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Open AccessArticle
3D Reconstruction Framework for Multiple Remote Robots on Cloud System
Symmetry 2017, 9(4), 55; doi:10.3390/sym9040055 -
Abstract
This paper proposes a cloud-based framework that optimizes the three-dimensional (3D) reconstruction of multiple types of sensor data captured from multiple remote robots. A working environment using multiple remote robots requires massive amounts of data processing in real-time, which cannot be achieved using
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This paper proposes a cloud-based framework that optimizes the three-dimensional (3D) reconstruction of multiple types of sensor data captured from multiple remote robots. A working environment using multiple remote robots requires massive amounts of data processing in real-time, which cannot be achieved using a single computer. In the proposed framework, reconstruction is carried out in cloud-based servers via distributed data processing. Consequently, users do not need to consider computing resources even when utilizing multiple remote robots. The sensors’ bulk data are transferred to a master server that divides the data and allocates the processing to a set of slave servers. Thus, the segmentation and reconstruction tasks are implemented in the slave servers. The reconstructed 3D space is created by fusing all the results in a visualization server, and the results are saved in a database that users can access and visualize in real-time. The results of the experiments conducted verify that the proposed system is capable of providing real-time 3D scenes of the surroundings of remote robots. Full article
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Open AccessArticle
An Efficient VQ Codebook Search Algorithm Applied to AMR-WB Speech Coding
Symmetry 2017, 9(4), 54; doi:10.3390/sym9040054 -
Abstract
The adaptive multi-rate wideband (AMR-WB) speech codec is widely used in modern mobile communication systems for high speech quality in handheld devices. Nonetheless, a major disadvantage is that vector quantization (VQ) of immittance spectral frequency (ISF) coefficients takes a considerable computational load in
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The adaptive multi-rate wideband (AMR-WB) speech codec is widely used in modern mobile communication systems for high speech quality in handheld devices. Nonetheless, a major disadvantage is that vector quantization (VQ) of immittance spectral frequency (ISF) coefficients takes a considerable computational load in the AMR-WB coding. Accordingly, a binary search space-structured VQ (BSS-VQ) algorithm is adopted to efficiently reduce the complexity of ISF quantization in AMR-WB. This search algorithm is done through a fast locating technique combined with lookup tables, such that an input vector is efficiently assigned to a subspace where relatively few codeword searches are required to be executed. In terms of overall search performance, this work is experimentally validated as a superior search algorithm relative to a multiple triangular inequality elimination (MTIE), a TIE with dynamic and intersection mechanisms (DI-TIE), and an equal-average equal-variance equal-norm nearest neighbor search (EEENNS) approach. With a full search algorithm as a benchmark for overall search load comparison, this work provides an 87% search load reduction at a threshold of quantization accuracy of 0.96, a figure far beyond 55% in the MTIE, 76% in the EEENNS approach, and 83% in the DI-TIE approach. Full article
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Open AccessArticle
Ear Detection under Uncontrolled Conditions with Multiple Scale Faster Region-Based Convolutional Neural Networks
Symmetry 2017, 9(4), 53; doi:10.3390/sym9040053 -
Abstract
Ear detection is an important step in ear recognition approaches. Most existing ear detection techniques are based on manually designing features or shallow learning algorithms. However, researchers found that the pose variation, occlusion, and imaging conditions provide a great challenge to the traditional
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Ear detection is an important step in ear recognition approaches. Most existing ear detection techniques are based on manually designing features or shallow learning algorithms. However, researchers found that the pose variation, occlusion, and imaging conditions provide a great challenge to the traditional ear detection methods under uncontrolled conditions. This paper proposes an efficient technique involving Multiple Scale Faster Region-based Convolutional Neural Networks (Faster R-CNN) to detect ears from 2D profile images in natural images automatically. Firstly, three regions of different scales are detected to infer the information about the ear location context within the image. Then an ear region filtering approach is proposed to extract the correct ear region and eliminate the false positives automatically. In an experiment with a test set of 200 web images (with variable photographic conditions), 98% of ears were accurately detected. Experiments were likewise conducted on the Collection J2 of University of Notre Dame Biometrics Database (UND-J2) and University of Beira Interior Ear dataset (UBEAR), which contain large occlusion, scale, and pose variations. Detection rates of 100% and 98.22%, respectively, demonstrate the effectiveness of the proposed approach. Full article
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Open AccessArticle
Dual Hesitant Fuzzy Probability
Symmetry 2017, 9(4), 52; doi:10.3390/sym9040052 -
Abstract
Intuitionistic fuzzy probabilities are an extension of the concept of probabilities with application in several practical problem solving tasks. The former are probabilities represented through intuitionistic fuzzy numbers, to indicate the uncertainty of the membership and nonmembership degrees in the value assigned to
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Intuitionistic fuzzy probabilities are an extension of the concept of probabilities with application in several practical problem solving tasks. The former are probabilities represented through intuitionistic fuzzy numbers, to indicate the uncertainty of the membership and nonmembership degrees in the value assigned to probabilities. Moreover, a dual hesitant fuzzy set (DHFS) is an extension of an intuitionistic fuzzy set, and its membership degrees and nonmembership degrees are represented by two sets of possible values; this new theory of fuzzy sets is known today as dual hesitant fuzzy set theory. This work will extend the notion of dual hesitant fuzzy probabilities by representing probabilities through the dual hesitant fuzzy numbers, in the sense of Zhu et al., instead of intuitionistic fuzzy numbers. We also give the concept of dual hesitant fuzzy probability, based on which we provide some main results including the properties of dual hesitant fuzzy probability, dual hesitant fuzzy conditional probability, and dual hesitant fuzzy total probability. Full article
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Open AccessArticle
Correlation Coefficients of Extended Hesitant Fuzzy Sets and Their Applications to Decision Making
Symmetry 2017, 9(4), 47; doi:10.3390/sym9040047 -
Abstract
Extended hesitant fuzzy sets (EHFSs), which allow the membership degree of an element to a set represented by several possible value-groups, can be considered as a powerful tool to express uncertain information in the process of group decision making. Therefore, we derive some
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Extended hesitant fuzzy sets (EHFSs), which allow the membership degree of an element to a set represented by several possible value-groups, can be considered as a powerful tool to express uncertain information in the process of group decision making. Therefore, we derive some correlation coefficients between EHFSs, which contain two cases, the correlation coefficients taking into account the length of extended hesitant fuzzy elements (EHFEs) and the correlation coefficients without taking into account the length of EHFEs, as a new extension of existing correlation coefficients for hesitant fuzzy sets (HFSs) and apply them to decision making under extended hesitant fuzzy environments. A real-world example based on the energy policy problem is employed to illustrate the actual need for dealing with the difference of evaluation information provided by different experts without information loss in decision making processes. Full article
Open AccessReview
Methods and Tools of Digital Triage in Forensic Context: Survey and Future Directions
Symmetry 2017, 9(4), 49; doi:10.3390/sym9040049 -
Abstract
Digital triage is the first investigative step of the forensic examination. The digital triage comes in two forms, live triage and post-mortem triage. The primary goal of the live triage is a rapid extraction of an intelligence from the potential sources. The live
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Digital triage is the first investigative step of the forensic examination. The digital triage comes in two forms, live triage and post-mortem triage. The primary goal of the live triage is a rapid extraction of an intelligence from the potential sources. The live triage raises legitimate concerns. The post-mortem triage is conducted in the laboratory and its main goal is ranking of the seized devices for the possible existence of the relevant evidence. The digital triage has the potential to quickly identify items that are likely to contain the evidential data. Therefore, it is a solution to the problem of case backlogs. However, existing methods and tools of the digital triage have limitations, especially, in the forensic context. Nevertheless, we have no better solution for the time being. In this paper, we critically review published research works and the proposed solutions for digital triage. The review is divided into four sections as follows: live triage, post-mortem triage, mobile device triage, and triage tools. We conclude that many challenges are awaiting for the developers in creating methods and tools of digital triage in order to keep pace with the development of new technologies. Full article
Open AccessArticle
Developmental Origins of Limb Developmental Instability in Human Fetuses: Many Abnormalities Make the Difference
Symmetry 2017, 9(4), 51; doi:10.3390/sym9040051 -
Abstract
Fluctuating asymmetry (FA) is the small random deviation from perfect symmetry in bilateral traits and is often used to assess developmental instability (DI) experienced by organisms. In this study, with a unique dataset of 1389 deceased human fetuses, we investigated the relationship between
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Fluctuating asymmetry (FA) is the small random deviation from perfect symmetry in bilateral traits and is often used to assess developmental instability (DI) experienced by organisms. In this study, with a unique dataset of 1389 deceased human fetuses, we investigated the relationship between abnormal development and human limb FA in different ways, using a more fundamental approach than usually done. We studied whether there is an underlying developmental basis of DI, as measured by FA, by investigating, first, whether limb FA can be attributed to developmental abnormalities associated with specific organ systems, germ layers or patterning processes, and second, whether limb FA increases with increasing number of developmental abnormalities either gradually, or in a threshold-like fashion. Limb FA was found to increase in fetuses with cardiovascular and nervous system abnormalities. Fetuses with ectoderm-derived abnormalities were also found to have significantly higher limb FA, but no other germ layers were found to be associated. We found no significant correlation between specific developmental processes, such as neural crest development, segmentation, midline and left-right patterning and limb FA. Although only some congenital abnormalities were correlated with limb FA, our results do suggest that limb FA increases when an increasing number of organ systems, germ layers or developmental pathways are disrupted. Therefore, we conclude that limb FA is mainly a good indicator for DI in the case of particularly severe perturbations of development and that FA does not reflect the subtler deviations from developmental stability. Full article
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Open AccessArticle
Enhanced Joint and Separable Reversible Data Hiding in Encrypted Images with High Payload
Symmetry 2017, 9(4), 50; doi:10.3390/sym9040050 -
Abstract
Recently, much attention has been paid to reversible data hiding (RDH) in encrypted images, since it preserves the data that the original image can be perfectly recovered after data extraction while protecting the confidentiality of image content. In this paper, we propose joint
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Recently, much attention has been paid to reversible data hiding (RDH) in encrypted images, since it preserves the data that the original image can be perfectly recovered after data extraction while protecting the confidentiality of image content. In this paper, we propose joint and separable RDH techniques using an improved embedding pattern and a new measurement function in encrypted images with a high payload. The first problem in recent joint data hiding is that the encrypted image is divided into blocks, and the spatial correlation in the block cannot fully reflect the smoothness of a natural image. The second problem is that half embedding is used to embed data and the prediction error is exploited to calculate the smoothness, which also fails to give good performance. To solve these problems, we divide the encrypted image into four sets, instead of blocks; the actual value of pixels is considered, rather than an estimated value, and the absolute difference between neighboring pixels is used in preference to prediction error to calculate the smoothness. Therefore, it is possible to use spatial correlation of the natural image perfectly. The experimental results show that the proposed joint and separable methods offer better performance over other works. Full article
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Open AccessArticle
Nested One-to-One Symmetric Classification Method on a Fuzzy SVM for Moving Vehicles
Symmetry 2017, 9(4), 48; doi:10.3390/sym9040048 -
Abstract
As a multi-classification problem, classification of moving vehicles has been studied by different statistical methods. These practical applications have various requirements, efficiencies, and performance, such as the size of training sample sets, convergence rate, and inseparable or ambiguous classification issues. With a reduction
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As a multi-classification problem, classification of moving vehicles has been studied by different statistical methods. These practical applications have various requirements, efficiencies, and performance, such as the size of training sample sets, convergence rate, and inseparable or ambiguous classification issues. With a reduction in its training time,the one-to-many support vector machine (SVM) method has an advantage over the standard SVM method by directly converting the binary classification problem into two multi-classification problems with short time and fast speed. When the number of training samples of a certain type is far less than the total number of samples, the accuracy of training, however, will be significantlydecreased,leading to theproblem of inseparable area. In this paper, the proposed nested one-to-one symmetric classification method on a fuzzy SVM symmetrically transforms the C multi-classification problems into the C(C-1)/2 binary classification problems with C(C-1)/2 classifiers, and solves the problem of inseparable area. According to the best combination factor of kernel function (γ, C) for the radial basis function (RBF) in the comparative experiments of training sample sets among the different algorithms, and the experimental results of many different training sample sets and test samples, the nested one-to-one symmetric classification algorithm on a fuzzy SVM for moving vehicle is able to obtain the best accuracy of recognition. Full article
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Open AccessLetter
Interweaving the Principle of Least Potential Energy in School and Introductory University Physics Courses
Symmetry 2017, 9(3), 45; doi:10.3390/sym9030045 -
Abstract
Understanding advanced physical phenomena such as vertically hanging elastic column, soap bubbles, crystals and cracks demands expressing and manipulating a system’s potential energy under equilibrium conditions. However, students at schools and universities are usually required to consider the forces acting on a system
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Understanding advanced physical phenomena such as vertically hanging elastic column, soap bubbles, crystals and cracks demands expressing and manipulating a system’s potential energy under equilibrium conditions. However, students at schools and universities are usually required to consider the forces acting on a system under equilibrium conditions, rather than taking into account its potential energy. As a result, they find it difficult to express the system’s potential energy and use it for calculations when they do need to do so. The principle of least potential energy is a powerful idea for solving static equilibrium physics problems in various fields such as hydrostatics, mechanics, and electrostatics. In the current essay, the authors describe this principle and provide examples where students can apply it. For each problem, the authors provide both the force consideration solution approach and the energy consideration solution approach. Full article
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Open AccessArticle
Symmetry in Domination for Hypergraphs with Choice
Symmetry 2017, 9(3), 46; doi:10.3390/sym9030046 -
Abstract
In this paper, we introduce the concept of (pair-wise) domination graphs for hypergraphs endowed with a choice function on edges. We are interested, for instance, in minimal numbers of edges for associated domination graphs. Theorems regarding the existence of balanced (zero-edge) domination graphs
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In this paper, we introduce the concept of (pair-wise) domination graphs for hypergraphs endowed with a choice function on edges. We are interested, for instance, in minimal numbers of edges for associated domination graphs. Theorems regarding the existence of balanced (zero-edge) domination graphs are presented. Several open questions are posed.
Full article
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Open AccessCommunication
Changes of Fluctuating Asymmetry with Age in Human Fetuses and Young Infants
Symmetry 2017, 9(3), 44; doi:10.3390/sym9030044 -
Abstract
(1) Background: Developmental instability (DI), often measured by fluctuating asymmetry (FA), increases with stress in humans, yet little is known about how stress affects the changes of asymmetry with age. More specifically, it is unknown if fetuses experiencing a major congenital abnormality will
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(1) Background: Developmental instability (DI), often measured by fluctuating asymmetry (FA), increases with stress in humans, yet little is known about how stress affects the changes of asymmetry with age. More specifically, it is unknown if fetuses experiencing a major congenital abnormality will express higher FA already during early development or only at a later age; (2) Methods: We combine two datasets to study associations between age and asymmetry in human fetuses and young infants. One population consists of fetuses from spontaneous abortions and early deceased infants where many experienced major congenital abnormalities, and a second from elicited abortions for social reasons; (3) Results: While the occurrence of major abnormalities did not seem to affect the way asymmetry decreased with age, differences between the two populations were observed; and (4) Conclusions: In one population where fetuses and young infants deceased of natural causes, asymmetry decreased rapidly until 20 weeks of age and then leveled off. Over the entire timespan (week 15–49), individuals with major congenital abnormalities showed higher FA, suggesting that developmental perturbations increase FA rapidly. In the second, more normal population with abortions solicited for social reasons, the decrease in asymmetry with age was less profound and not statistically significant, calling for further research toward understanding regional differences. Full article
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Open AccessArticle
Reference-Dependent Aggregation in Multi-AttributeGroup Decision-Making
Symmetry 2017, 9(3), 43; doi:10.3390/sym9030043 -
Abstract
To characterize the influence of decision makers’ psychological factors on the group decisionprocess, this paper develops a new class of aggregation operators based on reference-dependentutility functions (RUs) in multi-attribute group decision analysis. We consider two types of RUs:S-shaped, representing decision makers who are
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To characterize the influence of decision makers’ psychological factors on the group decisionprocess, this paper develops a new class of aggregation operators based on reference-dependentutility functions (RUs) in multi-attribute group decision analysis. We consider two types of RUs:S-shaped, representing decision makers who are risk-seeking for relative losses, and non-S-shaped,representing those that are risk-averse for relative losses. Based on these RUs, we establish twonew classes of reference-dependent aggregation operators; we study their properties and showthat their generality covers a number of existing aggregation operators. To determine the optimalweights for these aggregation operators, we construct an attribute deviation weight model and adecision maker (DM) deviation weight model. Furthermore, we develop a new multi-attribute groupdecision-making (MAGDM) approach based on these RU aggregation operators and weight models.Finally, numerical examples are given to illustrate the application of the approach.
Full article
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