Symmetry

21 pages, 3737 KiB

Open AccessArticle

Social Group Optimization Supported Segmentation and Evaluation of Skin Melanoma Images

by Nilanjan Dey, Venkatesan Rajinikanth, Amira S. Ashour and João Manuel R. S. Tavares

Symmetry 2018, 10(2), 51; https://doi.org/10.3390/sym10020051 - 22 Feb 2018

Cited by 127 | Viewed by 6149

The segmentation of medical images by computational methods has been claimed by the medical community, which has promoted the development of several algorithms regarding different tissues, organs and imaging modalities. Nowadays, skin melanoma is one of the most common serious malignancies in the [...] Read more.

The segmentation of medical images by computational methods has been claimed by the medical community, which has promoted the development of several algorithms regarding different tissues, organs and imaging modalities. Nowadays, skin melanoma is one of the most common serious malignancies in the human community. Consequently, automated and robust approaches have become an emerging need for accurate and fast clinical detection and diagnosis of skin cancer. Digital dermatoscopy is a clinically accepted device to register and to investigate suspicious regions in the skin. During the skin melanoma examination, mining the suspicious regions from dermoscopy images is generally demanded in order to make a clear diagnosis about skin diseases, mainly based on features of the region under analysis like border symmetry and regularity. Predominantly, the successful estimation of the skin cancer depends on the used computational techniques of image segmentation and analysis. In the current work, a social group optimization (SGO) supported automated tool was developed to examine skin melanoma in dermoscopy images. The proposed tool has two main steps, mainly the image pre-processing step using the Otsu/Kapur based thresholding technique and the image post-processing step using the level set/active contour based segmentation technique. The experimental work was conducted using three well-known dermoscopy image datasets. Similarity metrics were used to evaluate the clinical significance of the proposed tool such as Jaccard’s coefficient, Dice’s coefficient, false positive/negative rate, accuracy, sensitivity and specificity. The experimental findings suggest that the proposed tool achieved superior performance relatively to the ground truth images provided by a skin cancer physician. Generally, the proposed SGO based Kapur’s thresholding technique combined with the level set based segmentation technique is very effective for identifying melanoma dermoscopy digital images with high sensitivity, specificity and accuracy. Full article

(This article belongs to the Special Issue Advances in Medical Image Segmentation)

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15 pages, 292 KiB

Open AccessArticle

Single-Valued Neutrosophic Hesitant Fuzzy Choquet Aggregation Operators for Multi-Attribute Decision Making

by Xin Li and Xiaohong Zhang

Symmetry 2018, 10(2), 50; https://doi.org/10.3390/sym10020050 - 22 Feb 2018

Cited by 27 | Viewed by 2843

Abstract

This paper aims at developing new methods for multi-attribute decision making (MADM) under a single-valued neutrosophic hesitant fuzzy environment, in which each element has sets of possible values designed by truth, indeterminacy, and falsity membership hesitant functions. First, taking advantage of the Choquet [...] Read more.

This paper aims at developing new methods for multi-attribute decision making (MADM) under a single-valued neutrosophic hesitant fuzzy environment, in which each element has sets of possible values designed by truth, indeterminacy, and falsity membership hesitant functions. First, taking advantage of the Choquet integral and that it can reflect more correlations of attributes in MADM, two aggregation operators are defined based on the Choquet integral, specifically, the single-valued neutrosophic hesitant fuzzy Choquet ordered averaging (SVNHFCOA) operator and single-valued neutrosophic hesitant fuzzy Choquet ordered geometric (SVNHFCOG) operator, and their properties are also discussed in detail. Then, novel MADM approaches based on the SVNHFCOA and SVNHFCOG operators are established to process single-valued neutrosophic hesitant fuzzy information. Finally, this work provides a numerical example of investment alternatives to validate the application and effectiveness of the proposed approaches. Full article

10 pages, 2790 KiB

Open AccessArticle

Parameter Optimization on the Forced Ventilation of Symmetric Tunnel Construction Based on the Super-Short Bench-Cut Method

by Xiaokai Niu, Dingli Zhang, Jie Su and Hong Guo

Symmetry 2018, 10(2), 49; https://doi.org/10.3390/sym10020049 - 15 Feb 2018

Cited by 2 | Viewed by 3414

Abstract

To exploit the influence of the tunnel face and the distance between the diameter and the orifice of a blast pipe on the ventilation effect in symmetric tunnel construction, this paper uses Fluent to establish a three-dimensional model and numerical simulation. Firstly, the [...] Read more.

To exploit the influence of the tunnel face and the distance between the diameter and the orifice of a blast pipe on the ventilation effect in symmetric tunnel construction, this paper uses Fluent to establish a three-dimensional model and numerical simulation. Firstly, the accuracy of the numerical simulation is tested and then the distance between the orifice and tunnel face and the influence of the air duct diameter on the ventilation effect are studied, respectively. The results show that the ventilation effect is best when the wind pipe is arranged on one side of the tunnel wall (an asymmetrical layout), although the space in the tunnel is axisymmetric, and that the error of the numerical simulation is less than 5% of the measured value. When the distance between the orifice and tunnel face is 5 m, the uniformity of the air flow field near the tunnel face is poor; when the distance is 10 m and 12 m, an obvious vertex area appears in the tunnel. Furthermore, the uniformity of the wind velocity flow field is optimal when the distance is 8 m. When the air duct diameter is less than 1.4 m, there is a uniformity of the flow field near the tunnel face of the upper and lower benches; when the air duct diameter is more than 1.4 m, the tunnel face of the upper bench near the ground shows more obvious backflow. Therefore, it was determined that taking the air duct diameter as 1.4 m and the distance between the orifice and tunnel face as 8 m was the best combination for the design of ventilation in this project. It was also found that a better ventilation effect can be achieved when the distance between the nozzle of the ventilator and the tunnel face is 6 m–9 m and the wind speed of the nozzle is 6 m/s–8 m/s. In practical engineering, the wind speed and the required air volume should be taken into consideration to determine the diameter of the ventilator. Full article

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22 pages, 545 KiB

Open AccessArticle

MetrIntSimil—An Accurate and Robust Metric for Comparison of Similarity in Intelligence of Any Number of Cooperative Multiagent Systems

by Laszlo Barna Iantovics, Matthias Dehmer and Frank Emmert-Streib

Symmetry 2018, 10(2), 48; https://doi.org/10.3390/sym10020048 - 14 Feb 2018

Cited by 7 | Viewed by 3712

Abstract

Intelligent cooperative multiagent systems are applied for solving a large range of real-life problems, including in domains like biology and healthcare. There are very few metrics able to make an effective measure of the machine intelligence quotient. The most important drawbacks of the [...] Read more.

Intelligent cooperative multiagent systems are applied for solving a large range of real-life problems, including in domains like biology and healthcare. There are very few metrics able to make an effective measure of the machine intelligence quotient. The most important drawbacks of the designed metrics presented in the scientific literature consist in the limitation in universality, accuracy, and robustness. In this paper, we propose a novel universal metric called MetrIntSimil capable of making an accurate and robust symmetric comparison of the similarity in intelligence of any number of cooperative multiagent systems specialized in difficult problem solving. The universality is an important necessary property based on the large variety of designed intelligent systems. MetrIntSimil makes a comparison by taking into consideration the variability in intelligence in the problem solving of the compared cooperative multiagent systems. It allows a classification of the cooperative multiagent systems based on their similarity in intelligence. A cooperative multiagent system has variability in the problem solving intelligence, and it can manifest lower or higher intelligence in different problem solving tasks. More cooperative multiagent systems with similar intelligence can be included in the same class. For the evaluation of the proposed metric, we conducted a case study for more intelligent cooperative multiagent systems composed of simple computing agents applied for solving the Symmetric Travelling Salesman Problem (STSP) that is a class of NP-hard problems. STSP is the problem of finding the shortest Hamiltonian cycle/tour in a weighted undirected graph that does not have loops or multiple edges. The distance between two cities is the same in each opposite direction. Two classes of similar intelligence denoted IntClassA and IntClassB were identified. The experimental results show that the agent belonging to IntClassA intelligence class is less intelligent than the agents that belong to the IntClassB intelligence class. Full article

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14 pages, 4084 KiB

Open AccessFeature PaperArticle

Data Hiding Based on a Two-Layer Turtle Shell Matrix

by Xiao-Zhu Xie, Chia-Chen Lin and Chin-Chen Chang

Symmetry 2018, 10(2), 47; https://doi.org/10.3390/sym10020047 - 13 Feb 2018

Cited by 31 | Viewed by 4771

Abstract

Data hiding is a technology that embeds data into a cover carrier in an imperceptible way while still allowing the hidden data to be extracted accurately from the stego-carrier, which is one important branch of computer science and has drawn attention of scholars [...] Read more.

Data hiding is a technology that embeds data into a cover carrier in an imperceptible way while still allowing the hidden data to be extracted accurately from the stego-carrier, which is one important branch of computer science and has drawn attention of scholars in the last decade. Turtle shell-based (TSB) schemes have become popular in recent years due to their higher embedding capacity (EC) and better visual quality of the stego-image than most of the none magic matrices based (MMB) schemes. This paper proposes a two-layer turtle shell matrix-based (TTSMB) scheme for data hiding, in which an extra attribute presented by a 4-ary digit is assigned to each element of the turtle shell matrix with symmetrical distribution. Therefore, compared with the original TSB scheme, two more bits are embedded into each pixel pair to obtain a higher EC up to 2.5 bits per pixel (bpp). The experimental results reveal that under the condition of the same visual quality, the EC of the proposed scheme outperforms state-of-the-art data hiding schemes. Full article

(This article belongs to the Special Issue Emerging Data Hiding Systems in Image Communications)

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28 pages, 1717 KiB

Open AccessArticle

A Hybrid MCDM Technique for Risk Management in Construction Projects

by Kajal Chatterjee, Edmundas Kazimieras Zavadskas, Jolanta Tamošaitienė, Krishnendu Adhikary and Samarjit Kar

Symmetry 2018, 10(2), 46; https://doi.org/10.3390/sym10020046 - 13 Feb 2018

Cited by 126 | Viewed by 12357

Abstract

Multi-stakeholder based construction projects are subject to potential risk factors due to dynamic business environment and stakeholders’ lack of knowledge. When solving project management tasks, it is necessary to quantify the main risk indicators of the projects. Managing these requires suitable risk mitigation [...] Read more.

Multi-stakeholder based construction projects are subject to potential risk factors due to dynamic business environment and stakeholders’ lack of knowledge. When solving project management tasks, it is necessary to quantify the main risk indicators of the projects. Managing these requires suitable risk mitigation strategies to evaluate and analyse their severity. The existence of information asymmetry also causes difficulties with achieving Pareto efficiency. Hence, to ensure balanced satisfaction of all participants, risk evaluation of these projects can be considered as an important part of the multi-criteria decision-making (MCDM) process. In real-life problems, evaluation of project risks is often uncertain and even incomplete, and the prevailing methodologies fail to handle such situations. To address the problem, this paper extends the analytical network process (ANP) methodology in the D numbers domain to handle three types of ambiguous information’s, viz. complete, uncertain, and incomplete, and assesses the weight of risk criteria. The D numbers based approach overcomes the deficiencies of the exclusiveness hypothesis and completeness constraint of Dempster–Shafer (D–S) theory. Here, preference ratings of the decision matrix for each decision-maker are determined using a D numbers extended consistent fuzzy preference relation (D-CFPR). An extended multi-attributive border approximation area comparison (MABAC) method in D numbers is then developed to rank and select the best alternative risk response strategy. Finally, an illustrative example from construction sector is presented to check the feasibility of the proposed approach. For checking the reliability of alternative ranking, a comparative analysis is performed with different MCDM approaches in D numbers domain. Based on different criteria weights, a sensitivity analysis of obtained ranking of the hybrid D-ANP-MABAC model is performed to verify the robustness of the proposed method. Full article

(This article belongs to the Special Issue Civil Engineering and Symmetry)

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31 pages, 1993 KiB

Open AccessArticle

A Novel Approach for Evaluation of Projects Using an Interval–Valued Fuzzy Additive Ratio Assessment (ARAS) Method: A Case Study of Oil and Gas Well Drilling Projects

by Jalil Heidary Dahooie, Edmundas Kazimieras Zavadskas, Mahdi Abolhasani, Amirsalar Vanaki and Zenonas Turskis

Symmetry 2018, 10(2), 45; https://doi.org/10.3390/sym10020045 - 12 Feb 2018

Cited by 91 | Viewed by 6698

Abstract

The beginning of the 21st-century resulted in a more developed multi-attribute decision-making (MADM) tool and inspired new application areas that have resulted in discoveries in sustainable construction and building life cycle analysis. Construction and civil engineering stand for the central axis of a [...] Read more.

The beginning of the 21st-century resulted in a more developed multi-attribute decision-making (MADM) tool and inspired new application areas that have resulted in discoveries in sustainable construction and building life cycle analysis. Construction and civil engineering stand for the central axis of a body consisting of a multidisciplinary (multi-dimensional) world with ties to disciplines constituting the surface, and with the disciplines, as a consequence, tied to each other. When dealing with multi-attribute decision-making problems generally multiple solutions exist, especially when there is a large number of attributes, and the concept of Pareto-optimality is inefficient. The symmetry and structural regularity are essential concepts in many natural and man-made objects and play a crucial role in the design, engineering, and development of the world. The complexity and risks inherent in projects along with different effective indicators for success and failure may contribute to the difficulties in performance evaluation. In such situations, increasing the importance of uncertainty is observed. This paper proposes a novel integrated tool to find a balance between sustainable development, environmental impact and human well-being, i. e. to find symmetry axe with respect to goals, risks, and constraints (attributes) to cope with the complicated problems. The concept of “optimal solution” as the maximum degree of implemented goals (attributes) is very important. The model is built using the most relevant variables cited in the reviewed project literature and integrates two methods: the Step-Wise Weight Assessment Ratio Analysis (SWARA) method and a novel interval-valued fuzzy extension of the Additive Ratio Assessment (ARAS) method. This model was used to solve real case study of oil and gas well drilling projects evaluation. Despite the importance of oil and gas well drilling projects, there is lack of literature that describes and evaluates performance in this field projects. On the other hand, no structured assessment methodology has been presented for these types of projects. Given the limited research on performance evaluation in oil & gas well-drilling projects, the research identifies a set of performance criteria and proposes an evaluation model using fuzzy Delphi method. An illustrative example shows that the proposed method is a useful and alternative decision-making method. Full article

(This article belongs to the Special Issue Civil Engineering and Symmetry)

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13 pages, 325 KiB

Open AccessArticle

Constraining Forces Stabilizing Superconductivity in Bismuth

by Ekkehard Krüger

Symmetry 2018, 10(2), 44; https://doi.org/10.3390/sym10020044 - 12 Feb 2018

Cited by 5 | Viewed by 3451

Abstract

As shown in former papers, the nonadiabatic Heisenberg model presents a mechanism of Cooper pair formation generated by the strongly correlated atomic-like motion of the electrons in narrow, roughly half-filled “superconducting bands” of special symmetry. The formation of Cooper pairs is not only [...] Read more.

As shown in former papers, the nonadiabatic Heisenberg model presents a mechanism of Cooper pair formation generated by the strongly correlated atomic-like motion of the electrons in narrow, roughly half-filled “superconducting bands” of special symmetry. The formation of Cooper pairs is not only the result of an attractive electron–electron interaction but is additionally the outcome of quantum mechanical constraining forces. There is theoretical and experimental evidence that only these constraining forces operating in superconducting bands may produce eigenstates in which the electrons form Cooper pairs. Here, we report evidence that also the experimentally found superconducting state in bismuth at ambient as well as at high pressure is stabilized by constraining forces. Full article

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23 pages, 306 KiB

Open AccessArticle

Enhanced Matrix Power Function for Cryptographic Primitive Construction

by Eligijus Sakalauskas

Symmetry 2018, 10(2), 43; https://doi.org/10.3390/sym10020043 - 10 Feb 2018

Cited by 9 | Viewed by 2689

Abstract

A new enhanced matrix power function (MPF) is presented for the construction of cryptographic primitives. According to the definition in previously published papers, an MPF is an action of two matrices powering some base matrix on the left and right. The MPF inversion [...] Read more.

A new enhanced matrix power function (MPF) is presented for the construction of cryptographic primitives. According to the definition in previously published papers, an MPF is an action of two matrices powering some base matrix on the left and right. The MPF inversion equations, corresponding to the MPF problem, are derived and have some structural similarity with classical multivariate quadratic (MQ) problem equations. Unlike the MQ problem, the MPF problem seems to be more complicated, since its equations are not defined over the field, but are represented as left–right action of two matrices defined over the infinite near-semiring on the matrix defined over the certain infinite, additive, noncommuting semigroup. The main results are the following: (1) the proposition of infinite, nonsymmetric, and noncommuting algebraic structures for the construction of the enhanced MPF, satisfying associativity conditions, which are necessary for cryptographic applications; (2) the proof that MPF inversion is polynomially equivalent to the solution of a certain kind of generalized multivariate quadratic (MQ) problem which can be reckoned as hard; (3) the estimation of the effectiveness of direct MPF value computation; and (4) the presentation of preliminary security analysis, the determination of the security parameter, and specification of its secure value. These results allow us to make a conjecture that enhanced MPF can be a candidate one-way function (OWF), since the effective (polynomial-time) inversion algorithm for it is not yet known. An example of the application of the proposed MPF for the Key Agreement Protocol (KAP) is presented. Since the direct MPF value is computed effectively, the proposed MPF is suitable for the realization of cryptographic protocols in devices with restricted computation resources. Full article

21 pages, 3499 KiB

Open AccessArticle

Diagonally Implicit Multistep Block Method of Order Four for Solving Fuzzy Differential Equations Using Seikkala Derivatives

by Syahirbanun Isa, Zanariah Abdul Majid, Fudziah Ismail and Faranak Rabiei

Symmetry 2018, 10(2), 42; https://doi.org/10.3390/sym10020042 - 08 Feb 2018

Cited by 7 | Viewed by 3057

Abstract

In this paper, the solution of fuzzy differential equations is approximated numerically using diagonally implicit multistep block method of order four. The multistep block method is well known as an efficient and accurate method for solving ordinary differential equations, hence in this paper [...] Read more.

In this paper, the solution of fuzzy differential equations is approximated numerically using diagonally implicit multistep block method of order four. The multistep block method is well known as an efficient and accurate method for solving ordinary differential equations, hence in this paper the method will be used to solve the fuzzy initial value problems where the initial value is a symmetric triangular fuzzy interval. The triangular fuzzy number is not necessarily symmetric, however by imposing symmetry the definition of a triangular fuzzy number can be simplified. The symmetric triangular fuzzy interval is a triangular fuzzy interval that has same left and right width of membership function from the center. Due to this, the parametric form of symmetric triangular fuzzy number is simple and the performing arithmetic operations become easier. In order to interpret the fuzzy problems, Seikkala’s derivative approach is implemented. Characterization theorem is then used to translate the problems into a system of ordinary differential equations. The convergence of the introduced method is also proved. Numerical examples are given to investigate the performance of the proposed method. It is clearly shown in the results that the proposed method is comparable and reliable in solving fuzzy differential equations. Full article

(This article belongs to the Special Issue Fuzzy Sets Theory and Its Applications)

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15 pages, 364 KiB

Open AccessArticle

Lie Symmetry of the Diffusive Lotka–Volterra System with Time-Dependent Coefficients

by Vasyl’ Davydovych

Symmetry 2018, 10(2), 41; https://doi.org/10.3390/sym10020041 - 03 Feb 2018

Cited by 1 | Viewed by 3162

Abstract

Lie symmetry classification of the diffusive Lotka–Volterra system with time-dependent coefficients in the case of a single space variable is studied. A set of such symmetries in an explicit form is constructed. A nontrivial ansatz reducing the Lotka–Volterra system with correctly-specified coefficients to [...] Read more.

Lie symmetry classification of the diffusive Lotka–Volterra system with time-dependent coefficients in the case of a single space variable is studied. A set of such symmetries in an explicit form is constructed. A nontrivial ansatz reducing the Lotka–Volterra system with correctly-specified coefficients to the system of ordinary differential equations (ODEs) and an example of the exact solution with a biological interpretation are found. Full article

(This article belongs to the Special Issue Lie and Conditional Symmetries and Their Applications for Solving Nonlinear Models, II)

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91 pages, 19423 KiB

Open AccessArticle

Three Classes of Fractional Oscillators

by Ming Li

Symmetry 2018, 10(2), 40; https://doi.org/10.3390/sym10020040 - 30 Jan 2018

Cited by 48 | Viewed by 4785

Abstract

This article addresses three classes of fractional oscillators named Class I, II and III. It is known that the solutions to fractional oscillators of Class I type are represented by the Mittag-Leffler functions. However, closed form solutions to fractional oscillators in Classes II [...] Read more.

This article addresses three classes of fractional oscillators named Class I, II and III. It is known that the solutions to fractional oscillators of Class I type are represented by the Mittag-Leffler functions. However, closed form solutions to fractional oscillators in Classes II and III are unknown. In this article, we present a theory of equivalent systems with respect to three classes of fractional oscillators. In methodology, we first transform fractional oscillators with constant coefficients to be linear 2-order oscillators with variable coefficients (variable mass and damping). Then, we derive the closed form solutions to three classes of fractional oscillators using elementary functions. The present theory of equivalent oscillators consists of the main highlights as follows. (1) Proposing three equivalent 2-order oscillation equations corresponding to three classes of fractional oscillators; (2) Presenting the closed form expressions of equivalent mass, equivalent damping, equivalent natural frequencies, equivalent damping ratio for each class of fractional oscillators; (3) Putting forward the closed form formulas of responses (free, impulse, unit step, frequency, sinusoidal) to each class of fractional oscillators; (4) Revealing the power laws of equivalent mass and equivalent damping for each class of fractional oscillators in terms of oscillation frequency; (5) Giving analytic expressions of the logarithmic decrements of three classes of fractional oscillators; (6) Representing the closed form representations of some of the generalized Mittag-Leffler functions with elementary functions. The present results suggest a novel theory of fractional oscillators. This may facilitate the application of the theory of fractional oscillators to practice. Full article

(This article belongs to the Special Issue Symmetry and Complexity)

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15 pages, 779 KiB

Open AccessArticle

Prioritized Aggregation Operators and Correlated Aggregation Operators for Hesitant 2-Tuple Linguistic Variables

by Lidong Wang, Yanjun Wang and Xiaodong Liu

Symmetry 2018, 10(2), 39; https://doi.org/10.3390/sym10020039 - 30 Jan 2018

Cited by 10 | Viewed by 2806

Abstract

The aggregation operator is a potential tool to fuse the information derived from multisources, which has been applied in group decision, combination classification and scheduling clusters successfully. To better characterize complex decision situations and capture complex opinions of decision-makers (DMs), aggregation operators are [...] Read more.

The aggregation operator is a potential tool to fuse the information derived from multisources, which has been applied in group decision, combination classification and scheduling clusters successfully. To better characterize complex decision situations and capture complex opinions of decision-makers (DMs), aggregation operators are required to be explored from different viewpoints. In view of information fusion of hesitant 2-tuple linguistic variables, this paper establishes four new aggregation operators, which are called the hesitant 2-tuple linguistic prioritized weighted averaging (H2TLPWA) aggregation operator, hesitant 2-tuple linguistic prioritized weighted geometric (H2TLPWG) aggregation operator, hesitant 2-tuple linguistic correlated averaging (H2TLCA) aggregation operator, and hesitant 2-tuple linguistic correlated geometric (H2TLCG) aggregation operator, respectively. The H2TLPWA aggregation operator and H2TLPWG aggregation operator can characterize the prioritization relationship of the aggregated arguments. The H2TLCA aggregation operator and H2TLCG aggregation operator can describe dependencies between criteria in decision-making problem solving. Moreover all aggregation operation operators have the properties of idempotency, boundedness and monotonicity, and the H2TLCA aggregation operator and H2TLCG aggregation operator are also verified to be symmetric functions. In addition, the H2TLPWA aggregation operator and H2TLCA aggregation operator are employed to settle multicriteria decision-making problems with hesitant 2-tuple linguistic terms. By virtue of predefining discrete initial linguistic labels with symmetrical distribution, the detailed steps of the decision-making process with an example are given to illustrate their practicality and effectiveness. Full article

20 pages, 967 KiB

Open AccessArticle

Local Casimir Effect for a Scalar Field in Presence of a Point Impurity

by Davide Fermi and Livio Pizzocchero

Symmetry 2018, 10(2), 38; https://doi.org/10.3390/sym10020038 - 26 Jan 2018

Cited by 12 | Viewed by 3310

Abstract

The Casimir effect for a scalar field in presence of delta-type potentials has been investigated for a long time in the case of surface delta functions, modelling semi-transparent boundaries. More recently Albeverio, Cacciapuoti, Cognola, Spreafico and Zerbini have considered some configurations involving delta-type [...] Read more.

The Casimir effect for a scalar field in presence of delta-type potentials has been investigated for a long time in the case of surface delta functions, modelling semi-transparent boundaries. More recently Albeverio, Cacciapuoti, Cognola, Spreafico and Zerbini have considered some configurations involving delta-type potentials concentrated at points of

R^{3}

; in particular, the case with an isolated point singularity at the origin can be formulated as a field theory on

R^{3} \ {0}

, with self-adjoint boundary conditions at the origin for the Laplacian. However, the above authors have discussed only global aspects of the Casimir effect, focusing their attention on the vacuum expectation value (VEV) of the total energy. In the present paper we analyze the local Casimir effect with a point delta-type potential, computing the renormalized VEV of the stress-energy tensor at any point of

R^{3} \ {0}

; for this purpose we follow the zeta regularization approach, in the formulation already employed for different configurations in previous works of ours. Full article

(This article belongs to the Special Issue Casimir Physics and Applications)

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11 pages, 555 KiB

Open AccessFeature PaperArticle

Accounting for Dissipation in the Scattering Approach to the Casimir Energy

by Romain Guérout, Gert-Ludwig Ingold, Astrid Lambrecht and Serge Reynaud

Symmetry 2018, 10(2), 37; https://doi.org/10.3390/sym10020037 - 26 Jan 2018

Cited by 6 | Viewed by 3381

Abstract

We take dissipation into account in the derivation of the Casimir energy formula between two objects placed in a surrounding medium. The dissipation channels are considered explicitly in order to take advantage of the unitarity of the full scattering processes. We demonstrate that [...] Read more.

We take dissipation into account in the derivation of the Casimir energy formula between two objects placed in a surrounding medium. The dissipation channels are considered explicitly in order to take advantage of the unitarity of the full scattering processes. We demonstrate that the Casimir energy is given by a scattering formula expressed in terms of the scattering amplitudes coupling internal channels and taking dissipation into account implicitly. We prove that this formula is also valid when the surrounding medium is dissipative. Full article

(This article belongs to the Special Issue Casimir Physics and Applications)

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18 pages, 4755 KiB

Open AccessArticle

Efficient Data Hiding Based on Block Truncation Coding Using Pixel Pair Matching Technique

by Wien Hong

Symmetry 2018, 10(2), 36; https://doi.org/10.3390/sym10020036 - 25 Jan 2018

Cited by 34 | Viewed by 5300

Abstract

In this paper, an efficient data hiding method that embeds data into absolute moment block truncation coding (AMBTC) codes is proposed. The AMBTC method represents image blocks by trios, and each trio consists of two quantization levels and an asymmetrically distributed bitmap. However, [...] Read more.

In this paper, an efficient data hiding method that embeds data into absolute moment block truncation coding (AMBTC) codes is proposed. The AMBTC method represents image blocks by trios, and each trio consists of two quantization levels and an asymmetrically distributed bitmap. However, the asymmetric phenomena of bitmaps cause large degradation in image quality during data embedment. With the help of reference tables filled with symmetrical patterns, the proposed method exploits a symmetry adjustment model to modify the quantization levels in those smooth blocks to achieve the smallest distortion. If the block is complex, a lossless embedding method is performed to carry one additional bit. A sophisticated division switching mechanism is also proposed to modify a block from smooth to complex if the solution to the minimal distortion cannot be found. The payload can be adjusted by varying the threshold, or by embedding more bits into the quantization levels. The experiments indicate that the proposed work provides the best stego image quality under various payloads when comparing to the related prior works. Full article

(This article belongs to the Special Issue Emerging Data Hiding Systems in Image Communications)

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13 pages, 1523 KiB

Open AccessFeature PaperArticle

Symmetry and Topology: The 11 Uninodal Planar Nets Revisited

by Jean-Guillaume Eon

Symmetry 2018, 10(2), 35; https://doi.org/10.3390/sym10020035 - 24 Jan 2018

Cited by 4 | Viewed by 5025

Abstract

A description of the 11 well-known uninodal planar nets is given by Cayley color graphs or alternative Cayley color graphs of plane groups. By applying methods from topological graph theory, the nets are derived from the bouquet

B_{n}

with rotations mostly as [...] Read more.

A description of the 11 well-known uninodal planar nets is given by Cayley color graphs or alternative Cayley color graphs of plane groups. By applying methods from topological graph theory, the nets are derived from the bouquet

B_{n}

with rotations mostly as voltages. It thus appears that translation, as a symmetry operation in these nets, is no more fundamental than rotations. Full article

(This article belongs to the Special Issue Mathematical Crystallography)

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Graphical abstract

75 pages, 44501 KiB

Open AccessReview

Chiral Heterocycle-Based Receptors for Enantioselective Recognition

by Vaibhav N. Khose, Marina E. John, Anita D. Pandey, Victor Borovkov and Anil V. Karnik

Symmetry 2018, 10(2), 34; https://doi.org/10.3390/sym10020034 - 24 Jan 2018

Cited by 12 | Viewed by 7920

Abstract

The majority of biomolecules found in living beings are chiral, therefore chiral molecular recognition in living systems is crucial to life. Following Cram’s seminal work on the crown-based chiral recognition, prominent research groups have reported innumerable chiral receptors with distinctly different geometrical features [...] Read more.

The majority of biomolecules found in living beings are chiral, therefore chiral molecular recognition in living systems is crucial to life. Following Cram’s seminal work on the crown-based chiral recognition, prominent research groups have reported innumerable chiral receptors with distinctly different geometrical features and asymmetry elements. Main applications of such chiral receptors are found in chiral chromatography, as for analytical purposes and for bulk separation of racemates.Incorporation of heterocyclic rings in these recognition systems added a new dimension to the existing group of receptors. Heterocycles have additional features such as availability of unshared electron pairs, pronounced conformational features, introduction of hydrogen bonding and presence of permanent dipoles as well as specific spectral properties in certain cases. These features are found to enhance binding properties of the receptors and the selectivity factors between opposite enantiomers, allowing them to be effectively separated. The review presents the synthetic approaches towards these heterocyclic receptors and their distinctly different behavior vis-à-vis carbocyclic receptors. Full article

(This article belongs to the Special Issue Chiral Auxiliaries and Chirogenesis)

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13 pages, 4399 KiB

Open AccessArticle

Three-Dimensional Finite Element Analysis of Maxillary Sinus Floor Augmentation with Optimal Positioning of a Bone Graft Block

by Peter Schuller-Götzburg, Thomas Forte, Werner Pomwenger, Alexander Petutschnigg, Franz Watzinger and Karl Entacher

Symmetry 2018, 10(2), 33; https://doi.org/10.3390/sym10020033 - 23 Jan 2018

Cited by 6 | Viewed by 5501

Abstract

Purpose: the aim of the computational 3D-finite element study is to evaluate the influence of an augmented sinus lift with additional inserted bone grafting. The bone graft block stabilizes the implant in conjunction with conventional bone augmentation. Two finite element models were applied: [...] Read more.

Purpose: the aim of the computational 3D-finite element study is to evaluate the influence of an augmented sinus lift with additional inserted bone grafting. The bone graft block stabilizes the implant in conjunction with conventional bone augmentation. Two finite element models were applied: the real geometry based bone models and the simplified geometry models. The bone graft block was placed in three different positions. The implants were loaded first with an axial force and then with forces simulating laterotrusion and protrusion. This study examines whether the calculated stress behavior is symmetrical for both models. Having established a symmetry between the primary axis, the laterotrusion and protrusion behavior reduces calculation efforts, by simplifying the model. Material and Methods: a simplified U-shaped 3D finite element model of the molar region of the upper jaw and a more complex anatomical model of the left maxilla with less cortical bone were created. The bone graft block was placed in the maxillary sinus. Then the von Mises stress distribution was calculated and analyzed at three block positions: at contact with the sinus floor, in the middle of the implant helix and in the upper third of the implant. The two finite element models were then compared to simplify the modelling. Results: the position of the bone graft block significantly influences the magnitude of stress distribution. A bone graft block positioned in the upper third or middle of the implant reduces the quantity of stress compared to the reference model without a bone graft block. The low bone graft block position is clearly associated with lower stress distribution in compact bone. We registered no significant differences in stress in compact bone with regard to laterotrusion or protrusion. Conclusions: maximum values of von Mises stresses in compact bone can be reduced significantly by using a bone graft block. The reduction of stress is nearly the same for positions in the upper third and the middle of the implant. It is much more pronounced when the bone graft block is in the lower third of the implant near the sinus floor, which appeared to be the best position in the present study. Full article

(This article belongs to the Special Issue Advances in Medical Image Segmentation)

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Symmetry, Volume 10, Issue 2 (February 2018) – 19 articles

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