Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 8

Symmetry‎ Related Abstracts

8 Evaluation of Golden Beam Data for the Commissioning of 6 and 18 MV Photons Beams in Varian Linear Accelerator

Authors: Shoukat Ali, Abdul Qadir Jandga, Amjad Hussain


Objective: The main purpose of this study is to compare the Percent Depth dose (PDD) and In-plane and cross-plane profiles of Varian Golden beam data to the measured data of 6 and 18 MV photons for the commissioning of Eclipse treatment planning system. Introduction: Commissioning of treatment planning system requires an extensive acquisition of beam data for the clinical use of linear accelerators. Accurate dose delivery require to enter the PDDs, Profiles and dose rate tables for open and wedges fields into treatment planning system, enabling to calculate the MUs and dose distribution. Varian offers a generic set of beam data as a reference data, however not recommend for clinical use. In this study, we compared the generic beam data with the measured beam data to evaluate the reliability of generic beam data to be used for the clinical purpose. Methods and Material: PDDs and Profiles of Open and Wedge fields for different field sizes and at different depths measured as per Varian’s algorithm commissioning guideline. The measurement performed with PTW 3D-scanning water phantom with semi-flex ion chamber and MEPHYSTO software. The online available Varian Golden Beam Data compared with the measured data to evaluate the accuracy of the golden beam data to be used for the commissioning of Eclipse treatment planning system. Results: The deviation between measured vs. golden beam data was in the range of 2% max. In PDDs, the deviation increases more in the deeper depths than the shallower depths. Similarly, profiles have the same trend of increasing deviation at large field sizes and increasing depths. Conclusion: Study shows that the percentage deviation between measured and golden beam data is within the acceptable tolerance and therefore can be used for the commissioning process; however, verification of small subset of acquired data with the golden beam data should be mandatory before clinical use.

Keywords: Symmetry‎, percent depth dose, flatness, golden beam data

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7 Lie Symmetry Treatment for Pricing Options with Transactions Costs under the Fractional Black-Scholes Model

Authors: B. F. Nteumagne, E. Pindza, E. Mare


We apply Lie symmetries analysis to price and hedge options in the fractional Brownian framework. The reputation of Lie groups is well spread in the area of Mathematical sciences and lately, in Finance. In the presence of transactions costs and under fractional Brownian motions, analytical solutions become difficult to obtain. Lie symmetries analysis allows us to simplify the problem and obtain new analytical solution. In this paper, we investigate the use of symmetries to reduce the partial differential equation obtained and obtain the analytical solution. We then proposed a hedging procedure and calibration technique for these types of options, and test the model on real market data. We show the robustness of our methodology by its application to the pricing of digital options.

Keywords: Symmetry‎, Option Pricing, fractional brownian model, transaction cost

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6 Grammatical Parallelism in the Qurʼān

Authors: Yehudit Dror


Parallelism¬, or as it is called in Arabic, al-muqābala, occupies a central position in the rhetorical discipline of ʻilm al-bayān. Parallelism is used as a figure of textual ornamentation or embellishment and can be divided into several types that are based on the semantics of parallelism and its formative structure. Parallelism in Arabic has received a considerable amount of attention from the Arab rhetorician, which enables understanding the essence of parallelism in Arabic – its types, structure and meaning. However, there are some lacunae in their descriptions concerning the function and thematic restrictions of parallelism in the Qur’ān. In my presentation, which focuses on grammatical parallelism where the two stichos of the parallelism are the same with respect to syntax and morphology, I will show that parallelism has some important roles in the textual arrangement; it may, for example, conclude a thematic section, indicate a turning point in the text or to clarify what has been said previously. In addition, it will be shown that parallelism is not used randomly in the Qurʼān but rather is restricted to repeated themes which carry the most important messages of the Qurʼān, such as God's Might or behavioral patterns of the believers and the non-believers; or it can be used as a stylistic device.

Keywords: Symmetry‎, grammatical parallelism, half-line, Koran

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5 Dual Duality for Unifying Spacetime and Internal Symmetry

Authors: David C. Ni


The current efforts for Grand Unification Theory (GUT) can be classified into General Relativity, Quantum Mechanics, String Theory and the related formalisms. In the geometric approaches for extending General Relativity, the efforts are establishing global and local invariance embedded into metric formalisms, thereby additional dimensions are constructed for unifying canonical formulations, such as Hamiltonian and Lagrangian formulations. The approaches of extending Quantum Mechanics adopt symmetry principle to formulate algebra-group theories, which evolved from Maxwell formulation to Yang-Mills non-abelian gauge formulation, and thereafter manifested the Standard model. This thread of efforts has been constructing super-symmetry for mapping fermion and boson as well as gluon and graviton. The efforts of String theory currently have been evolving to so-called gauge/gravity correspondence, particularly the equivalence between type IIB string theory compactified on AdS5 × S5 and N = 4 supersymmetric Yang-Mills theory. Other efforts are also adopting cross-breeding approaches of above three formalisms as well as competing formalisms, nevertheless, the related symmetries, dualities, and correspondences are outlined as principles and techniques even these terminologies are defined diversely and often generally coined as duality. In this paper, we firstly classify these dualities from the perspective of physics. Then examine the hierarchical structure of classes from mathematical perspective referring to Coleman-Mandula theorem, Hidden Local Symmetry, Groupoid-Categorization and others. Based on Fundamental Theorems of Algebra, we argue that rather imposing effective constraints on different algebras and the related extensions, which are mainly constructed by self-breeding or self-mapping methodologies for sustaining invariance, we propose a new addition, momentum-angular momentum duality at the level of electromagnetic duality, for rationalizing the duality algebras, and then characterize this duality numerically with attempt for addressing some unsolved problems in physics and astrophysics.

Keywords: Algebra, Quantum Mechanics, General Relativity, string theory, Symmetry‎, Duality, correspondence, momentum-angular-momentum

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4 Extensions to Chen's Minimizing Equal Mass Paralellogram Solutions

Authors: Abdalla Manur, Daniel Offin, Alessandro Arsie


In this paper, we study the extension of the minimizing equal mass parallelogram solutions which was derived by Chen in 2001. Chen’s solution was minimizing for one quarter of the period [0; T], where numerical integration had been used in his proof. This paper focuses on extending the minimization property to intervals of time [0; 2T] and [0; 4T].

Keywords: Action, Symmetry‎, Hamiltoian, N-body

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3 Quantification and Preference of Facial Asymmetry of the Sub-Saharan Africans' 3D Facial Models

Authors: Anas Ibrahim Yahaya, Christophe Soligo


A substantial body of literature has reported on facial symmetry and asymmetry and their role in human mate choice. However, major gaps persist, with nearly all data originating from the WEIRD (Western, Educated, Industrialised, Rich and Developed) populations, and results remaining largely equivocal when compared across studies. This study is aimed at quantifying facial asymmetry from the 3D faces of the Hausa of northern Nigeria and also aimed at determining their (Hausa) perceptions and judgements of standardised facial images with different levels of asymmetry using questionnaires. Data were analysed using R-studio software and results indicated that individuals with lower levels of facial asymmetry (near facial symmetry) were perceived as more attractive, more suitable as marriage partners and more caring, whereas individuals with higher levels of facial asymmetry were perceived as more aggressive. The study conclusively asserts that all faces are asymmetric including the most beautiful ones, and the preference of less asymmetric faces was not just dependent on single facial trait, but rather on multiple facial traits; thus the study supports that physical attractiveness is not just an arbitrary social construct, but at least in part a cue to general health and possibly related to environmental context.

Keywords: Symmetry‎, Face, preference, Hausa, asymmetry

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2 Restrictedly-Regular Map Representation of n-Dimensional Abstract Polytopes

Authors: Antonio Breda d’Azevedo


Regularity has often been present in the form of regular polyhedra or tessellations; classical examples are the nine regular polyhedra consisting of the five Platonic solids (regular convex polyhedra) and the four Kleper-Poinsot polyhedra. These polytopes can be seen as regular maps. Maps are cellular embeddings of graphs (with possibly multiple edges, loops or dangling edges) on compact connected (closed) surfaces with or without boundary. The n-dimensional abstract polytopes, particularly the regular ones, have gained popularity over recent years. The main focus of research has been their symmetries and regularity. Planification of polyhedra helps its spatial construction, yet it destroys its symmetries. To our knowledge there is no “planification” for n-dimensional polytopes. However we show that it is possible to make a “surfacification” of the n-dimensional polytope, that is, it is possible to construct a restrictedly-marked map representation of the abstract polytope on some surface that describes its combinatorial structures as well as all of its symmetries. We also show that there are infinitely many ways to do this; yet there is one that is more natural that describes reflections on the sides ((n−1)-faces) of n-simplices with reflections on the sides of n-polygons. We illustrate this construction with the 4-tetrahedron (a regular 4-polytope with automorphism group of size 120) and the 4-cube (a regular 4-polytope with automorphism group of size 384).

Keywords: Symmetry‎, abstract polytope, automorphism group, N-simplicies

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1 The Effect of Symmetry on the Perception of Happiness and Boredom in Design Products

Authors: Michele Sinico


The present research investigates the effect of symmetry on the perception of happiness and boredom in design products. Three experiments were carried out in order to verify the degree of the visual expressive value on different models of bookcases, wall clocks, and chairs. 60 participants directly indicated the degree of happiness and boredom using 7-point rating scales. The findings show that the participants acknowledged a different value of expressive quality in the different product models. Results show also that symmetry is not a significant constraint for an emotional design project.

Keywords: Symmetry‎, Emotional Design, product experience, expressive qualities

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