Golden Ratio Research Articles

Comparison of facial attractiveness with golden proportion anthropometrically in young North Indian females

The purpose of this anthropometric study was to assess the facial attractiveness by directly measuring various facial proportions and comparing them to golden ratio in a sample of young adult North Indian females. 120 female sample subjects were assessed for facial attractiveness. Frontal facial photographs of these females were obtained and subjected to score evaluation for grouping into 3 groups viz group I unpleasant face group, group II acceptable face group, group III pleasant face group, by a group of 6 evaluators individually. Anthropometric measurements were taken on the subject’s face in frontal view by marking various landmarks. Various facial proportions were measured and recorded using calibrated calipers and then compared with golden proportion.In group I, facial indices ratio Al-Al/ Ch-Ch (0.697) shows a comparable ratio to the golden proportion. Group II showed no relationship with golden proportion for any facial ratios. In group III, facial ratio Al-Al/ N-Sn (0.685) shows a comparable ratio to the golden proportion. There was no statistically significant difference found in the golden proportion among the three groups viz unpleasant face group, acceptable face group and pleasant face group. Ideal golden proportions may partially govern the standards of beauty, but they were not analogous to the beauty or facial esthetics of the attractive females in the present study. This may be the result because beauty perception is subjective & depends on a variety of factors.

Comparative analysis on the validity of golden ratio, tri-bimaximal, hexagonal and bimaximal neutrino mixing patterns under the radiative corrections

We study the comparative analysis on the validity of four popular leptonic mixing patterns viz, golden ratio (GR), tri-bimaximal (TBM), hexagonal mixing (HM) and bimaximal (BM), which are assumed to be defined at high energy scale, M R = 1016 GeV. We perform numerical analysis of low energy neutrino oscillation parameters through the renormalisation group equations (RGEs) in both standard model (SM) and minimal supersymmetric standard model (MSSM) with the inclusion of scale dependent vacuum expectation value (VEV). The sum of three absolute neutrino mass eigenvalues obtained from the latest Planck cosmological data, ∑∣m i ∣ < 0.12 eV, is used as a constraint in the analysis of these four leptonic mixing patterns. We consider both normal hierarchical (NH) model and inverted hierarchical (IH) model in the analysis of these four leptonic mixing patterns, with SUSY breaking scale at m s = 1 TeV and tanβ=67 . Among the four mixing patterns, GR is found to satisfy the latest Planck cosmological data, ∑∣m i ∣ < 0.12 eV. Further analysis on the effect of the variation of SUSY breaking scale 1 TeV ≤ m s ≤ 14 TeV is also studied for GR neutrino mixing pattern in NH.

The Role of an Alternative Approach Educated Mind along with A Systematic Formal Quality Education in Economic, &amp; Peaceful Sustainable Growth of Better World for All

Alternative Forms of Education have developed since the late 20th century, such as distance learning, homeschooling, and many parallel or supplementary systems of education often designated as “conformal” and “popular” religious institutions also instruct the young and old alike in sacred knowledge as well. In that case in my assessment of education to educate the mind also be like this to achieve growth and to gain and add value to every individual by keeping it globally excess-able for all to acquire International standard Education to unleash the highest potential of every unique talents and exercise them to put it into great values. Our core focus is to solve the problems from the bottom and look for much clearer sustainable brilliant resources to obtain the finest results. Alternative education methods and approaches refer and to enhance an educational process that facilitates teaching and learning with a golden ratio. Evaluating different strategies begins by defining traditional methods of education with characteristics such as formalization, authoritarianism, memorization, and repetition. A differentiated learning approach is also mandatory to excel the individual learning patterns or styles. All institutions provide and follow the same rules for teaching and it’s a barrier for learners to flourish with their mind power. Rules always shrink the mind of a thinker to explore, therefore having principles is much more appropriate for knowledge to unfold all the layers and dynamics of the intellect Department of the human brain. Education writing, singing, dancing, music, painting, poetry, leadership, doctor, engineering, science, etc all are knowledge &amp; Education. Which is derived from the intellect department of our brain Memory is a crucial machine system to harnesses and harvests knowledge for anything and everything. Age, color, language, different faiths, etc should not be an agenda or set it in the rule book to stop someone from acquiring true knowledge to educate themselves. Once we are capable of re-shaping the education process and all are aware of it; it will lead us towards growth and greater development in human history. In the economic field, a peaceful and sustainable world. It requires spiritual enlightenment and emotional intelligence to navigate and curve them to build something for all. As a Social creature, we are part of each other and we are related to each other–therefore we all must take and understand the responsibility for collective development. The range comes from global unity to walk the talk in actionable performance. The role of improved schooling a central part of most development strategies, has become controversial because expansion of school attainment has not guaranteed improved economic conditions. This paper reviews the role of education in promoting economic well-being, and peaceful and sustainable growth for a better world, with a particular focus on the role of Education and an educated peaceful mind of quality results. It concludes that there is strong evidence that the cognitive skills of the population — rather than mere school attainment– are powerfully related to individuals’ unique earnings, the distribution of income, and economic growth. New empirical results show the importance of both minimal and high-level skills, the complementarity of skills and the quality of economic institutions, and the robustness of the relationship between skills and growth. International comparisons incorporating expanded data on cognitive skills reveal much larger skill deficits in developing countries than generally derived from just school enrolment and attainment. The magnitude of change needed makes clear that closing the economic gap with developed countries will require major structural changes in schooling institutions. Keywords: Economic growth, Education, Social creature, institutions

Physical layer security analysis for RIS-aided NOMA systems with non-colluding eavesdroppers

Within the realm of sixth-generation (6G) wireless systems, there exist two primary imperatives: establishing massive connections and ensuring robust data transmission security. Therefore, this paper delves into the realm of physical layer security (PLS) within the context of a reconfigurable intelligent surface (RIS)-assisted Non-Orthogonal Multiple Access (NOMA) network coupled with the Internet of Things (IoTs), while addressing the challenge of non-concluding eavesdroppers. Specifically, the utilization of NOMA technology is anticipated to yield a substantial enhancement in spectrum efficiency for 6G and forthcoming wireless networks. Furthermore, this study investigates the security aspects through metrics such as the secrecy outage probability (SOP) and the average secrecy capacity (ASC), with the derivation of closed-form approximations for these metrics. Based on these mathematical expressions, we unveil the asymptotic Secrecy Outage Probability (SOP) to extract comprehensive insights into the RIS-assisted NOMA system’s behavior. Furthermore, we employ an algorithm based on the Golden Section to showcase the optimal SOP for a more in-depth analysis. Our findings highlight that the number of RIS metasurface components and the average signal-to-noise ratio at the access point are the primary factors driving improvements in system performance. Finally, we confirmed the correctness of our derived expressions by conducting a comparative analysis between Monte-Carlo simulations and analytical results.

Implicit and Explicit Preferences for Golden Ratio

The golden ratio, also known as Phi (ϕ ≈ 1.618034), attracted the interest of mathematicians, artists, and intellectuals for many centuries, probably from when it was discovered in human anthropometry. Even in recent times, researchers found the presence of the golden ratio in Renaissance paintings and aesthetic preferences. The reasons behind the fascination with the golden ratio remain unclear, but it has been suggested that stimuli containing this proportion are often perceived as beautiful. However, evidence is conflicting, and the literature struggles to establish the existence of individual preferences for the golden ratio. To gain new insights into the nature of these preferences, one hundred participants completed an implicit association task, with either golden ratio or random stimuli presented with positive or negative words. Participants initially categorized the stimuli based on their assigned categories. Then, we assessed their explicit preferences by asking them to rate the stimuli in terms of pleasantness and by completing a line bisection task and the Ultimatum Game. The results revealed the typical effects observed in implicit association tasks, with improved response times and accuracy when golden ratio stimuli were associated with positive word categories. In contrast, explicit ratings yielded mixed results. We discuss our findings in relation to previous studies that have explored this issue, highlighting the ongoing debate surrounding preferences for the golden ratio.

A digital economy development index based on an improved hierarchical data envelopment analysis approach

The digital economy is playing an increasingly important role in the global economy. National and international organizations commonly utilize a composite index composed of multi-dimensional indicators to monitor performance, analyse policies, and communicate in the digital economy. This study introduces a hierarchical framework for constructing a Digital Economy Development Index (DEDI). One of the key challenges is determining the attribute weights to be assigned by aggregating the sub-indicators with hierarchical dimensions for DEDI. The current study shows that an H-DEA model can be transformed into a parametric linear programming problem and develops an improved golden section algorithm to search for approximate optimal solutions. The newly developed method is highly robust and provides an alternative procedure to determine the optimal weights for building a DEDI. We established a hierarchical evaluation framework and utilized a new approach to measure the DEDI of 30 provinces in China from 2015 to 2020. The results show that inter-provincial digital economy development in China shows a sequential weakening from the east, centre, and northeast to the west. The East leads the country's digital economy overall, while there is a clear gradient gap between provinces. The central region needs to create a cluster for the development of digital industries. The Northeast should enhance the competitiveness of the industry across the board. The West must strengthen the construction of innovative talent and new infrastructure for the digital economy. These findings can serve as guidelines for designing China's ongoing digital economy development.

Geometrías en el arte: la divina proporción y la proporción cordobesa

Since Euclid, it has been contemplated that the average and extreme ratio, known as the golden ratio or divine proportion according to Luca Pacioli, is the ultimate canon of beauty. Numerous studies have been conducted in an attempt to support this thesis. However, in the latter half of the 20th century, a new study emerged to confirm that in the city of Córdoba, a previously unknown proportion dominated, which had not been studied in either art or architecture. Rafael de la Hoz, the architect responsible for this discovery, referred to it as the Cordovan proportion or Human Proportion. Once discovered, it became evident that it was not a peculiarity unique to this Andalusian city, but rather, a canon of beauty that has been used on numerous occasions, albeit not explicitly acknowledged as such.

Analyzing Mushroom Structural Patterns of a Highly Compressible and Expandable Hemostatic Foam for Gastric Perforation Repair.

Nature presents the most beautiful patterns through evolving. Here, a layered porous pattern in golden ratio (0.618) is reported from a type of mushroom -Dictyophora Rubrovalvata stipe (DRS). The hierarchical structure shows a mathematical correlation with the golden ratio. This unique structure leads to superior mechanical properties. The gradient porous structure from outside to innermost endows it with asymmetrical hydrophilicity. A mathematical model is then developed to predict and apply to 3D printed structures. The mushroom is then explored to repair gastric perforation because the stomach is a continuous peristaltic organ, and the perforated site is subject to repeated mechanical movements and pressure changes. At present, endoscopic clipping is ineffective in treating ulcerative perforation with fragile surrounding tissues. Although endoscopic implant occlusion provides a new direction for the treatment of gastric ulcers, but the metal or plastic occluder needs to be removed, requiring a second intervention. Decellularized DRS (DDRS) is found with asymmetric water absorption rate, super-compressive elasticity, shape memory, and biocompatibility, making it a suitable occluder for the gastric perforation. The efficacy in blocking gastric perforation and promoting healing is confirmed by endoscopic observation and tissue analysis during a 2-month study.

Application of the Parabola Method in Nonconvex Optimization

We consider the Golden Section and Parabola Methods for solving univariate optimization problems. For multivariate problems, we use these methods as line search procedures in combination with well-known zero-order methods such as the coordinate descent method, the Hooke and Jeeves method, and the Rosenbrock method. A comprehensive numerical comparison of the obtained versions of zero-order methods is given in the present work. The set of test problems includes nonconvex functions with a large number of local and global optimum points. Zero-order methods combined with the Parabola method demonstrate high performance and quite frequently find the global optimum even for large problems (up to 100 variables).

Human Face Reconstruction using Divine Proportions and Gestalt for Occluded Video Face Recovery in Forensic Analysis using Deep Learning

Forensic video analysis has been used in diverse kind of high-profile cases, global discrepancies, and conflict zones. It is a three-phase process of scientific examination, comparison, and evaluation of video in legal matters. Human face reconstruction using deep learning for occluded video face recovery to aid in forensic analysis is the main objective of this paper. Forensic facial reconstruction is a combination of both scientific methods and artistic skill. In this paper, we introduce a method to reconstruct human faces occluded due to short noise innight-time video clips. A skull database is created with unique skull models with varying shapes, forms and proportions. Human body mathematical model biometric using golden ratio algorithm is proposed and used to find the occluded face proportions. Closure principle of gestalt theory of visual perception is used to fill in the missing parts of a face design and to create a whole face image using gan. The proposed model is found to have 50% lesser reduced Median error rate and 20% reduced Stdev than PrNet and 10% lower Mean error rate than 3Dddfav2.

Divine vulgarism: theorising the culturally sanctioned vulgarities

ABSTRACT This paper examines vulgarity’s cultural significance among the Zeliangrong Naga of Nagaland, Assam and Manipur. It is a sociological analysis of the ritual and social statuses maintained by senexes through ritualised vulgarities. The paper contends that vulgarities are not inherently vile. Vulgarities are believed to have divine power to protect humans by repelling evil spirits and causing them to despise humans who revel in utterly filthy vulgarism. Understanding the mythology of creation by divine intervention and propagation through sexual reproduction necessitates understanding ritualistic vulgarities. Men give something bad, like vulgarity, a divine meaning by giving it a good purpose and controlling how it is used in culture to keep their highest social and ritual statuses.

Assessment of Ultimate Bearing Capacity of Static Loading Pile Based on Cusp Catastrophe Theory

Determining the ultimate bearing capacity of pile is important for reasonable design of the pile. In this paper, a cusp catastrophe theory-based method was proposed for assessing the ultimate bearing capacity of static loading pile. Firstly, a three-parameter quartic polynomial in accordance with the standard form of cusp catastrophe model is proposed and used to fit the experimentally obtained Q–S curve. The parameters which allow the polynomial to produce best fitting to the Q–S curve are taken to identify the stability of the pile following a simple procedure. Then, the proposed method was verified against 10 Q–S curves obtained from field tests at Jinqiao-Meiya and Jinqiao-Chunyu areas of Shanghai. Results show that the ultimate bearing capacities of the piles identified by the proposed method were comparable to those identified by the JGJ 106-2014 standard method. Finally, it is found that the stability of the pile identified by the proposed method and the mechanical state of the pile identified by the Golden Section approach were correlated closely.

The golden section in the art of ancient Greece: an anthropometric study of the young warrior of Riace

More than half a century after their discovery in the Ionian Sea near Riace Marina (Italy, 1972 CE), the Riace Bronzes continue to fascinate and interest. They are a pair of statues most likely sculpted in Greece in the mid-5th century and are considered masterpieces of Classical Greek sculpture. Many studies have been conducted, yet there are no morphometric studies that delve into their facial features. The aim of this study is to determine dentofacial characteristics and the presence of golden ratios in the so-called “young-man” warrior statue, equipped with a silver foil to represent the upper teeth. The interpupillar, interalar, intercanthal distances and mesio-distal diameter of the upper central incisors were subjected to virtual photogrammetry (GIMP-GNU Image Manipulation Programme). The presence of vertical and horizontal golden ratios between different landmarks (intercanthal distance: centre of the nose; centre of pupils: base of nose: base of upper incisors; centre of pupil-base of nose: base of upper incisors-base of chin; centre of pupils- base of upper incisors: base of the chin) were analysed using a dedicated software (PhiMatrix). The face and teeth satisfy most of golden canons, as also corroborated by the one-way ANOVA-statistic test (p < 0.05) for repeated measurements by independent expert operators. The virtual golden facial grid should confirm an ovoid face, which should match the same dental shape. The statue design stems from the search for beauty as divine proportion, and a relatively small detail such as teeth seems to have been carefully programmed.

Mathematical Approaches to the Study of Human Information Processing

Introduction. We consider the Golden Ratio principle and the Fibonacci sequence in terms of its possible use in the production and perception of information. The correspondence between the Fibonacci sequence and the principle of symmetry is most clearly shown when numbers are replaced with concepts and judgments.Methodology and sources. Language is an integral part not only of consciousness, but also of reality, and therefore it is quite natural to assume that its formation and development took place in accordance with the objective laws of nature that ensure the effectiveness of the interaction of structural and systemic formations as part of the whole. Such an approach makes it possible to find answers to questions that have not been solved within the narrow linguistic framework of the study, and also contributes to the fact that language structures designed to describe the state of affairs in reality provide a methodological basis for cognition at the disposal of a person.Results and discussion. The simplest language phrases built on the models of «what is what», «what is which», «what/who does what», already contain all the essential elements of thought: 1) the separation of two objects; 2) comparing them with each other (in consciousness), and 3) inference (stating their separateness and differences from each other). Thus, symmetry and asymmetry are the essence of the process of obtaining new knowledge in any field of research. Each new judgment in the chain constructed in accordance with the Fibonacci sequence includes the two previous ones, but in a new quality – based on their synthesis. At the same time, all copies of the original and received structures remain in memory.Conclusion. The search for laws implies not only generalization of ideas, but also finding the simplest schemes according to which material objects are created and processes occurring in the natural environment are implemented. In accordance with the processes regulating the stability and variability of systems in the natural environment, the activity of consciousness is also carried out, aimed at obtaining knowledge and their formation on the basis of symmetry and asymmetry. Symmetry contributes to the preservation and assimilation of the original data, asymmetry allows you to extract new information based on them. The information coming from outside is transformed into linguistic structures – the only way possible for a person to reflect the results of logical and sensory analysis.

Comparative analysis of hydro energy determinants for European Economies using Golden Cut-oriented Quantum Spherical fuzzy modelling and causality analysis

This article presents a comparative analysis of the determinants of hydropower for European economies using Golden Cut oriented Quantum Spherical fuzzy modelling and causality analysis in 24 European countries over the period 2001–2020. The indicators chosen for the analysis are inflation, population, GDP per capita, CO2 and hydropower consumption. The analysis shows that the selected groups of countries are characterised by an inverse relationship between GDP per capita and hydropower consumption, suggesting a bi-directional causal relationship, which also confirms the novelty of this paper. Furthermore, another analysis is carried out using the fuzzy decision-making methodology. In this framework, the directions of influence of the five selected indicators are constructed: GDP per capita (criterion 1, D = 88.656, E = 88.083), hydropower consumption (criterion 2, D = 89.471, E = 88.677), population (criterion 3, D = 87.705, E = 89.228), CO2 emissions (criterion 4, D = 88.578, E = 89.186) and inflation (criterion 5, D = 88.943, E = 88.180). The Quantum Spherical fuzzy methodology is used for this purpose. The values of D and E are measures of the sum of the rows and columns of the overall relationship matrix. Hydropower consumption is the main criterion. It is understood that two different analyses give similar results, namely the bidirectional causal relationship between criteria 1 and 2.

An Adaptive Linear Programming Algorithm with Parameter Learning

When dealing with engineering design problems, designers often encounter nonlinear and nonconvex features, multiple objectives, coupled decision making, and various levels of fidelity of sub-systems. To realize the design with limited computational resources, problems with the features above need to be linearized and then solved using solution algorithms for linear programming. The adaptive linear programming (ALP) algorithm is an extension of the Sequential Linear Programming algorithm where a nonlinear compromise decision support problem (cDSP) is iteratively linearized, and the resulting linear programming problem is solved with satisficing solutions returned. The reduced move coefficient (RMC) is used to define how far away from the boundary the next linearization is to be performed, and currently, it is determined based on a heuristic. The choice of RMC significantly affects the efficacy of the linearization process and, hence, the rapidity of finding the solution. In this paper, we propose a rule-based parameter-learning procedure to vary the RMC at each iteration, thereby significantly increasing the speed of determining the ultimate solution. To demonstrate the efficacy of the ALP algorithm with parameter learning (ALPPL), we use an industry-inspired problem, namely, the integrated design of a hot-rolling process chain for the production of a steel rod. Using the proposed ALPPL, we can incorporate domain expertise to identify the most relevant criteria to evaluate the performance of the linearization algorithm, quantify the criteria as evaluation indices, and tune the RMC to return the solutions that fall into the most desired range of each evaluation index. Compared with the old ALP algorithm using the golden section search to update the RMC, the ALPPL improves the algorithm by identifying the RMC values with better linearization performance without adding computational complexity. The insensitive region of the RMC is better explored using the ALPPL—the ALP only explores the insensitive region twice, whereas the ALPPL explores four times throughout the iterations. With ALPPL, we have a more comprehensive definition of linearization performance—given multiple design scenarios, using evaluation indices (EIs) including the statistics of deviations, the numbers of binding (active) constraints and bounds, the numbers of accumulated linear constraints, and the number of iterations. The desired range of evaluation indices (DEI) is also learned during the iterations. The RMC value that brings the most EIs into the DEI is returned as the best RMC, which ensures a balance between the accuracy of the linearization and the robustness of the solutions. For our test problem, the hot-rolling process chain, the ALP returns the best RMC in twelve iterations considering only the deviation as the linearization performance index, whereas the ALPPL returns the best RMC in fourteen iterations considering multiple EIs. The complexity of both the ALP and the ALPPL is O(n2). The parameter-learning steps can be customized to improve the parameter determination of other algorithms.

Golden Laplacian Graphs

Many properties of the structure and dynamics of complex networks derive from the characteristics of the spectrum of the associated Laplacian matrix, specifically from the set of its eigenvalues. In this paper, we show that there exist graphs for which the ratio between the length of the spectrum (that is, the difference between the largest and smallest eigenvalues of the Laplacian matrix) and its spread (the difference between the second smallest eigenvalue and the smallest one) is equal to the golden ratio. We call such graphs Golden Laplacian Graphs (GLG). In this paper, we first find all such graphs with a number of nodes n≤10. We then prove several graph-theoretic and algebraic properties that characterize these graphs. These graphs prove to be extremely robust, as they have large vertex and edge connectivity along with a large isoperimetric constant. Finally, we study the synchronization properties of GLGs, showing that they are among the top synchronizable graphs of the same size. Therefore, GLGs represent very good candidates for engineering and communication networks.

Another appearance of the golden ratio

Another appearance of the golden ratio

From the Fibonacci Icosagrid to E8 (Part II): The Composite Mapping of the Cores

This paper is part of a series that describes the Fibonacci icosagrid quasicrystal (FIG) and its relation to the E8 root lattice. The FIG was originally constructed to represent the intersection points of an icosahedrally symmetric collection of planar grids in three dimensions, with the grid spacing of each following a Fibonacci chain. It was found to be closely related to a five-fold compound of 3D sections taken from the 4D Elser–Sloane quasicrystal (ESQC), which is derived via a cut-and-project process from E8. More recently, a direct cut-and-project from E8 has been found which yields the FIG (presented in another paper of this series). The present paper focuses not on the full quasicrystal, but on the relationship between the root polytope of E8 (Gosset’s 421 polytope) and the core polyhedron generated in the FIG, a compound of 20 tetrahedra referred to simply as a 20-Group. In particular, the H3 symmetry of the FIG can be seen as a five-fold or “golden” composition of tetrahedral symmetry (referring to the characteristic appearance of the golden ratio). This is shown to mirror a connection between tetrahedral and five-fold symmetries present in the 421. Indeed, the rotations that connect tetrahedra contained within the 421 are shown to induce, in a certain natural way, the tetrahedron orientations in the 20-Group.

On the long-run properties of income and stock prices: the stability of the “golden ratios”

PurposeThe challenge of predicting changes in aggregate income and stock prices is one that has occupied the research agendas of economists. This paper aims to use the consumption–income ratio and the dividend–price ratio to predict future income and stock prices.Design/methodology/approachTo examine the stability of the consumption–income ratio and the dividend–price ratio, the authors run a two-variable, two-lag reduced-form VAR in the vein of Cochrane (1994), using a lag of each respective ratio as exogenous to the VAR. Additionally, the authors estimate an AR(4) model for income and prices.FindingsThe consumption–income ratio and the dividend–price ratio remain key to understanding future movements in income and stock prices. The consumption–income ratio significantly predicts future income in the USA, and aggregate income is easier to predict than consumption in the VAR model. The dividend–price ratio does not significantly predict future price growth. Consumption and dividend shocks have lasting impacts on income and prices.Originality/valueThe consumption–income ratio and the dividend–price ratio are still key to understanding future movements in income and stock prices. The consumption–income ratio significantly predicts future income in the USA, and aggregate income is easier to predict than consumption in the VAR model. However, the dividend–price ratio does not significantly predict future price growth, a change from previous research from the 1990s, despite the increasing complexity of stock markets. Consumption and dividend shocks have lasting impacts on income and prices and appear to be significant drivers in both the short- and long-run variance in income and prices.