Calculators of the Harmony in Gradation

The following below have been made several calculators to implement Harmony in Gradation in various fields of science:
  1. Performance Simulation of 5G Cellular Network Explanation
  2. Measurement of Competition Level in the Industry Explanation
  3. Consistency Test Explanation
  4. Measurement of the Income Equality Index and Level Explanation
  5. Channel Cavity on Data Communications Explanation
  6. Measurement Index of “the Fairness over Inequality”  Explanation
  7. Equality Correlation Explanation
  8. The Human Development Index Inequality  Explanation
  9. Linear Regression Without Intercept  Explanation
  10. Smart_Estimation_ver H.1.0  Explanation
  11. The Equity Level of an Internet Service  Explanation
  12. Competition Levels among Students Explanation
  13. Fair Policy of TAX RATE Explanation
  14. A New Equilibrium Index for the science of Physics and Astronomy Explanation
  15. Linear Regression With Intercept

5.Brief Explanation of the Calculators

5.1. The Competition Law

(Explanation of theMeasurement of Competition Level in the Industry” Calculator) The Competition Law is used as a tool to maintain the sustainability of industry which is believed to happen when an industry has been run fair. In detail, the first step of the law is to measure the “Competition Level” on an industry consisting of several firms, and if the result indicates that it is unfair, the Economic Judge may order steps to make the firms can compete fairly. One possibility, not yet certain because there are many other considerations, is to force firms that have a small market to merge. The weakness of the current formula, the Herfindahl-Hirschman Index (HHI), contains only the “The Harmony” element, as a result that the judge may make the wrong decision, because they see the HHI generated index which happens in the simulation of merge situation (that means the number of firms is fewer) that does not change significantly, whereas by using Harmony in Gradation there will be a significant index change which can show the correct situation.
Harmony in Gradation is proposed to replace the Herfindahl Index
  1. 5.2. Consistency Score

    (Explanation of the Consistency Test Calculator)

    Picture Source (25/11/2018):  https://pixabay.com/en/human-observer-exhibition-2944065/
  1. One method used to measure emotional stability is the Pauli & Kraepelin test, which tells people to do the basic summation for 20 @ 3 minutes, then calculates 16 of the 20 measurement samples and interprets the average deviation as a consistency score. This shows that this method uses a formula that contains only “The Gradation”, and will cause the possibility that people with different emotional stability have been assessed equally. As a simple example of a test on two people, A who scores {5, 7, 5, 7, 5, 5, 7, 5, 5, 7, 7} and B {4, 6, 8, 6, 4, 6, 8, 6, 6, 4, 6, 8, 8, 6, 8, 4} will be judged to have the same emotional stability, since A and B are “seen” to have the same gradation. However, if the formula involves “The Harmony”, then B which has “the Harmony” more, but has the same average as A, will “look” has a larger gradation, meaning “The Harmony in Gradation” will cause B score will be smaller than A.

5.3.         Inequality Index

(Explanation of the Measurement of the Income Equality Index and Level and Human Development Index Inequality Calculator)
Picture source (25/11/2018):  https://pixabay.com/en/audio-mixer-music-sound-console-29400/ One of the formulas for calculating the Inequality Index is the Gini Index, whose formula contains only “The Gradation”, which makes it possible for two random variables having different properties to be interpreted as the same. If the Gini Index is only used to measure social inequalities such as inequality of people’s incomes, its “weakness” will not show potential economic losses, which must be handled by the state. But if the Inequality Index is also used to measure the inequality of facilities and services to communities in the cities or provinces of a country, then the economic problems will be more “visible”. In the calculation of such an inequality index, there is the possibility that big cities that have a nature “much higher” than the surrounding small towns, then considered to have the same index than small towns, because it is not “seen” by a formula that only has “The Gradation”, then the State manager lets it unconsciously this will be a driver of migration of the working age population to big cities, which will cause problems in big cities and reduce the productivity of small towns.
Harmony in Gradation is proposed to replace the Gini Index

5.4.         Information Entropy

(Explanation of the Channel Cavity on Data Communications (modified Information Entropy Formula) Calculator)
Picture source (25/11/2018):   https://pixabay.com/en/sound-audio-waves-equalizer-495859/ The information entropy formula developed by Claude Shannon only has “The Harmony”, it will cause problems when used in the field of cryptography, which “plays” the changes of the sample population, because the resulting index or entropy does not appear to change significantly when there is a change of sample size, whereas based on measurement results, it is believed there has been a very significant change in properties. Especially for the matter of information entropy, the formula of “The Harmony in Gradation” must be modified, therefore the formula is called “Channel Cavity” because, in this area, the preferred unit is bits, and is presented in the following equation. General Formula
Where: n = the size or number of symbols and pi = chance of the appearance of the ith symbol. Example formula:

5.5.         The Fairness Index

(Explanation of the Measurement Index of “the Fairness over Inequality Calculator) I have not found a formula for measuring the 100-year-old level of fairness, so this chapter does not write what formulas should be replaced by “The Harmony in Gradation”. The implementation concept of “The harmony in Gradation” to measure the level of fairness is described as follows:
    1. The assumption used is that although there is an imbalance on an affected variable, X, but the level of fairness of the action or policy against the affecting variable X expressed by variable Y, is fairer if the distribution of Y is more like the X distribution.
    2. The simple example in the field of taxation policy of a country, for example, there is an imbalance in the distribution of income of the population (affected variable), then the tax policy of the country may be fair if the tax rate distribution imposed is like the distribution of income population. Take a look at the reference, there is proof that by referring to my theory, the more “fair” this policy, then the state income derived from the tax will be the most optimum.
    3. Another example, in the field of a cellular telecommunication industry, for example, there is an imbalance in the distribution of the market share of its providers (affected variable), but if the distribution of the spectrum bandwidth provided by the state to the providers (affecting variable) is like the distribution of its market share, then the condition is said to be fair.

5.6.         Equality Correlation

(Explanation of the Equality Correlation and Linear Regression Without Intercept Calculator) Equality correlation method is a statistical measure showing the extent to which the random variable being measured has similarities with the reference variable, where the determination of the correlation index is done by calculating the Harmony in Gradation Index of the relationship between the random variable as measured by the reference variable. In this case, an index equal to one represents a perfect similarity between the elements of the variable as measured by the pairs of elements of the reference variable, let R be the reference variable = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11} and Y is random variable measured = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22}, then Y has an equity correlation index equal to one through the relationship function Y = 2R, since all elements of Y are equal to twice of the pairing elements of R. The Advantages compared to Pearson’s correlation are:
  • It would be better to use when we are sure that the regression equation has no intercept, which means the dependent variable is zero when the independent variable = zero
  • The hypothesis of the Regression equation, the correlation index between variables, and the confidence level of the regression equation will be obtained directly without the t test and F test
  • The result remains accurate for any sample population (sample > = 2).
Picture Idea:  https://pixabay.com/en/photos/equalizer/
  1. Note: I did not make the Harmony in Gradation calculator for regression that has an intercept, because it assumes that the statistical software experts more proficient to develop it.

    5.7. Fair Tax Policy

    (Explanation of the Fair Policy of TAX RATE Calculator)
The formula made here is to produce a perfect “Fairness over Inequality”, in the sense that the distribution of tax percentages to groups of people is exactly the same as the income distribution of these groups. Thus, the index of Harmony in Gradation is the same as one, and it can be proven that the state income from the income tax sector will be the maximum. In a real implementation, the government can modify the results of the calculation, but it must be remembered that this modification action will cause the state income from the tax sector to be not optimal.
  • In this calculator, the postulate used is “There cannot be a perfect equilibrium of a pair of objects in a union if we do not consider all objects in the union”. This very simple postulate is the key to compiling “Theory of Everything” or “Science of Everything”, which has been aspired by physicists since the last tens of years. Some examples of implementing the postulate are: 1. When we are studying the nature or property of celestial objects in the universe, where we are in a situation that until now we still don’t know the existence of all celestial objects in the universe, which means we cannot be in a state of perfect equilibrium, no matter how small the imbalance is, then it is obligatory for the use of a formula which contains both elements of “the Harmony” and “the Gradation”. Vice versa, if we use a formula that only contains one of the Harmony or the Gradation, then there are two types of errors that will occur, the first is a very small error, sometimes can negligible when calculating the property of a celestial body in the form of a planet or star, and the second is a big mistake when interpreting the nature of the universe. 2. When we are observing an object by applying Newton’s classical physical law “the magnitude of the reaction force of an object is the same as the force of action of the object”, where we often ignore the forces of many objects that we consider small, this shows that we have erroneously made the assumption that there has been perfect equilibrium in the system we observe. In other words, the formula we use should not only consist of one of the Harmony or the Gradation, but must involve both. Vice Versa, there will be a wrong conclusion. 3. When we are observing a moving object by applying the law of special relativity, where the existing formula derived by Lorenz only observes a system consisting of one light that moves at the speed of c and one object that moves at the speed v, even though in the real world conditions it must be very many objects that do not belong to our observation object that move at speeds of v1, v2, and so on and also many other lights that move at the speed of c/n1, c/n2 and so on. Thus, the act of not involving the whole objects and lights in the universe shows that equilibrium cannot be perfect. Then, the formula we use should not only consist of one of the Harmony or the Gradation, but must involve both. Vice Versa, there will be significantly wrong conclusions. Another possibility that must be considered is that the formula for the dilation of time and length derived by Lorenz is not experienced by the moving objects with velocity v, but precisely experienced by the light or anything that has the light-like nature moving at c or very close to c which “lives itself” and does not affect the surrounding environment. Thus, the lights can be assumed as a separate union whose members are themselves in the form as an object and in the form of a wave. So, a perfect equilibrium can occur in the light itself. Moreover, following the quantum theory, then the light causes itself to have a time and length dilation which the amount does not depend on all objects around it.  Thus, the process of special relativity can be explained as follows: the occurrence of changes in the frequency experienced by light in its form as a wave is related to causation with the dilation of time experienced by light in its form as an object and/or the changes in the wavelength of light in its form as a wave, if it occurs, is correlated with changes in the length of light in its shape as objects.

    5.9. Smart Estimation Ver .1.o.

    (Explanation of the Smart_Estimation_ver H.1.0 Calculator)
    Picture source (25/11//2018):  https://pixabay.com/en/businessman-board-immediately-soon-2556923/
  • In this calculator, Harmony in Gradation is only used to calculate the degree of confidence of the estimation results, while the estimation method on this calculator, which I call the H.1.0 version is to consider that the future events will be more affected by the events that have just happened than the effects of events that have taken place long time before.
NOTE: to broaden readers’ insights, we need to convey that technically, the estimation process is divided into two ways. The first way is to use the statistical data about past and present conditions to predict future conditions, so this process actually only produces estimates which, if true, only occur by chance, even if there is a level of confidence in the forecast, but only refers to statistical science. The second way is to take into account the chemical and/or physical processes of objects and/or waves, to take into account the conditions in the future, the predictions that are produced will certainly be true as long as the chemical and/or physical theory used is still valid.
    • 5.12. Performance Simulation of 5G Cellular Network

      (Explanation of the Performance Simulation of 5G Cellular Network Calculator) This calculator describes the implementation of the author’s invention of the fairness theory in the field of performance engineering in 5G mobile communication, especially in the new concept of the 5G cellular network that the 5G Ultra-Dense Cellular Networks, in which a macro cell has tens of G bps of throughput in a coverage area about 1 square km. However, the presence of tens of Evolved Node B on a 5G network macro cell may cause a performance loss in the form of latency and packet loss if every Evolved Node B (ENB) has a large variation of traffic intensity. Therefore, this calculator proposes a technique of arranging all Evolved Node B in the macro cell to have a traffic intensity of approximately the same value by adjusting the throughput allocation of each backhaul of the Evolved Node B so that its value is proportional to its traffic. In detail, the article in the reference proposes a new method of the resource allocation for the 5G ultra-dense cellular network based on the fairness concept the Harmony in-Gradation Resource Allocation. This fairness concept uses the harmony-in-gradation index which is a novel formula proposed as the fundamental key in reaching a good network performance on the 5G ultra-dense cellular network. The architectures of 5G network used in this calculator are a macro cell with one gateway and multiple gateways. In a single gateway architecture, a macrocell consists of one gateway and dozens of small cells. Each backhaul traffic from the small cell base station is forwarded to the gateway in the macro cell. The macrocell transmits data management and small cells transmit user data. Therefore, the task of a gateway is to allocate the backhaul throughput of the small cells which has a corresponding distribution to the traffic distribution of each Evolved Node B sent to the gateway. Therefore, the perfect allocation of resources reached wherein the distribution of throughput to the backhaul of each Evolved Node B (ENB) is exactly the same as the distribution of its traffic sent to the gateway. Contrarily, if the gateway does not set the resource allocation, then the backhaul throughput of each ENB is proportional to the effective radiated power of each transmitter, not by its traffic value, and cause the probability of unfair resource allocation will be very high. Then, unfairness in resource allocation will lead to a decrease in network performance. For that reason, it is necessary to have a method of resource allocation based on the theory of fairness, where there is a way to measure the index of fairness, then determine the level of fairness is in perfect, fair, unbalanced or unfair conditions, which corresponds to the level of network performance has been in a perfect, good, less good or poor conditions.

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