A New Approach to Overcoming Zero Trade in Gravity Models to Avoid Indefinite Values in Linear Logarithmic Equations and Parameter Verification Using Machine Learning

The presence of a high number of zero flow trades continues to provide a challenge in identifying gravity parameters to explain international trade using the gravity model. Linear regression with a logarithmic linear equation encounters an indefinite value on the logarithmic trade. Although several approaches to solving this problem have been proposed, the majority of them are no longer based on linear regression, making the process of finding solutions more complex. In this work, we suggest a two-step technique for determining the gravity parameters: first, perform linear regression locally to establish a dummy value to substitute trade flow zero, and then estimating the gravity parameters. Iterative techniques are used to determine the optimum parameters. Machine learning is used to test the estimated parameters by analyzing their position in the cluster. We calculated international trade figures for 2004, 2009, 2014, and 2019. We just examine the classic gravity equation and discover that the powers of GDP and distance are in the same cluster and are both worth roughly one. The strategy presented here can be used to solve other problems involving log-linear regression.Comment: 20 pages, 6 figure

Percolation Model for Proton Immobility in Ice

A simple Ising model and a statistical theory of gel formation in a polymer matrix were combined to explain the effect of temperature on the mobility of protons in ice. Cowin et al observed that protons in ice bulk were immobile at temperatures below 190 K, and suddenly become mobile at temperatures above 190 K [Nature 398, 405 (1999)]. We proposed here that the transport of protons is controlled by a percolation mechanism. The proton transport is facilitated by the occurrence of easily reoriented water molecules in the ice bulk. The fraction of this molecule depends on temperature and was calculated using a simple Ising model. The formation of network of these molecules which provides pathways for proton transport was calculated using a statistical theory of gel formation in a polymeric system. Our model succeeded to reproduce the variation of potential difference between the ice film surfaces with respect to temperature as observed by Cowin et al based on a soft landing experiment

Theoretical foundation for the Pareto distribution of international trade strength and introduction of an equation for international trade forecasting

I propose a new terminology, international trade strength, which is defined as the ratio of a country's total international trade to its GDP. This parameter represents a country's ability to generate international trade by utilizing its GDP. This figure is equivalent to GDP per capita, which represents a country's ability to use its population to generate GDP. Trade strength varies by country. The intriguing question is, what distribution function does the trade strength fulfill? In this paper, a theoretical foundation for predicting the distribution of trade strength and the rate of change of trade strength were developed. These two quantities were found to satisfy the Pareto distribution function. The equations were confirmed using data from the World Integrated Trade Solution (WITS) and the World Bank by comparing the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) to five types of distribution functions (exponential, lognormal, gamma, Pareto, and Weibull). I also discovered that the fitting Pareto power parameter is fairly close to the theoretical parameter. In addition, a formula for forecasting a country's total international trade in the following years was also developed.Comment: 27 pages, 5 figure

Percolation Model for Proton Immobility in Ice

A simple Ising model and a statistical theory of gel formation in a polymer matrix were combined to explain the effect of temperature on the mobility of protons in ice. Cowin et al observed that protons in ice bulk were immobile at temperatures below 190 K, and suddenly become mobile at temperatures above 190 K [Nature 398, 405 (1999)]. We proposed here that the transport of protons is controlled by a percolation mechanism. The proton transport is facilitated by the occurrence of easily reoriented water molecules in the ice bulk. The fraction of this molecule depends on temperature and was calculated using a simple Ising model. The formation of network of these molecules which provides pathways for proton transport was calculated using a statistical theory of gel formation in a polymeric system. Our model succeeded to reproduce the variation of potential difference between the ice film surfaces with respect to temperature as observed by Cowin et al based on a soft landing experiment

Sarong rolled around a body demonstrates the force for separating two sheets joined by folding and rolling is very large

There are a lot of new sciences that have been inspired by common phenomena and even by old traditions practiced in our daily lives. Eventually, it may induce unexpected new technologies after deeply explored. In this paper, inspired by the wearing of traditional cloth, named sarong, by the community in the South East Asian countries and others, we investigated the behavior of sheets folded like rolling of sarong around the stomach. Simple equipment was designed to qualitatively collect the data and combined with simple modeling. Rolling of the sarong around the stomach generates the joining force of two sheets, increasing proportionally to the square of the number of rolling. This finding is potentially applied for developing a method for strongly joining sheets by simply rolling and releasing the join by simply unrolling. This work can also be simply duplicated elsewhere so that it is worthy of teaching materials at undergraduate levels. Both scientific and teaching contents can be extracted simultaneously.Comment: 23 pages, 7 figures, 5 appendix image