This study focuses on modeling, prediction, and analysis of confirmed, recovered, and death cases of COVID-19 by using Fractional Calculus in comparison with other models for 8 countries including China, France, Italy, Spain, Turkey, the UK, and the US. First, the dataset is modeled using our previously proposed approach Deep Assessment Methodology, next, one step prediction of the future is made using two methods: Deep Assessment Methodology and Long Short-Term Memory. Later, a Gaussian prediction model is proposed to predict the short-term (30 Days) future of the pandemic, and prediction performance is evaluated. The proposed Gaussian model is compared to a time-dependent susceptible-infected-recovered (SIR) model. Lastly, an analysis of understanding the effect of history is made on memory vectors using wavelet-based denoising and correlation coefficients. Results prove that Deep Assessment Methodology successfully models the dataset with 0.6671%, 0.6957%, and 0.5756% average errors for confirmed, recovered, and death cases, respectively. We found that using the proposed Gaussian approach underestimates the trend of the pandemic and the fastest increase is observed in the US while the slowest is observed in China and Spain. Analysis of the past showed that, for all countries except Turkey, the current time instant is mainly dependent on the past two weeks where countries like Germany, Italy, and the UK have a shorter average incubation period when compared to the US and France.

In this study, a new approach for time series modeling and prediction, “deep assessment methodology,” is proposed and the performance is reported on modeling and prediction for upcoming years of Gross Domestic Product (GDP) per capita. The proposed methodology expresses a function with the finite summation of its previous values and derivatives combining fractional calculus and the Least Square Method to find unknown coefficients. The dataset of GDP per capita used in this study includes nine countries (Brazil, China, India, Italy, Japan, the UK, the USA, Spain and Turkey) and the European Union. The modeling performance of the proposed model is compared with the Polynomial model and the Fractional model and prediction performance is compared to a special type of neural network, Long Short-Term Memory (LSTM), that used for time series. Results show that using Deep Assessment Methodology yields promising modeling and prediction results for GDP per capita. The proposed method is outperforming Polynomial model and Fractional model by 1.538% and by 1.899% average error rates, respectively. We also show that Deep Assessment Method (DAM) is superior to plain LSTM on prediction for upcoming GDP per capita values by 1.21% average error.

Vehicle logo recognition has become an important part of object recognition in recent years because of its usage in surveillance applications. In order to achieve a higher recognition rates, several methods are proposed, such as Scale Invariant Feature Transform (SIFT), convolutional neural networks, bag-of-words and their variations. A fast logo recognition method based on reduced-dimension SIFT vectors using autoencoders is proposed in this paper. Computational load is decreased by applying dimensionality reduction to SIFT feature vectors. Feature vectors of size 128 are reduced to 64 and 32 by employing two layer neural nets called vanilla autoencoders. Publicly available vehicle logo images are used for testing purposes. Results suggest that the proposed method needs half of the original SIFT based method’s memory requirement with decreased processing time per image in return of a decrease in the accuracy less than 20%.

This study explores the modeling of the share of telecommunication revenues in gross domestic product from the year 2000 to 2018 for 5 countries including France, Germany, Italy, Turkey, the UK, and the OECD average. First, a new mathematical model based on Fractional Calculus and Least Square Method is proposed. Later, the telecommunication revenues in GDP dataset is modeled. Further, we compare the new Fractional approach to the classical Polynomial approach in three different settings. The results show that employing Fractional Calculus yields better modeling performance when compared to the classical Polynomial Approach in terms of Mean Absolute Percentage Error (MAPE). The Fractional approach outperforms the Polynomial approach by 0.1329 % MAPE on average. The largest MAPE is found for Turkey while the smallest MAPE is obtained for Italy in all settings.

Today, operators have become the resource of telecommunications data. Therefore, knowledge about subscriptions is easily available for most countries. In recent years, high-speed mobile internet access subscriptions are also increasing rapidly. There are two important subscriptions reviewed by The International Telecommunication Union (ITU): mobile broadband (MBB) subscriptions and Fixed broadband (FBB) subscriptions. In this study, we proposed an original mathematical model employing the fractional analysis theory and evaluate its validity by modeling the mobile broadband and fixed broadband subscriptions of six countries including France, Italy, Turkey, Germany, Spain, and the U.K. Later, we compared the Fractional Model we developed with the Polynomial Model. The results show that the Fractional Model is superior to the conventional Polynomial Model in modeling broadband subscriptions. For all selected countries, our proposed Fractional approach outperforms conventional polynomial regression. For all investigation categories, on average, the fractional approach works better by at least 10% and at most 30%.

This study focuses on modeling the daily deaths per new case of COVID-19 by using the Fractional Calculus and the Least Squares Method. Based on our prior work, we proposed a new modeling approach, assessed the strength of outbreak response, and analyzed possible underlying factors of the outbreak for 8 countries including China, France, Germany, Italy, Russia, Spain, the UK, and the US. First, we modeled weekly deaths per new case of COVID-19 using our new modeling method Deep Assessment Methodology - Second Derivative (DAM-SD). Later, we defined a performance indicator to understand how well each country copes with the pandemic. Lastly, Pearson correlations between the performance indicator and several economic, social, and environmental indices, such as Human Development Index, Human Freedom, Democracy, Competitiveness, and Trust Index are computed, and p-values are reported. Results showed that DAM-SD successfully models the daily new cases of COVID-19 with 3.7390% Mean Average Precision Error and outperforms the DAM by 1.5678% MAPE. China is the best-modeled country with 4.0975e-08% MAPE whereas the model produced the highest error rate for France as 8.8317% MAPE. According to the analysis with the performance indicators, China is the most successful country against the pandemic while the United States and France fail to confine COVID-19 outbreak compared to the others. Indicators such as Human Development Index, Human Freedom, Human Democracy, GINI Index, Workers Rights, the Trust Index, and Air Pollution are found significant for COVID-19 response according to the p-values. In the correlation analysis, Average Class Size, Government’s Long Term Vision, Responsiveness to Change, Better Life Index, and Population Density were the least significant indicators. Long Term Care Beds, Social Capital, and Global Social Mobility indicators are found correlated with the COVID-19 response. Household Spending and Student Skills are found insignificant.