Human development and planning is one of the most prominent activities in any country. There are several factors that can be effective in achieving this. One of the key elements in this way is ICT. In recent decades, this technology has evolved widely across all social and economic spheres and has had a profound impact on organizations, human resources and the economics of micro and macro societies. Considering the impact of using information and communication technology can be a good way to increase the level of productivity and development of each country. The purpose of this paper is to investigate the impact of information and communication technology on human development index. Therefore, the investigated model has been using panel data for 15 selected developing countries over the period of 2012 to 2017. The estimation results show that ICT has a positive and significant effect on human development index. While foreign direct investment and value added have a positive impact and inflation has a negative impact on the human development index.

R&D is one of the important factors affecting economic growth. Increased use of R&D will increase competition in manufacturing sectors, which will have a positive impact on the economy, improving product quality and diversity and improving productivity, which will increase production itself. The purpose of this study is to investigate the effects of R&D spending on economic growth using the GMM method for the 15 selected OECD countries from 2012 to 2018. The estimation results show that R&D has had a positive and significant effect on economic growth in the countries studied. Also, GDP of the last year, exchange rate and tax have had a positive impact on economic growth.

A Deep Neural Network (DNN) is a composite function of vector-valued functions, and in order to train a DNN, it is necessary to calculate the gradient of the loss function with respect to all parameters. This calculation can be a non-trivial task because the loss function of a DNN is a composition of several nonlinear functions, each with numerous parameters. The Backpropagation (BP) algorithm leverages the composite structure of the DNN to efficiently compute the gradient. As a result, the number of layers in the network does not significantly impact the complexity of the calculation. The objective of this paper is to express the gradient of the loss function in terms of a matrix multiplication using the Jacobian operator. This can be achieved by considering the total derivative of each layer with respect to its parameters and expressing it as a Jacobian matrix. The gradient can then be represented as the matrix product of these Jacobian matrices. This approach is valid because the chain rule can be applied to a composition of vector-valued functions, and the use of Jacobian matrices allows for the incorporation of multiple inputs and outputs. By providing concise mathematical justifications, the results can be made understandable and useful to a broad audience from various disciplines.

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