Linear algebra lies at the core of many algorithmic problems. Standard matrix multiplication and the Gaussian elimination method have arithmetic complexity that is cubic in terms of input size. In this article, we show that for most dense linear algebra problems—multiplication, inversion, determinant, system solving—more efficient algorithms exist with strictly sub-cubic complexity.

A number of factors influence linear growth, and one of the main causes of stunted growth in children is malnutrition. Finding the food intakes linked to stunting in the area of Mohammadpur, Dhaka, preschoolers was the aim of this study. To gain insights into children’s eating habits and the role of parental involvement in their growth in Bangladesh, this project will conduct interviews with parents and preschool-aged children. The aim is to predict which food habits may hinder growth in the near future and identify the underlying reasons behind them. By interviewing parents, valuable information about the dietary practices and food choices made within the household will be found. This includes understanding the types of foods provided to children, mealtime routines, and the strategies parents employ to encourage healthy eating. Additionally, the interviews will explore the factors that influence parents decisions regarding food, such as cultural traditions, economic constraints, and knowledge about nutrition. Furthermore, engaging directly with preschool-aged children will be enabled to gain insights into their food preferences, attitudes towards different foods, and their experiences during mealtimes. This can help identify any specific challenges or barriers that children may face when it comes to consuming nutritious foods. Through this comprehensive approach, the project aims to make predictions about which food habits may negatively impact children’s growth in the near future. By analyzing the gathered data, it can be identified patterns and trends in the children’s eating habits that may contribute to poor growth outcomes. For example, they may uncover patterns of limited vegetable intake, excessive consumption of processed foods, or inconsistent mealtime routines. Ultimately, this research aims to contribute to improved nutrition and overall growth outcomes for preschool-aged children. The results highlight the need for focused public health initiatives and community-based education programs that prioritize mothers' education on nutrition and health, as well as the provision of socioeconomic resources to help mothers meet their children's nutritional needs and avoid malnutrition. The current annual average rate of reduction is 2.7%, and this will need to be increased to 3.3% to achieve the target. This is not a phenomenal increase compared with the current rate of reduction, but it will require concerted planning and efforts. From an economic perspective, the cost to Bangladesh of not investing in accelerating this reduction will be huge in terms of lost gross domestic product and income. From a health perspective, it is essential to improve linear growth of children so that the negative effects of excess ponderal growth and resulting overweight and obesity are attenuated.

Arctic circle has become a focal point of geopolitical competition due to climate change, resource exploitation and emerging strategic interests. Arctic Nations- Russia, United States, Canada, Denmark and Norway are actively competing on regional claims, military dominance and economic occasions. Meanwhile, non-Arctic states such as China, India and Bangladesh are expanding their participation due to economic, environmental and strategic concerns. This study examines the underlying geopolitical stresses, evaluates policies of the Arctic and non-Arctic states, and assesses economic and security implications. Using a qualitative research approach, this paper highlights how Arctic geo -strategy can change the dynamics of global power.

Until now, Computer Scientists have concerned themselves with identifying efficient algorithms for solving the general case of some problem – that is finding one which performs well when the size of the input tends to infinity. However, this is the precise opposite of what is actually needed in practice. Effectively solving some real-world problem entails identifying an algorithm which works well for all (or some) inputs up to some fixed upper bound dictated by the concrete practical application. Such an algorithm may be distinct from the one which solves the general case. Furthermore, a general case algorithm may not exist at all or finding it might prove painstakingly hard for the human mind. Fortunately, in practice all that is needed is one which works on the finite cases involved in the real world situations, not one which can, unaltered, solve any input correctly. In this paper, we first introduce a theoretical framework for reasoning about finite algorithmics. It allows familiar concepts such as asymptotic complexity to be adapted to the case where the input size is bounded from above. We also present some elementary results within this theory. Secondly, we present a generic approach for automatically discovering an adequate algorithm for the finite case of some hard problem – if one exists. Thirdly, we argue why we expect the finite case of hard problems to be easier than the general case. Fourthly, we present some relevant ideas specific to three hard problems, namely 3CNF-SAT, String Compression and Integer Factorization. Fifthly, we discuss the significance of the theory and methods introduced in this paper – noting among other things that they can be used to automatically determine that either (i) P = NP, (ii) P <> NP or (iii) we don’t really care about the distinction for practical purposes. Finally, we present four directions for immediate further research and formulate an open question which, when answered will, for all practical purposes, decide P=NP. Enhancing the way Computer Scientists reason about hard problems is ultimately the single most important contribution we claim for this paper.