On a frame theoretic measure of quality of LTI systems

It is of practical significance to define the notion of a measure of quality of a control system, i.e., a quantitative extension of the classical notion of controllability. In this article we demonstrate that the three standard measures of quality involving the trace, minimum eigenvalue, and the determinant of the controllability grammian achieve their optimum values when the columns of the controllability matrix from a tight frame. Motivated by this, and in view of some recent developments in frame theoretic signal processing, we provide a measure of quality for LTI systems based on a measure of tightness of the columns of the reachability matrix

The role of the African Union in Economic and youth development in Africa: A case study of ECOWAS

This study examines the role of the African Union (AU) in fostering economic development and promoting youth political participation in Africa, with a specific focus on the Economic Community of West African States (ECOWAS). Despite the AU's efforts to promote regional integration and development, challenges persist, particularly in addressing youth unemployment and political apathy among the youth population. Through a case study of ECOWAS, this research sought to analyze the effectiveness of AU initiatives in driving economic growth and empowering young people to actively engage in the political process. The study employed both qualitative and quantitative methods, combining analysis of AU policies and programs with quantitative data collected from the Kobo toolbox questionnaire sent to participants based on youth political participation and economic integration in ECOWAS member states. The research objectives were to analyze the historicity and changes of the African Union's economic development plan and policies and examine key components in its economic development agenda since its formation. The present work e examines the African Union's programs and policies that focus on promoting youth political participation and representation locally and nationally and identify the perspectives and feedback from key stakeholders, including youth organizations and government officials, development practitioners, and youth advocates, on the impact and challenges of African Union interventions. The results of this study show how youths from different ECOWAS countries have different perceptions of the AU's efforts to promote youth political participation and representation. Age, gender, occupation, education, lack of political will, lobby, and youth exclusion emerged as significant predictors, reflecting the complex dynamics shaping youth engagement in economic and political processes in the ECOWAS region

Novel min-max reformulations of Linear Inverse Problems

In this article, we dwell into the class of so-called ill-posed Linear Inverse Problems (LIP) which simply refers to the task of recovering the entire signal from its relatively few random linear measurements. Such problems arise in a variety of settings with applications ranging from medical image processing, recommender systems, etc. We propose a slightly generalized version of the error constrained linear inverse problem and obtain a novel and equivalent convex-concave min-max reformulation by providing an exposition to its convex geometry. Saddle points of the min-max problem are completely characterized in terms of a solution to the LIP, and vice versa. Applying simple saddle point seeking ascend-descent type algorithms to solve the min-max problems provides novel and simple algorithms to find a solution to the LIP. Moreover, the reformulation of an LIP as the min-max problem provided in this article is crucial in developing methods to solve the dictionary learning problem with almost sure recovery constraints

Improved Shewhart Chart Using Multiscale Representation

Most univariate process monitoring techniques operate under three main assumptions, that the process residuals being evaluated are Gaussian, independent and contain a moderate level of noise. The performance of the conventional Shewhart chart, for example, is adversely affected when these assumptions are violated. Multiscale wavelet-based representation is a powerful data analysis tool that can help better satisfy these assumptions, i.e., decorrelate autocorrelated data, separate noise from features, and transform the data to better follow a Gaussian distribution at multiple scales. This research focused on developing an algorithm to extend the conventional Shewhart chart using multiscale representation to enhance its performance. Through simulated synthetic data, the developed multiscale Shewhart chart showed improved performance (with lower missed detection and false alarm rates) than the conventional Shewhart chart. The developed multiscale Shewhart chart was also applied to two real world applications, simulated distillation column data, and genomic copy number data, to illustrate the advantage of using the multiscale Shewhart chart for process monitoring over the conventional one

Nigerian English and the Dilemma of Standard English Language Learners

This paper reports on the dilemma learners face when learning English as a second language. Specifically the paper focuses on Nigerian englsih language learners considering various varieties of English use in Nigerian. The main objective of the paper is examines the variety of language learners in institutional settings often encounter in the process of learning English as a second language. Employing qualitative approach and desk-based method of data collection, the paper found out that, there are mainly three varieties of English in Nigeria viz: typical Nigerian English, Pidgin English and Broken English. The study concludes that more attention should be given to Standard English language in the instructional settings so that students should not be left in the dark