International Scientific Journals
of Scientific Technical Union of Mechanical Engineering "Industry 4.0"

Mathematical Optimization or Mathematical Programming is a set of theoretical and applied methods originating from applied mathematics to computer science, used to find the optimal value, given some predefined criterion for optimality and based on some input parameters. More precisely, it concerns finding the input parameters of a function (called the objective function) which maximize/minimize its output. Mathematical Optimization is widely used for various quantitative or computational problems that arise everywhere in science and engineering, ranging from statistics and applied math to aerospace engineering and finance. In the following paper, we demonstrate the use of two classical optimization algorithms – Gradient Descent and Lagrangian Multipliers method – in model development in finance and trading. The specific stochastic process on which the trading model is based is called the Ornstein-Uhlenbeck (O-U) process and the point of the use of these two optimization approaches is
to find the parameters that minimize the log likelihood function of this process. This fits the O-U process to the historical data and in the context of finance and trading, maximizes our profits and helps us hedge against losses

Topological Data Analysis (TDA) is relatively new filed of Applied Mathematics that emerged rapidly last years. The main tool of Topological Data Analysis is Persistent Homology. Persistent Homology provides some topological characteristics of the datasets. In this paper we will discuss classification of digital images using their topological signatures computed with Persistent Homology. We will experiment on the Fashion-MNIST dataset. Using Topological Data Analysis, the classification was improved.

Overcrowding in the Emergency Department (ED) is one of the most important issues in healthcare systems. Two major causes of this congestion are identified, the first one is unjustified Emergency Department visits and the second one a lack of downstream beds. The lack of downstream beds can deteriorate the quality of care for patients who need hospitalization after an ED visit. In this paper a generic simulation model is developed in order to analyse patient pathways from the ED to hospital discharge.