ABSTRACT. For predicting cardiovascular diseases, mathematical modelling of the cardiovascular system has been proven to be a powerful asset. The governing idea is to analyse it through compartments as multiple connected subsystems with inputs and outputs. In this paper, models were identified for four subsystems of input-output sequence (left ventricle - left atrium - ascending aorta - descending aorta - left common carotid artery) by modelling frequency response. A data set used for model identification consisted of blood pressure during four consecutive heart contractions of four circulatory segments from clinical trials performed on a pig. The goal is to discover a linear model with a non-integer order that succinctly represents the process, outperforming high-order ARX integer models. This model identification occurs non-parametrically, aiming to achieve the best smooth fit in the frequency domain by minimizing the difference between real measurements and model predictions using the PSO algorithm. 

ABSTRACT. The new types of truncated M-fractional exact soliton solutions for a important real world model known as truncated M-fractional (2+1)-Dimensional nonlinear Kadomt- sev Petviashvili-modified equal width (KP-mEW) equation are achieved. This model is used to explain the ocean waves, matter-wave pulses, waves in ferromagnetic media as wel as long wavelength water waves. We obtain these solutions by using modi- fied extended direct algebraic method and improved (G' /G)-expansion method. The obtained results consisting on trigonometric, hyperbolic trigonometric and mixed func- tions. We also discuss the effect of fractional order derivative. To validate our results, we utilized the Mathematica software. Additionally, we depict some of the obtained wave solitons, using two and three dimensional, and contour graphs. The obtained results are useful in the fields of fluid dynamics, nonlinear optics, ocean engineering and others. Stability analysis of the concerned model si also performed. Furthermore, these employed techniques are not only straightforward, but also highly effective when used to solve non-linear fractional partial differential equations (FPDEs).

ABSTRACT. The method of pseudodifferential mode parabolic equations is a computationally efficient and accurate tool for simulation of underwater noise in complex shallow-water environments. It can be used of estimating of sound exposure level and the impact of noise on the marine fauna, including fish and marine mammals. Numerical solution of pseudodifferential mode parabolic equations is discussed, including initial conditions and boundary conditions for artificial domain truncation. The efficiency of the resulting model is demonstrated in a shipping noise simulation problem.

ABSTRACT. During any business process, the carbon emissions arise through various ways which include transportation, processing, and storage of perishable food items. Eco-friendly techniques are often adopted to reduce waste and carbon emissions. Further, the assessment of how well resources are consumed and how efficiently waste is reduced, confirming that supplies and products continue in practice for as long as possible through reuse, reprocessing, and renewal can be measured through circular economy index. In this paper, a production inventory model for perishable products is proposed with demand as a function of time, selling price and circular economy index. It is observed that the investment in green technology decreases carbon emissions and consequently the total cost significantly. To validate the findings, graphical studies and numerical examples are provided. It is demonstrated how differences in inventory factors affect earnings and influence beneficiary choices.

ABSTRACT. We consider a zero-sum finite horizon linear-quadratic differential game. Suboptimal state-feedback controls of the players in this game are derived. This derivation is based on the approximate solution of the corresponding Riccati matrix differential equation by the method of artificial parameter. The theoretical results are illustrated by the approximate solution of the problem of pursuit-evasion engagement between two flying vehicles.

ABSTRACT. The talk deals with linear differential games with fixed terminal instant, convex geometric constraints of the players' controls, and convex terminal target set. The first player tries to guide the system to the target set at the terminal instant, the second one hinders this. In the 1960s, L. S. Pontryagin proposed a theoretic geometric procedure for approximate constructing time sections of the maximal stable bridge for games of this type. This procedure is known as the second Pontryagin's method. At the beginning of the 1980 in the Krasovskii Institute of Mathematics of Mechanics (Ekaterinburg, Russia), a computational algorithm for the procedure has been suggested and implemented as a computer program. However, this algorithm suitable only for games with two-dimensional equivalent phase vector (when the terminal set is located in some two-dimensional subspace of the phase space). The authors suggest a procedure suitable for games with multi-dimensional phase vector. For an implementation of this method, one needs implementations of convex hull construction, Minkowski sum and difference. The authors have taken known algorithms for convex hull construction and Minkowski sum. An algorithm for Minkowski difference as well as some procedures for conversion of different representations of multi-dimensional polyhedra to each other has been suggested. All these algorithms has been implemented as a computer program in C# by the authors. A series of model differential games has been computed.

ABSTRACT. Rapid developments in aerospace technologies demand reliable procedures to plan robust missions with high safety. To increase safety under uncertainties in model parameters or environmental conditions, multi-objective robust optimization methods via sensitivity minimization can be used. Thereby, an acceptable trade-off between operational nominal cost (e.g., time, energy) and robustness is searched to plan missions that are less prone to disturbances. As there are open-loop and closed-loop sensitivity minimization approaches, the presented analysis aims to exploit multi-objective optimization to assess the performance and the limitations of the open-loop and closed-loop methods. To solve the multi-objective optimization problems, scalarization techniques are utilized using weighted sums and cost bounds. By varying weights and cost bounds, multiple optima can be calculated, resulting in an approximate Pareto front and giving rise to an overview of the trade-off between optimality and robustness of the solutions. The analysis is performed for robust UAV trajectory optimization minimizing positional sensitivities.

ABSTRACT. The problem of optimizing trajectory tracking algorithms is considered. Based on measurements of a moving object, such algorithms iteratively make estimates of its state. These algorithms contain parameters that affect the quality of their work, for example, the noise variances in a mathematical model of the object's dynamics or the transition probabilities in a Hidden Markov Model, which describes switches in the dynamics mode. A multicriteria evolutionary optimization algorithm for such parameters is proposed based on genetic procedures. We also elaborate a procedure for using this algorithm on real data in which random measurement errors are simulated along the real trajectory. The system of criteria is proposed that assesses both the total mean square deviation of the trajectory tracking algorithm's output and the quality of its transition processes after a change of the object's motion mode. The algorithm was tested on model and real air traffic data.

ABSTRACT. A mathematical model of cerebral blood flow in the form of a dynamical system is considered. The cerebral blood flow autoregulation modeling problem is treated as an output regulation control problem. The cerebral autoregulation mechamism is described in terms of a feedback control law based on measurements of the arterial–arteriolar blood flow rate values and intracranial pressure estimates made by an asymtotic observer. The simulation results confirmed the good performance of the suggested cerebral blood flow autoregulation model.

ABSTRACT. The presented applied software implements an iterative algorithm based on the finite element method to calculate the partial pressure of oxygen in the tissue surrounding a blood vessel. The model includes nonlinear coupled differential equations describing the oxygen transport in a blood vessel and surrounding tissue. The software implementation of the algorithm is carried out using the package FreeFEM++.

ABSTRACT. In this paper, the 3-D simulation of a Newtonian fluid on sudden contraction geometries is presented. The main goal of the present work is the validation and verification of the proposed method with a larger and heavier parallel implementation in sight.

The fluid is modeled by the Navier-Stokes equations and solved using the projection method with first order in time and second order in space discretizations. Finite differences are used throughout the discretization process.

As a fully GPU-based implementation is the future objective of the research and also, as a means of lowering the memory usage, the Alternating Direction Implicit method is utilized to split the large resulting systems of linear equations into smaller problems, which are solved with the Thomas algorithm and the Successive Over-Relaxation method parallelized with OpenMP.

ABSTRACT. Epidemiological modelling is crucial to inform healthcare policies and to support decision making for disease prevention and control. The recent outbreak of COVID-19 pandemic raised a significant scientific and public debate regarding the quality of the mathematical models used to predict the effect of the pandemics and to choose an appropriate response strategy. To accurately capture how the disease spreads, we have to move beyond a usual assumption that the population is connected homogeneously (well--mixed), and towards network models of epidemics. Unfortunately, their complexity grows exponentially with the size of the network, that poses a significant computational challenge, known as the curse of dimensionality.

In this talk we discuss computational approaches to epidemiological models on networks, involving both numerical and symbolic computations. We also demonstrate that network models of moderate size can be solved accurately using the recently proposed algorithms based on low-rank tensor product factorisations. Finally, we discuss the inverse problem of inferring a contact network from epidemiological data, for which we employ black-box Bayesian optimisation techniques.

ABSTRACT. After an epidemic outbreak, government and medical institutions try to mitigate the consequences with suitable interventions. Unfortunately, interventions that seem to be successful in theory may be degraded in practice by manifold types of frictions such as delays and erroneous situation assessments. This paper discusses the effects of such frictions. For this purpose, a traditional compartmental model is supplemented by a rule-based control unit, which sets countermeasures into effect when situation assessments exceed critical threshold values.

The model is used to represent the chain of events which occurred in Italy in early 2020. Using analytical considerations, we focus on stability and on the calculation of the reproduction number. With the help of simulation runs, we also investigate the sensitivity of the model parameters and the potential influence of the control unit. The paper concludes with a discussion of the limitations of the underlying model and of the executed analysis.

ABSTRACT. The COVID-19 pandemic has shown that managing interventions involves more than just preventing new infections. The government has to take into account e.g.\ economic losses resulting from increased countermeasures and the mood of the population into account as well. Unfortunately, up to now only very few epidemic models integrate such cross-domain effects.

The paper presents a compartmental epidemiological model enhanced by psychological aspects. These aspects may influence the behavior of the population in response to epidemic conditions and governmental actions. The model incorporates frictions for being more realistic. The assessment of the epidemic's economic impact takes the incapacitated workforce due to both illness and lockdown regulations into account. The reproduction of fundamental economical and psychological effects occurring in an epidemics situation validates the chosen modeling approach.

Due to the limited availability of real-world data concerning psychology and economy, it was not possible to execute a model calibration. Thus, several model parameters have been chosen based on educated guesses. This restricts the usefulness of the model for quantitative predictive purposes. We conclude with a discussion and an outlook.