rss_2.0International Journal of Applied Mathematics and Computer Science FeedSciendo RSS Feed for International Journal of Applied Mathematics and Computer Science Journal of Applied Mathematics and Computer Science Feed the Analysis of a Mathematical Model of CAR–T Cell Therapy for Glioblastoma: Insights from a Mathematical Model<abstract> <title style='display:none'>Abstract</title> <p>Chimeric antigen receptor T (CAR-T) cell therapy has been proven to be successful against different leukaemias and lymphomas. Its success has led, in recent years, to its use being tested for different solid tumours, including glioblastoma, a type of primary brain tumour, characterised by aggressiveness and recurrence. This paper presents an analytical study of a mathematical model describing the competition of CAR-T and glioblastoma tumour cells, taking into account their immunosuppressive capacity. The model is formulated in a general way, and its basic properties are investigated. However, most of the analysis considers the model with exponential tumour growth, assuming this growth type for simplicity. The existence and stability of steady states are studied, and the subsequent focus is on two different types of treatment: constant and periodic. Finally, protocols for CAR-T cell therapy of glioblastoma are numerically derived; these are aimed at preventing the tumour from reaching a critical size and at prolonging the patients’ survival time as much as possible. The analytical and numerical results provide theoretical support for the treatment of glioblastoma using CAR-T cells.</p> </abstract>ARTICLEtrue Optimization Control Based on a Sandwich Model with Hysteresis for Piezo–Positioning Systems<abstract> <title style='display:none'>Abstract</title> <p>A nonsmooth optimization control (NOC) based on a sandwich model with hysteresis is proposed to control a micropositioning system (MPS) with a piezoelectric actuator (PEA). In this control scheme, the hysteresis phenomenon inherent in the PEA is described by a Duhem submodel embedded between two linear dynamic submodels that describe the behavior of the drive amplifier and the flexible hinge with load, respectively, thus constituting a sandwich model with hysteresis. Based on this model, a nonsmooth predictor for sandwich systems with hysteresis is constructed. To avoid the complicated online search for the optimal value of the generalized gradient at a nonsmooth point, the method of the so-called weighted estimation of generalized gradient is proposed. In order to compensate for the model error caused by model uncertainty, a model error compensator (MEC) is integrated into the online optimization control strategy. Afterwards, the stability of the control system is analyzed based on Lyapunov’s theory. Finally, the proposed NOC-MEC method is verified on an MPS with a PEA, and the corresponding experimental results are presented.</p> </abstract>ARTICLEtrue Control Problems without Terminal Constraints: The Turnpike Property with Interior Decay<abstract> <title style='display:none'>Abstract</title> <p>We show a turnpike result for problems of optimal control with possibly nonlinear systems as well as pointwise-in-time state and control constraints. The objective functional is of integral type and contains a tracking term which penalizes the distance to a desired steady state. In the optimal control problem, only the initial state is prescribed. We assume that a cheap control condition holds that yields a bound for the optimal value of our optimal control problem in terms of the initial data. We show that the solutions to the optimal control problems on the time intervals [0<italic>,T</italic> ] have a turnpike structure in the following sense: For large <italic>T</italic> the contribution to the objective functional that comes from the subinterval [<italic>T/</italic>2<italic>,T</italic> ], i.e., from the second half of the time interval [0<italic>,T</italic> ], is at most of the order 1<italic>/T</italic> . More generally, the result holds for subintervals of the form [<italic>rT,T</italic> ], where <italic>r ∈</italic> (0, 1<italic>/</italic>2) is a real number. Using this result inductively implies that the decay of the integral on such a subinterval in the objective function is faster than the reciprocal value of a power series in <italic>T</italic> with positive coefficients. Accordingly, the contribution to the objective value from the final part of the time interval decays rapidly with a growing time horizon. At the end of the paper we present examples for optimal control problems where our results are applicable.</p> </abstract>ARTICLEtrue Method of Lower and Upper Solutions for Control Problems and Application to a Model of Bone Marrow Transplantation<abstract> <title style='display:none'>Abstract</title> <p>A lower and upper solution method is introduced for control problems related to abstract operator equations. The method is illustrated on a control problem for the Lotka–Volterra model with seasonal harvesting and applied to a control problem of cell evolution after bone marrow transplantation.</p> </abstract>ARTICLEtrue a Mechanism for a Bayesian and Partially Observable Markov Approach<abstract> <title style='display:none'>Abstract</title> <p>The design of incentive-compatible mechanisms for a certain class of finite Bayesian partially observable Markov games is proposed using a dynamic framework. We set forth a formal method that maintains the incomplete knowledge of both the Bayesian model and the Markov system’s states. We suggest a methodology that uses Tikhonov’s regularization technique to compute a Bayesian Nash equilibrium and the accompanying game mechanism. Our framework centers on a penalty function approach, which guarantees strong convexity of the regularized reward function and the existence of a singular solution involving equality and inequality constraints in the game. We demonstrate that the approach leads to a resolution with the smallest weighted norm. The resulting individually rational and ex post periodic incentive compatible system satisfies this requirement. We arrive at the analytical equations needed to compute the game’s mechanism and equilibrium. Finally, using a supply chain network for a profit maximization problem, we demonstrate the viability of the proposed mechanism design.</p> </abstract>ARTICLEtrue Measures of an Ensemble Classifier Based on the Distributivity Equation to Predict the Presence of Severe Coronary Artery Disease<abstract> <title style='display:none'>Abstract</title> <p>The aim of this study is to apply and evaluate the usefulness of the hybrid classifier to predict the presence of serious coronary artery disease based on clinical data and 24-hour Holter ECG monitoring. Our approach relies on an ensemble classifier applying the distributivity equation aggregating base classifiers accordingly. Such a method may be helpful for physicians in the management of patients with coronary artery disease, in particular in the face of limited access to invasive diagnostic tests, i.e., coronary angiography, or in the case of contraindications to its performance. The paper includes results of experiments performed on medical data obtained from the Department of Internal Medicine, Jagiellonian University Medical College, Kraków, Poland. The data set contains clinical data, data from Holter ECG (24-hour ECG monitoring), and coronary angiography. A leave-one-out cross-validation technique is used for the performance evaluation of the classifiers on a data set using the WEKA (Waikato Environment for Knowledge Analysis) tool. We present the results of comparing our hybrid algorithm created from aggregation with the distributive equation of selected classification algorithms (multilayer perceptron network, support vector machine, <italic>k</italic>-nearest neighbors, naïve Bayes, and random forests) with themselves on raw data.</p> </abstract>ARTICLEtrue–Triggered Cooperative Control for High–Order Nonlinear Multi–Agent Systems with Finite–Time Consensus<abstract> <title style='display:none'>Abstract</title> <p>An event-triggered adaptive control algorithm is proposed for cooperative tracking control of high-order nonlinear multi-agent systems (MASs) with prescribed performance and full-state constraints. The algorithm combines dynamic surface technology and the backstepping recursive design method, with radial basis function neural networks (RBFNNs) used to approximate the unknown nonlinearity. The barrier Lyapunov function and finite-time stability theory are employed to prove that all agent states are semi-globally uniform and ultimately bounded, with the tracking error converging to a bounded neighborhood of zero in a finite time. Numerical simulations are provided to demonstrate the effectiveness of the proposed control scheme.</p> </abstract>ARTICLEtrue of the Fractional Sturm–Liouville Difference Problem to the Fractional Diffusion Difference Equation<abstract> <title style='display:none'>Abstract</title> <p>This paper deals with homogeneous and non-homogeneous fractional diffusion difference equations. The fractional operators in space and time are defined in the sense of Grünwald and Letnikov. Applying results on the existence of eigenvalues and corresponding eigenfunctions of the Sturm–Liouville problem, we show that solutions of fractional diffusion difference equations exist and are given by a finite series.</p> </abstract>ARTICLEtrue–Supervised vs. Supervised Learning for Mental Health Monitoring: A Case Study on Bipolar Disorder<abstract> <title style='display:none'>Abstract</title> <p>Acoustic features of speech are promising as objective markers for mental health monitoring. Specialized smartphone apps can gather such acoustic data without disrupting the daily activities of patients. Nonetheless, the psychiatric assessment of the patient’s mental state is typically a sporadic occurrence that takes place every few months. Consequently, only a slight fraction of the acoustic data is labeled and applicable for supervised learning. The majority of the related work on mental health monitoring limits the considerations only to labeled data using a predefined ground-truth period. On the other hand, semi-supervised methods make it possible to utilize the entire dataset, exploiting the regularities in the unlabeled portion of the data to improve the predictive power of a model. To assess the applicability of semi-supervised learning approaches, we discuss selected state-of-the-art semi-supervised classifiers, namely, label spreading, label propagation, a semi-supervised support vector machine, and the self training classifier. We use real-world data obtained from a bipolar disorder patient to compare the performance of the different methods with that of baseline supervised learning methods. The experiment shows that semi-supervised learning algorithms can outperform supervised algorithms in predicting bipolar disorder episodes.</p> </abstract>ARTICLEtrue of the Lombard Effect Based on a Machine Learning Approach<abstract> <title style='display:none'>Abstract</title> <p>The Lombard effect is an involuntary increase in the speaker’s pitch, intensity, and duration in the presence of noise. It makes it possible to communicate in noisy environments more effectively. This study aims to investigate an efficient method for detecting the Lombard effect in uttered speech. The influence of interfering noise, room type, and the gender of the person on the detection process is examined. First, acoustic parameters related to speech changes produced by the Lombard effect are extracted. Mid-term statistics are built upon the parameters and used for the self-similarity matrix construction. They constitute input data for a convolutional neural network (CNN). The self-similarity-based approach is then compared with two other methods, i.e., spectrograms used as input to the CNN and speech acoustic parameters combined with the <italic>k</italic>-nearest neighbors algorithm. The experimental investigations show the superiority of the self-similarity approach applied to Lombard effect detection over the other two methods utilized. Moreover, small standard deviation values for the self-similarity approach prove the resulting high accuracies.</p> </abstract>ARTICLEtrue Patterns and Chaos in a Map–Based Neuron Model<abstract> <title style='display:none'>Abstract</title> <p>The work studies the well-known map-based model of neuronal dynamics introduced in 2007 by Courbage, Nekorkin and Vdovin, important due to various medical applications. We also review and extend some of the existing results concerning <italic>β</italic>-transformations and (expanding) Lorenz mappings. Then we apply them for deducing important properties of spike-trains generated by the CNV model and explain their implications for neuron behaviour. In particular, using recent theorems of rotation theory for Lorenz-like maps, we provide a classification of periodic spiking patterns in this model.</p> </abstract>ARTICLEtrue Q–Transform–Based Deep Learning Architecture for Detection of Obstructive Sleep Apnea<abstract> <title style='display:none'>Abstract</title> <p>Obstructive sleep apnea (OSA) is a long-term sleep disorder that causes temporary disruption in breathing while sleeping. Polysomnography (PSG) is the technique for monitoring different signals during the patient’s sleep cycle, including electroencephalogram (EEG), electromyography (EMG), electrocardiogram (ECG), and oxygen saturation (SpO2). Due to the high cost and inconvenience of polysomnography, the usefulness of ECG signals in detecting OSA is explored in this work, which proposes a two-dimensional convolutional neural network (2D-CNN) model for detecting OSA using ECG signals. A publicly available apnea ECG database from PhysioNet is used for experimentation. Further, a constant Q-transform (CQT) is applied for segmentation, filtering, and conversion of ECG beats into images. The proposed CNN model demonstrates an average accuracy, sensitivity and specificity of 91.34%, 90.68% and 90.70%, respectively. The findings obtained using the proposed approach are comparable to those of many other existing methods for automatic detection of OSA.</p> </abstract>ARTICLEtrue Dynamic Model as a Tool for Design and Optimization of Propulsion Systems of Transport Means<abstract> <title style='display:none'>Abstract</title> <p>Designing power transmission systems is a complex and often time-consuming problem. In this task, various computational tools make it possible to speed up the process and verify a great many different solutions before the final one is developed. It is widely possible today to conduct computer simulations of the operation of various devices before the first physical prototype is built. The article presents an example of a dynamic model of power transmission systems, which has been developed to support work aimed at designing new and optimizing existing systems of that type, as well as to help diagnose them by designing diagnostic algorithms sensitive to early stages of damage development. The paper also presents sample results of tests conducted with the model, used at the gear design stage. In the presented model, the main goal is to reproduce the phenomena occurring in gears as well as possible, using numerous experiments in this direction featured in the literature. Many already historical models present different ways of modeling, but they often made significant simplifications, required by the limitations of the nature of computational capabilities. Differences also result from the purpose of the models being developed, and the analysis of these different ways of doing things makes it possible to choose the most appropriate approach.</p> </abstract>ARTICLEtrue Associative Memories with Complemented Operations<abstract> <title style='display:none'>Abstract</title> <p>Associative memories based on lattice algebra are of great interest in pattern recognition applications due to their excellent storage and recall properties. In this paper, a class of binary associative memory derived from lattice memories is presented, which is based on the definition of new complemented binary operations and threshold unary operations. The new learning method generates memories <bold>M</bold> and <bold>W</bold>; the former is robust to additive noise and the latter is robust to subtractive noise. In the recall step, the memories converge in a single step and use the same operation as the learning method. The storage capacity is unlimited, and in autoassociative mode there is perfect recall for the training set. Simulation results suggest that the proposed memories have better performance compared to other models.</p> </abstract>ARTICLEtrue Optimization Using a Two–Tier Hybrid Optimizer in an Internet of Things Network<abstract> <title style='display:none'>Abstract</title> <p>The growing use of the Internet of Things (IoT) in smart applications necessitates improved security monitoring of IoT components. The security of such components is monitored using intrusion detection systems which run machine learning (ML) algorithms to classify access attempts as anomalous or normal. However, in this case, one of the issues is the large length of the data feature vector that any ML or deep learning technique implemented on resource-constrained intelligent nodes must handle. In this paper, the problem of selecting an optimal-feature set is investigated to reduce the curse of data dimensionality. A two-layered approach is proposed: the first tier makes use of a random forest while the second tier uses a hybrid of gray wolf optimizer (GWO) and the particle swarm optimizer (PSO) with the k-nearest neighbor as the wrapper method. Further, differential weight distribution is made to the local-best and global-best positions in the velocity equation of PSO. A new metric, i.e., the reduced feature to accuracy ratio (RFAR), is introduced for comparing various works. Three data sets, namely, NSLKDD, DS2OS and BoTIoT, are used to evaluate and validate the proposed work. Experiments demonstrate improvements in accuracy up to 99.44%, 99.44% and 99.98% with the length of the optimal-feature vector equal to 9, 4 and 8 for the NSLKDD, DS2OS and BoTIoT data sets, respectively. Furthermore, classification improves for many of the individual classes of attacks: denial-of-service (DoS) (99.75%) and normal (99.52%) for NSLKDD, malicious control (100%) and DoS (68.69%) for DS2OS, and theft (95.65%) for BoTIoT.</p> </abstract>ARTICLEtrue–Symptom Measurement Based Fault Detection of the PEM Fuel Cell System<abstract> <title style='display:none'>Abstract</title> <p>The proper functioning of the fuel cell system depends on the proper operation of all its subsystems. One of the key subsystems is the oxidant supply system, which is responsible for supplying oxygen for the electrochemical reaction taking place in the cell. It also transports the reaction products, i.e., water, outside the fuel cell stack, and in some cases removes excess heat generated in the stack. Changes in the technical condition of machine individual elements always result in changes in operating or residual parameters; however, it is necessary to select appropriate diagnostic methods to be able to use these changes to assess the machine’s technical condition. This article presents the results of research focused on assessing the possibilities of diagnosing the oxidant supply subsystem, in particular, too low an oxidant flow leading to oxygen starvation and cathode flooding, based on the analysis of the voltage occurring in individual cells of the stack as well as on the basis of vibration and acoustic emission (AE) measurements. The presented results show that the faulty operation of that system can be indicated either through electrical and vibroacoustic/acoustic emission measurements.</p> </abstract>ARTICLEtrue Efficient Fault Tolerant Control Scheme for Euler–Lagrange Systems<abstract> <title style='display:none'>Abstract</title> <p>Every closed-loop system holds a level of fault tolerance, which could be increased by using a fault tolerant control (FTC) scheme. In this paper, an efficient FTC scheme for a class of nonlinear systems (Euler–Lagrange ones) is proposed, which guarantees high performance and stability in a faulty system. This scheme was designed on the basis of a cascade control structure in which the inner loop is the closed-loop system and the external loop is the FTC, a generalized proportional integral (GPI) observer-based controller, which manages the fault tolerance level increment. An important issue of the proposed scheme is that the GPI observer-based controller jointly estimates disturbances and faults, providing information about the state of health of the system, and then compensates their effect. The scheme is efficient because only the inertia matrix is required for the controller design, it is able to preserve the nominal control law unchanged and can operate properly without explicit information about system faults (fault diagnostic module). Simulation results, on a pendulum model, show the effectiveness of the proposed scheme for tracking control.</p> </abstract>ARTICLEtrue Quaternions for the Kinematic Description of a Fish–Like Propulsion System<abstract> <title style='display:none'>Abstract</title> <p>This study discusses the use of quaternions and dual quaternions in the description of artificial fish kinematics. The investigation offered here illustrates quaternion and dual quaternion algebra, as well as its implementation in the software chosen. When it comes to numerical stability, quaternions are better than matrices because a normalised quaternion always shows the correct rotation, while a matrix more easily loses its orthogonality due to rounding errors and oversizing. Although quaternions are more compact than rotation matrices, using quaternions does not always provide less numerical computation and the amount of memory needed. In this paper, an algebraic form of quaternion representation is provided which is less memory-demanding than the matrix representation. All the functions that were used to prepare this work are presented, and they can be employed to conduct more research on how well quaternions work in a specific assignment.</p> </abstract>ARTICLEtrue Approaches to Late Work Scheduling on Unrelated Machines<abstract> <title style='display:none'>Abstract</title> <p>We consider the scheduling problem on unrelated parallel machines in order to minimize the total late work. Since the problem is NP-hard, we propose a mathematical model and two dedicated exact approaches for solving it, based on the branching and bounding strategy and on enumerating combined with a dynamic programming algorithm. The time efficiencies of all three approaches are evaluated through computational experiments.</p> </abstract>ARTICLEtrue Dynamic Submerging Motion Model of the Hybrid–Propelled Unmanned Underwater Vehicle: Simulation and Experimental Verification<abstract> <title style='display:none'>Abstract</title> <p>Hybrid propulsion in underwater vehicles is the new idea of combining conventional propulsion systems such as screw propellers with other kinds of propulsion like oscillating biomimetic fins, glider wings or jet thrusters. Each of these propulsion systems has its own benefits and drawbacks, and the goal is to have them complement each other in certain conditions. This paper covers the topic of a dynamic model of the pitch and heave motion of the HUUV (hybrid unmanned underwater vehicle) using screw propellers and biomimetic lateral fins. Firstly, the simulation model of the vehicle performing depth and pitch change is presented. Secondly, the vehicle’s hydrodynamic coefficients obtained from CFD simulations are discussed. Thirdly, the results of the HUUV experimental studies in a swimming pool are presented. Lastly, simulation results are compared with those of the experiment to verify the correctness of the model. The vehicle’s motion in the swimming pool during the experiments was recorded using a submerged camcorder and then analysed using the Tracker software.</p> </abstract>ARTICLEtrue