Head and neck surgeries require skilled surgeons to avoid facial nerves and blood vessels. Using straight surgical instruments to create a deep and sealed operating environment is difficult. Continuum robots are particularly effective in head and neck surgery due to their extensive range of motion, adaptability, and ability to navigate confined anatomical spaces. This paper presents a new approach to examine the flexibility of the continuum robot in head and neck surgery, motivated by the advantages of continuum robots. This method uses a discretized kinematics model with a constant curvature and a piecewise assumption-fitting-approximation (PFA) method to find closed solutions for the continuum robot’s problem. We introduced the concept of spatial solid angle to assess the dexterity of the continuum robot, utilizing the inverse solution of the target point position as a reference. An intuitive dexterity index and dexterity area were proposed. The length of the continuum segment was optimized by simulation, and the efficacy of the approach was then validated through experiments. Experiments demonstrate that the piecewise assumption can cause the dual-section continuum robot to deform as expected. In comparison to previous similar tasks, the robot has exceptional position accuracy, with a position error of only 1.72% of the overall length. Additionally, it exhibits excellent real-time performance, with a maximum time consumption of 3.9 ms.

The aim of the present work was to identify the influence of visual feedback on the quality of users' work with variant human–computer interfaces and on the mastering of interfaces. The studies assessed the features of the generation of control commands by operators of ergatic (man–machine) systems using an oculographic interface, and hand- and head-based movement control interfaces were assessed. The presence of visual feedback was found to be important for accurate command generation in all cases. However, when controlling with the head and eyes, the presence of visual feedback led to greater deviations from the ideal trajectory and increases in the distance traveled by the cursor before reaching the target in untrained users. Analysis of typical reactions in all experiments allowed three types of control to be identified, these being different for eye and head movements but not for hand movements in the ergatic system. The first and second types showed greater numbers of errors in the presence of feedback than the third type. The results obtained here may be of value in the development of promising interfaces for ergatic systems, including determination of the required visual feedback components for this class of technical devices.

The work is devoted to the study of boundedness properties of integration and differentiation operators of Riemann–Liouville type on the real axis and semi–axis. The operators are acting in smoothness function spaces of Besov type with Muckenhoupt weight functions (weights) of standard and local type. The problem posed is solved by decomposing elements of the function spaces with respect to spline wavelet systems, which are the main solution tools. The article presents in detail a scheme for constructing such systems. In their terms, the corresponding decomposition theorems are established in the paper. The main results of the study are conditions on weights for the fulfilment of inequalities connecting the norms of images and pre–images of Riemann–Liouville integration operators.

A mathematical model of the air transport system, built using a system-dynamic approach, is proposed. With the help of the model, it is possible to improve the management of aviation transport systems according to the criterion of flight safety. When conducting experiments with the model, it is possible to predict the characteristics of the system and use the predictions when making decisions during control.

The behavior of real systems is often stochastic, and the connections between their elements can be adequately described as correlations. In recent years, there have been trends of increasing and complicating modern networks with the growth of their dependence on each other. We observe how several networks are combined into one interdependent network structure. This leads to an increase in the risks that the failure of nodes in one network may lead to the failure of dependent nodes in other networks. As a result of such failures, catastrophic cascade failures can occur in such interconnected network structures. Given the scale of such structures, which are often critical infrastructures, this problem becomes very relevant. The chapter considers the problem of the influence of correlation between individual nodes on the risk of cascading failures in networks. However, determining the correlation between networks is a difficult task in practice. Therefore, for the risk analysis of real network structures, it is first necessary to conduct a study on models, and only then move on to solving practical problems. Applied to Gaussian model network structures, the influence of the closeness of the relationship between subsystems on the risk of cascading failures has been studied. The value of the risk was estimated as the probability of such failures. As an indicator of the risk of cascading failures in the network structure, it is proposed to use the entropy indicator of the relationship between its subsystems. And to reduce the risk of cascading failures in the network structure, it is necessary to reduce the tightness of correlation between the most interconnected elements of subsystems.