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Given a set of points C = {x1, x2, ..., xm} ⊆ Rn, what is the minimum volume ellipsoid that encloses it? Equally interestingly, one may ask: What is the maximum volume ellipsoid that can be embedded in the set of points without containing any? These problems have a number of applications beside being interesting in their own right. In this paper we review the important results concerning these and suggest an evolutionary-type approach for their solution. We will also highlight computational results.

Relevance. Restoring the retinal integrity during surgical treatment of macular holes (MH) does not always guarantee a significant improvement in visual acuity in the postoperative period. The possibility of regeneration of the retinal ellipsoid zone (EZ), as well as the relationship between the structural restoration of the outer retina and the improvement of visual functions are very contradictory. Purpose. To assess the possibility and degree of repair of the ellipsoid zone in the early and long-term postoperative treatment of MH of medium and large diameters. Material and methods. A prospective study of 13 patients (13 eyes) – 12 women and 1 man with a MH of medium and large diameters was conducted. Patients were divided into 2 groups depending on the presence or absence of an EZ defect after 6 months postoperatively. The structure of the retina was evaluated according to OCT data and the visual acuity of patients in the distance before surgery, 1, 3 and 6 months after MR surgery. Results. In patients with complete restoration of retinal EZ, the initial size of the holes was 1.5 times smaller than in the comparison group, the time from the moment of diagnosis to surgery was 122.7±51.8 and 383.5±125.7 days, respectively. The defect of photoreceptors of the EZ by 1 month after surgery in patients of the first and second groups was 369.6±245.61 microns and 276.07±233.37 microns, respectively. By 6 months of follow–up in the first group, complete closure of the defect was observed, in the second group its decrease to 91.61±97.51 microns, while visual acuity in the first group was 0.46±0.83 by six months of followup and in 3 out of 5 cases it increased to 0.6–0.9, in the second group in all cases this indicator did not exceed 0.5. Conclusion. Complete regeneration of EZ was observed in 38.5% of cases 6 months after surgery, however, anatomical repair of the photoreceptor field of the macular area in the postoperative period does not guarantee improvement of visual functions in all patients. Key words: macular hole, ellipsoid zone, ellipsoid zone regeneration

The study examines a sustainable group decision-making model aimed at improving the efficiency and safety of ship operations. The sustainable group decision-making model is developed on the basis of the scenario describing the interaction between independent specialists from the expert community. It is revealed that developing the scenarios of ship operations and the procedures of the ship operations status control is based on the decisions made by expert groups. The study proposes the relations class of the individuals, where \"human elements\" are characterized by hierarchical vector criterion. When using such a criterion the analysis of equilibrium situations is focused on, and most of the results of the analysis are obtained for the case when the \"human elements\" share the resources defined through vector variables. It is shown that in the developed sustainable group decision-making model each expert could have two components of the global goal - personal and social constituents when choosing hazardous cases from ship operations patterns. These components should be achieved in the implementation of the ship key operation through the distribution of the vector resource. The algorithm for assessing the properties of \"group decisions stability\" is based on the principle of \"making group decisions of many individuals\", introduced in the work with the help of a solutions spheroid. Thus, for a finite number of steps, the algorithm estimates if the decisions of each expert belong to the group decisions spheroid, showing that there are no other solutions that would belong to this spheroid.

The relaxation dynamics of granular materials is more like that of complex fluids than that of thermal glass-forming systems, owing to the absence of the ‘cage effect’. Against the grain We can all claim familiarity with granular materials (think of sand, for example), so it might be surprising to find that there is still much to learn about their properties. When left undisturbed, a granular system will eventually settle into a stable structure; but perturb the system and the grains will move about, in a manner thought to resemble that of atoms in a slowly flowing glassy system. New results by Binquan Kou et al . show that this glassy analogy doesn't hold. The team used X-ray tomography to follow the three-dimensional motion of grains in a perturbed granular medium, and see dynamic behaviour that is distinct from that encountered in a glassy system. They trace this deviant behaviour to the presence of friction between the grains. Granular materials such as sand, powders and foams are ubiquitous in daily life and in industrial and geotechnical applications 1 , 2 , 3 , 4 . These disordered systems form stable structures when unperturbed, but in the presence of external influences such as tapping or shear they ‘relax’, becoming fluid in nature. It is often assumed that the relaxation dynamics of granular systems is similar to that of thermal glass-forming systems 3 , 5 . However, so far it has not been possible to determine experimentally the dynamic properties of three-dimensional granular systems at the particle level. This lack of experimental data, combined with the fact that the motion of granular particles involves friction (whereas the motion of particles in thermal glass-forming systems does not), means that an accurate description of the relaxation dynamics of granular materials is lacking. Here we use X-ray tomography to determine the microscale relaxation dynamics of hard granular ellipsoids subject to an oscillatory shear. We find that the distribution of the displacements of the ellipsoids is well described by a Gumbel law 6 (which is similar to a Gaussian distribution for small displacements but has a heavier tail for larger displacements), with a shape parameter that is independent of the amplitude of the shear strain and of the time. Despite this universality, the mean squared displacement of an individual ellipsoid follows a power law as a function of time, with an exponent that does depend on the strain amplitude and time. We argue that these results are related to microscale relaxation mechanisms that involve friction and memory effects (whereby the motion of an ellipsoid at a given point in time depends on its previous motion). Our observations demonstrate that, at the particle level, the dynamic behaviour of granular systems is qualitatively different from that of thermal glass-forming systems, and is instead more similar to that of complex fluids. We conclude that granular materials can relax even when the driving strain is weak.

For networked control systems with logarithmic quantization, the state estimation is important. Different from the traditional state estimation methods where the uncertainties are assumed to have known probability distributions, the set-membership estimation method used in this paper only supposes that the uncertainties are bounded. This assumption is more accurate and less conservative in practical application. This paper considers the ellipsoidal set-membership estimation of discrete-time linear systems with logarithmic quantized input. The set-membership estimator, which belongs to the ellipsoid, is proposed. The estimation error is analysed, and the sufficient conditions to guarantee the boundedness of the estimation error are given. Using the sector bound property of the logarithmic quantizer, the asymptotic stability of the system and the set-membership performance constraint are analysed, respectively. According to a numerical example, it is shown that the theoretical results obtained in this paper are effective and the set-membership estimation can estimate the system state effectively. The research presents an ellipsoidal set-membership estimation for networked control systems subject to logarithmic quantized control input. It has high computational efficiency and thus has great significance.

To investigate the behavior of a spacecraft near a pair of irregular bodies, consider a three-body configuration (one massless). Two massive bodies, P 1 and P 2 , form the primary system; each primary is modeled as a sphere or an ellipsoid. Two primary configurations are addressed: ‘synchronous’ and ‘non-synchronous’. Concepts and tools similar to those applied in the circular restricted three-body problem are exploited to construct periodic trajectories for a third body in synchronous systems. In non-synchronous systems, however, the search for third body periodic orbits is complicated by several factors. The mathematical model for the third-body motion is now time-variant and the motion of P 2 is not trivial.

Many natural micrometre-scale assemblies can be actuated to control their optical, transport and mechanical properties, yet such functionality is lacking in colloidal structures synthesized thus far. Here, we show with experiments and computer simulations that Janus ellipsoids can self-assemble into self-limiting one-dimensional fibres with shape-memory properties, and that the fibrillar assemblies can be actuated on application of an external alternating-current electric field. Actuation of the fibres occurs through a sliding mechanism that permits the rapid and reversible elongation and contraction of the Janus-ellipsoid chains by ~36% and that on long timescales leads to the generation of long, uniform self-assembled fibres. Colloidal-scale actuation might be useful in microrobotics and in applications of shape-memory materials. Experiments and computer simulations show that Janus ellipsoids can self-assemble into self-limiting fibres that have shape-memory properties and can be actuated by applying an external electric field.

The contact behaviour between an ellipsoid and a rigid plane is significant in research on bearing and assembly joint surfaces. However, an empirical relationship between an elastic–plastic ellipsoid and a rigid plane has not been established. In this study, the elastic–plastic contact behaviour between a deformable ellipsoid and a rigid plane was investigated by establishing a new finite element model. The proposed elastic–plastic ellipsoid contact model was designed considering the effects of the ellipticity and strain-hardening rate of the ellipsoid. The strain-hardening rate and ellipticity of the ellipsoid affected the contact area, load and mean pressure. Furthermore, the effect gradually increased with an increase in interference. New dimensionless empirical formulas for determining the contact load and contact area were proposed based on the analysis. The proposed model was validated by comparing the obtained results with previous experimental results and those of theoretical models. This study can be used to predict the elastic–plastic contact parameters between a single ellipsoid and a rigid body, such as bearings, gears and cams. It can also be used to investigate the elastic–plastic contact behaviour between anisotropic rough surfaces composed of asperities with different radii of curvature.

Spheroids provide a 3D environment with intensive cell–cell contacts. As a result of their excellent regenerative properties and rapid progress in their high-throughput production, spheroids are increasingly suggested as building blocks for tissue engineering. In this review, we focus on innovative biotechnological approaches that increase the quality of spheroids for this specific type of application. These include in particular the fabrication of coculture spheroids, mimicking the complex morphology and physiological tasks of natural tissues. In vitro preconditioning under different culture conditions and incorporation of biomaterials improve the function of spheroids and their directed fusion into macrotissues of desired shapes. The continuous development of these sophisticated approaches may markedly contribute to a broad implementation of spheroid-based tissue engineering in future regenerative medicine. Spheroids are increasingly used as building blocks in tissue engineering, because they ideally mimic the physiological 3D environment of tissues. Automatized large-scale production of spheroids is technically feasible. Compared to 2D cell systems, spheroids exhibit an enhanced regenerative capacity, which can be improved during the production process by adjusting the culture conditions and incorporation of biomaterials. The complexity of tissues can be mimicked by incorporation of multiple cell types in coculture spheroids. Macrotissues can be generated by seeding spheroids on scaffolds or by scaffold-free fusion of spheroids.

Background The worldwide demand for the organ replacement or tissue regeneration is increasing steadily. The advancements in tissue engineering and regenerative medicine have made it possible to regenerate such damaged organs or tissues into functional organ or tissue with the help of 3D bioprinting. The main component of the 3D bioprinting is the bioink, which is crucial for the development of functional organs or tissue structures. The bioinks used in 3D printing technology require so many properties which are vital and need to be considered during the selection. Combination of different methods and enhancements in properties are required to develop more successful bioinks for the 3D printing of organs or tissue structures. Main body This review consists of the recent state-of-art of polymer-based bioinks used in 3D printing for applications in tissue engineering and regenerative medicine. The subsection projects the basic requirements for the selection of successful bioinks for 3D printing and developing 3D tissues or organ structures using combinations of bioinks such as cells, biomedical polymers and biosignals. Different bioink materials and their properties related to the biocompatibility, printability, mechanical properties, which are recently reported for 3D printing are discussed in detail. Conclusion Many bioinks formulations have been reported from cell-biomaterials based bioinks to cell-based bioinks such as cell aggregates and tissue spheroids for tissue engineering and regenerative medicine applications. Interestingly, more tunable bioinks, which are biocompatible for live cells, printable and mechanically stable after printing are emerging with the help of functional polymeric biomaterials, their modifications and blending of cells and hydrogels. These approaches show the immense potential of these bioinks to produce more complex tissue/organ structures using 3D bioprinting in the future.