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This paper is dedicated to the analysis of medical and biological data obtained through locomotor training and testing of astronauts conducted both on Earth and during spaceflight. These experiments can be described as the astronaut’s movement on a treadmill according to a predefined regimen in various speed modes. During these modes, not only the speed is recorded but also a range of parameters, including heart rate, ground reaction force, and others, are collected. In order to analyze the dynamics of the astronaut’s condition over an extended period, it is necessary to perform a qualitative segmentation of their movement modes to independently assess the target metrics. This task becomes particularly relevant in the development of an autonomous life support system for astronauts that operates without direct supervision from Earth. The segmentation of target data is complicated by the presence of various anomalies, such as deviations from the predefined regimen, arbitrary and varying duration of mode transitions, hardware failures, and other factors. The paper includes a detailed review of several contemporary retrospective (offline) nonparametric methods for detecting multiple changepoints, which refer to sudden changes in the properties of the observed time series occurring at unknown moments. Special attention is given to algorithms and statistical measures that determine the homogeneity of the data and methods for detecting change points. The paper considers approaches based on dynamic programming and sliding window methods. The second part of the paper focuses on the numerical modeling of these methods using characteristic examples of experimental data, including both “simple” and “complex” speed profiles of movement. The analysis conducted allowed us to identify the preferred methods, which will be further evaluated on the complete dataset. Preference is given to methods that ensure the closeness of the markup to a reference one, potentially allow the detection of both boundaries of transient processes, as well as are robust relative to internal parameters.

Collective behavior can serve as a mechanism of thermoregulation and play a key role in the joint survival of a group of organisms. In higher animals, such phenomena are usually the subject of study of biology since sudden transitions to collective behavior are difficult to differentiate from the psychological and social adaptation of animals. However, in this paper, we indicate several important examples when a flock of higher animals demonstrates phase transitions similar to known phenomena in liquids and gases. This issue can also be studied experimentally within the framework of synthetic systems consisting of self-propelled robots that act according to a certain given algorithm. Generalizing both of these cases, we consider the problem of phase transitions in a dense group of interacting selfpropelled agents. Within the framework of microscopic theory, we propose a mathematical model of the phenomenon, in which agents are represented as bodies interacting with each other in accordance with an effective potential of a special type, expressing the desire of agents to move in the direction of the gradient of the joint thermal field. We show that the number of agents in the group, the group power, is the control parameter of the problem. A discrete model with individual dynamics of agents reproduces most of the phenomena observed both in natural flocks of higher animals engaged in collective thermoregulation and in synthetic complex systems. A first-order phase transition is observed, which symbolizes a change in the aggregate state in a group of agents. One observes the self-assembly of the initial weakly structured mass of agents into dense quasi-crystalline structures. We demonstrate also that, with an increase in the group power, a second-order phase transition in the form of thermal convection can occur. It manifests in a sudden liquefaction of the group and a transition to vortex motion, which ensures more efficient energy consumption in the case of a synthetic system of interacting robots and the collective survival of all individuals in the case of natural animal flocks.With an increase in the group power, secondary bifurcations occur, the vortex structure in agent medium becomes more complicated.

We consider a portfolio with call option and the corresponding underlying asset under the standard assumption that stock-market price represents a random variable with lognormal distribution. Minimizing the variance hedging risk of the portfolio on the date of maturity of the call option we find a fraction of the asset per unit call option. As a direct consequence we derive the statistically fair lookback call option price in explicit form. In contrast to the famous Black–Scholes theory, any portfolio cannot be regarded as  risk-free because no additional transactions are supposed to be conducted over the life of the contract, but the sequence of independent portfolios will reduce risk to zero asymptotically. This property is illustrated in the experimental section using a dataset of daily stock prices of 37 leading US-based companies for the period from April 2006 to January 2013.

The paper considers the problem of transverse impact on a thin preloaded fiber. The commonly accepted theory of transverse impact on a thin fiber is based on the classical works of Rakhmatulin and Smith. The simple relations obtained from the Rakhmatulin – Smith theory are widely used in engineering practice. However, there are numerous evidences that experimental results may differ significantly from estimations based on these relations. A brief overview of the factors that cause the differences is given in this article.

This paper focuses on the shear wave velocity, as it is the only feature that can be directly observed and measured using high-speed cameras or similar methods. The influence of the fiber preload on the wave speed is considered. This factor is important, since it inevitably arises in the experimental results. The reliable fastening and precise positioning of the fiber during the experiments requires its preload. This work shows that the preload significantly affects the shear wave velocity in the impacted fiber.

Numerical calculations were performed for Kevlar 29 and Spectra 1000 yarns. Shear wave velocities are obtained for different levels of initial tension. A direct comparison of numerical results and analytical estimations with experimental data is presented. The speed of the transverse wave in free and preloaded fibers differed by a factor of two for the setup parameters considered. This fact demonstrates that measurements based on high-speed imaging and analysis of the observed shear waves should take into account the preload of the fibers.

This paper proposes a formula for a quick estimation of the shear wave velocity in preloaded fibers. The formula is obtained from the basic relations of the Rakhmatulin – Smith theory under the assumption of a large initial deformation of the fiber. The formula can give significantly better results than the classical approximation, this fact is demonstrated using the data for preloaded Kevlar 29 and Spectra 1000. The paper also shows that direct numerical calculation has better corresponding with the experimental data than any of the considered analytical estimations.

A numerical simulation of fluid flow in a blood pump was performed using the FlowVision software package. This test problem, provided by the Center for Devices and Radiological Health of the US. Food and Drug Administration, involved considering fluid flow according to several design modes. At the same time for each case of calculation a certain value of liquid flow rate and rotor speed was set. Necessary data for calculations in the form of exact geometry, flow conditions and fluid characteristics were provided to all research participants, who used different software packages for modeling. Numerical simulations were performed in FlowVision for six calculation modes with the Newtonian fluid and standard $k-\varepsilon$ turbulence model, in addition, the fifth mode with the $k-\omega$ SST turbulence model and with the Caro rheological fluid model were performed. In the first stage of the numerical simulation, the convergence over the mesh was investigated, on the basis of which a final mesh with a number of cells of the order of 6 million was chosen. Due to the large number of cells, in order to accelerate the study, part of the calculations was performed on the Lomonosov-2 cluster. As a result of numerical simulation, we obtained and analyzed values of pressure difference between inlet and outlet of the pump, velocity between rotor blades and in the area of diffuser, and also, we carried out visualization of velocity distribution in certain cross-sections. For all design modes there was compared the pressure difference received numerically with the experimental data, and for the fifth calculation mode there was also compared with the experiment by speed distribution between rotor blades and in the area of diffuser. Data analysis has shown good correlation of calculation results in FlowVision with experimental results and numerical simulation in other software packages. The results obtained in FlowVision for solving the US FDA test suggest that FlowVision software package can be used for solving a wide range of hemodynamic problems.

The work focuses on mathematical modeling of light influence mechanisms on macromolecular composition of microalgae batch culture. It is shown that even with a single limiting factor, the growth of microalgae is associated with a significant change in the biochemical composition of the biomass in any part of the batch curve. The well-known qualitative models of microalgae are based on concepts of enzymatic kinetics and do not take into account the possible change of the limiting factor during batch culture growth. Such models do not allow describing the dynamics of the relative content of biochemical components of cells. We proposed an alternative approach which is based on generally accepted two-stage photoautotrophic growth of microalgae. Microalgae biomass can be considered as the sum of two macromolecular components — structural and reserve. At the first stage, during photosynthesis a reserve part of biomass is formed, from which the biosynthesis of cell structures occurs at the second stage. Model also assumes the proportionality of all biomass structural components which greatly simplifies mathematical calculations and experimental data fitting. The proposed mathematical model is represented by a system of two differential equations describing the synthesis of reserve biomass compounds at the expense of light and biosynthesis of structural components from reserve ones. The model takes into account that a part of the reserve compounds is spent on replenishing the pool of macroergs. The rates of synthesis of structural and reserve forms of biomass are given by linear splines. Such approach allows us to mathematically describe the change in the limiting factor with an increase in the biomass of the enrichment culture of microalgae. It is shown that under light limitation conditions the batch curve must be divided into several areas: unlimited growth, low cell concentration and optically dense culture. The analytical solutions of the basic system of equations describing the dynamics of macromolecular biomass content made it possible to determine species-specific coefficients for various light conditions. The model was verified on the experimental data of biomass growth and dynamics of chlorophyll $a$ content of the red marine microalgae Pоrphуridium purpurеum batch culture.

Mechanical properties of eukaryotic cells play an important role in life cycle conditions and in the development of pathological processes. In this paper we discuss the problem of parameters identification and verification of viscoelastic constitutive models based on force spectroscopy data of living cells. It is proposed to use one-dimensional continuous wavelet transform to calculate the relaxation function. Analytical calculations and the results of numerical simulation are given, which allow to obtain relaxation functions similar to each other on the basis of experimentally determined force curves and theoretical stress-strain relationships using wavelet differentiation algorithms. Test examples demonstrating correctness of software implementation of the proposed algorithms are analyzed. The cell models are considered, on the example of which the application of the proposed procedure of identification and verification of their parameters is demonstrated. Among them are a structural-mechanical model with parallel connected fractional elements, which is currently the most adequate in terms of compliance with atomic force microscopy data of a wide class of cells, and a new statistical-thermodynamic model, which is not inferior in descriptive capabilities to models with fractional derivatives, but has a clearer physical meaning. For the statistical-thermodynamic model, the procedure of its construction is described in detail, which includes the following. Introduction of a structural variable, the order parameter, to describe the orientation properties of the cell cytoskeleton. Setting and solving the statistical problem for the ensemble of actin filaments of a representative cell volume with respect to this variable. Establishment of the type of free energy depending on the order parameter, temperature and external load. It is also proposed to use an oriented-viscous-elastic body as a model of a representative element of the cell. Following the theory of linear thermodynamics, evolutionary equations describing the mechanical behavior of the representative volume of the cell are obtained, which satisfy the basic thermodynamic laws. The problem of optimizing the parameters of the statisticalthermodynamic model of the cell, which can be compared both with experimental data and with the results of simulations based on other mathematical models, is also posed and solved. The viscoelastic characteristics of cells are determined on the basis of comparison with literature data.

Muscle contraction is controlled by Ca2+ ions via regulatory proteins, troponin and tropomyosin, associated with thin actin filaments in sarcomeres. Depending on the Ca2+ concentration, the thin filament rearranges so that tropomyosin moves along its surface, opening or closing access to actin for the motor domains of myosin molecules, and causing contraction or relaxation, respectively. Numerous point amino acid substitutions in tropomyosin are known, leading to genetic pathologies — myo- and cardiomyopathies caused by changes in the structural and functional properties of the thin filament. The results of molecular dynamics modeling of a fragment of a thin filament of cardiac muscle sarcomeres formed by fibrillar actin and wildtype tropomyosin or with amino acid substitutions: the double stabilizing substitution D137L/G126R and the cardiomyopathic substitution S215L are presented. For numerical calculations, we used a new model of a thin filament fragment containing 26 actin monomers and 4 tropomyosin dimers, with a refined structure of the region of overlap of neighboring tropomyosin molecules in each of the two tropomyosin strands. The simulation results showed that tropomyosin significantly increases the bending stiffness of the thin filament, as previously found experimentally. The double stabilizing replacement D137L/G126R leads to a further increase in this rigidity, and the replacement S215L, on the contrary, leads to its decrease, which also corresponds to experimental data. At the same time, these substitutions have different effects on the angular mobility of the actin helix and only slightly modulate the angular mobility of tropomyosin cables relative to the actin helix and the population of hydrogen bonds between negatively charged tropomyosin residues and positively charged actin residues. The results of the verification of the new model demonstrate that its quality is sufficient for the numerical study of the effect of single amino acid substitutions on the structure and dynamics of thin filaments and study the effects leading to dysregulation of muscle contraction. This model can be used as a useful tool for elucidating the molecular mechanisms of some genetic diseases and assessing the pathogenicity of newly discovered genetic variants.

Photosynthetic apparatus of a plant cell consists of multiple photosynthetic electron transport chains (ETC). Each ETC is capable of capturing and utilizing light quanta, that drive electron transport along the chain. Light assimilation efficiency depends on the plant’s current physiological state. The energy of the part of quanta that cannot be utilized, dissipates into heat, or is emitted as fluorescence. Under high light conditions fluorescence levels gradually rise to the maximum level. The curve describing that rise is called fluorescence rise (FR). It has a complex shape and that shape changes depending on the photosynthetic apparatus state. This gives one the opportunity to investigate that state only using the non invasive measuring of the FR.

When measuring fluorescence in experimental conditions, we get a response from millions of photosynthetic units at a time. In order to reproduce the probabilistic nature of the processes in a photosynthetic ETC, we created a Monte Carlo model of this chain. This model describes an ETC as a sequence of electron carriers in a thylakoid membrane, connected with each other. Those carriers have certain probabilities of capturing light photons, transferring excited states, or reducing each other, depending on the current ETC state. The events that take place in each of the model photosynthetic ETCs are registered, accumulated and used to create fluorescence rise and electron carrier redox states accumulation kinetics. This paper describes the model structure, the principles of its operation and the relations between certain model parameters and the resulting kinetic curves shape. Model curves include photosystem II reaction center fluorescence rise and photosystem I reaction center redox state change kinetics under different conditions.

Many properties of ordinary differential equations systems solutions are determined by the properties of the equations in variations. An ODE system, which includes both the original nonlinear system and the equations in variations, will be called an extended system further. When studying the properties of the Cauchy problem for the systems of ordinary differential equations, the transition to extended systems allows one to study many subtle properties of solutions. For example, the transition to the extended system allows one to increase the order of approximation for numerical methods, gives the approaches to constructing a sensitivity function without using numerical differentiation procedures, allows to use methods of increased convergence order for the inverse problem solution. Authors used the Broyden method belonging to the class of quasi-Newtonian methods. The Rosenbroke method with complex coefficients was used to solve the stiff systems of the ordinary differential equations. In our case, it is equivalent to the second order approximation method for the extended system.

As an example of the proposed approach, several related mathematical models of the blood coagulation process were considered. Based on the analysis of the numerical calculations results, the conclusion was drawn that it is necessary to include a description of the factor XI positive feedback loop in the model equations system. Estimates of some reaction constants based on the numerical inverse problem solution were given.

Effect of factor V release on platelet activation was considered. The modification of the mathematical model allowed to achieve quantitative correspondence in the dynamics of the thrombin production with experimental data for an artificial system. Based on the sensitivity analysis, the hypothesis tested that there is no influence of the lipid membrane composition (the number of sites for various factors of the clotting system, except for thrombin sites) on the dynamics of the process.