Variational approach for recovering viscoelasticity from MRE data

This paper deals with an inverse problem for recovering the viscoelasticity of a living body from MRE (Magnetic Resonance Elastography) data. Based on a viscoelastic partial differential equation whose solution can approximately simulate MRE data, the inverse problem is transformed to a least square variational problem. This is to search for viscoelastic coefficients of this equation such that the solution to a boundary value problem of this equation fits approximately to MRE data with respect to the least square cost function. By computing the Gateaux derivatives of the cost function, we minimize the cost function by the projected gradient method is proposed for recovering the unknown coefficients. The reconstruction results based on simulated data and real experimental data are presented and discussed.

A method for estimating the statistical error of the solution in the inverse spectroscopy problem

A method for obtaining the interval of statistical error of the solution of the inverse spectroscopy problem, for the estimation of the statistical error of experimental data of which the normal distribution law can be applied, has been proposed. With the help of mathematical modeling of the statistical error of partial spectral components obtained from the numerically stable solution of the inverse problem, it has become possible to specify the error of the corresponding solution. The problem of getting the inverse solution error interval is actual because the existing methods of solution error evaluation are based on the analysis of smooth functional dependences under rigid restrictions on the region of acceptable solutions (compactness, monotonicity, etc.). Their use in computer processing of real experimental data is extremely difficult and therefore, as a rule, is not applied. Based on the extraction of partial spectral components and the estimation of their error, a method for obtaining an interval of statistical error for the solution of inverse spectroscopy problems has been proposed in this work. The necessity and importance of finding the solution error interval to provide reliable results is demonstrated using examples of processing Mössbauer spectra.

Network Structure of the Master Clock Is Important for Its Primary Function

A master clock located in the suprachiasmatic nucleus (SCN) regulates the circadian rhythm of physiological and behavioral activities in mammals. The SCN has two main functions in the regulation: an endogenous clock produces the endogenous rhythmic signal in body rhythms, and a calibrator synchronizes the body rhythms to the external light-dark cycle. These two functions have been determined to depend on either the dynamic behaviors of individual neurons or the whole SCN neuronal network. In this review, we first introduce possible network structures for the SCN, as revealed by time series analysis from real experimental data. It was found that the SCN network is heterogeneous and sparse, that is, the average shortest path length is very short, some nodes are hubs with large node degrees but most nodes have small node degrees, and the average node degree of the network is small. Secondly, the effects of the SCN network structure on the SCN function are reviewed based on mathematical models of the SCN network. It was found that robust rhythms with large amplitudes, a high synchronization between SCN neurons and a large entrainment ability exists mainly in small-world and scale-free type networks, but not other types. We conclude that the SCN most probably is an efficient small-world type or scale-free type network, which drives SCN function.

Comparison of Methods for Assessing the Assimilation Capacity of the Kazakhstani Sector of the Ili River

A mixed inverse problem for determining the biochemical oxygen demand of water ( L 0 ) and the rate of biochemical oxygen consumption ( k 0 ), which are important indicators of water quality, has been formulated and numerically solved based on real experimental data. The inverse problem is reduced to the optimization problem consisting in minimization of the deviation of the calculated values from the experimental data, which is solved numerically using the Nelder–Mead method (zero order) and the gradient method (first order). A number of examples of processing both model experimental data and field experimental data provided by hydrological stations monitoring pollutants in the Kazakhstani part of the Ili River basin are presented. A mathematical model that adequately describes the processes in the river system has been constructed.

Modeling the Tensile Strengths of Nickel-Based Superalloys at a Wide Range of Isothermal Exposures by Artificial Neural Networks

The nickel-based superalloys are unique high-temperature materials that are applied in gas-turbine engine manufacturing. The superalloys are compositions with complex doping. The master mechanical property of the alloys is the heat resistance, which is depicted by the values of the tensile strength after long isothermal exposures. However, for each superalloy, only certain temperature-time exposure parameters are known. The availability of information on the properties in the entire range of temperatures and holdings would significantly expand the possibilities of the superalloys applications. We have applied the artificial neural network to predict the missing tensile strength values for superalloys based on the chemical composition and the known tensile test conditions. The additional data preprocessing and the bootstrap have improved the model performance. A comparison of the modeled and the real experimental data has shown their convergence. The model verification has been carried out on the set of 10 common cast superalloys.

ADAPTIVE ALGORITHM FOR DETERMINING THE PARAMETERS OF AN INACCESSIBLE POINT OF AN OBJECT

In the present research the optimizing approach to the determination of the parameters of an inaccessible point of an object is developed. The common issues are revealed and essential steps of their resolution are identified. The essence of the problem is an objective contradiction between a requirement for the location of points A and B of the centers of the sighting tubes of optical devices in the same horizontal plane P1 and the lack of a real possibility to perform such to achieve this an identical one-level arrangement without error. The aim of the study is to develop strategies for determining the position of an inaccessible point of an object in the minimum domain between intersecting sighting rays as well as an adaptive algorithm for determining the values of the parameters of an inaccessible point under the given absolute and relative errors. To achieve this aim, the following problems are formulated and solved in the paper: 1. Develop strategies for determining the position of the inaccessible point of the object in the minimum domain between the intersecting sighting rays. 2. Develop an adaptive algorithm for determining the values of the parameters of an inaccessible point based on the specified absolute and relative errors. In the proposed optimizing approach, the three-dimensional geometrical model with crossed directional rays for the determination of coordinates of the inaccessible point of an object is developed. It is discussed that points С and C', coordinated of which to be determined, locates in domain [CDM, CEM], [C'D'M, C'E'M] of the minimum distance ρmin between crossed directional rays. The optimizing problem of the determination of coordinates of an inaccessible point of an object in space is reduced to a problem of the determination of the minimum distance between two crossed directional rays. It’s known from the theory of function of multiple variables that function ρ = f (tC'D', tC'E') reaches its extremum ρmin when its partial derivatives by each variable are equal to zero. Three strategies for selecting the position of the inaccessible point C (xC, yC, zC) in the found minimum region [CDM, CEM] are proposed. The required point C' (xC', yC', zC') can be located, for example, in the middle of the minimum segment [C'D'M, C'E'M]. The essence of the adaptive algorithm is in optimizing the variation of the initial values of data α, α', β, γ, γ', AB, at which the absolute and relative errors of the coordinates of the inaccessible point satisfy the error values set by the customer (0.0001-1.2%) The proposed approach is verified using real experimental data.

Coupling Analytical Models and Machine Learning Methods for Fast and Reliable Resolution of Effects in Multifrequency Eddy-Current Sensors

Eddy current (EC) measurements, widely used for diagnostics of conductive materials, are highly dependent on physical properties and geometry of a sample as well as on a design of an EC-sensor. For a sensor of a given design, the conductivity and thickness of a sample as well as the gap between the sample and the sensor (lift-off) are the most influencing parameters. Estimation of these parameters, based on signals acquired from the sensor, is quite complicated in case when all three parameters are unknown and may vary. In this paper, we propose a machine learning based approach for solving this problem. The approach makes it possible to avoid time and resource-consuming computations and does not require experimental data for training of the prediction models. The approach was tested using independent sets of measurements from both simulated and real experimental data.

PROGNOSTICATION OF STORAGE TERMS FOR PASTEURIZED SAUSAGES WITH ACTIVE PACKAGE ELEMENTS

The work is devoted to optimization modeling of an influence of pasteurization with oxygen absorbers on spoilage processes of lipids of boiled sausage products. According to the results, the influence on changes of peroxide and acid numbers of lipids of small sausages, pasteurized at presence of an oxygen absorber, has been mathematically prognosticated. At mathematical modeling, mathematic packages MathCad and «Data analysis» (ЕТ) MSExcel were used. The experiment was planned according to the plan of full factorial experiment. The dependence as to the influence of the recipe composition of sausage products at their storage on peroxide and acid number values has been revealed. The conducted modeling allows to state the adequacy of obtained regressive equations. The obtained empirical dependencies allow to prognosticate a storage term of boiled sausages products, pasteurized with elements of active package at using protecting barrier multi-layer polymeric materials. The optimization modeling was conducted by structuring a mathematical model as an analytic expression that reflects the connection of factor signs with a parametric index. The obtained response functions are adequate and have a high correspondence to real experimental data. Storage terms were substantiated for small sausages, which recipe included beef, pork, poultry meat and also food emulsions, based on animal proteins. The process of repeated pasteurization was conducted at temperature 85–90 °С during 15–20 minutes

Gait and Trajectory Optimization by Self-Learning for Quadrupedal Robots with an Active Back Joint

This paper presents an efficient technique for a self-learning dynamic walk for a quadrupedal robot. The cost function for such a task is typically complicated, and the number of parameters to be optimized is high. Therefore, a simple technique for optimization is of importance. We apply a genetic algorithm (GA) which uses real experimental data rather than simulations to evaluate the fitness of a tested gait. The algorithm actively optimizes 12 of the robot’s dynamic walking parameters. These include the step length and duration and the bending of an active back. For this end, a simple quadrupedal robot was designed and fabricated in a structure inspired by small animals. The fitness function was then computed based on experimental data collected from a camera located above the scene coupled with data collected from the actuators’ sensors. The experimental results demonstrate how walking abilities are improved in the course of learning, while including an active back should be considered to improve walking performances.

Quaternionic Assessment of EEG Traces on Nervous Multidimensional Hyperspheres

The nervous activity of the brain takes place in higher-dimensional functional spaces. Indeed, recent claims advocate that the brain might be equipped with a phase space displaying four spatial dimensions plus time, instead of the classical three plus time. This suggests the possibility to investigate global visualization methods for exploiting four-dimensional maps of real experimental data sets. Here we asked whether, starting from the conventional neuro-data available in three dimensions plus time, it is feasible to find an operational procedure to describe the corresponding four-dimensional trajectories. In particular, we used quaternion orthographic projections for the assessment of electroencephalographic traces (EEG) from scalp locations. This approach makes it possible to map three-dimensional EEG traces to the surface of a four-dimensional hypersphere, which has an important advantage, since quaternionic networks make it feasible to enlighten temporally far apart nervous trajectories equipped with the same features, such as the same frequency or amplitude of electric oscillations. This leads to an incisive operational assessment of symmetries, dualities and matching descriptions hidden in the very structure of complex neuro-data signals.