Coordinate Space Research Articles

Mathematical self-determination theory II: Affine space representation

Self-determination theory is a well-established theory of motivation. This theory provides for fundamental concepts related to human motivation, including self-determination. The mathematization of this theory has been envisaged in a series of two papers by the author. The first paper entitled “Mathematical self-determination theory I: Real representation” addressed the representation of the theory in reals. This second paper is in continuation of it. The representation of the first part allows to abstract the results in more general mathematical structures, namely, affine spaces. The simpler real representation is reobtained as a special instance. We take convexity as the pivotal starting point to generalize the whole exposition and represent self-determination theory in abstract affine spaces. This includes the affine space analogs of the notions of internal locus, external locus, and impersonal locus, of regulated and graded motivation, and self-determination. We also introduce polar coordinates in Euclidean affine motivation spaces to study self-determination on radial and angular line segments. We prove the distributivity of the lattice of general self-determination in the affine space formulation. The representation in an affine space is free in the choice of primitives. However, the different representations, in reals or affine, are shown to be unique up to canonical isomorphism. The aim of this paper is to extend on the results obtained in the first paper, thereby to further lay the mathematical foundations of self-determination motivation theory.

Stereo vision based robot welding

The most important advantages of robotic welding are precision and productivity. Introducing visual systems in welding allows one to easily position the elements that are welded. The robot will then perform welding without error after recording the welding points. The application of visual systems in robotics is very important because it enables the autonomous work of the robot. Stereo vision is used for three-dimensional reconstruction of the robot’s environment based on images captured by cameras. The stereo system consists of two cameras and a computer that processes the recorded images using appropriate programs and algorithms. The accuracy of estimating coordinates in space using a visual system is very important, it is necessary to estimate the parameters of the cameras and define their dependence. The relationship between the two cameras, as well as their basic parameters, are assessed by camera calibration. After calibrating the camera for each 2D coordinate, obtained from the camera sensor, it is possible to determine which set of points it belongs to in the 3D coordinate system. One of the most important and most difficult problems in the reconstruction of a 3D object is finding points on the planes of images that were created from the same physical point. The problem of correspondent points is also considered in this paper. To present the efficiency and reliability of the proposed solution for obtaining 3D coordinates of points in space, the proposed solution was tested in the laboratory and satisfactory results are obtained.

TONTOR ZONES MODEL FOR AUTOMATIVE OBJECT MONITORING

The paper presents the results of analytical modeling of the case of the presence zone of an abstract object characterized by a solid mass. It has several zones of presence based on the foundations of the TONTOR theory. Research determined that the discrete solid-state zone of the presence characterizes the solid part of the AE itself or the particles that form the surrounding space near the abstract entity and is the most powerful zone among the existing zones. The proposed model for determining the parameters of TONTOR zones of an object provides the possibility of analyzing the state of this object during its movements in the working space and metrological measurements of coordinates. These metrological aspects in the automatic mode of operation of object state analysis system determine the properties that increase the accuracy and speed of operations for calculating object movement trajectories in various fields of research.

Statistical processing of a small sample of raw data using artificial orthogonalisation technology

This paper addresses the task to devise a statistical estimation procedure in an event where the volume of the array of initial data used in processing is insufficient to correctly determine the parameters of the response function. The object of research is the technology of statistical processing of a small sample of data. The subject of the study is the methods of statistical estimation under conditions of a small sample of initial data. The main direction is to devise a special procedure for statistical processing of a small sample of initial data, which provides a correct statistical estimation of the parameters of the response function. The method for solving the problem is the selection of the most representative orthogonal replica-like subplan from the plan of a complete factorial experiment obtained by artificially orthogonalizing the results of a passive experiment. The necessity and expediency of the proposed procedure is a consequence of the unpredictability and uneven distribution of points in the phase space of coordinates. The result of the implementation of the corresponding procedure is a truncated orthogonal plan of the full factorial experiment, which provides the possibility of independent estimation of all coefficients of the regression polynomial describing the response function. Under conditions of a severe shortage of the number of measurements, the procedure makes it possible to isolate a representative orthogonal replica from the resulting plan of a complete factorial experiment. Using this subplan of the full factorial experiment plan makes it possible to evaluate all the coefficients of the regression polynomial that describes the desired response function. The corresponding computational procedure is based on solving the triaxial Boolean assignment problem

Distributed Coordination of Space–Ground Multiresources for Remote Sensing Missions

As data relay satellites (DRSs) play an increasingly important supporting role in remote sensing missions, efficient coordination across space–ground multiresources becomes a significant problem. Owing to the implementation problem of the centralized coordinate methods, this paper studies a distributed coordinate resource scheduling method which is realizable in the current space network structure. To be specific, we first formulate the multiple resource coordination problem into an MILP problem based on a modified time-expanded graph. Then, the problem is transferred and decomposed into subproblems for remote sensing satellite (RSS) systems and DRS systems to solve distributedly. Afterwards, we propose a distributed iterative scheme for the RSS systems and DRS systems based on alternating direction method of multipliers (ADMM), in which only the schedule information of the inter-satellite links are required to exchange between RSS systems and DRS systems. Simulation results are provided to validate the effectiveness of our distributed coordinated resource scheduling algorithm.

ELLIPSOIDAL TONTOR STEP MODEL OF SENSORS FOR AUTOMATED MECHATRONIC SYSTEMS

Modern medicine widely uses mechatronic modules in systems of various purposes, such as automated systems of diagnostics, scanning, irradiation. Recently, mechatronic modules in robotic surgical complexes are gaining importance. Thus, with the use of integrated sensors in mechatronic modules, executive manipulators of automated systems, positioning accuracy in defined spatial coordinates can be maintained. This data helps the medical staff to diagnose, monitor the patient's condition and make treatment decisions. The main purpose of sensor support in mechatronic systems is to ensure the accuracy and reliability of the system's functioning. Sensors must be sensitive and stable enough to provide measurements with high accuracy and respond to changes in real time. In addition, similar mechatronic modules are combined with sensors to create bionic limb prostheses, to restore human movement functions in various orthopedic diseases.
 At the same time, the trajectory of the movement of the executive bodies of the mechatronic medical system, regardless of its purpose, during spatial transformations of searching for the coordinates of a real object, must be determined taking into account possible deformations.
 Therefore, the accuracy of real-world displacement in space is determined by sensors that measure the parameters of physical objects. Thus, real transformations can be defined by spatial deviations that can be described using an ellipsoidal model. Accuracy, like the strength of the mechatronic module of a robot arm, is a variable value. They depend not only on the number of joints and the mobility of the hinges, but also on the position of the manipulators in space. At one point of coordinates, the module can apply more force than at another. The same is true for positioning accuracy, where the positioning error is greater at some points than at others. Therefore, an important actual problem in the creation of medical robotic systems is to determine the step-by-step movement of such a module in the workspace.
 Therefore, the purpose of this work is to determine the ellipsoidal TONTOR step model of sensors for automated mechatronic systems, as the motion of the executive manipulators and sensors of the system during transformations from imaginary coordinate space to real space determines trajectory errors. Based on the existing opportunities analyzed in the work application of mechatronic modules in automated medical systems, relevant tasks related to maintaining the positioning accuracy of diagnostic manipulators and sensors are defined. The importance of sensory complexes in measuring various biological parameters that determine the patient's condition is noted. And this involves the application of models of spatial movement of the sensor in the working space of automated equipment, in particular, a robotic mechatronic complex.
 In the work, it is proposed to use the TONTOR step model to increase the accuracy of the realization of the movement trajectory of the sensors of the mechatronic automated system. The results of creating an ellipsoidal model of the TONTOR step, which most accurately reflects the features of moving an object in space during transformations of the transition to real space, are given.

The enhanced search procedure in a coordinate domain for precise satellite positioning

Recently, there has been an increase in the availability of GNSS satellites for observation, which poses new challenges in the computational process of precise satellite positioning. Ambiguity resolution is a crucial step in achieving accurate relative positioning. In this regard, an improved version of a searching procedure in a three-dimensional coordinate domain has been proposed and tested. The method starts with a float solution, similar to classic methods like the LAMBDA. However, the subsequent step, the search procedure, is conducted in the coordinate space instead of the ambiguity space. This shift to a three-dimensional coordinate space leads to reduced computation time. A computational experiment was performed to validate the proposed method, which demonstrated a significant reduction in processing time. The advantages of this method are particularly prominent when dealing with a large number of satellites.

Analytical and Numerical Results for the Diffusion-Reaction Equation When the Reaction Coefficient Depends on Simultaneously the Space and Time Coordinates

We utilize the travelling-wave Ansatz to obtain novel analytical solutions to the linear diffusion–reaction equation. The reaction term is a function of time and space simultaneously, firstly in a Lorentzian form and secondly in a cosine travelling-wave form. The new solutions contain the Heun functions in the first case and the Mathieu functions for the second case, and therefore are highly nontrivial. We use these solutions to test some non-conventional explicit and stable numerical methods against the standard explicit and implicit methods, where in the latter case the algebraic equation system is solved by the preconditioned conjugate gradient and the GMRES solvers. After this verification, we also calculate the transient temperature of a 2D surface subjected to the cooling effect of the wind, which is a function of space and time again. We obtain that the explicit stable methods can reach the accuracy of the implicit solvers in orders of magnitude shorter time.

Integral transforms and [formula omitted]-symmetric Hamiltonians

Motivated by the fact that twice the Fourier transform plays the role of a parity operator. We systematically study the integral transforms of PT-symmetric Hamiltonians. First, we obtain a closed analytical formula for the exponential Fourier transform of a general PT-symmetric Hamiltonian. Using the Segal–Bargmann transform, we investigate the effect of the Fourier transforms on the eigenfunctions of the original Hamiltonian. As an immediate application, we comment on the holomorphic representation of non-Hermitian spin chains. In this case, the Hamiltonian is written in terms of analytical phase space coordinates and their partial derivatives in the Bargmann space instead of matrices in the vector Hilbert space. Finally, we discuss the effect of integral transforms in the study of the Swanson Hamiltonian.

An analytical technique to obtain traveling wave solutions to nonlinear models of fractional order

The (3, 3, 3) time-fractional Zakharov–Kuznetsov (TFZK) equation demonstrates the characteristic of traffic flows, the viscoelasticity waves, the material science, sound waves, signal processing, the financial mathematics, optical fibers, the electromagnetic field, water wave mechanics, ion acoustic waves in plasmas, the chemical physics and so many. The (3, 3, 3) TFZK equation is the specific event of the general (a,b,c) TFZK equation, where a,b denote the space coordinates and c denotes the temporal coordinate. The object of this investigation is to consider determining the (3, 3, 3) TFZK equation by the modified (G′/G)-expansion scheme (MGD/GES). The derivatives are in the beta-derivative sense. The fractional transformation equation is utilized to convert the proposed nonlinear models of fractional order (NLMFO) into non-linear models of integer order. Additionally, numerous new wave solutions (WSs) are formed. The attractive and easy technique of the MGD/GES recommends that this technique can be applied to WSs of other NLMFOs straightforwardly.

Non-contact type dynamic responses test of wind turbines

The performance analysis of wind turbine systems should be considered when calculating the wind speed relative to the wind turbine structure, and is essential for wind turbine design. Since the conditions are precarious in transient state and the operating environments are challenging, the wind turbine is a complex, multivariate, nonlinear system. This paper presents a novel dynamic response test method for wind turbines based on three-dimensional digital speckle measurement. This method use a real-time speckle image collection of objects in various stages using binocular stereo vision to perform stereo matching of deformation points on object surface. A digital image correlation algorithm is used to rebuild three-dimensional space coordinates of matching points so as to achieve wind turbine dynamic response. A laboratory-scale experimental platform is constructed to test the dynamic response of the wind turbine system. In order to verify the accuracy of the proposed method, a three-dimensional model of a wind turbine is built. With dynamic structure response process adopted to carry out dynamic analysis and compare theoretical results with test results, the results vary by less than 10 %, indicating that the test method presented in the paper is feasible and effective.

SITE CALIBRATION WITH PROJ AND WKT2

Abstract. In surveying projects, a site calibration is the solution to the problem of finding a transformation between the coordinate space of a site local coordinate reference system and a well known coordinate reference system given a set of pairs of corresponding coordinates. A site calibration enables the localization of new positions with cm accuracy using a RTK/PPK GNSS receiver and a transformation, which is a much more cost-effective than using a total station and much faster than other more traditional surveying methods. While site calibration is featured by almost every modern professional-grade GNSS receiver, the implementation is closed source and the output stored in proprietary file formats, tying the user to the vendor’s ecosystem. In this paper we propose a complete solution to the site calibration problem that can be fully implemented with open source software (in particular PROJ for coordinate transformations) and whose output can be represented in terms of an open standard (WKT version 2). Two methods and representations of a site calibration are described, a fully 3D one and a split horizontal and vertical one. Our main contribution is the openness and interoperability of the solution. Another important contribution is the analysis of the sensitivity of these solutions to measurement errors.

Моделирование объектов трубопроводного транспорта по данным дистанционного зондирования

The author considers the results of geospatial modeling of a production facility based on data from various types of surveys obtained during monitoring. The essence is to combine it in a single coordinate space for subsequent modeling with remote methods. The technological solutions are described; they enable performing geospatial modeling of pipeline transport objects on the basis of a single coordinate space due to the data from various types of remote studies. The site of the oil refinery, where reconstruction must have been carried out, was chosen as the object of the research. The remote sensing data were obtained through ground-based laser scanning and digital aerial photography using a drone. A scheme for remote sensing, information preprocessing and geospatial modeling of pipeline transportation facilities is provided. As a methodological basis for geospatial modeling, constructive methods are used, assuming the finiteness of the elements and the use of its basic components as an information unit.

Connectopic mapping techniques do not reflect functional gradients in the brain

Functional gradients, in which response properties change gradually across a brain region, have been proposed as a key organising principle of the brain. Recent studies using both resting-state and natural viewing paradigms have indicated that these gradients may be reconstructed from functional connectivity patterns via “connectopic mapping” analyses. However, local connectivity patterns may be confounded by spatial autocorrelations artificially introduced during data analysis, for instance by spatial smoothing or interpolation between coordinate spaces. Here, we investigate whether such confounds can produce illusory connectopic gradients. We generated datasets comprising random white noise in subjects’ functional volume spaces, then optionally applied spatial smoothing and/or interpolated the data to a different volume or surface space. Both smoothing and interpolation induced spatial autocorrelations sufficient for connectopic mapping to produce both volume- and surface-based local gradients in numerous brain regions. Furthermore, these gradients appeared highly similar to those obtained from real natural viewing data, although gradients generated from real and random data were statistically different in certain scenarios. We also reconstructed global gradients across the whole-brain – while these appeared less susceptible to artificial spatial autocorrelations, the ability to reproduce previously reported gradients was closely linked to specific features of the analysis pipeline. These results indicate that previously reported gradients identified by connectopic mapping techniques may be confounded by artificial spatial autocorrelations introduced during the analysis, and in some cases may reproduce poorly across different analysis pipelines. These findings imply that connectopic gradients need to be interpreted with caution.

HumanBrainAtlas: an in vivo MRI dataset for detailed segmentations

We introduce HumanBrainAtlas, an initiative to construct a highly detailed, open-access atlas of the living human brain that combines high-resolution in vivo MR imaging and detailed segmentations previously possible only in histological preparations. Here, we present and evaluate the first step of this initiative: a comprehensive dataset of two healthy male volunteers reconstructed to a 0.25 mm isotropic resolution for T1w, T2w, and DWI contrasts. Multiple high-resolution acquisitions were collected for each contrast and each participant, followed by averaging using symmetric group-wise normalisation (Advanced Normalisation Tools). The resulting image quality permits structural parcellations rivalling histology-based atlases, while maintaining the advantages of in vivo MRI. For example, components of the thalamus, hypothalamus, and hippocampus are often impossible to identify using standard MRI protocols—can be identified within the present data. Our data are virtually distortion free, fully 3D, and compatible with the existing in vivo Neuroimaging analysis tools. The dataset is suitable for teaching and is publicly available via our website (hba.neura.edu.au), which also provides data processing scripts. Instead of focusing on coordinates in an averaged brain space, our approach focuses on providing an example segmentation at great detail in the high-quality individual brain. This serves as an illustration on what features contrasts and relations can be used to interpret MRI datasets, in research, clinical, and education settings.

Teahouse or Not? Meng Jinghui’s Avant-garde Version of Lao She’s Classic Play

Lao She’s Teahouse is considered a masterpiece of Chinese theatre, a classic crystallized in the Beijing People’s Art Theatre’s production by Jiao Juyin from 1958, which has been regularly staged up to the present day. In 2018 a production by the well-known “pop avant-garde” director Meng Jinghui premiered at the Wuzhen Theatre Festival, giving rise to a heated debate about the concept of “classics.” This so-called “Teahouse incident” was one of the hot topics of the Chinese theatre scene in 2019, and this article explores the production’s polarized reception and debate. Meng Jinghui’s Teahouse is not examined as a one-way influence between Lao She’s source text and the new text/performance but from the perspective of a network relationship that sets the performance in a web that includes several other texts (plays, novellas, poems, etc.) by Chinese and foreign writers. This perspective shows how Meng Jinghui’s hybridization and his selection of intertexts and stage reminders aim to erase time and space coordinates in order to amplify the main themes of the play and, ultimately, reflect on the human condition. Based on this analysis, the polarized reception of the play and the reactions of the general public, critics, and academics are investigated, illuminating the reasons behind the controversy.

Machine Learning-Based Design of Ionic Liquids at the Atomic Scale for Highly Efficient CO2 Capture

Ionic liquids (ILs) are considered excellent substitutes for aqueous alkanolamine solutions in CO2 capture systems. However, the smart design of ILs, facing the small sparse data set and complex ionic structures, poses a huge challenge. To address this issue, a novel machine learning method based on a syntax-directed variational autoencoder (SDVAE), deep factorization machine (DeepFM), and gradient-based particle swarm optimization (GBPSO) was proposed in this work. The SDVAE converts the molecular structure and chemical space of the ILs, and then DeepFM predicts the solubility of each coordinate in the chemical space representing an IL. Finally, GBPSO identifies the coordinates that represent ILs with ideal properties. Our main optimization objective is a high solubility difference for CO2 between its absorption and desorption conditions in commercial plant capture systems, which represents the CO2 capture ability. The best IL generated has a predicted solubility difference that is 35.3% higher than that of the best one in the data set. A synthetic novel IL [EMIM][TOS] from the generated results was experimentally evaluated; it has a sufficiently high solubility difference to be a capture solvent with low energy consumption. Our model has proved to be a high-efficiency molecular design model that can be used for sparse small data sets.

Age-standardization and Standard Population

Objectives: The objective of this study is to provide examples of situations in which the relative ranking of age-standardized rates depends on the choice of standard population and to emphasize the importance of selecting an appropriate standard population.Methods: Mathematical methods are used for elaborate variance in the ranking of the age-standardized rates. Examples from the international comparisons of suicide rates and regional comparisons of cancer incidence in Korea were used.Results: The worldwide ranking of suicide rates for the Republic of Korea varies depending on the choice of the standard population (OECD standard vs. WHO standard). Similarly, the rank of South Korean cancer incidence rates by region also varied depending on the selected standard population (2000 mid-year population vs. 2020 mid-year population). This phenomenon has been demonstrated using coordinate space and vectors.Conclusions: An appropriate standard population should be selected according to the research purpose since there is no established recommendation. As conclusions may vary depending on the selection of the standard population, it is important to pay attention to the interpretation of the results.

Natural Variability of the Color of Beech Wood in the Color Space CIE L*a*b*

In this contribution, the color of dry beech wood from the zone, sapwood, mature wood and false heartwood of Fagus sylvatica L. trees was analyzed, and the measurement values were statistically processed in relation to the lightness coordinate L* as well as the chromatic coordinates of red color a* and yellow color b* in the color space CIE L*a*b*. The dispersion of color (color dispersion) ∆EuC of beech wood in coreless zones and the color of the wood of false heartwood were evaluated through the combined standard uncertainties of the individual coordinates of the color space. The visual color differences between the color of sapwood beech wood and the color of mature wood as well as between the color of sapwood and false heartwood are numerically documented through the values of total color differences ∆E* = 3.5 and ∆E* = 18.1. Within the framework of the categorization, the color difference between mature wood and sapwood belongs to the category of visible changes, and the difference between the color of the wood of the false heartwood and the color of the sapwood belongs to the category of significant color changes. By defining the boundaries of the color of beech wood for the color of sapwood, mature wood and false heartwood in the color space CIE L*a*b*, space is created to sort it into color groups in case of customer requests. At the same time, designers are expanding the possibilities of applying beech wood to color compositions, depending on the darkness and color of the beech wood identified by the values of the color space coordinates.

Nonlocal Kondo effect and two-fluid picture revealed in an exactly solvable model.

Understanding the nature of local-itinerant transition of strongly correlated electrons is one of the central problems in condensed matter physics. Heavy fermion systems describe the f-electron delocalization through Kondo interactions with conduction electrons. Tremendous efforts have been devoted to the so-called Kondo-destruction scenario, which predicts a dramatic local-to-itinerant quantum phase transition of f-electrons at zero temperature. On the other hand, two-fluid behaviors have been observed in many materials, suggesting coexistence of local and itinerant f-electrons over a broad temperature range but lacking a microscopic theoretical description. To elucidate this fundamental issue, here we propose an exactly solvable Kondo-Heisenberg model in which the spins are defined in the momentum space and the -space Kondo interaction corresponds to a highly nonlocal spin scattering in the coordinate space. Its solution reveals a continuous evolution of the Fermi surfaces with Kondo interaction and two-fluid behaviors similar to those observed in real materials. The electron density violates the usual Luttinger's theorem, but follows a generalized one allowing for partially enlarged Fermi surfaces due to partial Kondo screening in the momentum space. Our results highlight the consequence of nonlocal Kondo interaction relevant for strong quantum fluctuation regions and provide important insight into the microscopic description of two-fluid phenomenology in heavy fermion systems.