Space Research Articles

Collision Avoidance of UAV Formation Using Geometric Approach and Relative Velocity Vector in Three-dimensional Space

Collision Avoidance of UAV Formation Using Geometric Approach and Relative Velocity Vector in Three-dimensional Space

Asymptotic estimates of solution to damped fractional wave equation

It is known that the damped fractional wave equation has the diffusive structure as t→∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$t\\rightarrow \\infty $\\end{document}. Let u(t,x)=e−tcosh(tL)f(x)+e−tsinh(tL)L(f(x)+g(x))\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$u(t,x)=e^{-t}\\cosh (t\\sqrt{L})f(x)+e^{-t} \\frac{\\sinh (t\\sqrt{L})}{\\sqrt{L}}(f(x)+g(x))$\\end{document} be the solution of the Cauchy problem for the damped fractional wave equation, where L\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\sqrt{L}$\\end{document} involves the fractional Laplacian (−△)α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$(-\ riangle )^{\\alpha}$\\end{document} on the space variable. We can study the decay estimate of the solution u(t,x)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$u(t,x)$\\end{document} over the time t by means of the Cauchy problem for the parabolic equation. In this paper, we consider, for 0<α<1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$0<\\alpha <1$\\end{document}, the Cauchy problem in the two- and three-dimensional spaces for the damped fractional wave equation and the corresponding parabolic equation and obtain the Triebel–Lizorkin space estimate of the difference of solutions. At the same time, we also consider, for α=1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\alpha =1$\\end{document}, the case of the Cauchy problem in the four-dimensional space and obtain a Triebel–Lizorkin space estimate.

Spatial Localization of Transformer Inspection Robot Based on Adaptive Denoising and SCOT-β Generalized Cross-Correlation

In the detection process of the internal defects of large oil-immersed transformers, due to the huge size of large transformers and metal-enclosed structures, the positional localization of miniature inspection robots inside the transformer faces great difficulties. To address this problem, this paper proposes a three-dimensional positional localization method based on adaptive denoising and the SCOT weighting function with the addition of the exponent β (SCOT-β) generalized cross-correlation for L-type ultrasonic arrays of transformer internal inspection robots. Aiming at the strong noise interference in the field, the original signal is decomposed by an improved Empirical Mode Decomposition (EMD) method, and the optimal center frequency and bandwidth of each mode are adaptively searched. By extracting the modes in the frequency band of the positional localization signal, suppressing the modes in the noise frequency band, and reconstructing the Intrinsic Mode Function (IMF) of the independently selected superior modal components, a signal with a high signal-to-noise ratio is obtained. In addition, for the traditional mutual correlation algorithm with a large delay estimation error at a low signal-to-noise ratio, this paper adopts an improved generalized joint weighting function, SCOT-β, which improves the anti-jamming ability of the generalized mutual correlation method at a low signal-to-noise ratio by adding an exponential function to the denominator term of the SCOT weighting function’s generalized cross-correlation. Finally, the accurate positional localization of the transformer internal inspection robot is realized based on the quadratic L-array and search-based maximum likelihood estimation method. Simulation and experimental results show the following: the improved EMD denoising method better improves the signal-to-noise ratio of the positional localization signal with a lower distortion rate; in the transformer test tank, which is 120 cm in length, 100 cm in width, and 100 cm in height, based on the positional localization method in this paper, the average relative positional localization error of the transformer internal inspection robot in three-dimensional space is 2.27%, and the maximum positional localization error is less than 2 cm, which meets the requirements of engineering positional localization.

Spectroscopic Phenological Characterization of Mangrove Communities

Spaceborne spectroscopic imaging offers the potential to improve our understanding of biodiversity and ecosystem services, particularly for challenging and rich environments like mangroves. Understanding the signals present in large volumes of high-dimensional spectroscopic observations of vegetation communities requires the characterization of seasonal phenology and response to environmental conditions. This analysis leverages both spectroscopic and phenological information to characterize vegetation communities in the Sundarban riverine mangrove forest of the Ganges–Brahmaputra delta. Parallel analyses of surface reflectance spectra from NASA’s EMIT imaging spectrometer and MODIS vegetation abundance time series (2000–2022) reveal the spectroscopic and phenological diversity of the Sundarban mangrove communities. A comparison of spectral and temporal feature spaces rendered with low-order principal components and 3D embeddings from Uniform Manifold Approximation and Projection (UMAP) reveals similar structures with multiple spectral and temporal endmembers and multiple internal amplitude continua for both EMIT reflectance and MODIS Enhanced Vegetation Index (EVI) phenology. The spectral and temporal feature spaces of the Sundarban represent independent observations sharing a common structure that is driven by the physical processes controlling tree canopy spectral properties and their temporal evolution. Spectral and phenological endmembers reside at the peripheries of the mangrove forest with multiple outward gradients in amplitude of reflectance and phenology within the forest. Longitudinal gradients of both phenology and reflectance amplitude coincide with LiDAR-derived gradients in tree canopy height and sub-canopy ground elevation, suggesting the influence of surface hydrology and sediment deposition. RGB composite maps of both linear (PC) and nonlinear (UMAP) 3D feature spaces reveal a strong contrast between the phenological and spectroscopic diversity of the eastern Sundarban and the less diverse western Sundarban.

Simulation of tomato and corn growth using a modified intercropping model considering radiation interception in two-dimensional space and air temperature stress

Intercropping system has been widely applied in the agricultural production worldwide. However, the difference in agricultural productivity in tomato–corn intercropping system with different spatial arrangements has not been determined. Meanwhile, the existing intercropping models cannot precisely capture inter-species crop growth dynamics. Therefore, a 10-year (2010–2019) experimental field study was conducted in Hetao irrigation district, China, for the parameterization and evaluation of the model. The experiment data from the typical years (2018 and 2019) was adopted to analyze the crop growth dynamics in different hydrological years and different systems [two rows of tomato intercropping two rows of corn (IC2–2), four rows of tomato intercropping two rows of corn (IC4–2), sole corn (SC), and sole tomato (ST)]. Moreover, a modified intercropping model considering radiation interception in two-dimensional space and air temperature stress (MICG) was deduced. The results revealed that the MICG model can precisely simulate inter-species crop growth in tomato–corn intercropping system with different spatial arrangements. The mean relative error (MRE), normalized root mean square error (nRMSE), determination coefficient (R2), and percentage bias (PBIAS) of leaf area index (LAI) simulated by the MICG model in different spatial arrangements were 9.0 %, 7.8 %, 0.97, and –5.3 % for corn and 11.0 %, 7.8 %, 0.95, and 0.1 % for tomato, respectively. An apparent difference in the simulation accuracy was observed among different intercropping models in the rapid and senescence crop growth stages. The simulation accuracy of the MICG model was apparently higher than that of ICGw and ICG models. However, the MICG model still needs to be further improved considering its some limitations, e.g., the soil respiration and soil nitrogen transformation modules need be introduced in this model. Additionally, an apparent difference in crop growth dynamics in different spatial arrangements was observed, particularly in different hydrological years. The largest difference in crop growth dynamics in different spatial arrangements was observed in the middle crop growth stage (days after sowing [DAS] 20–100) in the wet year and in the late crop growth stage (DAS 101–140) in the dry year. In general, the highest aboveground biomass and yields of corn and tomato were observed in the IC2–2 and ST systems, respectively. However, the highest water use efficiency for corn (23.9) and tomato (268.7) was observed in the IC4–2 and ST systems, respectively. The agricultural production benefits in the IC4–2 system were better than in the IC2–2 system. Average land equivalent ratio and water equivalent ratio in both years increased by 0.8 % and 12.5 % in the IC4–2 system compared with those in the IC2–2 system, respectively. Overall, the IC4–2 system could be recommended as the most optimal spatial arrangement for the tomato–corn intercropping system.

Hilbert-curve assisted structure embedding method

MotivationChemical space embedding methods are widely utilized in various research settings for dimensional reduction, clustering and effective visualization. The maps generated by the embedding process can provide valuable insight to medicinal chemists in terms of the relationships between structural, physicochemical and biological properties of compounds. However, these maps are known to be difficult to interpret, and the ‘‘landscape’’ on the map is prone to ‘‘rearrangement’’ when embedding different sets of compounds.ResultsIn this study we present the Hilbert-Curve Assisted Space Embedding (HCASE) method which was designed to create maps by organizing structures according to a logic familiar to medicinal chemists. First, a chemical space is created with the help of a set of ‘‘reference scaffolds’’. These scaffolds are sorted according to the medicinal chemistry inspired Scaffold-Key algorithm found in prior art. Next, the ordered scaffolds are mapped to a line which is folded into a higher dimensional (here: 2D) space. The intricately folded line is referred to as a pseudo-Hilbert-Curve. The embedding of a compound happens by locating its most similar reference scaffold in the pseudo-Hilbert-Curve and assuming the respective position. Through a series of experiments, we demonstrate the properties of the maps generated by the HCASE method. Subjects of embeddings were compounds of the DrugBank and CANVASS libraries, and the chemical spaces were defined by scaffolds extracted from the ChEMBL database.Scientific contributionThe novelty of HCASE method lies in generating robust and intuitive chemical space embeddings that are reflective of a medicinal chemist’s reasoning, and the precedential use of space filling (Hilbert) curve in the process.Availabilityhttps://github.com/ncats/hcaseGraphical

Revisiting 3D visual grounding with Context-aware Feature Aggregation

3D visual grounding is the task of accurately locating objects in a three-dimensional scene based on textual descriptions. Current approaches mainly depend on downsampling and extracting the point features for fusion with text features. However, the main challenges of these methods are the poor point feature resolution and limited local context during multi-modal fusion, causing visual-linguistic misalignment, particularly for small objects described in the text. The intuitive solution is to get additional object-related point features, gathering more contextual information to augment the representation capability of multimodal features, thereby promoting the representation capabilities of multimodal features. Based on this, we introduce a novel 3D visual grounding framework named Context-aware Feature Aggregation (CFA). The CFA framework includes two key modules: (1) Point Augmented Aggregation Module (PAM), designed to compensate for downsampling-induced information loss by augmenting sampled points with neighboring context for more discriminative features; and (2) Dual Contextual Grouping Attention Module (DCGAM), which iteratively refines features and geometry coordinates from PAM, capturing more global context. We assess the performance of our CFA framework on two point-based datasets: ScanRefer and Nr3D/Sr3D. The CFA framework exhibits efficiency in 3D visual grounding, surpassing the performance of previous methods by experimental results.

An automated sleep staging tool based on simple statistical features of mice electroencephalography (EEG) and electromyography (EMG) data.

Electroencephalogram (EEG) and electromyogram (EMG) are fundamental tools in sleep research. However, investigations into the statistical properties of rodent EEG/EMG signals in the sleep-wake cycle have been limited. The lack of standard criteria in defining sleep stages forces researchers to rely on human expertise to inspect EEG/EMG. The recent increasing demand for analysing large-scale and long-term data has been overwhelming the capabilities of human experts. In this study, we explored the statistical features of EEG signals in the sleep-wake cycle. We found that the normalized EEG power density profile changes its lower and higher frequency powers to a comparable degree in the opposite direction, pivoting around 20-30 Hz between the NREM sleep and the active brain state. We also found that REM sleep has a normalized EEG power density profile that overlaps with wakefulness and a characteristic reduction in the EMG signal. Based on these observations, we proposed three simple statistical features that could span a 3D space. Each sleep-wake stage formed a separate cluster close to a normal distribution in the 3D space. Notably, the suggested features are a natural extension of the conventional definition, making it useful for experts to intuitively interpret the EEG/EMG signal alterations caused by genetic mutations or experimental treatments. In addition, we developed an unsupervised automatic staging algorithm based on these features. The developed algorithm is a valuable tool for expediting the quantitative evaluation of EEG/EMG signals so that researchers can utilize the recent high-throughput genetic or pharmacological methods for sleep research.

Updated Lagrangian particle hydrodynamics (ULPH) simulations of underwater bubble motions in three-dimensional space

Updated Lagrangian particle hydrodynamics (ULPH) simulations of underwater bubble motions in three-dimensional space

Guide RNA structure design enables combinatorial CRISPRa programs for biosynthetic profiling

Engineering metabolism to efficiently produce chemicals from multi-step pathways requires optimizing multi-gene expression programs to achieve enzyme balance. CRISPR-Cas transcriptional control systems are emerging as important tools for programming multi-gene expression, but poor predictability of guide RNA folding can disrupt expression control. Here, we correlate efficacy of modified guide RNAs (scRNAs) for CRISPR activation (CRISPRa) in E. coli with a computational kinetic parameter describing scRNA folding rate into the active structure (rS = 0.8). This parameter also enables forward design of scRNAs, allowing us to design a system of three synthetic CRISPRa promoters that can orthogonally activate (>35-fold) expression of chosen outputs. Through combinatorial activation tuning, we profile a three-dimensional design space expressing two different biosynthetic pathways, demonstrating variable production of pteridine and human milk oligosaccharide products. This RNA design approach aids combinatorial optimization of metabolic pathways and may accelerate routine design of effective multi-gene regulation programs in bacterial hosts.

Clarification of the transverse orbital angular momentum of spatiotemporal optical vortices

Advances in the generation and the application of spatiotemporal optical vortices (STOV) are proceeding fast, but fundamental aspects of their nature remain obscure. Bliokh (2023 Phys. Rev. A 107 L031501) (PRA) and Porras (2023 Prog. Electromagn. Res. 177 95) (PIER) provide contradictory results on the transverse orbital angular momentum (OAM) carried by STOVs. We show that the results by Porras in PIER and by Bliokh in PRA refer to different STOVs and are all correct. In PIER, STOVs are elliptical at given cross section and time, or in space-time, but not in three-dimensional space. In PRA, STOVs are elliptical in space but not in space-time. This is evidenced from two dual, equivalent theories on the transverse OAM where a wave packet is seen in space-time evolving with propagation distance or in space evolving in time, that account for all values of the total, intrinsic and extrinsic OAM in PIERS and PRA. However, the intrinsic OAM with respect to the photon wave function center in PRA is not generally conserved, which advocates for the energy center in PIER as the STOV center. We argue that STOVs are generated in experiments to purportedly have elliptical symmetry in space-time. The values provided in PIER should then be taken as the reference for elliptical STOVs, and the theory therein to evaluate the transverse OAM of other wave packets. Hancock et al (2021 Phys. Rev. Lett. 127 193901; 2024 Phys. Rev. X 14 011031) erroneously attribute the transverse OAM of elliptical STOVs in space to the elliptical STOVs in space-time that they consider theoretically and can generate in their experiments.

Three-dimensional line-of-sight-angle-constrained leader-following cooperative interception guidance law with prespecified impact time

To address the problem of multi-missile cooperative interception against maneuvering targets at a prespecified impact time and desired Line-of-Sight (LOS) angles in Three-Dimensional (3D) space, this paper proposes a 3D leader-following cooperative interception guidance law. First, in the LOS direction of the leader, an impact time-controlled guidance law is derived based on the fixed-time stability theory, which enables the leader to complete the interception task at a prespecified impact time. Next, in the LOS direction of the followers, by introducing a time consensus tracking error function, a fixed-time consensus tracking guidance law is investigated to guarantee the consensus tracking convergence of the time-to-go. Then, in the direction normal to the LOS, by combining the designed global integral sliding mode surface and the second-order Sliding Mode Control (SMC) theory, an innovative 3D LOS-angle-constrained interception guidance law is developed, which eliminates the reaching phase in the traditional sliding mode guidance laws and effectively saves energy consumption. Moreover, it effectively suppresses the chattering phenomenon while avoiding the singularity issue, and compensates for unknown interference caused by target maneuvering online, making it convenient for practical engineering applications. Finally, theoretical proof analysis and multiple sets of numerical simulation results verify the effectiveness, superiority, and robustness of the investigated guidance law.

Uncertain random variables and laws of large numbers under U-C chance space

Uncertainty theory was founded by Baoding Liu for modeling belief degrees about human uncertainty. And chance theory was pioneered by Yuhan Liu based on probability theory and uncertainty theory. In many cases, imprecise risk situation in subjective or objective setting and human uncertainty simultaneously appear in a complex system. To measure uncertain random events in this system, this paper combines uncertainty space with convex non-additive probability space into a new kind of two-dimensional chance space called U-C chance space. Moreover, a new framework for uncertain random variables combining uncertainty theory with convex non-additive probability theory is provided. For applications of this new framework, it can be applied to characterize some kinds of phenomena which possess the characteristics of both imprecise risk situations and belief degrees about human uncertainty in situations of great events, such as financial crisis, major natural disaster, etc. The main contribution of this paper is to derive the types of Kolmogorov and Marcinkiewicz-Zygmund LLNs for uncertain random variables satisfying some conditions under U-C chance space, where the convex non-additive probability is totally monotone. Furthermore, several examples are stated and explained.

Satellite-based InSAR Geodesy and Collocation with GNSS

Satellite radar interferometry (InSAR) enables large-scale monitoring of displacement with precision akin to ground-based methods. Using measurements from Sentinel-1 satellites, persistent scatterer networks cover areas up to hundreds of kilometers in size. One of the current challenges for the InSAR community is to tie these networks into a current and country-specific global terrestrial reference system through collocation with other geodetic techniques, especially Global Navigation Satellite Systems (GNSS). In this work, an optimal procedure for assessing a suitable collocation properties for InSAR and GNSS techniques is discussed, along with the proposal for the methodology to determine the spatial relationship between the reference points of both techniques. The study analyzes three collocation stations in Slovakia using their radar backscattering characteristics. InSAR achieves an intrinsic accuracy of up to 1 mm but has uncertainties several orders of magnitude larger in 3D space. A collocation of InSAR measurements with GNSS can tie relative InSAR displacement estimates to an absolute reference frame.

Identification of eupneic breathing using unsupervised machine learning.

The diaphragm muscle (DIAm) is unique to mammals and the primary muscle involved in breathing. In awake animals, considerable heterogeneity in DIAm electromyographic (EMG) activity reflects varied ventilatory and non-ventilatory behaviors. Experiments in awake animals are an essential component to understanding the neuromotor control of breathing; thus, it is paramount to unambiguously identify DIAm EMG activity that in fact reflects breathing. Current strategies for doing so in a reproducible, reliable, and efficient fashion are lacking. The present study used machine learning to evaluate DIAm EMG from awake rats using hierarchical clustering across four-dimensional feature space to classify eupneic breathing. Our model, which can be implemented with automated threshold of the clustering dendrogram, successfully identified eupneic breathing with high F1 score (0.92), specificity (0.70), and accuracy (0.88), indicating that it is a robust and reliable tool for investigating the neural control of breathing.

Three-dimensional fracture space characterization and conductivity evolution analysis of induced un-propped fractures in shale gas reservoirs

Huge numbers of induced unpropped (IU) fractures are generated near propped fractures during hydraulic fracturing in shale gas reservoirs. But it is still unclear how their fracture space and conductivity evolve under in-situ conditions. This paper prepares three types of samples, namely, manually split vertical/parallel to beddings (MSV, MSP) and parallel natural fractures (NFP), to represent the varied IU fractures as well as their surface morphology. Laser scan and reconstruction demonstrate that the initial fracture spaces of MSVs and MSPs are limited as the asperities of newly created surfaces are well-matched, and the NFPs have bigger space due to inhomogeneous geological corrosion. Surface slippage and consequent asperity mismatch increase the fracture width by several times, and the increase is proportional to surface roughness. Under stressful conditions, the slipped MSVs retain the smallest residual space and conductivity due to the newly sharp asperities. Controlled by the bedding structures and clay mineral hydrations, the conductivity of MSPs decreases most after treated with a fracturing fluid. The NFPs remain the highest conductivity, benefitting from their dispersive, gentle, and strong asperities. The results reveal the diverse evolution trends of IU fractures and can provide reliable parameters for fracturing design, post-fracturing evaluation, and productivity forecasting.

Enabling AI-Generated Content for Gadolinium-Free Contrast-Enhanced Breast Magnetic Resonance Imaging.

There is increasing interest in utilizing AI-generated content for gadolinium-free contrast-enhanced breast MRI. To develop a generative model for gadolinium-free contrast-enhanced breast MRI and evaluate the diagnostic utility of the generated scans. Retrospective. Two hundred seventy-six women with 304 breast MRI examinations (49 ± 13 years, 243/61 for training/testing). ZOOMit diffusion-weighted imaging (DWI), T1-weighted volumetric interpolated breath-hold examination (T1W VIBE), and axial T2 3D SPACE at 3.0 T. A generative model was developed to generate contrast-enhanced scans using precontrast T1W VIBE and DWI images. The generated and real images were quantitatively compared using the structural similarity index (SSIM), mean absolute error (MAE), and Dice similarity coefficient. Three radiologists with 8, 5, and 5 years of experience independently rated the image quality and lesion visibility on AI-generated and real images within various subgroups using a five-point scale. Four breast radiologists, with 8, 8, 5, and 5 years of experience, independently and blindly interpreted four reading protocols: unenhanced MRI protocol alone and combined with AI-generated scans, abbreviated MRI protocol, and full-MRI protocol. Results were assessed using t-tests and McNemar tests. Using pathology diagnosis as reference standard, sensitivity, specificity, positive predictive value (PPV), and negative predictive value (NPV) were calculated for each reading protocol. A P value <0.05 was considered significant. In the test set, the generated images showed similarity to the real images (SSIM: 0.935 ± 0.047 [SD], MAE: 0.015 ± 0.012 [SD], and Dice coefficient: 0.726 ± 0.177 [SD]). No significant difference in lesion visibility was observed between real and AI-generated scans of the mass, non-mass, and benign lesion subgroups. Adding AI-generated scans to the unenhanced MRI protocol slightly improved breast cancer detection (sensitivity: 92.86% vs. 85.71%, NPV: 76.92% vs. 70.00%); achieved non-inferior diagnostic utility compared to the AB-MRI protocol and full-protocol (sensitivity: 92.86%, 95.24%; NPV: 75.00%, 81.82%). AI-generated gadolinium-free contrast-enhanced breast MRI has potential to improve the sensitivity of unenhanced MRI in detecting breast cancer. 4 TECHNICAL EFFICACY: Stage 3.

Detection and Evaluation for High-Quality CPR Based on Motion Capture Devices: A Preliminary Test.

High-quality cardiopulmonary resuscitation (CPR) is important for successful revival. This test aimed to accurately and effectively assess parameters in CPR operations, particularly focusing on the non-quantified arm posture, to assist instructors in guiding students to enhance the quality of their performance. We used motion capture system (Mars series, Nokov, China) to collect compression data from four trained students about five rounds of CPR, recording dynamic data of each marker in three-dimensional space following time. Using the processed data, we calculated compression depth, frequency, and arm angles. Their performance still needed improvement, and there were variations in data within individuals. This suggests that when instructors conduct assessments, they should focus on not only the overall performance but also each compression. This experiment provides a new perspective for quantifying compression parameters, and future efforts should continue to optimize and incorporate new parameters for assessment.

The Unruh–DeWitt model and its joint interacting Hilbert space

In this work we make the connection between the Unruh–DeWitt (UDW) particle detector model applied to quantum field theory in curved spacetimes and the rigorous construction of the spin-boson (SB) model. With some modifications, we show that existing results about the existence of a SB ground state can be adapted to the UDW model. In the most relevant scenario involving massless scalar fields in (3+1)-dimensional globally hyperbolic spacetimes, where the UDW model describes a simplified model of light–matter interaction, we argue that common choices of the spacetime smearing functions regulate the ultraviolet behaviour of the model but can still exhibit infrared (IR) divergences. In particular, this implies the well-known expectation that the joint interacting Hilbert space of the model cannot be described by the tensor product of a two-dimensional complex Hilbert space and the Fock space of the vacuum representation. We discuss the conditions under which this problem does not arise and the relevance of the operator-algebraic approach for better understanding of particle detector models and their applications.Our work clarifies the connection between obstructions due to Haag’s theorem and IR bosons in the SB models, and paves the way for more rigorous study of entanglement and communication in the UDW framework involving multiple detectors.

Mathematical models and algorithms for designing main pipeline for transporting georesources

Relevance. The practical importance of the tasks of utility networks design, namely, the problems of optimizing the structure of the main pipeline according to given criteria, such as efficiency, reliability etc., under conditions of limitations, for example, the compatibility of various types of utilities. Since the main pipeline is laid on the ground with various physical and geological factors, natural and situational conditions, it is advisable to take the reliability of its operation as a global criterion. The task of network optimization is proposed in the form of displaying the main pipeline along the selected routes in three-dimensional space, which considers various existing communications and objects, as well as elevation marks of the area. The paper presents the problems of optimizing networks, both in the continuous case and in the discrete case, and also studies various indicators of the reliability of the operation of the main pipeline. Aim. To develop a model for laying the main pipeline in three-dimensional space, considering the reliability of the pipeline transport; to conduct a comparative analysis for various reliability indicators and topologies of the main pipeline. Objects. Utility communications and networks laid in three-dimensional space. Methods. Calculus of variations, discrete optimization methods, graph theory and hypernet theory methods, network reliability analysis methods. Results. The task of optimizing the main pipeline transport is given taking into account its nesting along the route in three-dimensional space with the choice of an optimization criterion (economic efficiency, reliability, etc.). The problem is presented in the form of continuous and discrete formulations, which is important for its development both within the theory of the calculus of variations and discrete optimization. In this work, the problem was studied within the framework of the theory of graphs and hypernets, which allow, firstly, taking into account the nesting of one structure (main pipeline) into another (a discrete analogue of three-dimensional space) and, secondly, clearly illustrating the results of numerical experiments. It is shown that under the conditions of a given variants for laying a secondary network along the primary channels, various optimal structures are obtained when considering various reliability indicators as a criterion, which can be used to implement a design solution for the construction and operation of pipeline transport for various purposes.