Space Research Articles

3D spacer fabric structured airflow channel for enhanced solar desalination with efficient multi-energy harvesting

Solar steam generation (SSG) is a sustainable way to drive seawater desalination and wastewater purification with green environmental energies including solar radiation, ambient heat, and airflow. Airflow is ubiquitous in outdoor environments, however, the utilization of airflow for accelerated evaporation through structure engineering remains unclear. Herein, environmental energies are efficiently utilized in an integrated way with the rational design of 3D spacer fabric. Carbon fiber bundles with broadband photothermal conversion ability and Tencel yarns with superior hydrophilicity are fabricated into the 3D spacer fabric. The stereoscopic airflow channel, wide evaporation surface area, and separated layers are constructed to optimize airflow pathways. Heat loss is reduced through the accelerated evaporation cooling effect. Extra ambient heat is harvested for cold evaporation by efficient airflow utilization. The evaporation rate of 3D spacer fabric reaches 5.15 kg·m−2·h−1 under a convective airflow of 3.5 m·s−1, which is twice the rate of traditional plain fabrics. The outstanding salt resistance is realized due to the separate design of photothermal and water supply layers as well as the continuous water circulation. The structural engineering of condenser devices is also investigated for enhanced airflow utilization. Overall, this work presents an effective and comprehensive multi-energy harvesting strategy to achieve rapid and durable SSG for practical clean water production.

Wearable accelerometers reveal objective assessment of walking symmetry and regularity in idiopathic scoliosis patients

Background Scoliosis is a multifaceted three-dimensional deformity that significantly affects patients’ balance function and walking process. While existing research primarily focuses on spatial and temporal parameters of walking and trunk/pelvic kinematics asymmetry, there remains controversy regarding the symmetry and regularity of bilateral lower limb gait. This study aims to investigate the symmetry and regularity of bilateral lower limb gait and examine the balance control strategy of the head during walking in patients with idiopathic scoliosis. Methods The study involved 17 patients with idiopathic scoliosis of Lenke 1 and Lenke 5 classifications, along with 17 healthy subjects for comparison. Three-dimensional accelerometers were attached to the head and L5 spinous process of each participant, and three-dimensional motion acceleration signals were collected during a 10-meter walking test. Analysis of the collected acceleration signals involved calculating five variables related to the symmetry and regularity of walking: root mean square (RMS) of the acceleration signal, harmonic ratio (HR), step regularity, stride regularity, and gait symmetry. Results Our analysis reveals that, during the walking process, the three-dimensional motion acceleration signals acquired from the lumbar region of patients diagnosed with idiopathic scoliosis exhibit noteworthy disparities in the RMS of the vertical axis (RMS-VT) and the HR of the vertical axis (HR-VT) when compared to the corresponding values in the healthy control (RMS-VT: 1.6 ± 0.41 vs. 3 ± 0.47, P < 0.05; HR-VT: 3 ± 0.72 vs. 3.9 ± 0.71, P < 0.05). Additionally, the motion acceleration signals of the head in three-dimensional space, including the RMS in the anterior-posterior and vertical axis, the HR-VT, and the values of step regularity in both anterior-posterior and vertical axis, as well as the values of stride regularity in all three axes, are all significantly lower than those in the healthy control group (P < 0.05). Conclusion The findings of the analysis suggest that the application of three-dimensional accelerometer sensors proves efficacious and convenient for scrutinizing the symmetry and regularity of walking in individuals with idiopathic scoliosis. Distinctive irregularities in gait symmetry and regularity manifest in patients with idiopathic scoliosis, particularly within the antero-posterior and vertical direction. Moreover, the dynamic balance control strategy of the head in three-dimensional space among patients with idiopathic scoliosis exhibits a relatively conservative nature when compared to healthy individuals.

A star-like photodetector for angle-based light sensing in 3D space

A star-like photodetector for angle-based light sensing in 3D space

On simulations of 3D fractional WBBM model through mathematical and graphical analysis with the assists of fractionality and unrestricted parameters

This study retrieves some novel exact solutions to the family of 3D space–time fractional Wazwaz–Benjamin–Bona–Mahony (WBBM) equations in the context of diverse nonlinear physical phenomena resulting from water wave mechanics. The family of WBBM equations is transformed for this purpose using a space and time fractional transformation into an ordinary differential equation (ODE). The ODE then uses a strong method, namely the Unified Method. Consequently, lump solutions, dark-bright soliton, singular and multiple soliton solutions, and periodic solutions are investigated. The disparities between the current study's conclusions and previously acquired solutions via other approaches are examined. All wave solutions produced are determined to be novel in terms of fractionality, unrestricted parameters, and implemented technique sense. The impact of unrestricted parameters and fractionality on the obtained solutions are visually presented, along with physical explanations. It is observed that the wave portents are varied with the increase of unrestricted parameters as well as fractionality. We dynamically showed that the appropriate transformation and the applied Unified approach more proficient in the study of water wave dynamics and might be used in future researches to clarify the many physical phenomena. The novelty of this work validate that the proposed method seem simple and useful tools for obtaining the solutions in PDEs and it is expected to use in mathematical physics and optical engineering.

Environmentally friendly lime melting slag-GBFS-titanium gypsum cementitious material: Mechanical properties, hydration characteristics and microstructure

Lime melting slag (LMS) is the solid waste produced when high-purity magnesium hydroxide is made utilizing the ammonia-lime combination technology. This study discusses the impact of LMS on the strength growth and hydration behavior of the granulated blast furnace slag (GBFS)-titanium gypsum (TG) system, with the aim of realizing the resource utilization of LMS. XRD, FTIR, SEM-EDS NMR and hydration heat characterization were employed to identify the types and development processes of hydration products at various stages. The findings indicate that incorporating 2 % LMS into the sample yields the most effective excitation, enhancing the mechanical characteristics of cementitious materials at various curing stage, particularly after 3d. The 3d compressive strength of the samples with 2 % LMS was 99.2 %, 36.9 %, 43.6 % and 72.4 % higher than that of the samples with 0 %, 4 %, 6 % and 10 % LMS, respectively. The undissolved Ca(OH)2 in the LMS can selectively adsorb dissolved Ca2+ and OH- to form a double layer structure. The higher the content of undissolved Ca(OH)2 in GBFS- titanium gypsum system, the higher the adsorption capacity of Ca2+ and OH-, and the relative content of ions used in alkali excitation slag decreased. Therefore, in the GBFS-titanium gypsum system, with the increase of LMS content, the hydration degree of GBFS gradually slows down, and the generation of hydration products correspondingly decreases, which shows that the compressive strength decreases on the macro level. The analysis of hydration products shows that the appropriate amount of LMS can promote the dissolution of GBFS, generate a large number of C-(A)-S-H gels and ettringite, form an interlocking effect in three-dimensional space, and improve the mechanical properties of hydration products. However, CO2 in the air dissolves in the water pool of the curing test block to form CO32-, which reacts with the three-dimensional network gel to form fine needle-like thaumasite, resulting in a decline in the flexural strength of GTL2, but this does not affect the development of the compressive strength of the test block. GTL cementitious materials also have good ecological and environmental benefits. This study provides a new idea for the resource utilization of LMS, and provides a rich theoretical basis for the research of solid waste cementitious materials.

The Unruh-DeWitt model and its joint interacting Hilbert space

Abstract In this work we make the connection between the Unruh-DeWitt particle detector model applied to quantum field theory in curved spacetimes and the rigorous construction of the spin-boson model. With some modifications, we show that existing results about the existence of a spin-boson ground state can be adapted to the Unruh-DeWitt model. In the most relevant scenario involving massless scalar fields in (3+1)-dimensional globally hyperbolic spacetimes, where the Unruh-DeWitt 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 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.

A New Perspective on the Homogeneous Coordinate System for Calculating Interatomic Distances and Their Derivatives in Terms of Internal Coordinates

AbstractIn many chemical physics calculations, efficient computation of interatomic distances and their derivatives using internal coordinates is essential for understanding molecular structure and dynamics. This paper explores the homogeneous coordinate system as an alternative framework to simplify these calculations. It is proven that computing interatomic distances using the Euclidean model of 3D space requires almost 60% more operations than the homogeneous model, which may represent a significant difference in molecular dynamics simulations.

Exploring motion using geometric morphometrics in microscopic aquatic invertebrates: ‘modes’ and movement patterns during feeding in a bdelloid rotifer model species

BackgroundMovement is a defining aspect of animals, but it is rarely studied using quantitative methods in microscopic invertebrates. Bdelloid rotifers are a cosmopolitan class of aquatic invertebrates of great scientific interest because of their ability to survive in very harsh environment and also because they represent a rare example of an ancient lineage that only includes asexually reproducing species. In this class, Adineta ricciae has become a model species as it is unusually easy to culture. Yet, relatively little is known of its ethology and almost nothing on how it behaves during feeding.MethodsTo explore feeding behaviour in A. ricciae, as well as to provide an example of application of computational ethology in a microscopic invertebrate, we apply Procrustes motion analysis in combination with ordination and clustering methods to a laboratory bred sample of individuals recorded during feeding.ResultsWe demonstrate that movement during feeding can be accurately described in a simple two-dimensional shape space with three main ‘modes’ of motion. Foot telescoping, with the body kept straight, is the most frequent ‘mode’, but it is accompanied by periodic rotations of the foot together with bending while the foot is mostly retracted.ConclusionsProcrustes motion analysis is a relatively simple but effective tool for describing motion during feeding in A. ricciae. The application of this method generates quantitative data that could be analysed in relation to genetic and ecological differences in a variety of experimental settings. The study provides an example that is easy to replicate in other invertebrates, including other microscopic animals whose behavioural ecology is often poorly known.

Voxelated bioprinting of modular double-network bio-ink droplets

Analogous of pixels to two-dimensional pictures, voxels—in the form of either small cubes or spheres—are the basic building blocks of three-dimensional objects. However, precise manipulation of viscoelastic bio-ink voxels in three-dimensional space represents a grand challenge in both soft matter science and biomanufacturing. Here, we present a voxelated bioprinting technology that enables the digital assembly of interpenetrating double-network hydrogel droplets made of polyacrylamide/alginate-based or hyaluronic acid/alginate-based polymers. The hydrogels are crosslinked via additive-free and biofriendly click reaction between a pair of stoichiometrically matched polymers carrying norbornene and tetrazine groups, respectively. We develop theoretical frameworks to describe the crosslinking kinetics and stiffness of the hydrogels, and construct a diagram-of-state to delineate their mechanical properties. Multi-channel print nozzles are developed to allow on-demand mixing of highly viscoelastic bio-inks without significantly impairing cell viability. Further, we showcase the distinctive capability of voxelated bioprinting by creating highly complex three-dimensional structures such as a hollow sphere composed of interconnected yet distinguishable hydrogel particles. Finally, we validate the cytocompatibility and in vivo stability of the printed double-network scaffolds through cell encapsulation and animal transplantation.

Content-state dimensions characterize different types of neuronal markers of consciousness.

Identifying the neuronal markers of consciousness is key to supporting the different scientific theories of consciousness. Neuronal markers of consciousness can be defined to reflect either the brain signatures underlying specific conscious content or those supporting different states of consciousness, two aspects traditionally studied separately. In this paper, we introduce a framework to characterize markers according to their dynamics in both the "state" and "content" dimensions. The 2D space is defined by the marker's capacity to distinguish the conscious states from non-conscious states (on the x-axis) and the content (e.g. perceived versus unperceived or different levels of cognitive processing on the y-axis). According to the sign of the x- and y-axis, markers are separated into four quadrants in terms of how they distinguish the state and content dimensions. We implement the framework using three types of electroencephalography markers: markers of connectivity, markers of complexity, and spectral summaries. The neuronal markers of state are represented by the level of consciousness in (i) healthy participants during a nap and (ii) patients with disorders of consciousness. On the other hand, the neuronal markers of content are represented by (i) the conscious content in healthy participants' perception task using a visual awareness paradigm and (ii) conscious processing of hierarchical regularities using an auditory local-global paradigm. In both cases, we see separate clusters of markers with correlated and anticorrelated dynamics, shedding light on the complex relationship between the state and content of consciousness and emphasizing the importance of considering them simultaneously. This work presents an innovative framework for studying consciousness by examining neuronal markers in a 2D space, providing a valuable resource for future research, with potential applications using diverse experimental paradigms, neural recording techniques, and modeling investigations.

A novel tool path planning method for 5-axis single-point diamond turning

5-Axis single-point diamond turning adds two linked axes based on 3-axis single-point diamond turning, which can smoothly and continuously process complex surfaces. Compared to 3-axis turning, tool path planning for 5-axis single-point diamond turning is a complex decision-making process, which is a novel problem in the existing studies and a difficulty in multi-axis turning. In this study, a novel path planning method for 5-axis single-point diamond turning is proposed. Firstly, the mapping relation from scallop height to the distribution of cutter contact (CC) points is established in the non-uniform rational B-spline (NURBS) parameter space, thereby the planning of CC points is quickly achieved under fewer constraints. Furthermore, the local interference and global interference generation mechanism of 5-axis single-point diamond turning are revealed by geometrical analysis, combining diamond tool parameters and tool shank parameters. By transforming the motion of the cutter axis posture in 3D space into swings in two planes, the posture accessibility diagram of the cutter axis is efficiently constructed. Finally, the feasibility and effectiveness of the tool path planning method are verified by 5-axis single-point diamond turning experiment. And the contour accuracy is improved through the quadratic planning of the CC points (the contour accuracy after compensation is 3.2 μm compared to normal one 9.6 μm). This study extends the traditional 3-axis turning to 5-axis turning, providing a new perspective for the machining of complex surfaces.

Holo-Stroke: Assessing for Immersive Stroke Care Through Stroke Hologram Teleportation.

Background: Augmented reality enables the wearer to see both their physical environment and virtual objects. Holograms could allow 3D video of providers to be transmitted to distant sites, allowing patients to interact with virtual providers as if they are in the same physical space. Our aim was to determine if Tele-Stroke augmented with Holo-Stroke, compared with Tele-Stroke alone, could improve satisfaction and perception of immersion for the patient. Methods: Kinect cameras positioned at 90-degree intervals around the hub practitioner were used. Cameras streamed real-time optical video to a unity point-cloud program where the data were stitched together in a 360-degree view. The resultant hologram was positioned in 3D space and was visible through the head-mounted display by the patient. Radiology images were shared in Tele-Stroke and via hologram. Likert satisfaction questions were administered. Wilcoxon signed-rank testing was used. Results: Each of the 30 neurology clinic participants scored both Tele-Stroke and Holo-Stroke. Out of these, 29 patients completed the assessments (1 failure owing to computer reboot). Average age was 52 years, with 53.3% of the patients being female, 70.0% being White, and 13.3% being Hispanic. Likert scale score median "Overall" was 32 Tele-Stroke versus 48 Holo-Stroke (p < 0.00001), "Immersion" was 5 versus 10 (p < 0.00001), "Beneficial Technique" was 6 versus 10 (p < 0.00001), and "Ability to See Images" was 5 versus 10 (p < 0.00001). Discussion: Holo-Stroke 3D holographic Tele-Stroke exams resulted in feasibility, satisfaction, and high perception of immersion for the patient. Patients were enthusiastic for the more immersive, personal discussion with their provider and a robust way to experience radiology images. Though further assessments are needed, Holo-Stroke can help the provider "be there, not just see there!"

Conformal trajectories in three-dimensional space forms

We introduce the notion of conformal trajectories in three-dimensional Riemannian manifolds [Formula: see text]. Given a conformal vector field [Formula: see text], a conformal trajectory of [Formula: see text] is a regular curve [Formula: see text] in [Formula: see text] satisfying [Formula: see text], for some fixed nonzero constant [Formula: see text]. In this paper, we study the conformal trajectories in the space forms [Formula: see text], [Formula: see text] and [Formula: see text]. For (non-Killing) conformal vector fields in [Formula: see text] (respectively, in [Formula: see text]), we prove that conformal trajectories have constant curvature and its torsion is a linear combination of trigonometric (respectively, hyperbolic) functions on the arc-length parameter. In the case of Euclidean space [Formula: see text], we obtain the same result for the radial vector field and characterizing all conformal trajectories.

A Property that Characterizes the Enneper Surface and Helix Surfaces

The main goal of this paper is to show that helix surfaces and the Enneper surface are the only surfaces in the 3-dimensional Euclidean space R3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {R}^{3}$$\\end{document} whose isogonal lines are generalized helices and pseudo-geodesic lines.

3D-Oculography: New Method of Determination of Human Gaze Point Position in Space

INTRODUCTION: Oculography — a method of recording movement of eyeballs of a human or animal by analyzing changes in electrical potentials recorded by two electrodes fixed on skin near the eye socket is used to solve various problems. Among them are the determination of pronounced nystagmus, of characteristic changes of oculomotor reactions in different conditions of observing video images. Of interest is the determination of the position of gaze point (GP) and of the area of increased attention in three-dimensional space. This information is associated with the cognitive system of the observer and is of interest not only to physiologists, but also to specialists of related fields. . AIM: To experimentally prove the effectiveness of the developed method of 3D-oculography providing determination of the GP position in space. MATERIALS AND METHODS: The possibility of restoring GP position based on the analysis of recorded oculograms even in the presence of additive noise induced by the external electromagnetic fields, is proven by the numeric modeling method. Direct experimental studies were conducted with recording oculograms of a human observer on a previously verified equipment. A ZB-2 oculograph was used, the data obtained were verified by the method of average values. RESULTS: The obtained modeling results permitted to determine the maximal values of dispersion of additive noise and amplitude shifts of signals, which make possible satisfactory restoration of the coordinates of the GP and parameters of its movement trajectory. The qualitative correspondence of the experimental results to the results of numerical modeling was proven. The correspondence between trajectories of the observed object moving in space and trajectories of GP movement synthesized from counts of recorded oculograms was confirmed. CONCLUSION: Multichannel record of oculographic signals permits restoring parameters of the GP trajectory. Creating systems for recording these signals requires minimization of the noise level. An increase in dispersion of the noise component of the signal leads to most significant errors in calculating the coordinates of trajectory points.

Compound 3D building modeling with structure-aware partition and primitive assembly from airborne laser scanning point clouds

ABSTRACT Urban digital twins and realistic three-dimensional (3D) scenes have further enhanced the ever-increasing demand for building models. Airborne Laser Scanning (ALS) point clouds are the predominant data source for 3D building reconstruction owing to their highly detailed spatial features. However, information on the reconstruction of compound buildings (i.e. buildings with diverse plane structures or various roof structures) is lacking. Existing methods often produce building models that suffer from topological inconsistencies and/or geometric errors. To address these issues, this study proposes an automatic building reconstruction approach based on ALS point cloud that offers both modeling flexibility and geometric consistency. Specifically, a structure-aware partitioning algorithm that partitions a complex building roof into several regular roof patches is incorporated. Subsequently, a primitive model library comprising representative primitives suitable for building reconstruction is created. Suitable primitive model selection and reconstruction optimization are employed to ensure the accuracy and compactness in the final model. To comprehensively evaluate the performance, two typical ALS point cloud datasets are tested. Experiments demonstrate the generated models can achieve a boundary consistency of 92% while ensuring Root Mean Square Error below 0.09 m. Comparative experiments with state-of-the-art methods further validate the effectiveness of the proposed approach in compound building reconstruction.

FLApy: A Python package for evaluating the 3D light availability heterogeneity within forest communities

Abstract Light availability (LAv) dictates a variety of biological and ecological processes across a range of spatiotemporal scales. Quantifying the spatial pattern of LAv in three‐dimensional (3D) space can promote the understanding of microclimates that are critical to fine‐scale species distribution. However, there is still a lack of tools that are robust to evaluate spatiotemporal heterogeneity of LAv in forests. Here, we propose the Forest Light Analyzer python package (FLApy), an open‐source computational tool designed for the analysis of intra‐forest LAv variation across multiple spatial scales. FLApy is freely invoked by Python, facilitating the processing of LiDAR point cloud data into a 3D data container constructed by voxels, as well as traversal calculations related to the LAv regime by high performance synthetic hemispherical algorithm. Furthermore, FLApy incorporates 37 indicators, enabling users to expediently export and visualize LAv patterns and the evaluation of heterogeneity of LAv at two scales (voxel scale and 3D‐cluster scale) for a range of fine‐scale ecological study purposes. To validate the efficacy of the FLApy, we employed a simulated point cloud dataset that simulates forests (varying in canopy closure). Furthermore, to evaluate real world forest, we executed the standard workflow of FLApy utilizing drone‐derived data from three subtropical evergreen broad‐leaved forest dynamics plots within the Ailao Mountain Reserve. Our findings underscore that a series of indices derived from FLApy provide a robust characterization of light availability heterogeneity within diverse forest settings. Additionally, when juxtaposed with conventional monitoring techniques, the metrics offered by FLApy demonstrated better generality in our field assessments. FLApy offers ecologists a solution for rapid quantification of understory light 3D‐regimes across multiple scales, addressing the disparity between traditional manual approaches and the precision required for contemporary ecological studies. Moreover, FLApy provides robust support for the establishment and expansion of heterogeneity indices based on 3D micro‐environments, enhancing our understanding of the largely uncharted 3D structural patterns. Anticipated outcomes suggest that FLApy will enhance our knowledge concerning the intra‐forest climatic conditions into a 3D context, proving pivotal in the delineation of microhabitats and the development of detailed 3D‐scale species distribution models.

FLApy: A Python package for evaluating the 3D light availability heterogeneity within forest communities

Abstract Light availability (LAv) dictates a variety of biological and ecological processes across a range of spatiotemporal scales. Quantifying the spatial pattern of LAv in three‐dimensional (3D) space can promote the understanding of microclimates that are critical to fine‐scale species distribution. However, there is still a lack of tools that are robust to evaluate spatiotemporal heterogeneity of LAv in forests. Here, we propose the Forest Light Analyzer python package (FLApy), an open‐source computational tool designed for the analysis of intra‐forest LAv variation across multiple spatial scales. FLApy is freely invoked by Python, facilitating the processing of LiDAR point cloud data into a 3D data container constructed by voxels, as well as traversal calculations related to the LAv regime by high performance synthetic hemispherical algorithm. Furthermore, FLApy incorporates 37 indicators, enabling users to expediently export and visualize LAv patterns and the evaluation of heterogeneity of LAv at two scales (voxel scale and 3D‐cluster scale) for a range of fine‐scale ecological study purposes. To validate the efficacy of the FLApy, we employed a simulated point cloud dataset that simulates forests (varying in canopy closure). Furthermore, to evaluate real world forest, we executed the standard workflow of FLApy utilizing drone‐derived data from three subtropical evergreen broad‐leaved forest dynamics plots within the Ailao Mountain Reserve. Our findings underscore that a series of indices derived from FLApy provide a robust characterization of light availability heterogeneity within diverse forest settings. Additionally, when juxtaposed with conventional monitoring techniques, the metrics offered by FLApy demonstrated better generality in our field assessments. FLApy offers ecologists a solution for rapid quantification of understory light 3D‐regimes across multiple scales, addressing the disparity between traditional manual approaches and the precision required for contemporary ecological studies. Moreover, FLApy provides robust support for the establishment and expansion of heterogeneity indices based on 3D micro‐environments, enhancing our understanding of the largely uncharted 3D structural patterns. Anticipated outcomes suggest that FLApy will enhance our knowledge concerning the intra‐forest climatic conditions into a 3D context, proving pivotal in the delineation of microhabitats and the development of detailed 3D‐scale species distribution models.

Deep learning based bilateral filtering for edge-preserving denoising of respiratory-gated PET

BackgroundResidual image noise is substantial in positron emission tomography (PET) and one of the factors limiting lesion detection, quantification, and overall image quality. Thus, improving noise reduction remains of considerable interest. This is especially true for respiratory-gated PET investigations. The only broadly used approach for noise reduction in PET imaging has been the application of low-pass filters, usually Gaussians, which however leads to loss of spatial resolution and increased partial volume effects affecting detectability of small lesions and quantitative data evaluation. The bilateral filter (BF) — a locally adaptive image filter — allows to reduce image noise while preserving well defined object edges but manual optimization of the filter parameters for a given PET scan can be tedious and time-consuming, hampering its clinical use. In this work we have investigated to what extent a suitable deep learning based approach can resolve this issue by training a suitable network with the target of reproducing the results of manually adjusted case-specific bilateral filtering.MethodsAltogether, 69 respiratory-gated clinical PET/CT scans with three different tracers ([18F]\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$[^{18}\ ext {F}]$$\\end{document}FDG, [18F]\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$[^{18}\ ext {F}]$$\\end{document}L-DOPA, [68Ga]\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$[^{68}\ ext {Ga}]$$\\end{document}DOTATATE) were used for the present investigation. Prior to data processing, the gated data sets were split, resulting in a total of 552 single-gate image volumes. For each of these image volumes, four 3D ROIs were delineated: one ROI for image noise assessment and three ROIs for focal uptake (e.g. tumor lesions) measurements at different target/background contrast levels. An automated procedure was used to perform a brute force search of the two-dimensional BF parameter space for each data set to identify the “optimal” filter parameters to generate user-approved ground truth input data consisting of pairs of original and optimally BF filtered images. For reproducing the optimal BF filtering, we employed a modified 3D U-Net CNN incorporating residual learning principle. The network training and evaluation was performed using a 5-fold cross-validation scheme. The influence of filtering on lesion SUV quantification and image noise level was assessed by calculating absolute and fractional differences between the CNN, manual BF, or original (STD) data sets in the previously defined ROIs.ResultsThe automated procedure used for filter parameter determination chose adequate filter parameters for the majority of the data sets with only 19 patient data sets requiring manual tuning. Evaluation of the focal uptake ROIs revealed that CNN as well as BF based filtering essentially maintain the focal SUVmax\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ext {SUV}_\ ext {max}$$\\end{document} values of the unfiltered images with a low mean ± SD difference of δSUVmaxCNN,STD\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\delta \ ext {SUV}_\ ext {max}^{\ ext {CNN},\ ext {STD}}$$\\end{document} = (−3.9 ± 5.2)% and δSUVmaxBF,STD\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\delta \ ext {SUV}_\ ext {max}^{\ ext {BF},\ ext {STD}}$$\\end{document} = (−4.4 ± 5.3)%. Regarding relative performance of CNN versus BF, both methods lead to very similar SUVmax\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ext {SUV}_\ ext {max}$$\\end{document} values in the vast majority of cases with an overall average difference of δSUVmaxCNN,BF\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\delta \ ext {SUV}_\ ext {max}^{\ ext {CNN},\ ext {BF}}$$\\end{document} = (0.5 ± 4.8)%. Evaluation of the noise properties showed that CNN filtering mostly satisfactorily reproduces the noise level and characteristics of BF with δNoiseCNN,BF\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\delta \ ext {Noise}^{\ ext {CNN},\ ext {BF}}$$\\end{document} = (5.6 ± 10.5)%. No significant tracer dependent differences between CNN and BF were observed.ConclusionsOur results show that a neural network based denoising can reproduce the results of a case by case optimized BF in a fully automated way. Apart from rare cases it led to images of practically identical quality regarding noise level, edge preservation, and signal recovery. We believe such a network might proof especially useful in the context of improved motion correction of respiratory-gated PET studies but could also help to establish BF-equivalent edge-preserving CNN filtering in clinical PET since it obviates time consuming manual BF parameter tuning.

D-terms in generalised complex geometry

Generalised Complex Geometry provides a natural interpretation of the N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 1 supersymmetry conditions for warped solutions of type II supergravity as differential equations on polyforms on the internal manifold. Written in this language the supersymmetry conditions correspond to calibration conditions for probe D-branes: D-string, domain-wall or space-filling branes, depending on the directions they span in the non-compact four-dimensional space. The BPS condition corresponding to the calibration of space-filling D-branes has been reformulated by Tomasiello, eliminating the explicit dependence on the metric. We generalise this derivation to the case of non-supersymmetric backgrounds violating the domain-wall and D-string calibration conditions. We use this reformulation to derive constraints that the ten-dimensional solutions with BPS space-filling sources must respect in order to dimensionally reduce to solutions of four-dimensional N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 1 supergravity with non-vanishing F-terms and potentially non-vanishing D-terms. We give the equations of motion for the class of type II vacua satisfying these constraints in the language of pure spinors. We investigate how restrictive these constraints are for the class of type IIB SU(3) backgrounds with BPS space-filling O5-planes.