Geometric Complexity Research Articles

Additively manufactured conformal cooling channels through topology optimization

Cooling channels play a critical role in various casting and molding processes, impacting both the cycle time and quality of the product. As additive manufacturing technologies become increasingly prevalent, conventional straight-drilled channels are being progressively substituted by intricate cooling lines that conform to the contours of the fabricated part. This transition can lead to a significant reduction of the solidification time and temperature gradients, consequently lowering the occurrence of part defects. However, designing such channels becomes challenging as geometric complexity and manufacturing constraints increase. In this work, we present a density-based topology optimization approach to generate conformal cooling channels in molds and dies inserts. To mitigate temperature variations, the objective function is penalized using the temperature standard deviation of the insert cavity surface. A density-gradient-based constraint is further utilized to reduce the generation of overhanging structures and promote manufacturability. In particular, the use of this constraint leads to the generation of channels characterized by a teardrop-shaped cross section. The cooling efficiency of a selected optimized design is confirmed through computations using a body-fitted solver. The geometry is subsequently manufactured by Laser Powder Bed Fusion (LPBF) and experiments are conducted to compare its performance in comparison to a design featuring straight-drilled channels. The results demonstrate that the optimized geometry significantly enhances the heat extraction rate and further leads to a 43% reduction of the cavity temperature standard deviation.

From constraints fusion to manifold optimization: A new directional transport manifold metaheuristic algorithm

The ascent of geometry-based models and methodologies, exemplified by geometric deep learning and manifold numerical optimization algorithms, has inaugurated a novel domain across various applications that grapple with geometric data complexities, such as electroencephalogram signals represented by symmetric positive definite matrix manifold, hierarchical data represented by hyperbolic manifold. The imperative fuels this inevitable paradigm shift to encapsulate the intricacies and richness inherent in data, areas where traditional methods prove inadequate. While metaheuristic algorithms are renowned for their versatile adaptability across applications, offering practical solutions within reasonable timeframes. However, the conventional metaheuristic algorithms fail on manifold applications with meaningless solutions. From an extrinsic optimization perspective, we treat manifold optimization problems as general optimization problems with multiple fused constraints that limit the optimization path to the manifold. This study pioneered the proposal and implementation of a metaheuristic manifold optimization, introducing a novel directional transport operator to rectify previously identified issues. Through experimentation across five sets of 25 problems, comparing against five algorithms, including both gradient-free and gradient-dominant counterparts, our proposed algorithm emerges as the optimal performer within the gradient-free category, demonstrating competitiveness even against gradient-dominant algorithms. Furthermore, we applied the proposed algorithm to the robot dynamic manipulation problem, achieving a close-optimal solution that eludes gradient-dominant approaches. This paper delves into the inherent capabilities and establishes the generalization of a metaheuristic algorithm within non-Euclidean functional landscapes. The source code will be available at https://github.com/lingping-fuzzy/metaheuristic-manifold-optimization.

Rupture segmentation on the East Anatolian fault (Turkey) controlled by along-strike variations in long-term slip rates in a structurally complex fault system

Abstract The East Anatolian fault in Turkey exhibits along-strike rupture segmentation, typically resulting in earthquakes with moment magnitude (Mw) up to 7.5 that are confined to individual segments. However, on 6 February 2023, a catastrophic Mw 7.8 earthquake struck near Kahramanmaraş (southeastern Turkey), defying previous expectations by rupturing multiple segments spanning over 300 km and overcoming multiple geometric complexities. We explore the mechanics of successive single- and multi-segment ruptures using numerical models of the seismic cycle calibrated to historical earthquake records and geodetic observations of the 2023 doublet. Our model successfully reproduces the observed historical rupture segmentation and the rare occurrence of multi-segment earthquakes. The segmentation pattern is influenced by variations in long-term slip rate along strike across the kinematically complex fault network between the Arabian and Anatolian plates. Our physics-based seismic cycle simulations shed light on the long-term variability of earthquake size that shapes seismic hazards.

Design optimization of advanced tow-steered composites with manufacturing constraints

Tow steering technologies, such as automated fiber placement, enable the fabrication of composite laminates with curvilinear fiber, tow, or tape paths. Designers may therefore tailor tow orientations locally according to the expected local stress state within a structure, such that strong and stiff orientations of the tow are (for example) optimized to provide maximal mechanical benefit. Tow path optimization can be an effective tool in automating this design process, yet has a tendency to create complex designs that may be challenging to manufacture. In the context of tow steering, these complexities can manifest in defects such as tow wrinkling, gaps, overlaps. In this work, we implement manufacturing constraints within the tow path optimization formulation to restrict the minimum tow turning radius and the maximum density of gaps between and overlaps of tows. This is achieved by bounding the local value of the curl and divergence of the vector field associated with the tow orientations. The resulting local constraints are effectively enforced in the optimization framework through the Augmented Lagrangian method. The resulting optimization methodology is demonstrated by designing 2D and 3D structures with optimized tow orientation paths that maximize stiffness (minimize compliance) considering various levels of manufacturing restrictions. The optimized tow paths are shown to be structurally efficient and to respect imposed manufacturing constraints. As expected, the more geometrical complexity that can be achieved by the feedstock tow and placement technology, the higher the stiffness of the resulting optimized design.

Bayesian linearized inversion for petrophysical and pore-connectivity parameters with seismic elastic data of carbonate reservoirs

Abstract Carbonate reservoirs are important targets for promoting the oil and gas reserve exploration and production in China. However, such reservoirs usually contain the developed complex pore structures, which heavily affect the precision in seismic prediction of petrophysical parameters. As one of the most important parameters to characterize reservoir rock, pore-related parameters can not only describe the pore structure, but also be used to evaluate the oil/gas bearing capabilities of potential reservoirs. The conventional rock-physics models (e.g. Gassmann's model) are formulated assuming fully-connected pores, which is unable to accurately capture the geometrical complexity in real rocks. In order to characterize the influences of multiple pores on the elastic properties, this work presents a rock-physics modelling method for carbonates, wherein the percentage composition of connected pores is equivalently quantified as the pore-connectivity factor. The method treats the pore-connectivity factor as an objective variable to characterize the spatial variations of pore structure. Specifically, the method combines the differential equivalent medium theory and Gassmann's model, and derives a linearized forward operator to quantitatively link porosity, water saturation, and pore-connectivity factor to seismic elastic parameters. According to the Bayesian linear inverse theory, the simultaneous estimation of petrophysical and pore-connectivity parameters is achieved. To characterize the statistical variations with multiple lithofacies, the Gaussian mixture model is employed to quantify the prior distribution of the objective variables. The posterior distribution of the objective variables is analytically expressed with the linearized forward operator. Numerical experiments show that the accuracy of the proposed method in predicting elastic parameters is improved. Compared with the conventional Xu-White model and the varying pore aspect ratio method, the accuracy of predicted P-wave velocity increases by 10.29% and 1.33%, respectively, and the predicted S-wave velocity increases by 6.44% and 0.03%, in terms of correlation coefficient. The application to the field data validates the effectiveness of the method, wherein the porosity and water saturation results help indicating the spatial distribution of potential reservoirs.

Effect of forefoot transverse arch stiffness on foot biomechanical response--based on finite element method.

The plantar vault, comprising the transverse and longitudinal arches of the human foot, is essential for impact absorption, elastic energy storage, and propulsion. Recent research underscores the importance of the transverse arch, contributing over 40% to midfoot stiffness. This study aimed to quantify biomechanical responses in the ankle-foot complex by varying the stiffness of the deep metatarsal transverse ligament (DTML). Using CT image reconstruction, we constructed a complex three-dimensional finite element model of the foot and ankle joint complex, accounting for geometric complexity and nonlinear characteristics. The focus of our study was to evaluate the effect of different forefoot transverse arch stiffness, that is, different Young's modulus values of DTML (from 135MPa to 405MPa), on different biomechanical aspects of the foot and ankle complex. Notably, we analyzed their effects on plantar pressure distribution, metatarsal stress patterns, navicular subsidence, and plantar fascial strain. Increasing the stiffness of the DTML has significant effects on foot biomechanics. Specifically, higher DTML stiffness leads to elevate von Mises stress in the 1st, 2nd, and 3rd metatarsals, while concurrently reducing plantar pressure by 14.2% when the Young's modulus is doubled. This stiffening also impedes navicular bone subsidence and foot lengthening. Notably, a 100% increase in the Young's modulus of DTML results in a 54.1% decrease in scaphoid subsidence and a 2.5% decrease in foot lengthening, which collectively contribute to a 33.1% enhancement in foot longitudinal stiffness. Additionally, doubling the Young's modulus of DTML can reduce the strain stretch of the plantar fascia by 38.5%. Preserving DTML integrity sustains the transverse arch, enhancing foot longitudinal stiffness and elastic responsiveness. These findings have implications for treating arch dysfunction and provide insights for shoe developers seeking to enhance propulsion.

Object Registration Techniques For 3D Particle Tracking

Image based 3D particle tracking is currently the most widely used technique for volumetric velocity measurements. Inspecting the flow-field around an object is however, hampered by the latter, obstructing the view across it. In this study, the problem of measurement limitations due to the above is addressed. The present work builds upon the recent proposal from Wieneke and Rockstroh (2024), whereby the information of the occluded lines of sight can be incorporated into the particle tracking algorithm. The approach, however, necessitates of methods that accurately evaluate the shape and position of the object within the measurement domain. Methods of object marking and the following 3D registration of a digital object model (CAD) are discussed. For the latter, the Iterative Closest Point (ICP) registration algorithm is adopted. The accuracy of object registration is evaluated by means of experiments, where marking approaches that include physical and optically projected markers are discussed and compared. Three objects with growing level of geometrical complexity are considered: a cube, a truncated wing and a scaled model of a sport cyclist. The registered CAD representations of the physical objects are included in aerodynamic experiments, and the flow field is measured by means of large-scale particle tracking using helium filled soap bubbles. Three operating regimes are studied and compared: monolithic, partitioned and object-aware (OA) monolithic. The results indicate that object registration enables a correct reconstruction of particle tracers and strongly reduces the domain clipping typical of the monolithic approach. Furthermore, the dynamical use of all views in the OA monolithic method offers clear benefits compared to the partitioned approach, namely a lower occurrence of ghost particles. Finally, the combined visualization of the object and the surrounding flow pattern offers means of insightful data inspection and interpretation, along with posing a basis for PIV data assimilation at the fluid-solid interface.

Three approaches on estimating geometric sensitivities in radiative transfer with Monte Carlo

The Monte Carlo method, renowned for its ability to handle the spectral and geometric complexities of 3D radiative transfer, is extensively utilized across various fields, including concentrated solar power design, atmospheric science, and computer graphics. The success of this method also extends to the estimation of sensitivity—the derivative of an observable with respect to a given system parameter, which is, however, particularly challenging when these parameters involve geometric deformation. Bridging statistical physics and computer graphics, distinct methodologies have emerged within these fields for estimating geometric sensitivity, each employing unique terminologies and mathematical frameworks, leading to seemingly disparate approaches. In this paper, we review the three main approaches to sensitivity estimation: (1) Expectation Differentiation, which employs a vectorized Monte Carlo algorithm to simultaneously estimate the intensity and its sensitivity; (2) Differentiable Rendering, predominantly used in computer graphics and applied in numerous contexts; (3) Transport Model for Sensitivity, which conceptualizes sensitivity as a physical quantity with its own transport equations and boundary conditions, thereby facilitating engineering and physics analyses. We aim to enhance readers’ ability to tackle sensitivity-related challenges by providing a comparative understanding of these three perspectives. We achieve this through a simplified one-dimensional radiative transfer case study, offering an accessible platform for comparing and classifying these approaches based on their theoretical underpinnings and practical application in Monte Carlo algorithms.

Printing path-dependent two-scale models for 3D printed planar auxetics by material extrusion

One particularly interesting class of mechanical metamaterials are those having a negative Poisson’s ratio, which are referred to as ‘auxetics’. Because of their geometrical complexity, auxetic designs cannot always be easily created. However, Additive Manufacturing (AM) methods like material extrusion in 3D printing present the opportunity to construct auxetic structures. Nevertheless, extruded 3D printed material can be highly anisotropic. Before 3D printed auxetics manufactured through material extrusion can be used in engineering applications, it is important to generate powerful simulation tools that can reliably reproduce and foretell their mechanical characteristics irrespective of their form and intricacy. In view of this, the current work proposes printing path-dependent models based on an experimentally validated multi-scale modelling scheme using the Lattice Beam Model (LBM). This is done by first representing idealized microstructures of extruded 3D printed polymers through geometric models and simulating these on the material scale. The aim is to explicitly model the inter-layer and intra-layer bonds that exist in material extruded 3D printed parts by assigning experimentally obtained interface properties that significantly differ from the bulk material. On the auxetic structure scale, two planar auxetic designs are modelled using the determined material scale relationships as input: Re-Entrant (RE) and Rotating Square (RS). In terms of mechanical response, the experimentally and numerically obtained force displacement curves agree reasonably well: the stiffness of the modelled auxetic designs fit well with the experimentally measured ones while the LBM simulations generally provide a good estimation in strength. Finally, it has been shown on both the material and auxetic structure scales that incorporation of the interfacial bond strengths in simulations of extruded 3D printed polymers is important, because neglecting these results in significant overestimation of the strength.

Model performance evaluation of build time using geometric shape complexity and process parameters in material extrusion

Additive Manufacturing (AM) is gaining widespread interest and recognition in both academia and industry due to its numerous advantages over traditional manufacturing processes. The AM process offers two significant benefits: mass customization and the ability to achieve higher shape complexity at no cost. The present study introduces a methodology for quantifying the shape complexity of feature-based parametric models that AM can produce. This method is exclusively a quantitative approach based on the “number of inputs” required to define the feature or integral sketch. Furthermore, an Artificial Neural Network (ANN) based predictive model for estimating the AM build time has been developed and validated. Supervised Machine Learning (ML) is employed to predict printing time by considering significant design and manufacturing parameters that affect the overall process time. A performance evaluation is conducted between the developed ANN model and a statistical Multiple Linear Regression (MLR) model. The validation Computer Aided Design (CAD) samples are chosen to evaluate the ANN and MLR model's performance to predict the build time. It is observed that the ANN model outperforms the MLR model in estimating the build time of complex geometries. Regarding the efficiency of models, the ANN model achieved an R square value of 0.880 and a lower prediction error of 15.543 %. However, the MLR model showed some sensitivity to high complexity and large volume parts when predicting printing time, with a R square value of 0.96. In contrast, the ANN model is more precise in forecasting FDM build time for complex geometries and large volume parts.

Injection-induced basement seismicity beneath the Raton Basin: constraints from refined fault architectures and basin structure.

Intraplate earthquakes induced by anthropogenic fluid injection present unexpected seismic risk to previously quiescent or low seismicity-rate regions. Despite many studies of induced seismicity, there are relatively few with detailed openly accessible constraints on the interaction between seismic sources and subsurface structures. In this study of the Raton Basin, we refine source observations from a dense nodal array and constrain basin structure using teleseismic receiver functions. The cross-correlation-based relocated hypocentres and a new set of focal mechanisms light up active fault segments and show clear spatiotemporal patterns. The geometric complexity of reactivated fault clusters appears greatest near higher rate injection wells. Simpler normal fault structure is found farther from injection wells and near abrupt structural transitions suggested by receiver functions. While less induced seismicity in the crystalline basement is expected when injection is >1 km from the top of the basement (like Raton), our receiver function analysis identified a basin thickness ~3 km beneath the nodal array and lateral variations in sedimentary structures. Our results explain potential fluid connectivity between the injection depths focused at ~1-1.5 km below the surface and basement fault activity that begins at ~3 km and reaches peak activity at ~4-8 km depths. This article is part of the theme issue 'Induced seismicity in coupled subsurface systems'.

Binder System Composition on the Rheological and Magnetic Properties of Nd-Fe-B Feedstocks for Metal Injection Molding

The applications of Nd-Fe-B-based magnets are experiencing significant diversification to achieve efficiency and miniaturization in different technologies. Metal injection molding (MIM) provides new opportunities to manufacture Nd-Fe-B magnets with high geometrical complexity efficiently. In this study, the impacts of the binder system composition and powder loading on the rheological behavior, contamination, and magnetic properties of the Nd-Fe-B MIM parts were investigated. A high-pressure capillary rheometer was used to measure the apparent viscosity and pressure drops for feedstocks with different binder formulations and powder contents. Also, oxygen and carbon contamination, density, and magnetic properties were measured for different feedstock formulations and powder loadings. From the rheological, density, and magnetic properties points of view, the binder system consisting of 45 vol.% LLDPE as backbone was selected as the optimum formulation. The findings indicated that the sample with this binder system and 55 vol.% powder content had a high density (6.83 g/cm3), remanence (0.591 T), and coercivity (744.6 kA/m) compared to other binder compositions. By using 58 vol.% powder loading, the values of density (7.54 g/cm3), remanence (0.618 T), and carbon residue (982 ppm) improved, and a suitable rheological behavior was still observed. Thus, a suitable feedstock formulation was developed.

Conditions and benefits of X-point radiation for the island divertor

We present a method to geometrically quantify the three magnetic island chains with the poloidal mode numbers m = 4, 5, and 6 (referred to in this paper as high-iota, standard, and low-iota islands, respectively), on which the W7-X divertor relies. The focus is on a comparative study of their detachment performance using a series of models of different physical and geometrical complexity, ranging from one- to three-dimensional (1D to 3D). In particular, it aims to identify the key physical elements behind the correlation between impurity radiation and island geometry and the associated detachment stability. Assuming intrinsic carbon as a radiator, we scan the three island chains with the EMC3-Eirene code based on otherwise identical code inputs. We find that the three islands behave differently in the radiation distribution, in the development of the radiation zones during detachment, and in the ‘radiation costs’, defined as the product of impurity and electron density near the last closed flux surface. While the radiation costs for the iota = 5/4 and 5/5 island chains linearly increase with the total radiation, the low-iota island with iota = 5/6 shows a bifurcation behavior in the sense that the radiation costs initially increase and then decrease when the total radiation exceeds a critical level. Consistent with the numerical trends, stable detachment, which is experimentally easy and robust to achieve with the standard iota = 5/5 island chain, remains an experimental challenge with the low-iota configuration. Dedicated numerical experiments show that the recycling neutrals and the ratio of parallel to perpendicular heat transport, which depends closely on the field line pitch, play a significant role in the formation and evolution of the radiation layer. A deeper understanding of the underlying physics relies on simpler models that explain why and how flux expansion can reduce the radiation costs. From these insights, we derive the conditions in which detached plasmas can benefit from the expansion of flux surfaces around the X-point. We show and explain why the current divertor design limits the actual capability of the high-iota configuration and propose solutions. The work is presented within a theoretical/numerical framework but cites relevant experimental evidence to emphasize its practical significance.

Cage-by-cage supramolecular polymerization via panel-decorated triphenylphosphine organic cage

Significant efforts have been dedicated to designing porous organic cage compounds with geometric complexity and topological diversity. However, the use of these cage molecules as premade building units for constructing infinite cage-based superstructures remains unexplored. Here, we report the use of a panel-decorated phosphine organic cage as a special monomer to achieve supramolecular polymerization, resulting in cage-by-cage noncovalent polymers through the synergy of metal-coordination and intercage π–π dimerization. At a monomer concentration of 122 mM, the average degree of polymerization reaches 17, corresponding to a molecular weight of 26 kDa. The obtained cage-based supramolecular polymers can further hierarchically self-assemble into vesicular morphologies or one-dimensional nanofiber architectures. Selective control over the cosolvents can regulate their structural hierarchy and assembled morphology. This approach paves a new way for the construction of cage-based hierarchical assemblies and materials.

Non-dimensional parameters governing the crashworthy performance of tubes with complex cross-sections

The crashworthiness of thin-walled tubes with various designs under axial compression has been extensively investigated. Despite this, the parameters that govern the performance of tubes and can be applied across different cross-sectional topologies have not hitherto been available. In this paper, twenty types of thin-walled tubes with different cross-sectional shapes (e.g., multi-celled, bi-tubular, and hierarchical square, hexagonal and circular tubes) have been numerically simulated and theoretically analysed. All the tubes are made from identical material and possess identical apparent cross-sectional area, height and mass. Six indicators are employed to characterise the crashworthiness performance of the tubes. Two novel non-dimensional indices, the geometric complexity index (RG) which is the ratio of the total length of solid segments in the cross-section of a tube to that of the square tube, and the topological index (RT) which is the non-dimensional coefficient in the expression of plastic energy dissipation closely related to the types and numbers of the wall junctions in cross-section, are identified for the first time. Both the indices RG and RT are used in a regression analysis of the indicators that characterise the crashworthiness of the tubes. The results reveal that the crashworthiness indicators of the tubes, the mean crushing force (MCF), the specific energy absorption (SEA) and the effectiveness of energy absorption (EEA) do not exclusively vary with RG. Instead, MCF, SEA and EEA are all properly fitted by linear relations with a single non-dimensional parameter ω, which is a simple function of RG and RT, i.e., ω=RT/RG. Increasing the magnitude of ω ultimately improves the crashworthiness of tubes, including enhanced specific energy absorption, effectiveness of energy absorption and crushing force efficiency, while reducing the force fluctuation during the crushing process. Of the tubes studied, the edge-based hierarchical circular tube (EH_C) has the highest SEA of 22.17 J/g, which is 133%, 60% and 41% larger than that of single-celled square, hexagonal and circular tubes, respectively.

Detection of slow slip events along the southern Peru - northern Chile subduction zone

Detections of slow slip events (SSEs) are now common along most plate boundary fault systems at the global scale. However, no such event has been described in the south Peru - north Chile subduction zone so far, except for the early preparatory phase of the 2014 Iquique earthquake. We use geodetic template matching on GNSS-derived time series of surface motion in Northern Chile to extract SSEs hidden within the geodetic noise. We detect 33 events with durations ranging from 9 to 40 days and magnitudes from Mw 5.6 to 6.2. The moment released by these aseismic events seems to scale with the cube of their duration, suggesting a dynamic comparable to that of earthquakes. We compare the distribution of SSEs with the distribution of coupling along the megathrust derived using Bayesian inference on GNSS- and InSAR-derived interseismic velocities. From this comparison, we obtain that most SSEs occur in regions of intermediate coupling where the megathrust transitions from locked to creeping or where geometrical complexities of the interplate region have been proposed. We finally discuss the potential role of fluids as a triggering mechanism for SSEs in the area.

A Multiplex Rupture Sequence Under Complex Fault Network Due To Preceding Earthquake Swarms During the 2024 Mw 7.5 Noto Peninsula, Japan, Earthquake

AbstractA devastating earthquake with moment magnitude 7.5 occurred in the Noto Peninsula in central Japan on 1 January 2024. We estimate the rupture evolution of this earthquake from teleseismic P‐wave data using the potency‐density tensor inversion method, which provides information on the spatiotemporal slip distribution including fault orientations. The results show a long and quiet initial rupture phase that overlaps with regions of preceding earthquake swarms and associated aseismic deformation. The following three major rupture episodes evolve on segmented, differently oriented faults bounded by the initial rupture region. The irregular initial rupture process followed by the multi‐scale rupture growth is considered to be controlled by the preceding seismic and aseismic processes and the geometric complexity of the fault system. Such a discrete rupture scenario, including the triggering of an isolated fault rupture, adds critical inputs on the assessment of strong ground motion and associated damages for future earthquakes.

TECHNOLOGY FOR COMBINING THE RESULTS OF 3D LASER SCANNING FROM DIFFERENT STATIONS USING PLANE MARKS

3D laser scanning is a promising technology gaining popularity and active use worldwide. One of the advantages of 3D laser scanning is the speed of the scanning process and processing of the results. Compared to other geodetic instruments, this technology allows for displaying large objects in a much shorter time and more efficiently. For example, at the construction stage of an industrial plant, scanning enables monitoring the shapes and sizes of all its elements in real time, which is critical for controlling and optimising construction processes. Another important aspect is the geometric complexity of objects. Many objects can have complex shapes or similar elements of considerable length. When combining scanning results from different stations, it is necessary to ensure the accuracy and correct geometry of the object. To combine scan results, designated markers in the form of spheres and plane marks are used. However, unlike spheres, plane markers can be more convenient and economical. In addition, they can be left on the object for a long time, which significantly simplifies the additional scanning or data correction. It is also notable that in our time, the development of laser scanning technologies has led to new scanners that can automatically stitch together scan results by using advanced technology to track characteristic points in the environment. Despite the significant advantages of this new technology in terms of efficiency and accuracy, it is worth noting that it is rather expensive. Accordingly, scanners that do not have this advanced technology rely on alternative methods of stitching together scan results, such as placing plane marks on the object. The article aims to develop a technology for combining the results of 3D laser scanning from different stations using plane marks. The article considers the evaluation of the technical characteristics of the Trimble TX6 laser scanner, the analysis of options for using plane marks to ensure scanning accuracy, and the identification of the advantages and disadvantages of this method. Keywords: 3D laser scanning, plane marks, stitching algorithm, point cloud, Trimble RealWorks.

HyperGCN: an effective deep representation learning framework for the integrative analysis of spatial transcriptomics data

BackgroundAdvances of spatial transcriptomics technologies enabled simultaneously profiling gene expression and spatial locations of cells from the same tissue. Computational tools and approaches for integration of transcriptomics data and spatial context information are urgently needed to comprehensively explore the underlying structure patterns. In this manuscript, we propose HyperGCN for the integrative analysis of gene expression and spatial information profiled from the same tissue. HyperGCN enables data visualization and clustering, and facilitates downstream analysis, including domain segmentation, the characterization of marker genes for the specific domain structure and GO enrichment analysis.ResultsExtensive experiments are implemented on four real datasets from different tissues (including human dorsolateral prefrontal cortex, human positive breast tumors, mouse brain, mouse olfactory bulb tissue and Zabrafish melanoma) and technologies (including 10X visium, osmFISH, seqFISH+, 10X Xenium and Stereo-seq) with different spatial resolutions. The results show that HyperGCN achieves superior clustering performance and produces good domain segmentation effects while identifies biologically meaningful spatial expression patterns. This study provides a flexible framework to analyze spatial transcriptomics data with high geometric complexity.ConclusionsHyperGCN is an unsupervised method based on hypergraph induced graph convolutional network, where it assumes that there existed disjoint tissues with high geometric complexity, and models the semantic relationship of cells through hypergraph, which better tackles the high-order interactions of cells and levels of noise in spatial transcriptomics data.

Identifying imaging challenges for 1D and 3D geometric complexity (LG space)

In some situations, it is difficult to image seismic data even when factors such as illumination, anisotropy, and attenuation are resolvable. An often-overlooked but dominant factor affecting imaging is the geometric complexity of subsurface reflectors. In some of these settings, we propose that geometric complexity plays a dominant role in the quality of seismic imaging. This has been documented in subsalt regions with poor image quality where 3D vertical seismic profiles (VSPs) are available. VSPs often demonstrate that there is good illumination below salt, but the complexity of the observed downgoing wave and diffractions cannot be simulated with smooth earth models. We use synthetic examples with high geometric complexity and no other complications to analyze the imaging process: a 2D sediment-salt model with rough salt-top topography, and a 1D model with complex reflectivity. In these models, it is difficult to estimate velocity, and it is challenging to image the data. These synthetic examples are useful to understand the limitations of imaging with smooth models, to create guidelines to identify geometric complexity in field data, and to develop possible mitigations to improve imaging. Further real data examples will be needed to test geometric complexity.