Shape Space Research Articles

An efficient heuristic for geometric analysis of cell deformations.

Sickle cell disease causes erythrocytes to become sickle-shaped, affecting their movement in the bloodstream and reducing oxygen delivery. It has a high global prevalence and places a significant burden on healthcare systems, especially in resource-limited regions. Automated classification of sickle cells in blood images is crucial, allowing the specialist to reduce the effort required and avoid errors when quantifying the deformed cells and assessing the severity of a crisis. Recent studies have proposed various erythrocyte representation and classification methods (Jennifer et al., 2023 [1]). Since classification depends solely on cell shape, a suitable approach models erythrocytes as closed planar curves in shape space (Epifanio et al., 2020). This approach employs elastic distances between shapes, which are invariant under rotations, translations, scaling, and reparameterizations, ensuring consistent distance measurements regardless of the curves' position, starting point, or traversal speed. While previous methods exploiting shape space distances had achieved high accuracy, we refined the model by considering the geometric characteristics of healthy and sickled erythrocytes. Our method proposes (1) to employ a fixed parameterization based on the major axis of each cell to compute distances and (2) to align each cell with two templates using this parameterization before computing distances. Aligning shapes to templates before distance computation, a concept successfully applied in areas such as molecular dynamics (Richmond et al., 2004 [2]), and using a fixed parameterization, instead of minimizing distances across all possible parameterizations, simplifies calculations. This strategy achieves 96.03% accuracy rate in both supervised classification and unsupervised clustering. Our method ensures efficient erythrocyte classification, maintaining or improving accuracy over shape space models while significantly reducing computational costs.

Active axial motion compensation in multiphoton-excited fluorescence microscopy.

In living organisms, the natural motion caused by heartbeat, breathing, or muscle movements leads to the deformation of tissue caused by translation and stretching of the tissue structure. This effect results in the displacement or deformation of the plane of observation for intravital microscopy and causes motion-induced aberrations of the resulting image data. This, in turn, places severe limitations on the time during which specific events can be observed in intravital imaging experiments. These limitations can be overcome if the tissue motion can be compensated such that the plane of observation remains steady. We have developed a mathematical shape space model that can predict the periodic motion of a cylindrical tissue phantom resembling blood vessels. This model is then used to rapidly calculate the future position of the plane of observation of a two-photon laser scanning fluorescence microscope. The focal plane is continuously adjusted to the calculated position with a piezo-actuated objective lens holder. We demonstrate active motion compensation for non-harmonic axial displacements of the vessel phantom with a field of view up to 400 µm × 400 µm, vertical amplitudes of more than 100 µm, and at a rate of 0.5 Hz.

Riemannian Shape Optimization of Thin Shells Using Isogeometric Analysis

ABSTRACTIn this contribution, we consider the optimal shape design of thin elastic shell structures based on a linearized shell model of Koiter's type, whose shape can be described by a surface immersed in three‐dimensional Euclidean space. We regard the set of unparametrized immersions of the surface as an infinite‐dimensional Riemannian shape space and perform optimization in this setting using the Riemannian shape gradient. Nonuniform rational basis splines (NURBS) are employed to discretize the shell and numerically solve the underlying equations that govern its mechanical behavior via isogeometric analysis. By representing NURBS patches as B‐spline patches in real projective space, NURBS weights can also be incorporated into the optimization routine. We discuss the practical implementation of the method and demonstrate our approach on the compliance minimization of a half‐cylindrical shell under static load and fixed area constraint.

How does optimal prey abundance shape space use by a territorial raptor?

Understanding predator-prey interactions is important to determine the inter-relationships between species. Optimal foraging theory states that predators balance out energy expended with the energy gained from their prey. In the Iberian Peninsula, the European rabbit (Oryctolagus cuniculus) is a key prey species for endangered Bonelli’s eagle (Aquila fasciata). Thus, it is vital to understand how changes in rabbit abundance can influence habitat selection and territory use by Bonelli’s eagle. We studied 11 radio-tagged Bonelli’s eagles in their territories in Catalonia (NE Iberian Peninsula) and analysed the relationship between rabbit relative abundance, habitat selection and territory use of eagles. Rabbit relative abundance varied between territories, with shrublands hosting more rabbits, and eagles preferred shrublands and open areas for foraging and avoided dense forests. Spatial use by territorial eagles correlated positively with rabbit abundance in rabbit-rich territories, thereby supporting the idea that prey availability influences habitat selection. This result confirms optimal foraging strategies given that open habitats including shrublands tended to host more rabbits, thus providing better opportunities for prey detection and capture. Therefore, maintaining rabbit populations and their habitats (i.e., preserving open Mediterranean shrublands) would seem to be crucial for Bonelli’s eagle conservation. Our findings improve our understanding of predator-prey interactions and highlight the relationship between habitat structure, prey abundance and predator behaviour. In addition, our results emphasize the need for targeted conservation strategies designed to safeguard endangered species such as Bonelli’s eagle and maintain ecosystem integrity.

Writing Transpacifically: Planning Theory / Theorist Yet-To-Come

This paper ponders the transpacific flows from a planning perspective. We planners and planning theorists, whose job shapes space, know transpacific financial, material and labour flows condensing as real estate can exacerbate imperial geographies. We know the ’trans‘ in the transpacific has an unmappable speed. Given these conditions, how might planning’s theoretical texts look like, while critically engaging the transpacific flows as well as planning’s role in exacerbation of imperial geographies? How could planning theory refuse the frequent demand for it to produce images of the future? Could texts be tools made of visual, conceptual or visual forces that readers can connect to other texts or social actions to initiate other ways to unsettle imperial geographies? To explore theoretical-texts as tools, this papers weaves in a quasi autoethnographic style, in the main-text and a series of collages, to query its own writing and thinking processes in this unimageable transpacific: What is a theorist or theory’s role in the transpacific, their relation to practice, and to ethics and hope? How to open the relation between theorist, people, knowledge, thinking and place? It asks as a refrain: What is the concept of ‘writing transpacifically’ becoming while writing, reading and thinking in the transpacific?

Classification of Red Blood Cells in the Kendall Space of Reflection Shapes

Classification of Red Blood Cells in the Kendall Space of Reflection Shapes

Shape-based disease grading via functional maps and graph convolutional networks with application to Alzheimer’s disease

Shape analysis provides methods for understanding anatomical structures extracted from medical images. However, the underlying notions of shape spaces that are frequently employed come with strict assumptions prohibiting the analysis of incomplete and/or topologically varying shapes. This work aims to alleviate these limitations by adapting the concept of functional maps. Further, we present a graph-based learning approach for morphometric classification of disease states that uses novel shape descriptors based on this concept. We demonstrate the performance of the derived classifier on the open-access ADNI database differentiating normal controls and subjects with Alzheimer’s disease. Notably, the experiments show that our approach can improve over state-of-the-art from geometric deep learning.

‘The next five years will be a crucial time’: meet the analyst shaping space policy

‘The next five years will be a crucial time’: meet the analyst shaping space policy

“Girls doing a big job” in diaspora: cosmopolitan minority and making modern Chinese women associations in white Australia

ABSTRACT During Australia's “White Australia” policy (1901-1973), Chinese women in Sydney defied limitations through voluntary work. Starting with social clubs and local relief funds, their efforts culminated in the 1954 Chinese Women's Association of Australia (CWAA). This study explores how these women navigated inclusion and exclusion by leveraging their voluntary efforts. Fundraising, cultural events, and community activities became platforms for them to express their evolving identities and reshape social dynamics. The paper argues that cultural practices empowered women-led Chinese voluntary organizations in the diaspora. It introduces the concept of a “cosmopolitan minority,” where “Chineseness” is performed identities transcending race or ethnicity alone. Cosmopolitan life allowed these women to leverage intercultural understanding for navigating their complex situation and fostering resilience. Through collaboration and community building, they strategically performed their heritage, ultimately shaping associations and spaces to assert agency and define their ideal lives within the diaspora.

Badania nad zachowaniem zasad ładu przestrzennego w perspektywach rozwoju miasta Nowy Targ

The study aims to analyse the functioning of the city of Nowy Targ in the context of maintaining the principles of spatial order. The concept of spatial order is used not only by city planners, but also by other representatives of sciences related to spatial management. Spatial order is an interdisciplinary concept as it appears in many fields of sciences, not only technical ones. Inextricably linked to the idea of sustainable development, spatial order combines issues from urban planning, architecture, economy, and environmental protection. It can be considered in relation to several categories, such as: conscious space design, development of appropriate spatial patterns, protection of characteristic spatial systems, shaping space in accordance with tradition and culture, and counteracting spatial disharmony trends. This study begins by discussing various definitions of spatial order found in the literature. A study on the maintenance of the principles of spatial order in Nowy Targ covered a range of factors from the socio-economic, functional, cultural, environmental to compositional and aesthetic. While developing such a topic it is important to verify the stages of implementation of the assumptions of source documentation, like the ‘Nowy Targ City Development Strategy for 2019-2023 with an outlook to 2030’. The following research tools were used in the study: Desk Research (a review of publicly available data, including a study of legal regulations and a review of the literature on the subject) and CAWI (Computer Assisted Web Interviews – an online survey addressed to a wider audience). The results of the analyses showed Nowy Targ’s significant potential for the implementation of spatial order principles and high social awareness of the need to respect them by its inhabitants.

Museum Educators Perspective of Failure: A Collective Frame Analysis

ABSTRACTMuseums offer a unique role and safe space in shaping how youth view and react to experiences with failure. The purpose of this study was to add to the conversation around failure in out‐of‐school learning, particularly from the perspective of educators within museum settings that implement STEAM‐related making exhibits, workshops, and/or camps for youth. We analyzed approximately 9 h of video data from two sources: video recordings of virtual group meetings with 14 museum educators from six partnering institutions, and video recordings from five of the individual partnering sites discussing failure as a concept within their organization and programming. In this article, we demonstrate how the framings of failure by museum educators are bounded, and transformed, by un/seen external forces that ultimately impact the professional practices of educators in their organizations. We contend that the significance of this study lies in how perspectives around failure are produced and how they influence educators' professional practice, specifically in how failure is framed and communicated within STEAM‐related learning opportunities in museum settings.

Designing a Psychiatric Center in Ngaoundéré : When Architecture Becomes Therapeutic

Architecture plays a crucial role in shaping spaces that influence human behavior and well-being. In the context of mental health, therapeutic architecture has emerged as a powerful tool to enhance patient care and recovery. This article focuses on the design of a psychiatric center in Ngaoundere, where the principles of therapeutic architecture are applied to create a healing environment. By incorporating thoughtful spatial layouts, natural light, and soothing materials, the center aims to support the mental well-being of its patients. The project highlights how architectural design can specifically address the needs of psychiatric care in Ngaoundere, offering a new approach to healthcare in the region.

Relation Constrained Capsule Graph Neural Networks for Non-Rigid Shape Correspondence

Non-rigid 3D shape correspondence aims to establish dense correspondences between two non-rigidly deformed 3D shapes. However, the variability and symmetry of non-rigid shapes usually lead to mismatches due to shape deformation, topological changes, or data with severe noise. To finding an accurate correspondence between 3D dynamic shapes for the local deformation complexity, this article proposes a Relation Constrained Capsule Graph Network (RC-CGNet), which combines global and local features by encouraging the relation constraints between the embedding feature space and the input shape space based on the functional maps framework. Specifically, we design a Diffusion Graph Attention Network (DGANet) to segment the surface into parts with correct edge boundary between two regions. The Minimum Spanning Tree (MST) of geodesic curves among the singularities obtained from the segmented parts is added as relation constraints, which can compute isometric correspondences in both direct and symmetric directions. Besides that, the relation-and-attention constrained neural networks are designed to learn the shape correspondence via attention-aware CapsNet and functional maps under relation constraints. To improve the convergence speed and matching accuracy, we propose an optimized residual network structure based on the Nesterov Accelerated Gradient (NAG) to extract local features, and use graph convolution structure to extract global features. Moreover, a lightweight Gated Attention Module (GAM) is designed to fuse global and local features to obtain a richer feature representation. Since the capsule network has better spatial reasoning ability than the traditional convolutional neural network, our novel network architecture is a dual-route capsule network based on Routing Attention Fusion Block (RAFB), filtering low-discriminative capsules from a holistic view by exploiting geometric hierarchical relationships of semantic parts. Experiments on open datasets show that our method has excellent accuracy and wide adaptability.

Shape Mediation Analysis in Alzheimer's Disease Studies.

As a crucial tool in neuroscience, mediation analysis has been developed and widely adopted to elucidate the role of intermediary variables derived from neuroimaging data. Typically, structural equation models (SEMs) are employed to investigate the influences of exposures on outcomes, with model coefficients being interpreted as causal effects. While existing SEMs have proven to be effective tools for mediation analysis involving various neuroimaging-related mediators, limited research has explored scenarios where these mediators are derived from the shape space. In addition, the linear relationship assumption adopted in existing SEMs may lead to substantial efficiency losses and decreased predictive accuracy in real-world applications. To address these challenges, we introduce a novel framework for shape mediation analysis, designed to explore the causal relationships between genetic exposures and clinical outcomes, whether mediated or unmediated by shape-related factors while accounting for potential confounding variables. Within our framework, we apply the square-root velocity function to extract elastic shape representations, which reside within the linear Hilbert space of square-integrable functions. Subsequently, we introduce a two-layer shape regression model to characterize the relationships among neurocognitive outcomes, elastic shape mediators, genetic exposures, and clinical confounders. Both estimation and inference procedures are established for unknown parameters along with the corresponding causal estimands. The asymptotic properties of estimated quantities are investigated as well. Both simulated studies and real-data analyses demonstrate the superior performance of our proposed method in terms of estimation accuracy and robustness when compared to existing approaches for estimating causal estimands.

Surface Flux Transport Modeling Using Physics-informed Neural Networks

Studying the magnetic field properties on the solar surface is crucial for understanding the solar and heliospheric activities, which in turn shape space weather in the solar system. Surface flux transport (SFT) modeling helps us to simulate and analyze the transport and evolution of magnetic flux on the solar surface, providing valuable insights into the mechanisms responsible for solar activity. In this work, we demonstrate the use of machine learning techniques in solving magnetic flux transport, making it accurate. We have developed a novel physics-informed neural network (PINN)-based model to study the evolution of bipolar magnetic regions using SFT in one-dimensional azimuthally averaged and also in two dimensions. We demonstrate the efficiency and computational feasibility of our PINN-based model by comparing its performance and accuracy with that of a numerical model implemented using the Runge–Kutta implicit–explicit scheme. The mesh-independent PINN method can be used to reproduce the observed polar magnetic field with better flux conservation. This advancement is important for accurately reproducing observed polar magnetic fields, thereby providing insights into the strength of future solar cycles. This work paves the way for more efficient and accurate simulations of solar magnetic flux transport and showcases the applicability of PINNs in solving advection–diffusion equations with a particular focus on heliophysics.

Relationships between capnogram parameters by mainstream and sidestream techniques at different breathing frequencies

Capnography, routinely used in operating rooms and intensive care units, reveals essential information on lung ventilation and ventilation–perfusion matching. Mainstream capnography directly measures CO2 in the breathing circuit for accurate analysis and is considered a reference technique. Sidestream capnography, however, analyzes gas away from the patient leading to potentially less accurate measures. While these methodological differences impact the capnogram indices in mechanically ventilated patients, such assessments during spontaneous breathing are essentially lacking. Accordingly, we aimed to compare mainstream and sidestream capnography in spontaneously breathing subjects, focusing on differences in capnogram shape and dead space indices at various respiratory rates. Simultaneous mainstream and sidestream time and volumetric capnography were performed on spontaneously breathing adults (n = 35). Measurements were performed during controlled low (10/min), medium (12/min), and high (20/min) breathing rates as a challenge. Correlation and Bland–Altman analyses were used to assess trends and agreements between time and volumetric capnography indices obtained by the mainstream and sidestream techniques, including end-tidal CO2 (ETCO2), shape factors reflecting the slopes of phases 2 and 3, and anatomical and physiological dead space fractions. ETCO2 and physiological dead space measured by mainstream and sidestream techniques showed excellent correlations (r > 0.90, p < 0.001 for all breathing rates) and agreements. While strong correlations and moderate agreements were evidenced in the parameters reflecting the late phase of expiration (phase 3 slope and exhaled CO2 volume), these relationships were weaker for indices related to the early phase of expiration (phase 2 slope, anatomical dead space). Changing breathing frequency caused significant alterations in all capnography parameters, which were detectable by both mainstream and sidestream techniques. Sidestream capnography cannot substitute the more accurate mainstream technique for measuring the absolute values of shape factors and ventilation dead space fractions. However, sidestream capnography is also able to detect and track changes in uneven alveolar emptying, ventilation–perfusion matching and ventilation dead space fraction in spontaneously breathing subjects.

Enhanced energy harvesting in low-velocity water by downstream interference for piezoelectric energy harvester

The vibration of a single-degree-of-freedom bluff body positioned in water is intensified by the positive excitation, which is affected by the upstream interfering body and also by the downstream obstacles. This paper investigates the effect of downstream interference on galloping piezoelectric energy harvester performance. A mathematical model of the piezoelectric energy harvester under disturbance is established based on the extended Hamilton’s principle, and the theoretical output is further derived. The accuracy of proposed model is verified by the results of circulating water channel experiment. The effect of interference shape and approximate spacing (L/D) on system output is further analyzed, and the results show that the harvester performance is substantially improved when the distance between the bluff body and downstream interference is sufficiently small, and the interference is an elliptical cylinder with an aspect ratio of 0.6, i.e., the output power is 0.624 mW, which is improved by 24.39 % when L/D=1.8 and U=0.5m/s. Precise numerical calculations are further utilized to indicate that the harvester’s output performance is optimal when the downstream interference angle is 30°.

Trabecular Meshwork Abnormalities in a Model of Congenital Glaucoma Due to LTBP2 Mutation.

To characterize early trabecular meshwork (TM) morphologic abnormalities in a feline model of human primary congenital glaucoma (PCG) caused by mutation in LTBP2. Eyes from 41 cats, including 19 normal and 22 homozygous for LTBP2 mutation, across various postnatal stages (birth, 2 weeks, 5 weeks, and 12 weeks) were paraformaldehyde fixed, anterior segments dissected, post-fixed in glutaraldehyde, osmicated, and processed and sectioned for transmission electron microscopy. Cell morphology, nuclear shape, and intertrabecular space (ITS) were quantitatively assessed, and the structure of the fibrillar extracellular matrix in the TM was systematically evaluated. The earliest differences in TM morphology between PCG and normal cats were identified at 2 weeks postnatally. Elastic fibers in the TM were discontinuous and disorganized (P = 0.0122), and by 5 weeks of age PCG cats presented significantly less ITS (P = 0.0076) and morphologically rounder TM cells than normal cats (P = 0.0293). By 12 weeks of age, the ITS was further collapsed (P < 0.0001), and the TM cells were morphologically elongated and attenuated in PCG compared to controls (P = 0.0028). In this feline model of PCG due to LTBP2 mutation, development of ultrastructural TM extracellular matrix abnormalities are first observed by 2 weeks and cellular abnormalities by 5 weeks of age. By 12 weeks of age, when intraocular pressure becomes significantly elevated, the TM morphologic abnormalities are already well established. These findings suggest that the postnatal period between 0 and 5 weeks of age is critical for TM and PCG development and progression in cats.

Enhanced Drag Force Estimation in Automotive Design: A Surrogate Model Leveraging Limited Full-Order Model Drag Data and Comprehensive Physical Field Integration

In this paper, a novel surrogate model for shape-parametrized vehicle drag force prediction is proposed. It is assumed that only a limited dataset of high-fidelity CFD results is available, typically less than ten high-fidelity CFD solutions for different shape samples. The idea is to take advantage not only of the drag coefficients but also physical fields such as velocity, pressure, and kinetic energy evaluated on a cutting plane in the wake of the vehicle and perpendicular to the road. This additional “augmented” information provides a more accurate and robust prediction of the drag force compared to a standard surface response methodology. As a first step, an original reparametrization of the shape based on combination coefficients of shape principal components is proposed, leading to a low-dimensional representation of the shape space. The second step consists in determining principal components of the x-direction momentum flux through a cutting plane behind the car. The final step is to find the mapping between the reduced shape description and the momentum flux formula to achieve an accurate drag estimation. The resulting surrogate model is a space-parameter separated representation with shape principal component coefficients and spatial modes dedicated to drag-force evaluation. The algorithm can deal with shapes of variable mesh by using an optimal transport procedure that interpolates the fields on a shared reference mesh. The Machine Learning algorithm is challenged on a car concept with a three-dimensional shape design space. With only two well-chosen samples, the numerical algorithm is able to return a drag surrogate model with reasonable uniform error over the validation dataset. An incremental learning approach involving additional high-fidelity computations is also proposed. The leading algorithm is shown to improve the model accuracy. The study also shows the sensitivity of the results with respect to the initial experimental design. As feedback, we discuss and suggest what appear to be the correct choices of experimental designs for the best results.

Dental arch shape in twins: A morphometric study of genetic influences

The objective of this study was to assess the relative contribution of genes to shape variation in the permanent dental arches in individuals of Western European descent. The dental casts from 64 monozygotic and 38 dizygotic twins, housed in the Adelaide Dental School's twin record collection, Australia, were assessed. The subjects were of Western European descent, with a mean age of 19.4 ± 5.4 years. Dental casts were scanned using a 3-dimensional scanner (3Shape E4, 3Shape, Copenhagen, Denmark), and landmarks were placed on incisal edges and cusp tips of canines, premolars, and molars. Procrustes superimposition and principal components analysis were applied to examine shape variation. Two-block partial least-squares analysis was used to assess shape covariation between arches. Structural equation modeling was utilized to decompose observed shape variation into genetic and environmental components using the normal assumptions of the twin model. The first 3 principal components (PCs) of the maxillary and mandibular arch were meaningful, accounting for 53% and 50% of the variation in shape space, respectively. The PCs represented shape variability as follows: PC1 - arch depth-width ratio, PC2 - arch taper, canine position (and first premolar rotation for the mandibular arch), and PC3 - incisor displacement and rotation. Genetic modeling indicated that a model incorporating additive genetic and unique environmental factors optimally explained the observed variation for all meaningful PCs. Within shape space, most of the variation in maxillary and mandibular arches exhibited moderate to high heritability (h2= 0.61-0.74). Maxillary and mandibular dental arches had strong and significant shape covariation, with high heritability in their reciprocal influences on shape (h2= 0.72-0.74; rpls coefficient= 0.87; P<0.05). In this cohort, dental arch shape variation was predominantly influenced by genetic factors. High covariation and heritability were observed between the maxillary and mandibular dental arches. This information may help inform decisions around orthodontic intervention.