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1. Cortical Morphometry Analysis based on Worst Transportation Theory

   Zhang, Min; An, Dongsheng; Lei, Na; Wu, Jianfeng; Zhao, Tong; Xu, Xiaoyin; Wang, Yalin; Gu, Xianfeng (October 2021, IPMI 2021: Information Processing in Medical Imaging)

   null (Ed.)

   Biomarkers play an important role in early detection and intervention in Alzheimer’s disease (AD). However, obtaining effective biomarkers for AD is still a big challenge. In this work, we propose to use the worst transportation cost as a univariate biomarker to index cortical morphometry for tracking AD progression. The worst transportation (WT) aims to find the least economical way to transport one measure to the other, which contrasts to the optimal transportation (OT) that finds the most economical way between measures. To compute the WT cost, we generalize the Brenier theorem for the OT map to the WT map, and show that the WT map is the gradient of a concave function satisfying the Monge-Ampere equation. We also develop an efficient algorithm to compute the WT map based on computational geometry. We apply the algorithm to analyze cortical shape difference between dementia due to AD and normal aging individuals. The experimental results reveal the effectiveness of our proposed method which yields better statistical performance than other competiting methods including the OT. 

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2. Topological Surface States in a Gyroid Acoustic Crystal

   https://doi.org/10.1002/advs.202205723  

   Guo, Yuning; Rosa, Matheus_I_N; Ruzzene, Massimo (December 2022, Advanced Science)

   Abstract The acoustic properties of an acoustic crystal consisting of acoustic channels designed according to the gyroid minimal surface embedded in a 3D rigid material are investigated. The resulting gyroid acoustic crystal is characterized by a spin‐1 Weyl and a charge‐2 Dirac degenerate points that are enforced by its nonsymmorphic symmetry. The gyroid geometry and its symmetries produce multi‐fold topological degeneracies that occur naturally without the need for ad hoc geometry designs. The non‐trivial topology of the acoustic dispersion produces chiral surface states with open arcs, which manifest themselves as waves whose propagation is highly directional and remains confined to the surfaces of a 3D material. Experiments on an additively manufactured sample validate the predictions of surface arc states and produce negative refraction of waves at the interface between adjoining surfaces. The topological surface states in a gyroid acoustic crystal shed light on nontrivial bulk and edge physics in symmetry‐based compact continuum materials, whose capabilities augment those observed in ad hoc designs. The continuous shape design of the considered acoustic channels and the ensuing anomalous acoustic performance suggest this class of phononic materials with semimetal‐like topology as effective building blocks for acoustic liners and load‐carrying structural components with sound proofing functionality. 

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3. Dynamic Neural Surfaces for Elastic 4D Shape Representation and Analysis

   Nizamani, A; Laga, H; Wang, G; Boussaid, F; Bennamoun, M; Srivastava, A (July 2025, Proceedings IEEE Computer Society Conference on Computer Vision and Pattern Recognition)

   We propose a novel framework for the statistical analysis of genus-zero 4D surfaces, i.e., 3D surfaces that deform and evolve over time. This problem is particularly challenging due to the arbitrary parameterizations of these surfaces and their varying deformation speeds, necessitating effective spatiotemporal registration. Traditionally, 4D surfaces are discretized, in space and time, before computing their spatiotemporal registrations, geodesics, and statistics. However, this approach may result in suboptimal solutions and, as we demonstrate in this paper, is not necessary. In contrast, we treat 4D surfaces as continuous functions in both space and time. We introduce Dynamic Spherical Neural Surfaces (D-SNS), an efficient smooth and continuous spatiotemporal representation for genus-0 4D surfaces. We then demonstrate how to perform core 4D shape analysis tasks such as spatiotemporal registration, geodesics computation, and mean 4D shape estimation, directly on these continuous representations without upfront discretization and meshing. By integrating neural representations with classical Riemannian geometry and statistical shape analysis techniques, we provide the building blocks for enabling full functional shape analysis. We demonstrate the efficiency of the framework on 4D human and face datasets. The source code and additional results are available at https://4d-dsns.github.io/DSNS/. 

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4. Understanding monocyte-driven neuroinflammation in Alzheimer’s disease using human cortical organoid microphysiological systems

   https://doi.org/10.1126/sciadv.adu2708  

   Tian, Chunhui; Ao, Zheng; Cerneckis, Jonas; Cai, Hongwei; Chen, Lei; Niu, Hengyao; Takayama, Kazuo; Kim, Jungsu; Shi, Yanhong; Gu, Mingxia; et al (August 2025, Science Advances)

   Increasing evidence strongly links neuroinflammation to Alzheimer’s disease (AD) pathogenesis. Peripheral monocytes are crucial components of the human immune system, but their contribution to AD pathogenesis is still largely understudied partially due to limited human models. Here, we introduce human cortical organoid microphysiological systems (hCO-MPSs) to study AD monocyte-mediated neuroinflammation. By culturing doughnut-shape organoids on 3D-printed devices within standard 96-well plates, we generate hCO-MPSs with reduced necrosis, minimized hypoxia, and improved viability. Using these models, we found that monocytes from AD patients exhibit increased infiltration ability, decreased amyloid-β clearance capacity, and stronger inflammatory response than monocytes from age-matched control donors. Moreover, we observed that AD monocytes induce pro-inflammatory effects such as elevated astrocyte activation and neuronal apoptosis. Furthermore, the marked increase in IL1B and CCL3 expression underscores their pivotal role in AD monocyte-mediated neuroinflammation. Our findings provide insight into understanding monocytes’ role in AD pathogenesis, and our lab-compatible MPS models may offer a promising way for studying various neuroinflammatory diseases. 

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5. Approximating the Shape Operator with the Surface Hellan–Herrmann–Johnson Element

   https://doi.org/10.1137/22M1531968  

   Walker, Shawn W (April 2024, SIAM Journal on Scientific Computing)

   We present a finite element technique for approximating the surface Hessian of a discrete scalar function on triangulated surfaces embedded in $$\R^{3}$$, with or without boundary. We then extend the method to compute approximations of the full shape operator of the underlying surface using only the known discrete surface. The method is based on the Hellan--Herrmann--Johnson (HHJ) element and does not require any ad-hoc modifications. Convergence is established provided the discrete surface satisfies a Lagrange interpolation property related to the exact surface. The convergence rate, in $L^2$, for the shape operator approximation is $O(h^m)$, where $$m \geq 1$$ is the polynomial degree of the surface, i.e. the method converges even for piecewise linear surface triangulations. For surfaces with boundary, some additional boundary data is needed to establish optimal convergence, e.g. boundary information about the surface normal vector or the curvature in the co-normal direction. Numerical examples are given on non-trivial surfaces that demonstrate our error estimates and the efficacy of the method. 

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