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1. Boundary Sketching with Asymptotically Optimal Distance and Rotation

   Dani, Varsha ; Islam, Abir ; Saia, Jared ( July 2023 , Structural Information and Communication Complexity)

   Rajsbaum, Sergio ; Balliu, Alkida ; Daymude, Joshua J. ; Olivetti, Dennis (Ed.)

   We address the problem of designing a distributed algorithm for two robots that sketches the boundary of an unknown shape. Critically, we assume a certain amount of delay in how quickly our robots can react to external feedback. In particular, when a robot moves, it commits to move along path of length at least λ, or turn an amount of radians at least λ for some positive λ ≤ (1/2)^6, that is normalized based on a unit diameter shape. Then, our algorithm outputs a polygon that is an ϵ-sketch, for ϵ = 8λ^(1/2), in the sense that every point on the shape boundary is within distance ϵ of the output polygon. Moreover, our costs are asymptotically optimal in two key criteria for the robots: total distance travelled and total amount of rotation. Additionally, we implement our algorithm, and illustrate its output on some specific shapes. 

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2. Characterizing Cell Shape Distributions Using k-Mode Kernel Mixtures

   https://doi.org/10.1109/ICPR56361.2022.9956604  

   Deng, Ximu ; Srivastava, Anuj ; Sarkar, Rituparna ; Labruyere, Elisabeth ; Olivo-Marin, Jean-Christophe ( August 2022 , 26th International Conference on Pattern Recognition (ICPR))

   This paper addresses the problem of characterizing statistical distributions of cellular shape populations using shape samples from microscopy image data. This problem is challenging because of the nonlinearity and high-dimensionality of shape manifolds. The paper develops an efficient, nonparametric approach using ideas from k-modal mixtures and kernel estimators. It uses elastic shape analysis of cell boundaries to estimate statistical modes and clusters given shapes around those modes. (Notably, it uses a combination of modal distributions and ANOVA to determine k automatically.) A population is then characterized as k-modal mixture relative to this estimated clustering and a chosen kernel (e.g., a Gaussian or a flat kernel). One can compare and analyze populations using the Fisher-Rao metric between their estimated distributions. We demonstrate this approach for classifying shapes associated with migrations of entamoeba histolytica under different experimental conditions. This framework remarkably captures salient shape patterns and separates shape data for different experimental settings, even when it is difficult to discern class differences visually. 

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3. Specimen alignment with limited point-based homology: 3D morphometrics of disparate bivalve shells (Mollusca: Bivalvia)

   https://doi.org/10.7717/peerj.13617  

   Edie, Stewart M. ; Collins, Katie S. ; Jablonski, David ( January 2022 , PeerJ)

   Background Comparative morphology fundamentally relies on the orientation and alignment of specimens. In the era of geometric morphometrics, point-based homologies are commonly deployed to register specimens and their landmarks in a shared coordinate system. However, the number of point-based homologies commonly diminishes with increasing phylogenetic breadth. These situations invite alternative, often conflicting, approaches to alignment. The bivalve shell (Mollusca: Bivalvia) exemplifies a homologous structure with few universally homologous points—only one can be identified across the Class, the shell ‘beak’. Here, we develop an axis-based framework, grounded in the homology of shell features, to orient shells for landmark-based, comparative morphology. Methods Using 3D scans of species that span the disparity of shell morphology across the Class, multiple modes of scaling, translation, and rotation were applied to test for differences in shell shape. Point-based homologies were used to define body axes, which were then standardized to facilitate specimen alignment via rotation. Resulting alignments were compared using pairwise distances between specimen shapes as defined by surface semilandmarks. Results Analysis of 45 possible alignment schemes finds general conformity among the shape differences of ‘typical’ equilateral shells, but the shape differences among atypical shells can change considerably, particularly those with distinctive modes of growth. Each alignment corresponds to a hypothesis about the ecological, developmental, or evolutionary basis of morphological differences, but we suggest orientation via the hinge line for many analyses of shell shape across the Class, a formalization of the most common approach to morphometrics of shell form. This axis-based approach to aligning specimens facilitates the comparison of approximately continuous differences in shape among phylogenetically broad and morphologically disparate samples, not only within bivalves but across many other clades. 

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4. A modal‐based Kalman filtering framework for mode extraction and decomposition of damped structures

   https://doi.org/10.1111/mice.12963  

   Hwang, Jae‐Seung ; Kwon, Dae Kun ; Kareem, Ahsan ( December 2022 , Computer-Aided Civil and Infrastructure Engineering)

   The mode shape is one of the important modal parameters that enables to visualize the intrinsic behavior of a structure as well as the quantity of interest by extracting or separating modal response from measurements. In this study, a new output‐only framework is proposed to extract modes using a modal‐based Kalman filter defined in the modal space and identify the mode shape by manipulating the correlation between the separated modes and the measured responses. It is also shown that the proposed framework can be extended to estimate the mode shapes of a non‐classically damped structure in state space when the state variable is constructed from the measured responses and applied to the modal‐based Kalman filter. The mode shape estimation framework proposed in this study was verified by numerical simulations and full‐scale measurements. From the verification examples and their results, it was noted that the proposed modal identification framework is not influenced by the presence of noise, and it can be applied to identify the state‐space mode shapes of non‐classically damped systems as well as systems with very closely distributed modes such as buildings equipped with tuned mass dampers.

    

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5. Experimental tests of bivalve shell shape reveal potential tradeoffs between mechanical and behavioral defenses

   https://doi.org/10.1038/s41598-020-76358-x  

   Johnson, Erynn H. ( November 2020 , Scientific Reports)

   Bivalves protect themselves from predators using both mechanical and behavioral defenses. While their shells serve as mechanical armor, bivalve shells also enable evasive behaviors such as swimming and burrowing. Therefore, bivalve shell shape is a critical determinant of how successfully an organism can defend against attack. Shape is believed to be related to shell strength with bivalve shell shapes converging on a select few morphologies that correlate with life mode and motility. In this study, mathematical modeling and 3D printing were used to analyze the protective function of different shell shapes against vertebrate shell-crushing predators. Considering what life modes different shapes permit and analyzing the strength of these shapes in compression provides insight to evolutionary and ecological tradeoffs with respect to mechanical and behavioral defenses. These empirical tests are the first of their kind to isolate the influence of bivalve shell shape on strength and quantitatively demonstrate that shell strength is derived from multiple shape parameters. The findings of this theoretical study are consistent with examples of shell shapes that allow escape behaviors being mechanically weaker than those which do not. Additionally, shell elongation from the umbo, a metric often overlooked, is shown to have significant effects on shell strength.

    

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