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1. Universal deformations and inhomogeneities in isotropic Cauchy elasticity

   https://doi.org/10.1098/rspa.2024.0229  

   Yavari, Arash (July 2024, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences)

   For a given class of materials, universal deformations are those deformations that can be maintained in the absence of body forces and by applying solely boundary tractions. For inhomogeneous bodies, in addition to the universality constraints that determine the universal deformations, there are extra constraints on the form of the material inhomogeneities—universal inhomogeneity constraints. Those inhomogeneities compatible with the universal inhomogeneity constraints are called universal inhomogeneities. In a Cauchy elastic solid, stress at a given point and at an instance of time is a function of strain at that point and that exact moment in time, without any dependence on prior history. A Cauchy elastic solid does not necessarily have an energy function, i.e. Cauchy elastic solids are, in general, non-hyperelastic (or non-Green elastic). In this paper, we characterize universal deformations in both compressible and incompressible inhomogeneous isotropic Cauchy elasticity. As Cauchy elasticity includes hyperelasticity, one expects the universal deformations of Cauchy elasticity to be a subset of those of hyperelasticity both in compressible and incompressible cases. It is also expected that the universal inhomogeneity constraints to be more stringent than those of hyperelasticity, and hence, the set of universal inhomogeneities to be smaller than that of hyperelasticity. We prove the somewhat unexpected result that the sets of universal deformations of isotropic Cauchy elasticity and isotropic hyperelasticity are identical, in both the compressible and incompressible cases. We also prove that their corresponding universal inhomogeneities are identical as well. 

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2. Condition Monitoring and Fault Diagnosis of Generators in Power Networks

   Yang, Bowen; Li, Fangyu; Ye, Jin; Song, Wenzhan. (August 2019, IEEE Power & Energy Society General Meeting)

   In this paper, a novel hierarchical signal processing methodology is proposed for generator condition monitoring and fault diagnosis based on raw electrical waveform data in power networks, which can often be measured by strategically located waveform sensors. The impact of generator short circuit faults on strategically located electrical waveform sensors in power networks are firstly investigated and validated in Matlab Simulink. Based on the large set of electrical waveform data produced by Matlab Simulink, a hierarchical algorithm is then designed to locate fault site location and monitor the condition of generators in power networks. Finally, the proposed methodology is validated in 14-bus IEEE standard power network under different scenarios (e.g, one generator fault, two-generator-fault, various aging levels, etc). Our results show that we can locate fault site location and monitor the aging condition of generators in power networks. Compared to traditional condition monitoring and fault diagnosis based on generator sensors, our proposed methodology can monitor a large number of generators based on a limited number of waveform sensors, which promises to reduce the cost of the maintenance and improve the reliability of the power grid. 

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3. Private Vector Mean Estimation in the Shuffle Model: Optimal Rates Require Many Messages

   Asi, Hilal; Feldman, Vitaly; Nelson, Jelani; Nguyen, Huy L; Talwar, Kunal; Zhou, Samson (July 2024, Proceedings of Machine Learning Research)

   We study the problem of private vector mean estimation in the shuffle model of privacy where n users each have a unit vector v^{(i)} in R^d. We propose a new multi-message protocol that achieves the optimal error using O~(min(n*epsilon^2, d)) messages per user. Moreover, we show that any (unbiased) protocol that achieves optimal error requires each user to send Omega(min(n*epsilon^2,d)/log(n)) messages, demonstrating the optimality of our message complexity up to logarithmic factors. Additionally, we study the single-message setting and design a protocol that achieves mean squared error O(dn^{d/(d+2)} * epsilon^{-4/(d+2)}). Moreover, we show that any single-message protocol must incur mean squared error Omega(dn^{d/(d+2)}), showing that our protocol is optimal in the standard setting where epsilon = Theta(1). Finally, we study robustness to malicious users and show that malicious users can incur large additive error with a single shuffler. 

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4. Rates of Protein Evolution across the Marsupial Phylogeny: Heterogeneity and Link to Life-History Traits

   https://doi.org/10.1093/gbe/evab277  

   Luzuriaga-Neira, Agusto R; Alvarez-Ponce, David (January 2022, Genome Biology and Evolution)

   Storz, Jay (Ed.)

   Abstract Despite the importance of effective population size (Ne) in evolutionary and conservation biology, it remains unclear what factors have an impact on this quantity. The Nearly Neutral Theory of Molecular Evolution predicts a faster accumulation of deleterious mutations (and thus a higher dN/dS ratio) in populations with small Ne; thus, measuring dN/dS ratios in different groups/species can provide insight into their Ne. Here, we used an exome data set of 1,550 loci from 45 species of marsupials representing 18 of the 22 extant families, to estimate dN/dS ratios across the different branches and families of the marsupial phylogeny. We found a considerable heterogeneity in dN/dS ratios among families and species, which suggests significant differences in their Ne. Furthermore, our multivariate analyses of several life-history traits showed that dN/dS ratios (and thus Ne) are affected by body weight, body length, and weaning age. 

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5. Uncovering material deformations via machine learning combined with four-dimensional scanning transmission electron microscopy

   https://doi.org/10.1038/s41524-022-00793-9  

   Shi, Chuqiao; Cao, Michael C.; Rehn, Sarah M.; Bae, Sang-Hoon; Kim, Jeehwan; Jones, Matthew R.; Muller, David A.; Han, Yimo (May 2022, npj Computational Materials)

   Abstract Understanding lattice deformations is crucial in determining the properties of nanomaterials, which can become more prominent in future applications ranging from energy harvesting to electronic devices. However, it remains challenging to reveal unexpected deformations that crucially affect material properties across a large sample area. Here, we demonstrate a rapid and semi-automated unsupervised machine learning approach to uncover lattice deformations in materials. Our method utilizes divisive hierarchical clustering to automatically unveil multi-scale deformations in the entire sample flake from the diffraction data using four-dimensional scanning transmission electron microscopy (4D-STEM). Our approach overcomes the current barriers of large 4D data analysis without a priori knowledge of the sample. Using this purely data-driven analysis, we have uncovered different types of material deformations, such as strain, lattice distortion, bending contour, etc., which can significantly impact the band structure and subsequent performance of nanomaterials-based devices. We envision that this data-driven procedure will provide insight into materials’ intrinsic structures and accelerate the discovery of materials. 

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