M&amp;M: blending medicine and music

Bronstein, Marcello D.

doi:10.20945/2359-3997000000161

Cited by 5 publications

(7 citation statements)

References 1 publication

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“…The algorithm is implemented on a 64-bit 32GB memory Windows 10 system, using Matlab 2019b as a visual development environment. The TOSCA high-resolution dataset 37 , SHREC2010 dataset 38 and SHREC2015-Canonical Forms dataset 39 are used for non-rigid 3D shape analysis experiments. The TOSCA high-resolution dataset contains 80 shapes with different isometric transformation postures and is divided into 9 categories, which including cats (11), dogs (9), wolves (3), horses (8), centaur (6), gorillas (4), victoria (12) and michael and david (7 and 20, respectively).…”

Section: Resultsmentioning

confidence: 99%

Scale-invariant Mexican Hat wavelet descriptor for non-rigid shape similarity measurement

Yan

Zhou

Zhang

et al. 2023

Sci Rep

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The Mexican Hat wavelet (MHW) is strictly derived from the heat kernel by taking its negative first-order derivative with respect to time t. As a solution to the heat equation that the heat kernel has a clear initial condition, the Laplace–Beltrami operator. Although the MHW descriptor can effectively characterize the model information, but it has poor robustness to the model with scale transformation, and the feature description performance is affected to some extent. Following a popular mathematical method, in this paper, we bases on the MHW to study scaling invariance and proposes a new shape descriptor, the scale-invariant Mexican Hat wavelet (SIMHW), which by logarithmic sampling and Fourier transform that obtains the expression of SIMHW in Fourier domain. The experimental results show that SIMHW has finer information description ability and stronger recognition ability, and has better robustness to various non-rigid transformations. It can correctly calculate the similarity between 3D shapes and realize the effective shape retrieval.

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Section: Resultsmentioning

confidence: 99%

Scale-invariant Mexican Hat wavelet descriptor for non-rigid shape similarity measurement

Yan

Zhou

Zhang

et al. 2023

Sci Rep

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“…However, this approach would amount to averaging the pairwise similarities without considering the higher-order structure of individual graphs. Other approaches include making the graph Laplacians commute approximately (Bronstein et al, 2013), or equivalently, jointly diagonalizing the graph Laplacians approximately (Eynard et al, 2015), as well as finding the geometric mean of the graph Laplacians (El Gheche et al, 2020).…”

Section: Mathematical Structure Of Graphsmentioning

confidence: 99%

Spectral clustering of single-cell multi-omics data on multilayer graphs

Zhang

Leistico

Cho

et al. 2022

Preprint

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Single-cell sequencing technologies that simultaneously generate multimodal cellular profiles present opportunities for improved understanding of cell heterogeneity in tissues. How the multimodal information can be integrated to obtain a common cell type identification, however, poses a computational challenge. Multilayer graphs provide a natural representation of multi-omic single-cell sequencing datasets, and finding cell clusters may be understood as a multilayer graph partition problem. We introduce two spectral algorithms on multilayer graphs, spectral clustering on multilayer graphs (SCML) and the weighted locally linear (WLL) method, to cluster cells in multi-omic single-cell sequencing datasets. We connect these algorithms through a unifying mathematical framework that represents each layer using a Hamiltonian operator and a mixture of its eigenstates to integrate the multiple graph layers, demonstrating in the process that the WLL method is a rigorous multilayer spectral graph theoretic reformulation of the popular Seurat weighted nearest neighbor (WNN) algorithm. Implementing our algorithms and applying them to a CITE-seq dataset of cord blood mononuclear cells yields results similar to the Seurat WNN analysis. Our work thus extends spectral methods to multimodal single-cell data analysis.

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“…The negatively charged IrCl6 2and PtCl6 2− are expected to mainly coordinate to cationic pyridinium groups by an electrostatic interaction. 51 A series of ten immersion baths were investigated in this work (see Supporting Information Table S3), where the immersion time was held constant for 10 min, only six of the baths are shown in Table 1. Each immersion bath is defined to include 100 mM H2SO4 and a total metal ion concentration of 10 mM, each differentiated by the following Pt:Ir molar ratios: 10:0, 9.75:0.25, 9.5:0.5, 9.0:1.0, 8.0:2.0, 7.5:2.5, 7.0:3.0, 5.0:5.0, 2.4:7.6, and 0:10.…”

Section: Arrays Of Ptir Nps From Diblock Copolymer Templatesmentioning

confidence: 99%