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Multidimensional Size Functions for Shape Comparison
TLDR
We prove that in Size Theory the comparison of multidimensional size functions can be reduced to the 1-dimensional case by a suitable change of variables. Expand
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Size Functions and Formal Series
  • P. Frosini, C. Landi
  • Mathematics, Computer Science
  • Applicable Algebra in Engineering, Communication…
  • 1 August 2001
TLDR
We prove that every size function can be represented as a set of points and lines in the real plane, with multiplicities. Expand
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Betti numbers in multidimensional persistent homology are stable functions
Multidimensional persistence mostly studies topological features of shapes by analyzing the lower level sets of vector-valued functions, called filtering functions. As is well known, in the case ofExpand
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Natural Pseudo-Distance and Optimal Matching between Reduced Size Functions
TLDR
This paper studies the properties of a new lower bound for the natural pseudo-distance. Expand
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A Mayer–Vietoris Formula for Persistent Homology with an Application to Shape Recognition in the Presence of Occlusions
TLDR
We show that persistent homology has a Mayer–Vietoris sequence that is generally not exact but only of order 2. Expand
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Describing shapes by geometrical-topological properties of real functions
TLDR
Differential topology, and specifically Morse theory, provide a suitable setting for formalizing and solving several problems related to shape analysis by combining the topological exploration of a shape with quantitative measurement of geometrical properties provided by a real function defined on the shape. Expand
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Solubilization methods and reference 2-DE map of cow milk fat globules.
Milk fat globules (MFGs) are secretory vesicles assembled and secreted by mammary epithelial cells during lactation. They consist of fat globules surrounded by a lipid bilayer membrane which isExpand
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Zebrafish Collagen Type I: Molecular and Biochemical Characterization of the Major Structural Protein in Bone and Skin
Over the last years the zebrafish imposed itself as a powerful model to study skeletal diseases, but a limit to its use is the poor characterization of collagen type I, the most abundant protein inExpand
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Protein pathways working in human follicular fluid: the future for tailored IVF?
The human follicular fluid (HFF) contains molecules and proteins that may affect follicle growth, oocyte maturation and competence acquiring. Despite the numerous studies, an integrated broadExpand
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Using matching distance in size theory: A survey
TLDR
In this survey we illustrate how the matching distance between reduced size functions can be applied for shape comparison. Expand
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