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The Surgery Step and ξ-Bordism
In this chapter manifolds are assumed to be smooth and we will take the first steps towards the solution of the following problem.
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Sullivan’s Juvenilia: Surgery and Algebraic Topology
Dennis Sullivan’s early work, despite being strongly motivated by geometric problems, had a strong algebraic nature, certainly much more so than his...
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Geometric Computing for Minimal Invasive Surgery
In this chapter, we show the treatment of a variety of tasks of medical robotics handled using a powerful, non-redundant coefficient geometric...
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Homotopy Spheres
This is a beautiful and illuminating example. It shows how the general surgery methods, which we have developed so far, apply to a concrete problem,...
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From Hyperbolic Dehn Filling to Surgeries in Representation Varieties
Hyperbolic Dehn surgery and the bending procedure provide two ways which can be used to describe hyperbolic deformations of a complete hyperbolic...
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The Centroid-Deformation Decomposition for Buoyant Vortex Patch Motion
The motion of a two-dimensional buoyant vortex patch, i. e., a vortex patch with a uniform density different from the uniform density of the...
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Biomimetic amelioration of zirconium nanoparticles on a rigid substrate over viscous slime — a physiological approach
In this article, an investigation is conducted to study the precise role of zirconium nanoparticles that exist in a slime-like fluid subject to...
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Classification of Pathologies on Medical Images Using the Algorithm of Random Forest of Optimal-Complexity Trees
The authors propose an approach to the construction of classifiers in the class of Random Forest algorithms. A genetic algorithm is used to determine...
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Areas in space, volumes
The area of polyhedral surfaces relies on the definitions and the properties of area of plane figures. Thus, the area of the surface of a rectangular...
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Artificial Intelligence for Digital Dentistry
Digital dentistry is evolving rapidly with the rapid innovation of artificial intelligence (AI) and the advancement of an AI-based digital platform...
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Equilibrium stressability of multidimensional frameworks
We prove an equilibrium stressability criterion for trivalent multidimensional frameworks. The criterion appears in different languages: (1) in terms...
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Ricci Solitons
This chapter provides the basic theory of Ricci flow, Ricci solitons, their examples, important properties and known results.
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Balian–Low Type Theorems on Homogeneous Groups
We prove strict necessary density conditions for coherent frames and Riesz sequences on homogeneous groups. Let N be a connected, simply connected...
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Peabodies of constant width
We describe a new family of 3-dimensional bodies of constant width that we have called peabodies, obtained from the Reuleaux tetrahedron by replacing...
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Families of Legendrians and Lagrangians with unbounded spectral norm
Viterbo has conjectured that any Lagrangian in the unit codisc bundle of a torus which is Hamiltonian isotopic.
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Slow–Fast Model and Therapy Optimization for Oncolytic Treatment of Tumors
The present work studies models of oncolytic virotherapy without space variable in which virus replication occurs at a faster time scale than tumor...
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Numerical Methods for Diagnosis and Therapy Design of Cerebral Palsy by Bilevel Optimal Control of Constrained Biomechanical Multi-Body Systems
In this chapter, we describe how to use mathematical optimization for diagnosis and treatment planning of cerebral palsy. We give background...
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Four-dimensional complete gradient shrinking Ricci solitons with half positive isotropic curvature
In this paper, we investigate the geometry of 4-dimensional complete gradient shrinking Ricci solitons with half positive isotropic curvature (half...