Biological Shape Analysis with Geometric Statistics and Learning

Snapshots of modern mathematics from Oberwolfach

Biological Shape Analysis with Geometric Statistics and Learning

The advances in biomedical imaging techniques have enabled us to access the 3D shapes of a variety of structures: organs, cells, proteins. Since biological shapes are related to physiological functions, shape data may hold the key to unlocking outstanding mysteries in biomedicine. This snapshot introduces the mathematical framework of geometric statistics and learning and its applications to biomedicine.

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Mathematical subjects

Geometry and Topology
Probability Theory and Statistics

Connections to other fields

Computer Science
Life Science

Author(s)

Saiteja Utpala, Nina Miolane

License

DOI (Digital Object Identifier)

10.14760/SNAP-2022-008-EN

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snapshot-2022-008.pdf

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snapshots: overview

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The geometry of fair division
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The periodic tables of algebraic geometry
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Patterns and waves in theory, experiment, and application
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Closed geodesics on surfaces
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Route planning for bacteria
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Characterizations of intrinsic volumes on convex bodies and convex functions
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A tale of three curves
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Biological Shape Analysis with Geometric Statistics and Learning
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The Robinson–Schensted algorithm
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Finite geometries: pure mathematics close to applications
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Quantum symmetry
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The Enigma behind the Good–Turing formula
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Reflections on hyperbolic space
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Ultrafilter methods in combinatorics
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Zopfgruppen, die Yang–Baxter-Gleichung und Unterfaktoren
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Invitation to quiver representation and Catalan combinatorics
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Searching for structure in complex data: A modern statistical quest
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C∗-algebras: structure and classification
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From the dollar game to the Riemann-Roch Theorem
Steven Rayan, Laura P. Schaposnik
Higgs bundles without geometry
Behrend Heeren, Martin Rumpf
Shape space - a paradigm for character animation in computer graphics
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Rotating needles, vibrating strings, and Fourier summation
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Quantum symmetry
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Determinacy versus indeterminacy
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Vertex-to-Self Trajectories on the Platonic Solids
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Random matrix theory: Dyson Brownian motion
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Positive Scalar Curvature and Applications
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The codimension
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The mathematics of aquatic locomotion
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Topological recursion
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Solving quadratic equations in many variables
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Spaces of Riemannian metrics
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Computational Optimal Transport
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A few shades of interpolation
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Molecular quantum dynamics
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Closed geodesics on surfaces and Riemannian manifolds
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Mathematische Modellierung von Krebswachstum
Michael Baake, David Damanik, Uwe Grimm
Aperiodic Order and Spectral Properties
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News on quadratic polynomials
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Winkeltreue zahlt sich aus
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Towards a Mathematical Theory of Turbulence in Fluids
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Profinite groups
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The adaptive finite element method
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Footballs and donuts in four dimensions
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Prime Tuples in Function Fields
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Polyhedra and commensurability
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High performance computing on smartphones
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Symmetry and characters of finite groups
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Domino tilings of the Aztec Diamond
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Quantum diffusion
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Zero-dimensional symmetry
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Minimizing energy
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Billiards and flat surfaces
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Swallowtail on the shore
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Arrangements of lines
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What does ">" really mean?
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The ternary Goldbach Problem
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Matrixfaktorisierungen
John E. McCarthy
Dirichlet Series

Mathematical subjects

Algebra and Number Theory
Analysis
Didactics and Education
Discrete Mathematics and Foundations
Geometry and Topology
Numerics and Scientific Computing
Probability Theory and Statistics

Connections to other fields

Chemistry and Earth Science
Computer Science
Engineering and Technology
Finance
Humanities and Social Sciences
Life Science
Physics
Reflections on Mathematics

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