Biological Shape Analysis with Geometric Statistics and Learning

Oberwolfach'tan

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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Matematiksel konular

Geometri ve Topoloji
Olasılık Kuramı ve İstatistik

Diğer alanlarla ilişkiler

Bilgisayar Bilimeri
Yaşam Bilimleri

Yazar(lar)

Saiteja Utpala, Nina Miolane

Lisans

DOI (Dijital nesne belirteci)

10.14760/SNAP-2022-008-EN

PDF indir

snapshot-2022-008.pdf

PDF

snapshots: overview

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Algebras and quantum games
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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
Michael Baake, Uwe Grimm, Robert V. Moody
What is Pattern?
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Biological Shape Analysis with Geometric Statistics and Learning
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Representations and degenerations
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Solving inverse problems with Bayes’ theorem
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Jewellery from tessellations of hyperbolic space
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Seeing through rock with help from optimal transport
David A. Craven
Searching for the Monster in the Trees
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The Robinson–Schensted algorithm
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Emergence in biology and social sciences
Jason D. Lotay
Lagrangian mean curvature flow
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Finite geometries: pure mathematics close to applications
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Describing distance: from the plane to spectral triples
Martijn Caspers
Quantum symmetry
Fadoua Balabdaoui, Yulia Kulagina
The Enigma behind the Good–Turing formula
Anna Haensch
Reflections on hyperbolic space
Isaac Goldbring
Ultrafilter methods in combinatorics
Gandalf Lechner
Zopfgruppen, die Yang–Baxter-Gleichung und Unterfaktoren
Baptiste Rognerud
Invitation to quiver representation and Catalan combinatorics
Po-Ling Loh
Searching for structure in complex data: A modern statistical quest
David Kerr
C∗-algebras: structure and classification
Sara Lamboglia, Martin Ulirsch
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
Joshua Zahl
Rotating needles, vibrating strings, and Fourier summation
Moritz Weber
Quantum symmetry
Christian Berg
Determinacy versus indeterminacy
Jayadev S. Athreya, David Aulicino
Vertex-to-Self Trajectories on the Platonic Solids
Gianluca Finocchio
Random matrix theory: Dyson Brownian motion
Holger Kammeyer, Roman Sauer
From Betti numbers to l2-Betti numbers
Martin J. Gander
Is it possible to predict the far future before the near future is known accurately?
Jan-Bernhard Kordaß
The Interaction of Curvature and Topology
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The Mathematics of Fluids and Solids
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A surprising connection between quantum mechanics and shallow water waves
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Formation Control and Rigidity Theory
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Expander graphs and where to find them
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Deep Learning and Inverse Problems
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Mixed-dimensional models for real-world applications
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Configuration spaces and braid groups
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On Logic, Choices and Games
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Nonlinear Acoustics
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Random permutations
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Algebra, matrices, and computers
Jonathan Rosenberg, David Wraith
Positive Scalar Curvature and Applications
Hector Pasten
Diophantine equations and why they are hard
Martin Buhmann, Janin Jäger
On radial basis functions
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Snake graphs, perfect matchings and continued fractions
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Estimating the volume of a convex body
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Mixed volumes and mixed integrals
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A short story on optimal transport and its many applications
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Number theory in quantum computing
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Data assimilation: mathematics for merging models and data
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The codimension
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The mathematics of aquatic locomotion
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Tropical geometry
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Fast Solvers for Highly Oscillatory Problems
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Topological Complexity, Robotics and Social Choice
Thomas Sauer
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Computing with symmetries
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Topological recursion
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The Algebraic Statistics of an Oberwolfach Workshop
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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
Marco Radeschi
Closed geodesics on surfaces and Riemannian manifolds
Christian Engwer, Markus Knappitsch
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
Laurent Bartholdi
Profinite groups
Dietmar Gallistl
The adaptive finite element method
Steven Klee
Footballs and donuts in four dimensions
Nikolai Nowaczyk
The Willmore Conjecture
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Prime Tuples in Function Fields
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Polyhedra and commensurability
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Wie steuert man einen Kran?
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Symmetry and characters of finite groups
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On the containment problem
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Random sampling of domino and lozenge tilings
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Swarming robots
Ulrich Krähmer
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Domino tilings of the Aztec Diamond
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Quantum diffusion
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Modelling the spread of brain tumours
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Ideas of Newton-Okounkov bodies
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Darcy’s law and groundwater flow modelling
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Tom Solomon
Chaos and chaotic fluid mixing
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Friezes and tilings
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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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Operator theory and the singular value decomposition
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The Kadison-Singer problem
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Swallowtail on the shore
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Statistics and dynamical phenomena
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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
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Dirichlet Series

Matematiksel konular

Cebir ve Sayılar Kuramı
Analiz
Eğitim ve Eğitim Bilimi
Ayrık Matematik ve Matematiğin Temelleri
Geometri ve Topoloji
Nümerik ve Hesap Analizi
Olasılık Kuramı ve İstatistik

Diğer alanlarla ilişkiler

Kimya ve Yer Bilimler
Bilgisayar Bilimeri
Mühendislik ve Teknoloji
Finans
Beşeri ve Sosyal Bilimler
Yaşam Bilimleri
Fizik
Matematik Üzerine Düşünceler

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