Learning with transformed data using diffeomorphisms.
problem Training data transformation for improved prediction accuracy.
method Minimizes prediction error penalized by diffeomorphism distance to identity.
result Demonstrates potential of diffeomorphisms in large-dimensional estimation.
The paper proposes a deep learning approach to efficiently approximate diffeomorphisms for shape alignment.
problem Finding optimal reparameterizations of shapes for computing geodesic distances.
method The authors develop a neural network-based algorithm to construct approximations of diffeomorphisms using PyTorch.
result The proposed method achieves universal approximation properties and bounds on Lipschitz constants for the constructed diffeomorphisms.
DID measures similarity invariant to diffeomorphisms.
problem Measuring similarity invariance to diffeomorphisms.
method DID measures similarity as the solution to an optimization problem in a Reproducing Kernel Hilbert Space.
result DID is invariant to diffeomorphisms and can be efficiently approximated.
Diffeomorphic Time Warping (DiffTW) is a novel method for time series classification that learns a diffeomorphic mapping between time series.
problem Time series classification
method Diffeomorphic Time Warping (DiffTW)
result Outperforms DTW on 60 out of 86 datasets
Study on controllability and groups of manifolds with boundaries.
problem Controllability of vector fields on manifolds with boundaries.
method Establish controllability results for diffeomorphism groups of manifolds with smooth boundaries.
result Diffeomorphism groups of manifolds with smooth boundaries form fibre bundles and are generated by the exponential map.
Bayesian method learns optimal momentum for landmark matching.
problem Finding a diffeomorphism between two sets of landmarks.
method Ensemble Kalman filter for derivative-free Bayesian inverse method.
result Efficient algorithm for various target shapes.
Smooth manifolds have equivalent diffeomorphism groups if and only if they are diffeomorphic.
problem Understanding when diffeomorphism groups of smooth manifolds are elementarily equivalent.
method Analyzing the equivalence of Cr and Cs diffeomorphism groups of smooth manifolds. result Equivalent diffeomorphism groups imply diffeomorphic manifolds, strengthening previous results.
Constructs entropy-minimizing pseudo-Anosov diffeomorphisms on K3 surfaces.
problem Finding minimal entropy diffeomorphisms on K3 surfaces.
method Constructs pseudo-Anosov diffeomorphisms minimizing entropy.
result Obtains infinitely many entropy-minimizing diffeomorphisms.
FineMorphs models smooth transformations for multivariate regression.
problem Efficiently modeling complex transformations for multivariate regression.
method Optimal control of affine and diffeomorphic transformations using smooth vector fields.
result FineMorphs can reduce dimensionality and adapt to large datasets.
A neural network method tackles high-dimensional diffeomorphic mapping problems.
problem High-dimensional diffeomorphic mapping struggles with the curse of dimensionality.
method Combines variational principles with quasi-conformal theory for accurate, bijective mappings.
result Validated accuracy, robustness, and effectiveness in complex registration scenarios.
The study proves diffeomorphisms can be localized to simpler submanifolds.
problem Localization of exotic diffeomorphisms on compact simply-connected 4-manifolds.
method Localization theorem for diffeomorphisms isotopic to identity after stabilization.
result Diffeomorphisms can be isotoped to simpler submanifolds.
Paper derives explicit expression of Alekseev-Meinrenken diffeomorphism.
problem Understanding the Alekseev-Meinrenken diffeomorphism.
method Via the Stokes phenomenon of meromorphic linear systems of ODEs with Poncaré rank 1.
result Explicit expression of the Alekseev-Meinrenken diffeomorphism.
According to Pixton, there are Morse-Smale diffeomorphisms of the 3-sphere which have no energy function, that is a Lyapunov function whose critical points are all periodic points of the diffeomorphism. We introduce the concept of quasi-energy function for a Morse-Smale diffeomorphism as a Lyapunov function with the le…
We determine the Riemannian manifolds for which the group of exact volume preserving diffeomorphisms is a totally geodesic subgroup of the group of volume preserving diffeomorphisms, considering right invariant L2-metrics. The same is done for the subgroup of Hamiltonian diffeomorphisms as a subgroup of the group of…
Generalizes π2-diffeomorphism finiteness to non-zero first homotopy groups.
problem Bounding diffeomorphic types of compact manifolds with vanishing first and second homotopy groups.
method Generalizing the π2-diffeomorphism finiteness theorem to include non-zero first homotopy groups. result Diffeomorphic types of compact manifolds with non-zero first homotopy groups can be bounded.
Study on group cocycles for volume-preserving diffeomorphisms.
problem Understanding group cocycles on volume-preserving diffeomorphisms.
method Constructed two types of group cocycles on the volume-preserving diffeomorphism group.
result One cocycle yields the Euler class of flat sphere bundles for the sphere.
Book introduces Hofer's metric on symplectic diffeomorphisms.
problem Understanding dynamics and growth in symplectic geometry.
method Introduces Hofer's metric and analyzes its properties.
result Provides insights into the structure of symplectic diffeomorphisms.
Study partially hyperbolic diffeomorphisms on 3-manifolds, proving some classification results.
problem Classifying partially hyperbolic diffeomorphisms on 3-manifolds.
method Detailed proofs of results on partially hyperbolic diffeomorphisms on 3-manifolds, focusing on dynamically coherent cases.
result Some results towards the classification of partially hyperbolic diffeomorphisms on 3-manifolds.
Study local diffeomorphisms of conformal circles in pseudo-Riemannian manifolds.
problem Understanding local diffeomorphisms of conformal circles.
method Variations of conformal circles and pseudo-Riemannian manifolds.
result Local diffeomorphisms of conformal circles are conformal local diffeomorphisms.
Survey on foliations and diffeomorphism groups.
problem Relationship between algebraic and homotopical properties.
method Survey and analysis of existing literature.
result Explains the connection between diffeomorphism groups and foliations.
The paper explores the transitivity of orbifold diffeomorphisms.
problem Understanding the transitivity of orbifold diffeomorphisms.
method Investigates the group of compactly supported diffeomorphisms of orbifolds.
result The group of orbifold diffeomorphisms is n-transitive. The paper shows Thurston geometries don't support Anosov diffeomorphisms.
problem The existence of Anosov diffeomorphisms on Thurston geometries.
method Analyzing Thurston geometries and their properties.
result Thurston geometries do not support transitive Anosov diffeomorphisms.
New exotic 4D spaces found using knot slicing techniques.
problem Finding non-diffeomorphic exotic 4D spaces.
method Using RBG links to create slice knots with non-diffeomorphic complements.
result Distinguished new exotic 4D spaces using end Floer homology.
The paper explores simplifying manifold equivalence to actual equivalence.
problem Does R-diffeomorphism imply diffeomorphism or homeomorphism for compact manifolds?
method Analysis of manifold theory, including h- and s-cobordism theorems and recent classification results.
result Presentation of known results and new classifications of R-diffeomorphisms.
The paper proves n-transitivity for equivariant diffeomorphisms of manifolds.
problem Proving n-transitivity for equivariant diffeomorphisms. method Analyzing the group of equivariant diffeomorphisms on proper smooth G-manifolds. result The group of equivariant diffeomorphisms acts n-transitively on M. Optimizes metric in LDDMM for better image registration and classification.
problem Improving image registration and predictive modeling in medical imaging.
method Machine learning approach using kernel Fischer Linear Discriminant Analysis (KLDA) to optimize the Riemannian metric on diffeomorphisms.
result Significant improvement in ROC AUC for schizophrenia control prediction.
New 4-manifolds with exotic diffeomorphisms found.
problem Existence of exotic diffeomorphisms in 4-manifolds.
method Proves existence of infinitely many contractible 4-manifolds with exotic diffeomorphisms.
result Infinitely many contractible 4-manifolds with absolutely exotic diffeomorphisms.
Study exotic Dehn twists in 4-manifolds, producing first known exotic diffeomorphisms.
problem Detecting exotic diffeomorphisms in 4-manifolds.
method 2-parameter families Seiberg-Witten theory over RP2. result Constructed the smallest closed 4-manifold with exotic diffeomorphisms.
New Lie groups found for Poisson diffeomorphisms.
problem Finding Lie group structures on Poisson diffeomorphism groups.
method Using Poisson groupoids, develop Lie group structures.
result Poisson diffeomorphism groups of various Poisson manifolds are regular Lie groups.
Entropy norm on surface diffeomorphisms is unbounded.
problem Bounding entropy norm on surface diffeomorphisms.
method Analyzing the group of diffeomorphisms of a closed orientable surface.
result Entropy norm is unbounded on the group of diffeomorphisms of a closed orientable surface.
Study shows mean action of periodic orbits in annuli is bounded by their Calabi invariant.
problem Understanding the average distortion of periodic orbits in area-preserving annuli.
method Analyzes action functions and Calabi invariants of diffeomorphisms near annulus boundaries.
result Infimum of mean action of periodic orbits is bounded by their Calabi invariant.
Paper finds exotic diffeomorphisms on specific 4-manifolds.
problem Understanding exotic diffeomorphisms on 4-manifolds with b2+=2. method Comparing winding numbers of parameter families.
result 2\mathbb{C}\mathbb{P}^2 \# 10 (-\mathbb{C}\mathbb{P}^2) admits exotic diffeomorphisms.
Theta graph diffeomorphism shows nontrivial mapping class of 4-sphere.
problem Identifying nontrivial elements in the smooth mapping class group of 4-sphere.
method Diagrammatic calculus for smooth mapping class group of 4-sphere, Watanabe's clasper surgery construction.
result Theta graph diffeomorphism is isotopic to a nontrivial element of (1,2)-subgroup.
Positive paths connect diffeomorphisms on contact manifolds.
problem Defining and analyzing positivity in diffeomorphism groups of manifolds with contact structures.
method By examining paths of diffeomorphisms that are positively transverse to the contact distribution, showing flexibility and connecting diffeomorphisms.
result Any two diffeomorphisms on standard contact structure of R^(2n+1) can be connected by a positive path.
The paper finds diffeomorphic complex intersections with distinct Hodge numbers.
problem Identifying complex intersections with different Hodge numbers.
method Provided three pairs of 3-dimensional and one pair of 5-dimensional complex complete intersections, all diffeomorphic but with different Hodge numbers.
result Diffeomorphic complex intersections can have different Hodge numbers.
Proves transitivity of real Anosov diffeomorphisms with specific properties.
problem Transitivity of real Anosov diffeomorphisms with specific properties.
method Proves transitivity using specific properties of real Anosov diffeomorphisms.
result Proves transitivity of real Anosov diffeomorphisms.
Complex surfaces show non-simply connected diffeomorphism groups with non-homotopic loops.
problem Complex surfaces with non-simply connected diffeomorphism groups and non-homotopic loops.
method Exhibited examples of complex surfaces.
result Diffeomorphism groups of complex surfaces are not simply-connected and contain non-homotopic loops.
Using the categorical description of supergeometry we give an explicit construction of the diffeomorphism supergroup of a compact finite-dimensional supermanifold. The construction provides the diffeomorphism supergroup with the structure of a Frechet supermanifold. In addition, we derive results about the structure of…
We give examples of harmonic cellular maps between negatively curved manifolds which are not diffeomorphisms but are homotopic to diffeomorphisms.
A new type of diffeomorphic normalizing flow for flexible density estimation.
problem Flexible density estimation and variational inference.
method Constructs a diffeomorphic flow using an ODE with a neural network to parametrize the smooth vector field and a recursive neural network for approximating the solution.
result End-to-end trained DDNF achieves competitive results on density estimation and variational inference tasks.
Study controllability of diffeomorphisms of simple polytopes.
problem Controllability of diffeomorphisms of simple polytopes.
method Lie group structure and controllability results for diffeomorphisms of simple polytopes.
result Identity component of the diffeomorphism group is generated by the exponential image.
Diffeomorphisms of convex polytopes form a Lie group.
problem Understanding transformations of convex polytopes.
method Forming a Lie group from diffeomorphisms of convex polytopes.
result The group of diffeomorphisms of a convex polytope is a regular Lie group.
An orientation preserving diffeomorphism over a surface embedded in a 4-manifold is called extendable, if this diffeomorphism is a restriction of an orientation preserving diffeomorphism on this 4-manifold. In this paper, we investigate conditions for extendability of diffeomorphisms over surfaces in the complex projec…
Authors prove existence of exotic surfaces and invariants not detecting self-diffeomorphisms.
problem Existence and properties of exotic surfaces and diffeomorphisms.
method Vanishing theorem of family Bauer--Furuta invariant for diffeomorphisms on spin 4-manifolds.
result Family Bauer--Furuta invariants do not detect exotic self-diffeomorphisms on S4 or S2imesS2. Dual pairs constructed for volume preserving diffeomorphisms using symplectic geometry.
problem Understanding the group of volume preserving diffeomorphisms through symplectic geometry.
method Using cotangent bundles of spaces of smooth embeddings, symplectic reduction, and nonlinear Grassmannians of augmented submanifolds.
result Descriptions of coadjoint orbits of the group of volume preserving diffeomorphisms in terms of submanifolds of augmented spaces.
We prove that a compactly supported homeomorphism of a smooth manifold of dimension greater or equal to 5 can be approximated uniformly by compactly supported diffeomorphisms if and only if it is isotopic to a diffeomorphism. If the given homeomorphism is in addition volume preserving, then it can be approximated unifo…
Global diffeomorphism proof between tame Fréchet spaces.
problem Existence of global diffeomorphism between Fréchet spaces.
method Mountain Pass Theorem and sufficient conditions for diffeomorphism.
result Existence of global diffeomorphism between tame Fréchet spaces.
Exotic diffeomorphisms found on complex surfaces and 4-manifolds.
problem Finding exotic diffeomorphisms on 4-manifolds.
method Minimal complex surfaces and spin 4-manifolds with S3 boundary. result First known instances of exotic diffeomorphisms of irreducible 4-manifolds.