A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Proves constraints on groups extending Möbius transformations on spheres.
FineMorphs models smooth transformations for multivariate regression.
Study projective derivative cocycles for circle diffeomorphisms.
We show that the action of Cremona transformations on the real points of quadrics exhibits the full complexity of the diffeomorphisms of the sphere, the torus, and of all non-orientable surfaces. The main result says that if X is rational, then Aut(X), the group of algebraic automorphisms, is dense in Diff(X), the grou…
We introduce in this paper a learning paradigm in which the training data is transformed by a diffeomorphic transformation before prediction. The learning algorithm minimizes a cost function evaluating the prediction error on the training set penalized by the distance between the diffeomorphism and the identity. The ap…
Classification of Finslerian spaces with nontrivial concircular transformations.
The paper examines convergence of currents and forms under smooth diffeomorphisms.
Diffeomorphism freedom induces a gauge dependence in the theory of spacetime perturbations. We derive a compact formula for gauge transformations of perturbations of arbitrary order. To this end, we develop the theory of Taylor expansions for one-parameter families (not necessarily groups) of diffeomorphisms. First, we…
Paper proves CFlows can approximate any diffeomorphism and applies it in Bayesian optimization.
In this paper, we study generalized symmetric Finsler spaces. We first study symmetry preserving diffeomorphisms, then we show that the group of symmetry preserving diffeomorphisms is a transitive Lie transformation group. Finally we give some existence theorems.
Compact Finslerian manifolds don't admit non-trivial circle-preserving transformations.
Gradient flow on diffeomorphisms for image registration, with well-posedness proven.
Researchers relax the CVF's smoothness requirement to create more flexible flow models.
Let S be a compact surface - or the interior of a compact surface - and let V be the manifold of cooriented contact elements of S equiped with its canonical contact structure. A diffeomorphism of V that preserves the contact structure and its coorientation is called a contact transformation over S. We prove the followi…
Causal spacetimes with Ricci tensor have unique transformations.
Study constructs transverse metrics using transformations commuting with elliptic operators.
In the double field theory, gauge symmetries are realized as generalized diffeomorphisms in the doubled spacetime. By consistency of the theory, dependence of tensor fields on the doubled coordinates is strongly constrained. This causes finite transformation law highly complicated, both technically and conceptually. In…
The paper extends LDDMM framework to include Lie group actions in large deformation shape registration.
The paper explores simple and relatively simple transformation groups and their universal coverings.
Diffeomorphic Time Warping (DiffTW) is a novel method for time series classification that learns a diffeomorphic mapping between time series.
We introduce the spherical phylon group, a subgroup of the group of all formal diffeomorphisms of that fix the origin. The invariant theory of the spherical phylon group is used to understand the invariants of the Laplace transform.
We consider the following problem: given two parallel and identically oriented bundles of light rays in n-dimensional Euclidean space and given a diffeomorphism between the rays of the former bundle and the rays of the latter one, is it possible to realize this diffeomorphism by means of several mirror reflections? We …
We introduce two operations named biflip and puzzle-move on simple polytopes producing polytopes with diffeomorphic moment-angle manifolds.
We address the following problem: given two smooth densities on a manifold, find an optimal diffeomorphism that transforms one density into the other. Our framework builds on connections between the Fisher-Rao information metric on the space of probability densities and right-invariant metrics on the infinite-dimension…
Smooth manifold structure on Möbius transformations of quaternionic ball identified.
New framework uses elliptic operators to study projective maps.
In this note we study logarithmic transformations in the sense of differential topology on two fibers of the Hopf surface. It is known that such transformations are susceptible to yield exotic smooth structures on four-manifolds. We will show here that this is not the case for the Hopf surface, all integer homology Hop…
The study examines lower and upper bounds of Wasserstein distances for affine transformations of random vectors.
There are eight possible Pin groups that can be used to describe the transformation behaviour of fermions under parity and time reversal. We show that only two of these are compatible with general relativity, in the sense that the configuration space of fermions coupled to gravity transforms appropriately under the spa…
Corks transform complex curves without changing topology.
The paper studies how geometric transformations affect semi-classical operators on specific Lie groups.
New sampling method for heavy-tailed distributions using Langevin Algorithm.
Paper proves a quantitative estimate for transforming almost complex structures into standard ones.
In this paper, we will introduce a cut and paste move, called a geometrically null log transform, and prove that any two manifolds related by a sequence of these moves become diffeomorphic afte r one stabilization. To motivate the cut and paste move, we will use the symplec tic fiber sum, and a construction of Fintushe…
In this paper we extend some well-known rigidity results for conformal changes of Einstein metrics to the class of generalized quasi-Einstein (GQE) metrics, which includes gradient Ricci solitons. In order to do so, we introduce the notions of conformal diffeomorphisms and vector fields that preserve a GQE structure. W…
Cookbook transforms constrained statistical inference into unconstrained problems.
In the paper \cite{wall_1}, C.T.C. Wall proved that two smooth closed simply connected 4-manifolds which are homeomorphic are in fact stably diffeomorphic. We prove a similar result which states that two smooth closed 4-manifolds satisfying certain properties are stably diffeomorphic if and only if their signatures agr…
One of the most challenging problems in the domain of 2-D image or 3-D shape is to handle the non-rigid deformation. From the perspective of transformation groups, the conformal transformation is a key part of the diffeomorphism. According to the Liouville Theorem, an important part of the conformal transformation is t…
Paper proves every stable 4-sphere has a unique diffeomorphism class.
Study fundamental groups of geometric transformation groups using loop spaces.
Constructs minimal surfaces over Pitot quadrilaterals using harmonic diffeomorphisms.
The paper provides a link between ergodic theory and symplectic topology. A classical notion of ergodic theory is a skew product map associated with a loop in a group of transformations. We study skew products which come from loops in the group of Hamiltonian diffeomorphisms of a symplectic manifold. Our main question …
The paper proves bounded cohomology properties of Euclidean space groups.
Here, by extending the definition of circle to Finsler geometry, we show that, every circle-preserving local diffeomorphism is conformal. This result implies that in Finsler geometry, the definition of concircular change of metrics, a priori, does not require the conformal assumption.
We introduce a geometric framework to study Newton's equations on infinite-dimensional configuration spaces of diffeomorphisms and smooth probability densities. It turns out that several important PDEs of hydrodynamical origin can be described in this framework in a natural way. In particular, the Madelung transform be…
We prove that any regular integral invariant of volume-preserving transformations is equivalent to the helicity. Specifically, given a functional defined on exact divergence-free vector fields of class on a compact 3-manifold that is associated with a well-behaved integral kernel, we prove that $\mat…
The paper develops stochastic methods on geometric spaces for transformations.
Suppose M is a noncompact connected smooth 2-manifold without boundary and let D(M)_0 denote the identity component of the diffeomorphism group of M with the compact-open C^infty-topology. In this paper we investigate the topological type of D(M)_0 and show that D(M)_0 is a topological ell_2-manifold and it has the hom…