Related papers: Polar Transform and Local Positivity for Curves
We introduce and study a number of invariants of locally compact quantum groups defined by their scaling and modular groups and the spectrum of their modular elements. Focusing mainly on compact quantum groups we consider the question…
Translational invariance induced by pooling operations is an inherent property of convolutional neural networks, which facilitates numerous computer vision tasks such as classification. Yet to leverage rotational invariant tasks,…
The Kreck-Stolz $s$-invariant is a classic path-component invariant for the space and moduli space of positive scalar curvature metrics. It is an absolute (as opposed to relative) invariant, but this strength comes at the expense of being…
We use the hyperK\"aler geometry define an disc-counting invariants with deformable boundary condition on hyperK\"ahler manifolds. Unlike the reduced Gromov-Witten invariants, these invariants can have non-trivial wall-crossing phenomenon…
We construct invariants for any closed semipositive symplectic manifold which count rational curves satisfying tangency constraints to a local divisor. More generally, we introduce invariants involving multibranched local tangency…
The polar wavelet transform (PWT) has been proven to be a powerful mathematical tool for signal and image processing in recent years. Due to the increasing demand for directional representations of signals in engineering, it is impossible…
Using the integral representations of the solutions of Schr\"odinger equation, which are the essential ingredients of the Gel'fand-Levitan and Marchenko integral equations of inverse scattering theory, we obtain a general theorem on the…
The stable pairs theory of local curves in 3-folds (equivariant with respect to the scaling 2-torus) is studied with stationary descendent insertions. Reduction rules are found to lower descendents when higher than the degree. Factorization…
Differential analysis aims at inferring global properties of nonlinear behaviors from the local analysis of the linearized dynamics. The paper motivates and illustrates the use of differential analysis on the nonlinear pendulum model, an…
Pseudo-cones are a class of unbounded closed convex sets, not containing the origin. They admit a kind of polarity, called copolarity. With this, they can be considered as a counterpart to convex bodies containing the origin in the…
We establish cross-ratio invariants for surfaces in 4-space in an analogous way to Uribe-Vargas's work for surfaces in 3-space. We study the geometric locii of local and multi-local singularities of ortogonal projections of the surface. The…
Any sufficiently often differentiable curve in the orbit space of a compact Lie group representation can be lifted to a once differentiable curve into the representation space.
We present results and examples which show that the consideration of a certain tubular mutation is advantageous in the study of noncommutative curves which parametrize the simple regular representations of a tame bimodule. We classify all…
We study statistical properties of turbulent inverse cascades in a class of nonlinear models describing a scalar field transported by a two-dimensional incompressible flow. The class is characterized by a linear relation between the…
Structured optimization uses a prescribed set of atoms to assemble a solution that fits a model to data. Polarity, which extends the familiar notion of orthogonality from linear sets to general convex sets, plays a special role in a simple…
We present a novel, log-radius profile representation for convex curves and define a new operation for combining the shape features of curves. Unlike the standard, angle profile-based methods, this operation accurately combines the shape…
This is a significantly improved version with new applications. We show that there are many cohomogeneity one manifolds which do not admit an analytic invariant metric with non-negative sectional curvature, although they do have a smooth…
In the second part of the paper we consider a convolution of probability measures on spaces of locally finite configurations (subsets of a phase space) as well as their connection with the convolution of the corresponding correlation…
In this paper, we improve Polyak's local convexity result for quadratic transformations. Extension and open problems are also presented.
In this article we revisit a new notion of positivity in real semisimple Lie groups that at the same time generalizes total positivity in split real Lie groups as well as positive Lie semigroups in Hermitian Lie groups of tube type. We…