Related papers: Local, Smooth, and Consistent Jacobi Set Simplific…
Majorization-minimization schemes are a broad class of iterative methods targeting general optimization problems, including nonconvex, nonsmooth and stochastic. These algorithms minimize successively a sequence of upper bounds of the…
This paper establishes closed-string mirror symmetry for all log Calabi-Yau surfaces with generic parameters, where the exceptional divisor are sufficiently small. We demonstrate that blowing down a $(-1)$-divisor removes a single geometric…
Majorization-minimization algorithms consist of successively minimizing a sequence of upper bounds of the objective function so that along the iterations the objective function decreases. Such a simple principle allows to solve a large…
We propose a decomposition framework for the parallel optimization of the sum of a differentiable function and a (block) separable nonsmooth, convex one. The latter term is typically used to enforce structure in the solution as, for…
We present two improvements to arithmetic in the Jacobian of global function fields based on the approach of Hess. The first reduces the number of expensive reduction steps by optimizing for typical inputs rather than worst-case behavior,…
Semantic segmentation is the task of assigning a class-label to each pixel in an image. We propose a region-based semantic segmentation framework which handles both full and weak supervision, and addresses three common problems: (1) Objects…
In many naturally occurring optimization problems one needs to ensure that the definition of the optimization problem lends itself to solutions that are tractable to compute. In cases where exact solutions cannot be computed tractably, it…
The canonical functional action in the path integral in phase space is discretized by linking each pair of consecutive vertebral points --${\bf q}_k$ and ${\bf p}_{k+1}$ or ${\bf p}_k$ and ${\bf q}_{k+1}$-- through the invariant complete…
Cosmological correlators are fundamental observables in an expanding universe and are highly non-trivial functions even at tree-level. In this work, we uncover novel structures in the space of such tree-level correlators that enable us to…
In this paper, locally Lipschitz functions acting between infinite dimensional normed spaces are considered. When the range is a dual space and satisfies the Radon--Nikod\'ym property, Clarke's generalized Jacobian will be extended to this…
By using the scheme of Jacobi elliptic functions with their duality symmetries we present a formulation of the Jacobi- Gordon field theory that will manifest the strong/weak coupling duality at classical level; for certain continuous limits…
The standard formulation of Jacobi manifolds in terms of differential operators on line bundles, although effective at capturing most of the relevant geometric features, lacks a clear algebraic interpretation similar to how Poisson algebras…
Jacobi matrices are parametrized by their eigenvalues and norming constants (first coordinates of normalized eigenvectors): this coordinate system breaks down at reducible tridiagonal matrices. The set of real symmetric tridiagonal matrices…
In studies of smooth maps with good differential topological conditions such as immersions, embeddings, Morse functions and their higher dimensional versions including fold maps and application to geometry, especially algebraic and…
We consider the problem of approximating a smooth function from finitely-many pointwise samples using $\ell^1$ minimization techniques. In the first part of this paper, we introduce an infinite-dimensional approach to this problem. Three…
We present a simple direct discretization for functionals used in the variational mesh generation and adaptation. Meshing functionals are discretized on simplicial meshes and the Jacobian matrix of the continuous coordinate transformation…
Composite minimization involves a collection of smooth functions which are aggregated in a nonsmooth manner. In the convex setting, we design an algorithm by linearizing each smooth component in accordance with its main curvature. The…
We consider finite pencils of Jacobi matrices \[ J_n(w)=A+wB, \] where $A$ is diagonal and $B$ is tridiagonal with zero diagonal. The spectral curve is the affine plane curve \[ \chi_n(\lambda,w)=\det(\lambda I+J_n(w))=0 . \] The main…
In this paper we show that every area minimizing cone C^{n-1} in R^n can be approximated by entirely smooth area minimizing hypersurfaces. This extensively uses hyperbolic unfoldings of such hypersurfaces and the resulting potential theory…
We propose a decomposition framework for the parallel optimization of the sum of a differentiable (possibly nonconvex) function and a (block) separable nonsmooth, convex one. The latter term is usually employed to enforce structure in the…