相关论文: A nongraphical obstacle problem for elastic curves
In the framework of linearized elasticity, we study thin elastic composite plates with thickness $\delta$. The plates contain small, rigid rectangular plates distributed periodically along $\varepsilon$. Between two neighboring rigid plates…
We study global optimization of non-convex functions through optimal control theory. Our main result establishes that (quasi-)optimal trajectories of a discounted control problem converge globally and practically asymptotically to the set…
Crossing minimization is one of the central problems in graph drawing. Recently, there has been an increased interest in the problem of minimizing crossings between paths in drawings of graphs. This is the metro-line crossing minimization…
The thin obstacle problem or $n$-dimensional Signorini problem is a classical variational problem arising in several applications, starting with its first introduction in elasticity theory. The vast literature concerns mostly quadratic…
We study recovery of piecewise-constant signals on graphs by the estimator minimizing an $l_0$-edge-penalized objective. Although exact minimization of this objective may be computationally intractable, we show that the same statistical…
The classical Euler's problem on optimal configurations of elastic rod in the plane with fixed endpoints and tangents at the endpoints is considered. The global structure of the exponential mapping that parameterises extremal trajectories…
We consider a variational problem with a polyconvex integrand and nonstandard boundary conditions that can be treated as minimization of the stress energy during the suturing process in the plastic surgery. Ex- istence of minimizers is…
Problems from metric graph theory like Metric Dimension, Geodetic Set, and Strong Metric Dimension have recently had a strong impact in parameterized complexity by being the first known problems in NP to admit double-exponential lower…
We attempt to describe surface defects in smectic A thin films by formulating a free discontinuity problem - that is, a variational problem in which the order parameter is allowed to have jump discontinuities on some (unknown) set. The free…
We consider perimeter perturbations of a class of attractive-repulsive energies, given by the sum of two nonlocal interactions with power-law kernels, defined over sets with fixed measure. We prove that there exists curves in the…
A developable cone ("d-cone") is the shape made by an elastic sheet when it is pressed at its center into a hollow cylinder by a distance $\epsilon$. Starting from a nonlinear model depending on the thickness $h > 0$ of the sheet, we prove…
Here, we address a dimension-reduction problem in the context of nonlinear elasticity where the applied external surface forces induce bending-torsion moments. The underlying body is a multi-structure in $\mathbb{R}^3$ consisting of a thin…
We study critical surfaces for a surface energy which contains the squared $L^2$ norm of the difference of the mean curvature $H$ and the spontaneous curvature $c_o$, coupled to the elastic energy of the boundary curve. We investigate the…
We study the problem of finding a maximum cardinality minimal separator of a graph. This problem is known to be NP-hard even for bipartite graphs. In this paper, we strengthen this hardness by showing that for planar bipartite graphs, the…
For an input graph $G$, an additive spanner is a sparse subgraph $H$ whose shortest paths match those of $G$ up to small additive error. We prove two new lower bounds in the area of additive spanners: 1) We construct $n$-node graphs $G$ for…
In this work we introduce the obstacle-mass constraint problem for a multidimensional scalar hyperbolic conservation law. We prove existence of an entropy solution to this problem by a penalization/viscosity method. The mass constraint…
Plateau problems with elastic boundary energies have been of recent theoretical and applied interest. However, strong assumptions have to be made to avoid self-intersections of the boundary curve during energy minimization. We introduce a…
We consider the problem of learning a sparse graph under the Laplacian constrained Gaussian graphical models. This problem can be formulated as a penalized maximum likelihood estimation of the Laplacian constrained precision matrix. Like in…
The notion of a (polynomial) kernelization from parameterized complexity is a well-studied model for efficient preprocessing for hard computational problems. By now, it is quite well understood which parameterized problems do or…
Converting a parametric curve into the implicit form, which is called implicitization, has always been a popular but challenging problem in geometric modeling and related applications. However, the existing methods mostly suffer from the…