Related papers: Extremal Configurations of Hinge Structures
This work proposes an algorithm to bound the minimum distance between points on trajectories of a dynamical system and points on an unsafe set. Prior work on certifying safety of trajectories includes barrier and density methods, which do…
We consider the extremal pointset configuration problem of maximizing a kernel-based energy subject to the geometric constraints that the points are contained in a fixed set, the pairwise distances are bounded below, and that every closed…
This expository article describes applications of topological configuration spaces to the control of robotic systems. In particular, we review recent work by the authors on configuration spaces of graphs. These are lovely spaces: we show…
We study the correspondence between four-dimensional supersymmetric gauge theories and two-dimensional conformal field theories in the case of N=2* gauge theory. We emphasize the genus expansion on the gauge theory side, as obtained via…
The analytic structure of the Regge action on a cone in $d$ dimensions over a boundary of arbitrary topology is determined in simplicial minisuperspace. The minisuperspace is defined by the assignment of a single internal edge length to all…
Additive robotic construction of building-scale discrete bar structures, such as trusses and space frames, is increasingly attractive due to the potential improvements in efficiency, safety, and design possibilities. However, programming…
This paper analyzes the support of the conditional distribution of optimal martingale transport plans in higher dimension. In the context of a distance coupling in dimension larger than 2, previous results established by Ghoussoub, Kim &…
We consider the Monge problem of optimal transport between a compactly supported source measure and a target probability measure with unbounded support. We consider the convergence of optimal maps and potential functions when the target…
We consider the problem of approximating a two-dimensional shape contour (or curve segment) using discrete assembly systems, which allow to build geometric structures based on limited sets of node and edge types subject to edge length and…
We derive a new bound on the dimension of images of period maps of global pure polarized integral variations of Hodge structures with generic Hodge datum of level at least 3. When the generic Mumford-Tate domain of the variation is a period…
We study brane realizations of chiral matter in N=1 supersymmetric gauge theories in four dimensions. A "cross" configuration which leads to "flavor doubling" is found to have a superpotential. The main example is realized using a special…
In this paper, we characterize the extreme points of a class of multidimensional monotone functions. This result is then applied to large contests, where it provides a useful representation of optimal allocation rules under a broad class of…
In this short note, we show that the distance function to any finite set $X\subset \mathbb{R}^n$ is a topological Morse function, regardless of whether $X$ is in general position. We also precisely characterize its topological critical…
Using homological techniques we show that a pin-anchored frame that involves only moments and shears provides a conceptual bridge between the statics of moment frames and the kinematics of pin-jointed trusses. One immediate result is a long…
Recently, through development of several 3d vision systems, widely used in various applications, medical and biometric fields. Microsoft kinect sensor have been most of used camera among 3d vision systems. Microsoft kinect sensor can obtain…
For a given Markov chain Monte Carlo (MCMC) algorithm, we define the distance between configurations that quantifies the difficulty of transitions. This distance enables us to investigate MCMC algorithms in a geometrical way, and we…
Multi-robot formation control enables robots to cooperate as a working group in completing complex tasks, which has been widely used in both civilian and military scenarios. Before moving to reach a given formation, each robot should choose…
Rotational bands in $^{158}$Er at ultra-high spin have been studied in the framework of relativistic and non-relativistic nuclear density functional theories. Consistent results are obtained across the theoretical models used but some…
We present a large scale exact diagonalization study of the one dimensional spin $1/2$ Heisenberg model in a random magnetic field. In order to access properties at varying energy densities across the entire spectrum for system sizes up to…
Electronic structure of strongly correlated transition metal oxides (TMOs) is a complex phenomenon due to competing interaction among the charge, spin, orbital and lattice degrees of freedom. Often individual compounds are examined to…