Related papers: Tableau Stabilization and Lattice Paths
This work establishes rigorous, novel and widely applicable stability guarantees and transferability bounds for graph convolutional networks -- without reference to any underlying limit object or statistical distribution. Crucially,…
We define a special case of tree decompositions for planar graphs that respect a given embedding of the graph. We study the analogous width of the resulting decomposition we call the embedded-width of a plane graph. We show both upper…
We propose an exact renormalization group equation for Lattice Gauge Theories, that has no dependence on the lattice spacing. We instead relate the lattice spacing properties directly to the continuum convergence of the support of each…
We introduce a new type of lattice path, called brick-wall lattice path, and we derive a formula which counts the number of paths on these lattices imposing certain restrictions on the Cartesian plane. Connections to the Fibonacci sequence,…
In recent decades, much attention has been focused on the topic of optimal paths in weighted networks due to its broad scientific interest and technological applications. In this work we revisit the problem of the optimal path between two…
We study the navigation problem for a robot moving amidst static and dynamic obstacles and rely on a hierarchical approach to solve it. First, the reference trajectory is planned by the safe interval path planning algorithm that is capable…
We study the stability margin of a vehicular formation with distributed control, in which the control at each vehicle only depends on the information from its neighbors in an information graph. We consider a D-dimensional lattice as…
Structure-aware Taylor (SAT) methods are a class of timestepping schemes designed for propagating linear hyperbolic solutions within a tent-shaped spacetime region. Tents are useful to design explicit time marching schemes on unstructured…
We give a simple approximation algorithm for a common generalization of many previously studied extensions of the maximum size stable matching problem with ties. These generalizations include the existence of critical vertices in the graph,…
The emerging field of passive macro-scale tile-based self-assembly (TBSA) shows promise in enabling effective manufacturing processes by harnessing TBSA's intrinsic parallelism. However, current TBSA methodologies still do not fulfill their…
Randomized coordinate descent (RCD) is a popular optimization algorithm with wide applications in solving various machine learning problems, which motivates a lot of theoretical analysis on its convergence behavior. As a comparison, there…
Visibility graph reconstruction, which asks us to construct a polygon that has a given visibility graph, is a fundamental problem with unknown complexity (although visibility graph recognition is known to be in PSPACE). We show that two…
Solitary waves in a general nonlinear lattice are discussed, employing as a model the nonlinear Schr\"odinger equation with a spatially periodic nonlinear coefficient. An asymptotic theory is developed for long solitary waves, that span a…
The graph bisection problem is the problem of partitioning the vertex set of a graph into two sets of given sizes such that the sum of weights of edges joining these two sets is optimized. We present a semidefinite programming relaxation…
Imposing orthogonality on the layers of neural networks is known to facilitate the learning by limiting the exploding/vanishing of the gradient; decorrelate the features; improve the robustness. This paper studies the theoretical properties…
It is well known in the Reduced Basis approximation of saddle point problems that the Galerkin projection on the reduced space does not guarantee the inf-sup approximation stability even if a stable high fidelity method was used to generate…
We characterize the values of the stable rank for Leavitt path algebras, by giving concrete criteria in terms of properties of the underlying graph.
We present an algorithm, based on the iteration of conformal maps, that produces independent samples of self-avoiding paths in the plane. It is a discrete process approximating radial Schramm-Loewner evolution growing to infinity. We focus…
The study of nonlinear phenomena in systems with many degrees of freedom often relies on complex numerical simulations. In trying to model realistic situations, these systems may be coupled to an external environment which drives their…
This article deals with stability of continuous-time switched linear systems under constrained switching. Given a family of linear systems, possibly containing unstable dynamics, we characterize a new class of switching signals under which…