Related papers: Implicit Linear Algebra and Basic Circuit Theory I…
This article is concerned with the rigidity properties of geometric realizations of incidence geometries of rank two as points and lines in the Euclidean plane; we care about the distance being preserved among collinear points. We discuss…
Recently, Dvir, Golovnev, and Weinstein have shown that sufficiently strong lower bounds for linear data structures would imply new bounds for rigid matrices. However, their result utilizes an algorithm that requires an $NP$ oracle, and…
The rolling pad instability is caused by electromagnetic interactions in systems of horizontal layers with strongly different electric conductivities. We analyze the instability for a simplified model of a liquid metal battery (LMB), a…
We introduce the concept of strongly independent matrices over any field, and prove the existence of such matrices for certain fields and the non-existence for algebraically closed fields. Then we apply strongly independent matrices over…
We explore the rigidity of generic frameworks in 3-dimensions whose underlying graph is close to being planar. Specifically we consider apex graphs, edge-apex graphs and their variants and prove independence results in the generic…
One of the most important classes of even $\Delta$-matroids arises from orientable ribbon graphs, which play a role analogous to that of graphic matroids in matroid theory. Motivated by a natural correspondence between strong…
The introduction of covering-based rough sets has made a substantial contribution to the classical rough sets. However, many vital problems in rough sets, including attribution reduction, are NP-hard and therefore the algorithms for solving…
A rigidity theory is developed for frameworks in a metric space with two types of distance constraints. Mixed sparsity graph characterisations are obtained for the infinitesimal and continuous rigidity of completely regular bar-joint…
We consider a port-Hamiltonian system on a spatial domain $\Omega \subseteq \mathbb{R}^n$ that is bounded with Lipschitz boundary. We show that there is a boundary triple associated to this system. Hence, we can characterize all boundary…
The paper is dedicated to the study of strong duality for a problem of linear copositive programming. Based on the recently introduced concept of the set of normalized immobile indices, an extended dual problem is deduced. The dual problem…
We provide a unified framework in which the interlace polynomial and several related graph polynomials are defined more generally for multimatroids and delta-matroids. Using combinatorial properties of multimatroids rather than…
We show algorithms for computing representative families for matroid intersections and use them in fixed-parameter algorithms for set packing, set covering, and facility location problems with multiple matroid constraints. We complement our…
Implicit neural networks are a general class of learning models that replace the layers in traditional feedforward models with implicit algebraic equations. Compared to traditional learning models, implicit networks offer competitive…
A 2-dimensional point-line framework is a collection of points and lines in the plane which are linked by pairwise constraints that fix some angles between pairs of lines and also some point-line and point-point distances. It is rigid if…
A new general formalism for determining the electric multipole polarizabilities of quantum (atomic and nuclear) bound systems based on the use of the transition matrix in momentum space has been developed. As distinct from the conventional…
Matroid intersection is a classical optimization problem where, given two matroids over the same ground set, the goal is to find the largest common independent set. In this paper, we show that there exists a certain "sparsifer": a subset of…
We show that, for points along the moment curve, the bar-and-joint rigidity matroid and the hyperconnectivity matroid coincide, and that both coincide with the $C^{d-2}_{d-1}$-cofactor rigidity of points along any (non-degenerate) conic in…
We characterize the combinatorial types of symmetric frameworks in the plane that are minimally generically symmetry-forced infinitesimally rigid when the symmetry group consists of rotations and translations. Along the way, we use tropical…
The MAC-BC duality of information theory and wireless communications is an intriguing concept for efficient algorithm design. However, no concept is known so far for the important cellular channel. To make progress on this front, we…
Discrete polymatroids are the multi-set analogue of matroids. In this paper, we explore the connections among linear network coding, linear index coding and representable discrete polymatroids. We consider vector linear solutions of…