Related papers: Scaled Relative Graph of Normal Matrices
Graphs serve as generic tools to encode the underlying relational structure of data. Often this graph is not given, and so the task of inferring it from nodal observations becomes important. Traditional approaches formulate a convex inverse…
Let G be an arbitrary finite weighted digraph with weights in the set of complex rational functions. A general procedure is proposed which allows for the reduction of G to a smaller graph with a less complicated structure having the same…
We consider solving a probably ill-conditioned linear operator equation, where the operator is not modeled by physical laws but is specified via training pairs (consisting of images and data) of the input-output relation of the operator. We…
Random feature maps are ubiquitous in modern statistical machine learning, where they generalize random projections by means of powerful, yet often difficult to analyze nonlinear operators. In this paper, we leverage the "concentration"…
Robots rely heavily on sensors, especially RGB and depth cameras, to perceive and interact with the world. RGB cameras record 2D images with rich semantic information while missing precise spatial information. On the other side, depth…
Coordinating multi-robot systems (MRS) to search in unknown environments is particularly challenging for tasks that require semantic reasoning beyond geometric exploration. Classical coordination strategies rely on frontier coverage or…
Let $D$ be an oriented graph with skew adjacency matrix $S(D)$. Two oriented graphs $D$ and $C$ are said to share the same generalized skew spectrum if $S(D)$ and $S(C)$ have the same eigenvalues, and $J-S(D)$ and $J-S(C)$ also have the…
Stochastic variance reduced gradient (SVRG) is an accelerated version of stochastic gradient descent based on variance reduction, and is promising for solving large-scale inverse problems. In this work, we analyze SVRG and a regularized…
We define a graded graph, called the Schur--Weyl graph, which arises naturally when one considers simultaneously the RSK algorithm and the classical duality between representations of the symmetric and general linear groups. As one of the…
Graph-based methods have been proposed as a unified framework for discrete calculus of local and nonlocal image processing methods in the recent years. In order to translate variational models and partial differential equations to a graph,…
A matrix-weighted graph is an undirected graph with a $k\times k$ positive semidefinite matrix assigned to each edge. There are natural generalizations of the Laplacian and adjacency matrices for such graphs. These matrices can be used to…
This work addresses a modification of the random geometric graph (RGG) model by considering a set of points uniformly and independently distributed on the surface of a $(d-1)$-sphere with radius $r$ in a $d-$dimensional Euclidean space,…
A conjugate skew gain graph is a skew gain graph with the labels (also called, the conjugate skew gains) from the field of complex numbes on the oriented edges such that they get conjugated when we reverse the orientation. In this paper we…
Regression analysis is used for prediction and to understand the effect of independent variables on dependent variables. Symbolic regression (SR) automates the search for non-linear regression models, delivering a set of hypotheses that…
Regular ring lattices (RRLs) are defined as peculiar undirected circulant graphs constructed from a cycle graph, wherein each node is connected to pairs of neighbors that are spaced progressively in terms of vertex degree. This kind of…
A graph is a mathematical object consisting of a set of vertices and a set of edges connecting vertices. Graphs can be drawn on paper in various ways, but until recently all published methods of drawing graphs have had undesirable…
The spherical Radon transform (SRT) is an integral transform that maps a function to its integrals over concentric spherical shells centered at specified sensor locations. It has several imaging applications, including synthetic aperture…
Graph is an abstract representation commonly used to model networked systems and structure. In problems across various fields, including computer vision and pattern recognition, and neuroscience, graphs are often brought into comparison (a…
Radiative symmetry breaking (RSB) is a theoretically appealing framework for the generation of mass scales through quantum effects. It can be successfully implemented in models with extended scalar and gauge sectors. We provide a systematic…
A multi-relational graph maintains two or more relations over a vertex set. This article defines an algebra for traversing such graphs that is based on an $n$-ary relational algebra, a concatenative single-relational path algebra, and a…