Related papers: Stable Independence in Perfect Maps
In this paper, we consider the problem of testing independence in high-dimensional settings with missing data. Building upon a recently proposed Kendall-based statistic, we introduce two new modifications specifically designed to…
This paper is concerned with path-complete barrier functions which offer a graph-based methodology for verifying safety properties in switched systems. The path-complete framework leverages algebraic (barrier functions) as well as…
This paper revisits the Pearson Chi-squared independence test. After presenting the underlying theory with modern notations and showing new way of deriving the proof, we describe an innovative and intuitive graphical presentation of this…
This paper investigates observability/controllability of a networked dynamic system (NDS) in which system matrices of its subsystems are expressed through linear fractional transformations (LFT). Some relations have been obtained between…
Traditional centralized stability analysis struggles with scalability in large complex modern power grids. This two-part paper proposes a compositional and equilibrium-free approach to analyzing power system stability. In Part I, we prove…
The goal of this work is to identify steady-state solutions to dynamical systems defined on large, random families of networks. We do so by passing to a continuum limit where the adjacency matrix is replaced by a non-local operator with…
We consider a 2 d.o.f. Hamiltonian system with one degree of freedom corresponding to fast motion and the other corresponding to slow motion. The ratio of the time derivatives of slow and fast variables is of order $0<\eps \ll 1$. At frozen…
Recent work of Lazarovich provides necessary and sufficient conditions on a graph L for there to exist a unique simply-connected (k,L)-complex. The two conditions are symmetry properties of the graph, namely star-transitivity and…
The so-called permutation separability criteria are simple operational conditions that are necessary for separability of mixed states of multipartite systems: (1) permute the indices of the density matrix and (2) check if the trace norm of…
Graph convolutional networks have been successful in addressing graph-based tasks such as semi-supervised node classification. Existing methods use a network structure defined by the user based on experimentation with fixed number of layers…
This paper presents a novel approach to stability analysis for grid-connected converters utilizing Scaled Relative Graphs (SRG). Our method effectively decouples grid and converter dynamics, thereby establishing a comprehensive and…
We propose a generalization of the classical stable marriage problem. In our model, the preferences on one side of the partition are given in terms of arbitrary binary relations, which need not be transitive nor acyclic. This generalization…
We discuss properties of distributions that are multivariate totally positive of order two (MTP2) related to conditional independence. In particular, we show that any independence model generated by an MTP2 distribution is a compositional…
Necessary and sufficient conditions for a finite connected graph with a strict partial order on vertices to be a combinatorial invariant of pseudoharmonic function are obtained.
A graph is called $d$-rigid if there exists a generic embedding of its vertex set into $\mathbb{R}^d$ such that every continuous motion of the vertices that preserves the lengths of all edges actually preserves the distances between all…
Given a hereditary family $\mathcal{G}$ of admissible graphs and a function $\lambda(G)$ that linearly depends on the statistics of order-$\kappa$ subgraphs in a graph $G$, we consider the extremal problem of determining…
In the present paper, complete designs of graphs are considered. The notion of (regular) sampling is introduced and analyzed in detail, showing that the trivial necessary condition for its existence is actually sufficient. Some examples are…
We continue and extend previous work on the parameterized complexity analysis of the NP-hard Stable Roommates with Ties and Incomplete Lists problem, thereby strengthening earlier results both on the side of parameterized hardness as well…
This work proposes a novel distributed framework for verifying the incremental stability of large-scale systems with unknown dynamics and known interconnection structures using graph neural networks. Our proposed approach relies on the…
This paper deals with the controllability for a class of non-autonomous neutral differential equations of fractional order with infinite delay in an abstract space. The semi-group theory of bounded linear operators, fractional calculus, and…