10 research outputs found
On Stability and Consensus of Signed Networks: A Self-loop Compensation Perspective
Positive semidefinite is not an inherent property of signed Laplacians, which
renders the stability and consensus of multi-agent system on undirected signed
networks intricate. Inspired by the correlation between diagonal dominance and
spectrum of signed Laplacians, this paper proposes a self-loop compensation
mechanism in the design of interaction protocol amongst agents and examines the
stability/consensus of the compensated signed networks. It turns out that
self-loop compensation acts as exerting a virtual leader on these agents that
are incident to negative edges, steering whom towards origin. Analytical
connections between self-loop compensation and the collective behavior of the
compensated signed network are established. Necessary and/or sufficient
conditions for predictable cluster consensus of signed networks via self-loop
compensation are provided. The optimality of self-loop compensation is
discussed. Furthermore, we extend our results to directed signed networks where
the symmetry of signed Laplacian is not free. Simulation examples are provided
to demonstrate the theoretical results
Dynamics over Signed Networks
A signed network is a network with each link associated with a positive or
negative sign. Models for nodes interacting over such signed networks, where
two different types of interactions take place along the positive and negative
links, respectively, arise from various biological, social, political, and
economic systems. As modifications to the conventional DeGroot dynamics for
positive links, two basic types of negative interactions along negative links,
namely the opposing rule and the repelling rule, have been proposed and studied
in the literature. This paper reviews a few fundamental convergence results for
such dynamics over deterministic or random signed networks under a unified
algebraic-graphical method. We show that a systematic tool of studying node
state evolution over signed networks can be obtained utilizing generalized
Perron-Frobenius theory, graph theory, and elementary algebraic recursions.Comment: In press, SIAM Revie
Bures-Wasserstein Means of Graphs
Finding the mean of sampled data is a fundamental task in machine learning
and statistics. However, in cases where the data samples are graph objects,
defining a mean is an inherently difficult task. We propose a novel framework
for defining a graph mean via embeddings in the space of smooth graph signal
distributions, where graph similarity can be measured using the Wasserstein
metric. By finding a mean in this embedding space, we can recover a mean graph
that preserves structural information. We establish the existence and
uniqueness of the novel graph mean, and provide an iterative algorithm for
computing it. To highlight the potential of our framework as a valuable tool
for practical applications in machine learning, it is evaluated on various
tasks, including k-means clustering of structured aligned graphs,
classification of functional brain networks, and semi-supervised node
classification in multi-layer graphs. Our experimental results demonstrate that
our approach achieves consistent performance, outperforms existing baseline
approaches, and improves the performance of state-of-the-art methods
On the local metric property in multivariate extremes
Many multivariate data sets exhibit a form of positive dependence, which can
either appear globally between all variables or only locally within particular
subgroups. A popular notion of positive dependence that allows for localized
positivity is positive association. In this work we introduce the notion of
extremal positive association for multivariate extremes from threshold
exceedances. Via a sufficient condition for extremal association, we show that
extremal association generalizes extremal tree models. For H\"usler--Reiss
distributions the sufficient condition permits a parametric description that we
call the metric property. As the parameter of a H\"usler--Reiss distribution is
a Euclidean distance matrix, the metric property relates to research in
electrical network theory and Euclidean geometry. We show that the metric
property can be localized with respect to a graph and study surrogate
likelihood inference. This gives rise to a two-step estimation procedure for
locally metrical H\"usler--Reiss graphical models. The second step allows for a
simple dual problem, which is implemented via a gradient descent algorithm.
Finally, we demonstrate our results on simulated and real data.Comment: 22 pages, 4 figure
Stability Bounds of Droop-Controlled Inverters in Power Grid Networks
The energy mix of future power systems will include high shares of electricity generation by wind turbines and solar photovoltaics. These generation facilities are generally connected via power-electronic inverters. While conventional generation responds dynamically to the state of the electric power system, inverters are power-electronic hardware and need to be programmed to react to the state of the system. Choosing an appropriate control scheme and the corresponding parameters is necessary to guarantee that the system operates safely. A prominent control scheme for inverters is droop control, which mimics the response of conventional generation. In this work, we investigate the stability of coupled systems of droop-controlled inverters in arbitrary network topologies. Employing linear stability analysis, we derive effective local stability criteria that consider both the overall network topology as well as its interplay with the inverters’ intrinsic parameters. First, we explore the stability of an inverter coupled to an infinite grid and uncover stability and instability regions. Second, we extend the analysis to a generic topology of inverters and provide mathematical criteria for the stability and instability of the system. Last, we showcase the usefulness of the criteria by examining two model systems using numerical simulations. The developed criteria show which parameters might lead to an unstable operating state.Stability Bounds of Droop-Controlled Inverters in Power Grid NetworkspublishedVersio
LIPIcs, Volume 261, ICALP 2023, Complete Volume
LIPIcs, Volume 261, ICALP 2023, Complete Volum