Related papers: Modeling of Physical Network Systems
Kirchhoff's Matrix-Tree Theorem asserts that the number of spanning trees in a finite graph can be computed from the determinant of any of its reduced Laplacian matrices. In many cases, even for well-studied families of graphs, this can be…
Transmission line failures in power systems propagate non-locally, making the control of the resulting outages extremely difficult. In this work, we establish a mathematical theory that characterizes the patterns of line failure propagation…
The diagrammatic analysis of interacting particle assemblies harbors a fundamental mismatch between two of its main implementations: Phi-derivable (conserving) approximations and parquet (crossing symmetric) models. No termwise expansion,…
This work clarifies the relation between network circuit (topology) and behavior (information transmission and synchronization) in active networks, e.g. neural networks. As an application, we show how to determine a network topology that is…
The design of robust supply and distribution systems is one of the fundamental challenges at the interface of network science and logistics. Given the multitude of performance criteria, real-world constraints, and external influences acting…
The characterization of the notions of complex and detailed balancing for mass action kinetics chemical reaction networks is revisited from the perspective of algebraic graph theory, in particular Kirchhoff's Matrix Tree theorem for…
We introduce nonlocal dynamics on directed networks through the construction of a fractional version of a nonsymmetric Laplacian for weighted directed graphs. Furthermore, we provide an analytic treatment of fractional dynamics for both…
Many physical systems -- such as optical waveguide lattices and dense neuronal or vascular networks -- can be modeled by metric graphs, where slender "wires" (edges) support wave or diffusion equations subject to Kirchhoff conditions at the…
We consider spectral methods that uncover hidden structures in directed networks. We establish and exploit connections between node reordering via (a) minimizing an objective function and (b) maximizing the likelihood of a random graph…
We propose a linear programming (LP) framework for steady-state diffusion and flux optimization on geometric networks. The state variable satisfies a discrete diffusion law on a weighted, oriented graph, where conductances are scaled by…
To describe the flow of a miscible quantity on a network, we introduce the graph wave equation where the standard continuous Laplacian is replaced by the graph Laplacian. This is a natural description of an array of inductances and…
This paper proposes a general framework for structure-preserving model reduction of a secondorder network system based on graph clustering. In this approach, vertex dynamics are captured by the transfer functions from inputs to individual…
The structure of continuous Hopfield networks is revisited from a system-theoretic point of view. After adopting a novel electrical network interpretation involving nonlinear capacitors, it is shown that Hopfield networks admit a…
Signed networks appear naturally in contexts where conflict or animosity is apparent. In this book chapter we review some of the literature on signed networks, especially in the context of partitioning. Most of the work is founded in what…
We present a stochastic optimal control problem for a tree network. The dynamics of the network are governed by transport equations with a special emphasis on the non-linear damping function. Demand profiles at the network sinks are…
The fundamental theory of energy networks in different energy forms is established following an in-depth analysis of the nature of energy for comprehensive energy utilization. The definition of an energy network is given. Combining the…
We study the emergence of a power law distribution in the systems which can be characterized by a hierarchically organized supplying network. It is shown that conservation laws on the branches of the network can, at some approximation,…
Understanding and interacting with everyday physical scenes requires rich knowledge about the structure of the world, represented either implicitly in a value or policy function, or explicitly in a transition model. Here we introduce a new…
We develop inductive biases for the machine learning of complex physical systems based on the port-Hamiltonian formalism. To satisfy by construction the principles of thermodynamics in the learned physics (conservation of energy,…
Distributed Port-Hamiltonian (dPHS) theory provides a powerful framework for modeling physical systems governed by partial differential equations and has enabled a broad class of boundary control methodologies. Their effectiveness, however,…