Related papers: On Networks Over Finite Rings
Large-scale Dynamic Networks (LDNs) are becoming increasingly important in the Internet age, yet the dynamic nature of these networks captures the evolution of the network structure and how edge weights change over time, posing unique…
We study primary submodules and primary decompositions from a differential and computational point of view. Our main theoretical contribution is a general structure theory and a representation theorem for primary submodules of an arbitrary…
Efficient and robust control using spiking neural networks (SNNs) is still an open problem. Whilst behaviour of biological agents is produced through sparse and irregular spiking patterns, which provide both robust and efficient control,…
Purpose: To develop the algebraic foundation of finite commutative ternary $\Gamma$-semirings by identifying their intrinsic invariants, lattice organization, and radical behavior that generalize classical semiring and $\Gamma$-ring…
Let R be a commutative ring with unity, M a module over R and let S be a G-set for a finite group G. We define a set MS to be the set of elements expressed as the formal finite sum of the form similar to the elements of group ring RG. The…
The effectiveness of many optimal network control algorithms (e.g., BackPressure) relies on the premise that all of the nodes are fully controllable. However, these algorithms may yield poor performance in a partially-controllable network…
In this paper, we introduce and study two new classes of commutative rings, namely semi transitional rings and transitional rings, which extend several classical ideas arising from rings of continuous functions and their variants. A general…
Tensor ring (TR) decomposition is an efficient approach to discover the hidden low-rank patterns for higher-order tensors, and streaming tensors are becoming highly prevalent in real-world applications. In this paper, we investigate how to…
Unveiling the underlying control principles of complex networks is one of the ultimate goals of network science. We introduce a novel concept, control hub, to reveal a cornerstone of the control structure of a network. The control hubs of a…
Fixed-size commutative rings are quasi-ordered such that all scalar linearly solvable networks over any given ring are also scalar linearly solvable over any higher-ordered ring. As consequences, if a network has a scalar linear solution…
In this paper, we elaborate ring theoretic properties of nodal orders. In particular, we prove that they are closed under taking crossed products with finite groups.
The ability to control complex networks is of crucial importance across a wide range of applications in natural and engineering sciences. However, issues of both theoretical and numerical nature introduce fundamental limitations to…
Controlling a complex network towards a desired state is of great importance in many applications. A network can be controlled by inputting suitable external signals into some selected nodes, which are called driver nodes. Previous works…
An algorithm for irreducible decomposition of representations of finite groups over fields of characteristic zero is described. The algorithm uses the fact that the decomposition induces a partition of the invariant inner product into a…
We develop two generalizations of contraction theory, namely, semi-contraction and weak-contraction theory. First, using the notion of semi-norm, we propose a geometric framework for semi-contraction theory. We introduce matrix…
In areas such as computer software and hardware, manufacturing systems, and transportation, engineers encounter networks with arbitrarily large numbers of isomorphic subprocesses. Parameterized systems provide a framework for modeling such…
We define a notion of network capacity region of networks that generalizes the notion of network capacity defined by Cannons et al. and prove its notable properties such as closedness, boundedness and convexity when the finite field is…
A two-layer control architecture is proposed, which promotes scalable implementations for model predictive controllers. The top layer acts as both a reference governor for the bottom layer and as a feedback controller for the regulated…
We consider discrete-time dynamics, for cascading failure in DC networks, whose map is composition of failure rule with control actions. Supply-demand at the nodes is monotonically non-increasing under admissible control. Under the failure…
Recently, we have introduced and modified two graph-decomposition theorems based on a new graph product, motivated by applications in the context of synchronising periodic real-time processes. This vertex-removing synchronised product…