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Comprehending complex systems by simplifying and highlighting important dynamical patterns requires modeling and mapping higher-order network flows. However, complex systems come in many forms and demand a range of representations,…
Recently, graph neural networks have been widely used for network embedding because of their prominent performance in pairwise relationship learning. In the real world, a more natural and common situation is the coexistence of pairwise…
In this paper we consider random linear under-determined systems with block-sparse solutions. A standard subvariant of such systems, namely, precisely the same type of systems without additional block structuring requirement, gained a lot…
Additive manufacturing methods together with topology optimization have enabled the creation of multiscale structures with controlled spatially-varying material microstructure. However, topology optimization or inverse design of such…
Networks are one of the most valuable data structures for modeling problems in the real world. However, the most recent node embedding strategies have focused on undirected graphs, with limited attention to directed graphs, especially…
This paper investigates the consensus problem in almost sure sense for uncertain multi-agent systems with noises and fixed topology. By combining the tools of stochastic analysis, algebraic graph theory, and matrix theory, we analyze the…
Hypergraphs, increasingly utilised to model complex and diverse relationships in modern networks, have gained significant attention for representing intricate higher-order interactions. Among various challenges, cohesive subgraph discovery…
In this work, we introduce an iterative linearised finite element method for the solution of Bingham fluid flow problems. The proposed algorithm has the favourable property that a subsequence of the sequence of iterates generated converges…
In this paper we examine the model matching problem that concerns nonlinear input - output discrete systems, containing products among delays of input and output signals, through a special factorization. The algebraic framework of $\de…
We solve the problem of identifying (reconstructing) network topology from steady state network measurements. Concretely, given only a data matrix $\mathbf{X}$ where the $X_{ij}$ entry corresponds to flow in edge $i$ in configuration…
We introduce a framework for automatically defining and learning deep generative models with problem-specific structure. We tackle problem domains that are more traditionally solved by algorithms such as sorting, constraint satisfaction for…
We study the problem of identifying different behaviors occurring in different parts of a large heterogenous network. We zoom in to the network using lenses of different sizes to capture the local structure of the network. These network…
We present a complexity reduction algorithm for a family of parameter-dependent linear systems when the system parameters belong to a compact semi-algebraic set. This algorithm potentially describes the underlying dynamical system with…
In this paper, we present a general framework for efficiently computing diverse solutions to combinatorial optimization problems. Given a problem instance, the goal is to find $k$ solutions that maximize a specified diversity measure; the…
Recently, with the significant developments in deep learning techniques, solving underdetermined inverse problems has become one of the major concerns in the medical imaging domain. Typical examples include undersampled magnetic resonance…
Managing heterogeneous network systems is a difficult task because each of these networks has its own curious management system. These networks usually are constructed on independent management protocols which are not compatible with each…
The heterogeneous network is a robust data abstraction that can model entities of different types interacting in various ways. Such heterogeneity brings rich semantic information but presents nontrivial challenges in aggregating the…
The challenge of finding exact and finite-dimensional Koopman embeddings of nonlinear systems has been largely circumvented by employing data-driven techniques to learn models of different complexities (e.g., linear, bilinear, input…
In the present work, a simple algorithm for stabilizing an unknown linear time-invariant system is proposed, assuming only that this system is stabilizable. The suggested algorithm is based on first performing a partial identification of…
We present algorithms used in the computational part of the article "Special homogeneous linear systems on Hirzebruch surfaces".