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Denoising-based models, including diffusion and flow matching, have led to substantial advances in graph generation. Despite this progress, such models remain constrained by two fundamental limitations: a computational cost that scales…

Most statistical models for networks focus on pairwise interactions between nodes. However, many real-world networks involve higher-order interactions among multiple nodes, such as co-authors collaborating on a paper. Hypergraphs provide a…

We present a general, flexible modeling abstraction for building and working with distributed optimization problems called a RemoteOptiGraph. This abstraction extends the OptiGraph model in Plasmo$.$jl, where optimization problems are…

Accurately modeling chemical reactions in molecular dynamics simulations requires detailed pre- and post-reaction templates, often created through labor-intensive manual workflows. This work introduces a Python-based algorithm that…

In real world domains, most graphs naturally exhibit a hierarchical structure. However, data-driven graph generation is yet to effectively capture such structures. To address this, we propose a novel approach that recursively generates…

Resource allocation and scheduling are a common problem in various distributed systems. Although widely studied, the state-of-the-art solutions either do not scale or lack the expressive power to capture the most complex instances of the…

Network interactions that are nonlinear in the state of more than two nodes - also known as higher-order interactions - can have a profound impact on the collective network dynamics. Here we develop a coupled cell hypernetwork formalism to…

In the first part of this paper, we propose new optimization-based methods for the computation of preferred (dense, sparse, reversible, detailed and complex balanced) linearly conjugate reaction network structures with mass action dynamics.…

Urban intersections are prone to delays and inefficiencies due to static precedence rules and occlusions limiting the view on prioritized traffic. Existing approaches to improve traffic flow, widely known as automatic intersection…

We present an extension of our Molecular Transformer architecture combined with a hyper-graph exploration strategy for automatic retrosynthesis route planning without human intervention. The single-step retrosynthetic model sets a new state…

Reaction-diffusion systems offer a powerful framework for understanding self-organized patterns in biological systems, yet controlling these patterns remains a significant challenge. As a consequence, we present a rigorous framework of…

Many real-world graphs involve different types of nodes and relations between nodes, being heterogeneous by nature. The representation learning of heterogeneous graphs (HGs) embeds the rich structure and semantics of such graphs into a…

Complex systems often show macroscopic coherent behavior due to the interactions of microscopic agents like molecules, cells, or individuals in a population with their environment. However, simulating such systems poses several…

Graph-based signal processing techniques have become essential for handling data in non-Euclidean spaces. However, there is a growing awareness that these graph models might need to be expanded into `higher-order' domains to effectively…

In this paper, we introduce a self-supervised learning method to enhance the graph-level representations with the help of a set of subgraphs. For this purpose, we propose a universal framework to generate subgraphs in an auto-regressive way…

Nested regular path queries are used for querying graph databases and RDF triple stores. We propose a new algorithm for evaluating nested regular path queries on a graph from a set of start nodes in combined linear time. We show that this…

Mechanistic network models specify the mechanisms by which networks grow and change, allowing researchers to investigate complex systems using both simulation and analytical techniques. Unfortunately, it is difficult to write likelihoods…

A nonlinear multigrid solver for two-phase flow and transport in a mixed fractional-flow velocity-pressure-saturation formulation is proposed. The solver, which is under the framework of the full approximation scheme (FAS), extends our…

In complex systems (e.g., communication, transportation, and biological networks), high robustness ensures sustained functionality and stability even when resisting attacks. However, the inherent structure complexity and the…

In this paper, the synchronization in a hyper-network of coupled dynamical systems is investigated for the first time. An evolving hyper-network model is proposed for better describing some complex systems. A concept of joint degree is…