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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…
To cope with the intractability of answering Conjunctive Queries (CQs) and solving Constraint Satisfaction Problems (CSPs), several notions of hypergraph decompositions have been proposed -- giving rise to different notions of width,…
Highly periodic structures are often said to convey the beauty of nature. However, most material properties are strongly influenced by the defects they contain. On the mesoscopic scale, molecular self-assembly exemplifies this interplay;…
Recent advancements in the synthesis of anisotropic macromolecules and nanoparticles have spurred an immense interest in theoretical and computational studies of self-assembly. The cornerstone of such studies is the role of shape in…
Self-assembly processes are widespread in nature, and lie at the heart of many biological and physical phenomena. The characteristics of self-assembly building blocks determine the structures that they form. Two crucial properties are the…
High-rate bivariate bicycle (BB) codes are promising low-overhead quantum memories, but their stabilizer checks typically have weight $6$ or higher, making syndrome extraction challenging. We introduce subsystem bivariate bicycle (SBB)…
Complex systems are often driven by higher-order interactions among multiple units, naturally represented as hypergraphs. Understanding dependency structures within these hypergraphs is crucial for understanding and predicting the behavior…
The mathematical formalisms used to model biological systems induce both latent and ambiguous assumptions that can limit or distort their representational capabilities. Developing formalisms that can represent systems more precisely is…
We introduce a high-performance linear-scaling electronic structure method that employs chromatic superposition states (CSS) as a low-dimensional, high-fidelity representation, which can be orders of magnitude smaller than the full Hilbert…
Assembly planning is a difficult problem for companies. Many disciplines such as design, planning, scheduling, and manufacturing execution need to be carefully engineered and coordinated to create successful product assembly plans. Recent…
Understanding and navigating large-scale codebases remains a significant challenge in software engineering. Existing methods often treat code as flat text or focus primarily on local structural relationships, limiting their ability to…
It is discussed how the superstatistical formulation of effective Boltzmann factors can be related to the concept of Kolmogorov complexity, generating an infinite set of complexity measures (CMs) for quantifying information. At this level,…
Spontaneous self-assembly in molecular systems is a fundamental route to both biological and engineered soft matter. Simple micellisation, emulsion formation, and polymer mixing principles are well understood. However, the principles behind…
Self-assembly of dilute sequence-defined macromolecules is a complex phenomenon in which the local arrangement of chemical moieties can lead to the formation of long-range structure. The dependence of this structure on the sequence…
Hypergraphs naturally represent group interactions, which are omnipresent in many domains: collaborations of researchers, co-purchases of items, joint interactions of proteins, to name a few. In this work, we propose tools for answering the…
Assessing the synergistic high-order behaviors (HOBs) that emerge from underlying structural mechanisms is crucial to characterize complex systems. This work leverages the combined use of predictability and information measures to detect…
Modern cyber-physical systems (CPS) integrate physics, computation, and learning, demanding modeling frameworks that are simultaneously composable, learnable, and verifiable. Yet existing approaches treat these goals in isolation: causal…
Hypergraphs naturally represent group interactions, which are omnipresent in many domains: collaborations of researchers, co-purchases of items, and joint interactions of proteins, to name a few. In this work, we propose tools for answering…
In a previous work a procedure was decribed for dividing the $3 \times N$-dimensional conformational space of a molecular system into a number of discrete cells, this partition allowed the building of a combinatorial structure from data…
Due to the subtle balance of intermolecular interactions that govern structure-property relations, predicting the stability of crystal structures formed from molecular building blocks is a highly non-trivial scientific problem. A…