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The richness of many complex systems stems from the interactions among their components. The higher-order nature of these interactions, involving many units at once, and their temporal dynamics constitute crucial properties that shape the…
We introduce the Insertion Chain Complex, a higher-dimensional extension of insertion graphs, as a new framework for analyzing finite sets of words. We study its topological and combinatorial properties, in particular its homology groups,…
Nanoparticles with "sticky patches" have long been proposed as building blocks for the self-assembly of complex structures. The synthetic realizability of such patchy particles, however, greatly lags behind predictions of patterns they…
Introduced the quantitative measure of the structural complexity of the graph (complex network, etc.) based on a procedure similar to the renormalization process, considering the difference between actual and averaged graph structures on…
Higher-order networks, naturally described as hypergraphs, are essential for modeling real-world systems involving interactions among three or more entities. Stochastic block models offer a principled framework for characterizing mesoscale…
The bond graph approach to modelling biochemical networks is extended to allow hierarchical construction of complex models from simpler components. This is made possible by representing the simpler components as thermodynamically open…
Hypergraphs provide a natural way to represent polyadic relationships in network data. For large hypergraphs, it is often difficult to visually detect structures within the data. Recently, a scalable polygon-based visualization approach was…
Hierarchically designed mechanical metamaterials involve nested levels of structural organization, mimicking natural structures (such as bones, wood, and bird feathers) to create advanced functional materials. Compositional hierarchy, a…
We describe a new generation of algorithms capable of mapping the structure and conformations of macromolecules and their complexes from large ensembles of heterogeneous snapshots, and demonstrate the feasibility of determining both…
The Program Semantic Graph (PSG) introduced in prior work on Dimensional Type Systems and Deterministic Memory Management encodes compilation-relevant properties as binary edge relations between computation nodes. This representation is…
In recent years, the creation of block-structured dictionary has attracted a lot of interest. Learning such dictionaries involve two step process: block formation and dictionary update. Both these steps are important in producing an…
Self-supervised semantic segmentation methods often suffer from structural errors, including merging distinct objects or fragmenting coherent regions, because they rely primarily on low-level appearance cues such as color and texture. These…
At the cutting edge of materials science, matter is designed to self-organize into structures that perform a wide range of functions. The past two decades have witnessed major innovations in the versatility of building blocks, ranging from…
Providing an abstract representation of natural and human complex structures is a challenging problem. Accounting for the system heterogenous components while allowing for analytical tractability is a difficult balance. Here I introduce…
Most existing popular methods for learning graph embedding only consider fixed-order global structural features and lack structures hierarchical representation. To address this weakness, we propose a novel graph embedding algorithm named…
The rise in complexity of network data in neuroscience, social networks, and protein-protein interaction networks has been accompanied by several efforts to model and understand these data at different scales. A key multiscale network…
On the basis of a model system of pillars built of unit cubes, a two-component entropic measure for the multiscale analysis of spatio-compositional inhomogeneity is proposed. It quantifies the statistical dissimilarity per cell of the…
We study the problem of conjunctive query evaluation relative to a class of queries; this problem is formulated here as the relational homomorphism problem relative to a class of structures A, wherein each instance must be a pair of…
Structure-Based Drug Design (SBDD) is a powerful strategy in computational drug discovery, utilizing three-dimensional protein structures to guide the design of molecules with improved binding affinity. However, capturing complex…
Efforts toward a comprehensive description of behavior have indeed facilitated the development of representation-based approaches that utilize deep learning to capture behavioral information. As behavior complexity increases, the expressive…