Related papers: Structural and Compositional Complexities of Hiera…
An important question in the study of constraint satisfaction problems (CSP) is understanding how the graph or hypergraph describing the incidence structure of the constraints influences the complexity of the problem. For binary CSP…
We introduce constructible directed complexes, a combinatorial presentation of higher categories inspired by constructible complexes in poset topology. Constructible directed complexes with a greatest element, called atoms, encompass common…
Large language models show great potential in unstructured data understanding, but still face significant challenges with graphs due to their structural hallucination. Existing approaches mainly either verbalize graphs into natural…
In a previous work arXiv:physics/0611108v2, it was shown that the volume spanned by a molecular system in its conformational space can be effectively bounded by a polyhedral cone, this cone is described by means of a simple combinatorial…
The Constructive Solid Geometry (CSG) is a data model providing a set of binary Boolean operators such as Union, Difference and Intersection. In this work, these operators are used to compute topological relations between objects defined by…
Within the framework of generalized combinatorial approach, the complexity is determined for infinite set of self-similar hierarchical ensembles. This complexity is shown to increase with strengthening of the hierarchy coupling to the…
A graph theoretic approach is proposed for object shape representation in a hierarchical compositional architecture called Compositional Hierarchy of Parts (CHOP). In the proposed approach, vocabulary learning is performed using a hybrid…
Metamaterials exhibit materials response deviation from conventional elasticity. This phenomenon is captured by the generalized elasticity as a result of extending the theory at the expense of introducing additional parameters. These…
We produce a class of $\omega$-categorical structures with finite signature by applying a model-theoretic construction -- a refinement of the Hrushosvki-encoding -- to $\omega$-categorical structures in a possibly infinite signature. We…
Heterogeneous graph neural networks have become popular in various domains. However, their generalizability and interpretability are limited due to the discrepancy between their inherent inference flows and human reasoning logic or…
Co-assembly of inorganic nanoparticles (NPs) and nanostructured polymer matrix represents an intricate interplay of enthalpic or entropic forces. Particle size largely affects the phase behavior of the nanocomposite. Theoretical studies…
The problem of accelerating drug discovery relies heavily on automatic tools to optimize precursor molecules to afford them with better biochemical properties. Our work in this paper substantially extends prior state-of-the-art on…
Evaluating the (dis)similarity of crystalline, disordered and molecular compounds is a critical step in the development of algorithms to navigate automatically the configuration space of complex materials. For instance, a structural…
We study the problem of building generative models of natural source code (NSC); that is, source code written and understood by humans. Our primary contribution is to describe a family of generative models for NSC that have three key…
Characterization of medium-range order in amorphous materials and its relation to short-range order is discussed. A new topological approach is presented here to extract a hierarchical structure of amorphous materials, which is robust…
Publicly available collections of drug-like molecules have grown to comprise 10s of billions of possibilities in recent history due to advances in chemical synthesis. Traditional methods for identifying "hit" molecules from a large…
In this paper, we introduce the concept of self-amplifying structures for hypergraphs, positioning it as a key element for understanding propagation and internal reinforcement in complex systems. To quantify this phenomenon, we define the…
Because of its promising contribution to the bottom-up approach for nanofabrication of complex molecular architectures, self-organization is widely studied nowadays. Numerous studies have tackled supramolecular chirality or low-dimensional…
Hierarchies allow feature sharing between objects at multiple levels of representation, can code exponential variability in a very compact way and enable fast inference. This makes them potentially suitable for learning and recognizing a…
Topological subsystem codes were proposed by Bombin based on 3-face-colorable cubic graphs. Suchara, Bravyi and Terhal generalized this construction and proposed a method to construct topological subsystem codes using 3-valent hypergraphs…