相关论文: Category theoretic analysis of hierarchical protei…

Many complex systems can be represented as networks composed by distinct layers, interacting and depending on each others. For example, in biology, a good description of the full protein-protein interactome requires, for some organisms, up…

The topology of any complex system is key to understanding its structure and function. Fundamentally, algebraic topology guarantees that any system represented by a network can be understood through its closed paths. The length of each path…

Membrane particles such as proteins and lipids organize into zones that perform unique functions. Here, I introduce a topological and category-theoretic framework to represent particle and zone intra-scale interactions and inter-scale…

In this perspective article, we present a multidisciplinary approach for characterizing protein structure networks. We first place our approach in its historical context and describe the manner in which it synthesizes concepts from quantum…

Cellular function is widely believed to be organized in a modular fashion. On all scales and at all levels of complexity, relatively independent sub-units perform relatively independent sub-tasks of biological function. This functional…

Many complex systems in nature and society can be described in terms of networks capturing the intricate web of connections among the units they are made of. A key question is how to interpret the global organization of such networks as the…

Given a category fibered in groupoids over schemes with a log structure, one produces a category fibered in groupoids over log schemes. We classify the groupoid fibrations over log schemes that arise in this manner in terms of a categorical…

The linear representation hypothesis is the informal idea that semantic concepts are encoded as linear directions in the representation spaces of large language models (LLMs). Previous work has shown how to make this notion precise for…

Sequence comparison and alignment has had an enormous impact on our understanding of evolution, biology, and disease. Comparison and alignment of biological networks will likely have a similar impact. Existing network alignments use…

The principle of similarity, or homophily, is often used to explain patterns observed in complex networks such as transitivity and the abundance of triangles (3-cycles). However, many phenomena from division of labor to protein-protein…

We develop a representation theory of categories as a means to explore characteristic structures in algebra. Characteristic structures play a critical role in isomorphism testing of groups and algebras, and their construction and…

Chiral heteropolymers such as larger globular proteins can simultaneously support multiple length scales. The interplay between different scales brings about conformational diversity, and governs the structure of the energy landscape.…

One of the classical questions in evolutionary biology is how evolutionary processes are coupled at the gene and species level. With this motivation, we compare the topological properties (mainly the depth scaling, as a characterization of…

The natural world is full of complex systems characterized by intricate relations between their components: from social interactions between individuals in a social network to electrostatic interactions between atoms in a protein.…

Knowledge silos emerge when structural properties of organizational interaction networks limit the diffusion of information. These structural barriers are known to take many forms at different scales - hubs in otherwise sparse…

Allosteric regulation in proteins is often accompanied by conformational changes that facilitate transmission of mechanical signals between distant ligand binding sites. Typically, these deformations are classified in terms of specific…

Formation of a hierarchy within an organization is a natural way of assigning the duties, delegating responsibilities and optimizing the flow of information. Only for the smallest companies the lack of the hierarchy, that is, a flat one, is…

Living systems are often described utilizing informational analogies. An important open question is whether information is merely a useful conceptual metaphor, or intrinsic to the operation of biological systems. To address this question,…

This paper presents findings from a study of the email network of a large scientific research organization, focusing on methods for visualizing and modeling organizational hierarchies within large, complex network datasets. In the first…

Protein-Text Question Answering (QA) is crucial for interpreting biological sequences through natural language. The integration of Large Language Models (LLMs) with Retrieval-Augmented Generation (RAG) that efficiently leverages biological…