Related papers: Topological Structures of Large Scale Interacting …
In our previous article with Yukio Kametani, we investigated the geometric structure underlying a large scale interacting system on infinite graphs, via constructing a suitable cohomology theory called uniformly local cohomology, which…
We prove a uniform version of Varadhan decomposition for shift-invariant closed uniform forms associated to large scale interacting systems on general crystal lattices. In particular, this result includes the case of translation invariant…
We rigorously formulate and prove for a relatively general class of interactions Varadhan's Decomposition of shift-invariant closed $L^2$-forms for a large scale interacting system on the Euclidean lattice with finite range. Such…
Stochastic large scale interacting systems can be studied via the observables, i.e. functions on the underlying configuration space. In our previous article, we introduced the concept of uniform functions, which are suitable class of…
We investigate the dynamics of forward or backward self-similar systems (iterated function systems) and the topological structure of their invariant sets. We define a new cohomology theory (interaction cohomology) for forward or backward…
The study of complex systems has captured widespread attention in recent years, emphasizing the exploration of interactions and emergent properties among system units. Network analysis based on graph theory has emerged as a powerful…
Interactions in complex systems are widely observed across various fields, drawing increased attention from researchers. In mathematics, efforts are made to develop various theories and methods for studying the interactions between spaces.…
We will study a class of system composed of interacting unicyclic machines placed in contact with a hot and cold thermal baths subjected to a non-conservative driving worksource. Despite their simplicity, these models showcase an intricate…
Complex systems are difficult to study not only because they are nonlinear, multiscale, and often nonstationary, but because their scientifically relevant organization is often invisible at the level of individual components, pairwise…
Graphs serve as powerful tools for modeling pairwise interactions in diverse fields such as biology, material science, and social networks. However, they inherently overlook interactions involving more than two entities. Simplicial…
Tate cohomology has been generalised by several authors using different constructions that have applications in group theory, ring theory and homotopical algebra. Therefore, there is a need for a uniform account that explains why their…
In this note we introduce a notion of a morphism between two hyperbolic iterated function systems. We prove that the graph of a morphism is the attractor of an iterated function system, giving a Closed Graph Theorem, and show how it can be…
Hyperuniformity, the suppression of density fluctuations at large length scales, is observed across a wide variety of domains, from cosmology to condensed matter and biological systems. Although the standard definition of hyperuniformity…
We show that a fairly arbitrary Frechet space topology on the space of holomorphic functions on a domain controls the topology of uniform convergence on compact sets. In fact it turns out that the result we present can be proved more simply…
The "theory of open sub-functorial dynamics" is a new theory that defines interacting generalized dynamical systems. The interactions between these dynamics produce new dynamics which, of course, can then enter into other interactions. A…
We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part we discus the main structures…
Multilayer networks have permeated all the sciences as a powerful mathematical abstraction for interdependent heterogenous complex systems such as multimodal brain connectomes, transportation, ecological systems, and scientific…
The application of modern topology optimization techniques to single physics systems has seen great advances in the last three decades. However, the application of these tools to sophisticated multiphysics systems such as fluid-structure…
Over the past decade, a number of researchers in systems biology have sought to relate the function of biological systems to their network-level descriptions -- lists of the most important players and the pairwise interactions between them.…
In the context of complex algebraic varieties, the decomposition theorem for semi-small maps provides a decomposition of the direct image of the constant sheaf. In this work, we develop a decomposition theorem for branched coverings of…