相关论文: Natural Topology
We discuss tipping phenomena (critical transitions) in nonautonomous systems using an example of a bistable ecosystem model with environmental changes represented by time-varying parameters [Scheffer et al., Ecosystems, 11 (2008), pp.…
Topological phase of matter is now a mainstream of research in condensed matter physics, of which the classification, synthesis, and detection of topological states have brought excitements over the recent decade while remain incomplete…
The central idea of metamaterials and metaoptics is that, besides their base materials, the geometry of structures offers a broad extra dimension to explore for exotic functionalities. Here, we discover that the topology of structures…
Statistical Topology emerged since topological aspects continue to gain importance in many areas of physics. It is most desirable to study topological invariants and their statistics in schematic models that facilitate the identification of…
Physics-informed neural networks (PINNs) effectively embed physical principles into machine learning, but often struggle with complex or alternating geometries. We propose a novel method for integrating geometric transformations within…
At its core, the physics paradigm adopts a reductionist approach, aiming to understand fundamental phenomena by decomposing them into simpler, elementary processes. While this strategy has been tremendously successful in physics, it has…
The framework Topology of Sustainable Management by Heitzig et al. (2016) distinguishes qualitatively different regions in state space of dynamical models representing manageable systems with default dynamics. In this paper, we connect the…
A generalized-homology bordism-theory is constructed, such that for certain manifold homotopy stratified sets (MHSS; Quinn-spaces) homeomorphism-invariant geometric fundamental-classes exist. The construction combines three ideas: Firstly,…
The paper studies the concepts of hedging and arbitrage in a non probabilistic framework. It provides conditions for non probabilistic arbitrage based on the topological structure of the trajectory space and makes connections with the usual…
We develop a language for describing the relationship among observations, mathematical models, and the underlying principles from which they are derived. Using Information Geometry, we consider geometric properties of statistical models for…
I give a geometric construction of certain first order natural dynamical observables in multifield cosmological models with arbitrary target space topology and discuss a system of related dynamical approximations and regimes for such…
The predictions of mean-field electrodynamics can now be probed using direct numerical simulations of random flows and magnetic fields. When modelling astrophysical MHD, it is important to verify that such simulations are in agreement with…
Topological phenomena typically govern the behavior of delocalized waves, giving rise to robust transport in electronic, photonic, and mechanical systems. Whether similar principles can directly control the motion of a localized particle,…
Unlike the case of surfaces of topologically finite type, there are several different Teichm\"uller spaces that are associated to a surface of topological infinite type. These Teichm\"uller spaces first depend (set-theoretically) on whether…
Various kinds of data are routinely represented as discrete probability distributions. Examples include text documents summarized by histograms of word occurrences and images represented as histograms of oriented gradients. Viewing a…
I explain the difficulty of making various concepts of and relating to probability precise, rigorous and physically significant when attempting to apply them in reasoning about objects (e.g., spacetimes) living in infinite-dimensional…
We present a physically-inspired model and an efficient algorithm to infer hierarchical rankings of nodes in directed networks. It assigns real-valued ranks to nodes rather than simply ordinal ranks, and it formalizes the assumption that…
Topological interactions are an essential ingredient for building consistent low-energy theories of fermions, gauge fields and Nambu-Goldstone bosons in the absence of explicit UV completions, such as in Little Higgs models. These…
We consider the problem of inferring the topology of a network using the measurements available at the end nodes, without cooperation from the internal nodes. To this end, we provide a simple method to obtain path interference which…
Emergent patterns in complex systems are related to many intriguing phenomena in modern science and philosophy. Several conceptions such as weak, strong and robust emergence have been proposed to emphasize different epistemological and…