Related papers: Topology and experimental distinguishability
Experimental science usually relies on laboratory procedures that, after finitely many steps, terminate with numerical reports on physical quantities. This paper argues that such procedures can be understood as algorithmic once the…
The non-classical features of quantum mechanics are reproduced using models constructed with a classical theory - general relativity. The inability to define complete initial data consistently and independently of future measurements,…
In quantum theory, observables with a continuous spectrum are known to be fundamentally different from those with a discrete and finite spectrum. While some fundamental tests and applications of quantum mechanics originally formulated for…
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…
Some of the basic concepts of topology are explored through known physics problems. This helps us in two ways, one, in motivating the definitions and the concepts, and two, in showing that topological analysis leads to a clearer…
This paper presents the first approach to visualize the importance of topological features that define classes of data. Topological features, with their ability to abstract the fundamental structure of complex data, are an integral…
Represented spaces form the general setting for the study of computability derived from Turing machines. As such, they are the basic entities for endeavors such as computable analysis or computable measure theory. The theory of represented…
Entropy can signify different things: For instance, heat transfer in thermodynamics or a measure of information in data analysis. Many entropies have been introduced and it can be difficult to ascertain their different importance and…
Natural data offer a hard challenge to data analysis. One set of tools is being developed by several teams to face this difficult task: Persistent topology. After a brief introduction to this theory, some applications to the analysis and…
Working in the soft-element (classical) viewpoint, we introduce \emph{soft bitopological groups}: soft groups endowed with two soft topologies such that the induced topologies on the set of soft elements make the soft-element group into a…
The concept of identifiability describes the possibility of inferring the parameters of a dynamic model by observing its output. It is common and useful to distinguish between structural and practical identifiability. The former property is…
Using nonstandard analysis we define a topology on the ring of germs of functions: $(mathbb R^n,0)\rightarrow(mathbb R,0)$. We prove that this topology is absolutely convex, Hausdorff, that convergent nets of continuous germs have…
We say a model is continuous in utilities (resp., preferences) if small perturbations of utility functions (resp., preferences) generate small changes in the model's outputs. While similar, these two questions are different. They are only…
Basic pairs and their morphisms are the most elementary framework in which standard topological notions can be defined. We present here a new interpretation of topological concepts as those which can be communicated faithfully between the…
Conformational transitions are ubiquitous in biomolecular systems, have significant functional roles and are subject to evolutionary pressures. Here we provide a first theoretical framework for topological transition, i.e. conformational…
Topology transcends boundaries that conventionally delineate physical, biological and engineering sciences. Our ability to mathematically describe topology, combined with our access to precision tracking and manipulation approaches, has…
Persistence modules are a central algebraic object arising in topological data analysis. The notion of interleaving provides a natural way to measure distances between persistence modules. We consider various classes of persistence modules,…
The central goal of this thesis is to develop methods to experimentally study topological phases. We do so by applying the powerful toolbox of quantum simulation techniques with cold atoms in optical lattices. To this day, a complete…
Empirical substantive research, such as in the life or social sciences, is commonly categorized into the two modes exploratory and confirmatory, both of which are essential to scientific progress. The former is also referred to as…
Category theory has foundational importance because it provides conceptual lenses to characterize what is important in mathematics. Originally the main lenses were universal mapping properties and natural transformations. In recent decades,…