Related papers: String Diagrams for Optics
Microscopy and optical imaging are drastically limited by the inhomogeneities encountered by the light while propagating from the object of interest to the detection system. In this context, adaptive optics and wavefront manipulation are…
4-dimensional optics is here introduced axiomatically as the space that supports a Universal wave equation which is applied to the postulated Higgs field. Self-guiding of this field is shown to produce all the modes necessary to provide…
Concept lattice drawings are an important tool to visualize complex relations in data in a simple manner to human readers. Many attempts were made to transfer classical graph drawing approaches to order diagrams. Although those methods are…
We provide a visual and intuitive introduction to effectively calculating in 2-groups along with explicit examples coming from non-abelian 1- and 2-form gauge theory. In particular, we utilize string diagrams, tools similar to tensor…
We introduce M\"obius strip diagram algebras (and their monoid and categorical versions) as subalgebras of a partition-style diagram calculus in which strands may carry handles and M\"obius strip features. We identify the resulting diagram…
Categories of polymorphic lenses in computer science, and of open games in compositional game theory, have a curious structure that is reminiscent of compact closed categories, but differs in some crucial ways. Specifically they have a…
The use of rewriting-based visual formalisms is on the rise. In the formal methods community, this is due also to the introduction of adhesive categories, where most properties of classical approaches to graph transformation, such as those…
Spin glasses are paradigmatic models that deliver concepts relevant for a variety of systems. However, rigorous analytical results are difficult to obtain for spin-glass models, in particular for realistic short-range models. Therefore…
The original idea of proof nets can be formulated by means of interaction nets syntax. Additional machinery as switching, jumps and graph connectivity is needed in order to ensure correspondence between a proof structure and a correct proof…
Lenses are programs that can be run both "front to back" and "back to front," allowing updates to either their source or their target data to be transferred in both directions. Lenses have been extensively studied, extended, and applied.…
Graph embedding algorithms are used to efficiently represent (encode) a graph in a low-dimensional continuous vector space that preserves the most important properties of the graph. One aspect that is often overlooked is whether the graph…
The machine learning community currently has no standardized process for documenting datasets, which can lead to severe consequences in high-stakes domains. To address this gap, we propose datasheets for datasets. In the electronics…
Graph-based signal processing techniques have become essential for handling data in non-Euclidean spaces. However, there is a growing awareness that these graph models might need to be expanded into `higher-order' domains to effectively…
Order diagrams are an important tool to visualize the complex structure of ordered sets. Favorable drawings of order diagrams, i.e., easily readable for humans, are hard to come by, even for small ordered sets. Many attempts were made to…
We commonly think of mathematics as bringing precision to application domains, but its relationship with computer science is more complex. This experience report on the use of Racket and Haskell to teach a required first university CS…
There is increasing focus on analyzing data represented as hypergraphs, which are better able to express complex relationships amongst entities than are graphs. Much of the critical information about hypergraph structure is available only…
The study of abstraction and composition - the focus of category theory - naturally leads to sophisticated diagrams which can encode complex algebraic semantics. Consequently, these diagrams facilitate a clearer visual comprehension of…
We survey work on the paradigm called "computing by observing." Its central feature is that one considers the behavior of an evolving system as the result of a computation. To this end an observer records this behavior. It has turned out…
Diagrams are common tools for representing complex concepts, relationships and events, often when it would be difficult to portray the same information with natural images. Understanding natural images has been extensively studied in…
In quantum electrodynamics, optical processes are theoretically described by double-sided Feynman diagrams. This formalism is powerful in the case of molecules but proves inappropriate to account for light-matter interactions within complex…