Related papers: String Diagrams for Optics
We analyze the core structure of string defects in various condensed matter systems, such as nematic liquid crystals and superfluid helium, and argue that in certain cases the variation of the refractive index near the core is such that it…
Optics are bidirectional accessors of data structures; they provide a powerful abstraction of many common data transformations. This abstraction is compositional thanks to a representation in terms of profunctors endowed with an algebraic…
Traditional treatments of formal logic provide: 1. A syntax for formulas. 2. An inference relation between sets of formulas. 3. A rule for assigning meaning to formulas (semantics) that is sound with respect to the inference relation. First…
Lenses may be characterised as objects in the category of algebras over a monad, however they are often understood instead as morphisms, which propagate updates between systems. Working internally to a category with pullbacks, we define…
Lenses, optics and dependent lenses (or equivalently morphisms of containers, or equivalently natural transformations of polynomial functors) are all widely used in applied category theory as models of bidirectional processes. From the…
The unprecedented pace of machine learning research has lead to incredible advances, but also poses hard challenges. At present, the field lacks strong theoretical underpinnings, and many important achievements stem from ad hoc design…
We present a form of algebraic reasoning for computational objects which are expressed as graphs. Edges describe the flow of data between primitive operations which are represented by vertices. These graphs have an interface made of…
This is a general work on gravitational lensing. We present new expressions for the optical scalars and the deflection angle in terms of the energy-momentum tensor components of matter distributions. Our work generalizes standard references…
It is shown that the one-lens system in para-axial optics can serve as an optical computer for contraction of Wigner's little groups and an analogue computer which transforms analytically computations on a spherical surface to those on a…
The derivation of a function is a fundamental tool for solving problems in calculus. Consequently, the motivations for investigating physical systems capable of performing this task are numerous. Furthermore, the potential to develop an…
Calculi of string diagrams are increasingly used to present the syntax and algebraic structure of various families of circuits, including signal flow graphs, electrical circuits and quantum processes. In many such approaches, the semantic…
Modern applications of strong gravitational lensing require the ability to use precise and varied observational data to constrain complex lens models. I discuss two sets of computational methods for lensing calculations. The first is a new…
The description of light diffraction using catastrophe optics is one of the most intriguing theoretical invention in the field of classical optics of the last four decades. Its practical implementation has faced some resistance over the…
In modern mathematics, graphs figure as one of the better-investigated class of mathematical objects. Various properties of graphs, as well as graph-processing algorithms, can be useful if graphs of a certain kind are used as denotations…
A string diagram is a two-dimensional graphical representation that can be described as a one-dimensional term generated from a set of primitives using sequential and parallel compositions. Since different syntactic terms may represent the…
Although reasoning about equations over strings has been extensively studied for several decades, little research has been done for equational reasoning on general clauses over strings. This paper introduces a new superposition calculus…
Optical forces have been fruitfully applied in a broad variety of areas that not only span the traditional scientific fields such as physics, chemistry, and biology, but also in more applied fields. It is customary and useful to split the…
Functional programmers have an established tradition of using traversals as a design pattern to work with recursive data structures. The technique is so prolific that a whole host of libraries have been designed to help in the task of…
We establish a formal bridge between qubit-based and photonic quantum computing. We do this by defining a functor from the ZX calculus to linear optical circuits. In the process we provide a compositional theory of quantum linear optics…
We present explicit expressions for the optical scalars and the deection angle in terms of the energymomentum tensor components of matter distributions. Our work generalizes standard references in the literature where normally stringent…