Related papers: String Diagrams for Optics
Diagram chasing is not an easy task. The coherence holds in a generalized sense if we have a mechanical method to judge whether given two morphisms are equal to each other. A simple way to this end is to reform a concerned category into a…
We establish a general unified formulation which, using the optical theorem of electromagnetic helicity, shows that dichorism is a phenomenon arising in any scattering -or diffraction- process, elastic or not, of chiral electromagnetic…
We extend to higher order a recently published method for calculating the deflection angle of light in a general static and spherically symmetric metric. Since the method is convergent we obtain very accurate analytical expressions that we…
Alignments, i.e., position-wise comparisons of two or more strings or ordered lists are of utmost practical importance in computational biology and a host of other fields, including historical linguistics and emerging areas of research in…
In this article we discuss a data structure, which combines advantages of two different ways for representing graphs: adjacency matrix and collection of adjacency lists. This data structure can fast add and search edges (advantages of…
Mathematics is the language of science. Fluent and productive use of mathematics requires one to understand the meaning embodied in mathematical symbols, operators, syntax, etc., which can be a difficult task. For instance, in algebraic…
We review some of the recent developments in the construction of $W$-string theories. These are generalisations of ordinary strings in which the two-dimensional ``worldsheet'' theory, instead of being a gauging of the Virasoro algebra, is a…
We introduce string diagrams for physical duoidal categories (normal $\otimes$-symmetric duoidal categories): they consist of string diagrams with wires forming a zigzag-free partial order and order-preserving nodes whose inputs and outputs…
Spreadsheets are used extensively in industry, often for business critical purposes. In previous work we have analyzed the information needs of spreadsheet professionals and addressed their need for support with the transition of a…
The operations of linear algebra, calculus, and statistics are routinely applied to measurement scales but certain mathematical conditions must be satisfied in order for these operations to be applicable. We call attention to the conditions…
String diagrams are a powerful tool for reasoning about physical processes, logic circuits, tensor networks, and many other compositional structures. The distinguishing feature of these diagrams is that edges need not be connected to…
In category theory, the use of string diagrams is well known to aid in the intuitive understanding of certain concepts, particularly when dealing with adjunctions and monoidal categories. We show that string diagrams are also useful in…
Simple optics are defined using actions of monoidal categories. Compound optics arise, for instance, as natural transformations between polynomial functors. Since a monoidal category is a special case of a bicategory, we formulate complex…
The versatility of optics enables the design of a wide range of elegant beam instrumentation. Multiple properties of particle beams can be precisely measured by various optical techniques, which include: direct sampling of optical radiation…
It is common to introduce optical tweezers using either geometric optics for large particles or the Rayleigh approximation for very small particles. These approaches are successful at conveying the key ideas behind optical tweezers in their…
Proof nets are a syntax for linear logic proofs which gives a coarser notion of proof equivalence with respect to syntactic equality together with an intuitive geometrical representation of proofs. In this paper we give an alternative…
The various non-linear transformations incurred by the rays in an optical system can be modelled by matrix products up to any desired order of approximation. Mathematica software has been used to find the appropriate matrix coefficients for…
We study limits of convergent sequences of string graphs, that is, graphs with an intersection representation consisting of curves in the plane. We use these results to study the limiting behavior of a sequence of random string graphs. We…
The representation of graphs is commonly based on the adjacency matrix concept. This formulation is the foundation of most algebraic and computational approaches to graph processing. The advent of deep learning language models offers a wide…
A string graph is an intersection graph of curves in the plane. A $k$-string graph is a graph with a string representation in which every pair of curves intersects in at most $k$ points. We introduce the class of $(=k)$-string graphs as a…