Related papers: Toy operads
The overall aim of this paper is to define a structure of graph operads, thus generalizing the celebrated pre-Lie operad on rooted trees. More precisely, we define two operads on multigraphs, and exhibit a non trivial link between them and…
The purpose of this paper is to study the derived category of simplicial multicategories with arbitrary sets of objects (also known as, colored operads in simplicial sets). Our main result is a derived Morita theory for operads-where we…
Deformable linear objects (e.g., cables, ropes, and threads) commonly appear in our everyday lives. However, perception of these objects and the study of physical interaction with them is still a growing area. There have already been…
Deformable object manipulation requires computationally efficient representations that are compatible with robotic sensing modalities. In this paper, we present VIRDO:an implicit, multi-modal, and continuous representation for…
A rectangular "shifting cloak", which visually shifts the cloaked object for a certain distance from the original place, is proposed. Comparing with the previously proposed similar cloaks, this rectangular shifting cloak has a much simpler…
Adaptive optics workbenches are fully functional optical systems that can be used to illustrate and teach a variety of concepts and cognitive processes. Four systems have been funded, designed and constructed by various institutions and…
This monograph provides a coherent development of operads, infinity operads, and monoidal categories, equipped with equivariant structures encoded by an action operad. A group operad is a planar operad with an action operad equivariant…
When talking to secondary school students, first impressions are crucial. Accidentally say something that sounds boring and you'll lose them in seconds. A physical demonstration can be an eye-catching way to begin an activity or spark off a…
Work in progress concerning alternative formalizations of arithmetic.
We describe four classical undergraduate physics experiments that were done with everyday objects and low-cost sensors: mechanical oscillations, transmittance of light through a slab of matter, beam deformation under load, and thermal…
The author considers a class of mechatronic puzzles falling in the mixed-reality category, present examples of such devices, and propose a way to categorize them. Close relationships of such devices with the Tangible User Interface are…
Circuit algebras are a symmetric version of Jones's planar algebras. They originated in quantum topology as a framework for encoding virtual crossings. This paper extends existing results for modular operads to construct a graphical…
The oscillation periods bounded by a simple pendulum and an oscillating rigid rod are illustrated using a multiple pendulum. Oscillation periods between these two limits are obtained. A theoretical approach using the Lagrangian formalism…
This paper provides a general operadic definition for the notion of splitting the operations of algebraic structures. This construction is proved to be equivalent to some Manin products of operads and it is shown to be closely related to…
Manipulatives used in the right way help improve mathematical concepts leading to better learning outcomes. In this paper, we present a phygital (physical + digital) curriculum inspired teaching system for kids aged 5-8 to learn geometry…
We characterize disjoint hypercyclic sequences of wedge operators. Also, we give some sufficient conditions for a sequence of the dual wedge operators to be disjoint topologically transitive. Finally, we give some concrete examples and…
Although algebraic structures are frequently analyzed using unary and binary operations, they can also be effectively defined and unified through ternary operations. In this context, we introduce structures that contain two constants and a…
Algebraic structures with multiple copies of a given type of operations interrelated by various compatibility conditions have long being studied in mathematics and mathematical physics. They are broadly referred as linearly compatible,…
A straightforward argument shows that, by allowing counterfactual elements of physical reality, any arbitrary discrete finite-dimensional operator corresponds to an observable.
One of the main virtues of trees is to represent formal solutions of various functional equations which can be cast in the form of fixed point problems. Basic examples include differential equations and functional (Lagrange) inversion in…