Related papers: Mechanizing Operads with Event-B
Operads were originally defined as V-operads, that is, enriched in a symmetric or braided monoidal category V. The symmetry or braiding in V is required in order to describe the associativity axiom the operads must obey, as well as the…
Probabilistic specifications are fast gaining ground as a tool for statistical modeling of probabilistic systems. One of the main goals of formal methods in this domain is to ensure that specific behavior is present or absent in the system,…
In functional programming, monads are supposed to encapsulate computations, effectfully producing the final result, but keeping to themselves the means of acquiring it. For various reasons, we sometimes want to reveal the internals of a…
Online Analytical Processing (OLAP) comprises tools and algorithms that allow querying multidimensional databases. It is based on the multidimensional model, where data can be seen as a cube, where each cell contains one or more measures…
Models of complicated systems can be represented in different ways - in scientific papers, they are represented using natural language text as well as equations. But to be of real use, they must also be implemented as software, thus making…
This thesis is intended to provide an account of the theory and applications of Operational Methods that allow the "translation" of the theory of special functions and polynomials into a "different" mathematical language. The language we…
We introduce a functorial construction which, from a monoid, produces a set-operad. We obtain new (symmetric or not) operads as suboperads or quotients of the operads obtained from usual monoids such as the additive and multiplicative…
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…
In this paper, we investigate the power of nearly purely operational techniques in the study of umbral calculus. We present a concise reconstruction of the theory based on a systematic use of linear operators, with particular attention to…
The tools, ideas, and insights from linear algebra, abstract algebra, and functional analysis can be extremely useful to signal processing and system theory in various areas of engineering, science, and social science including…
Hybrid computation combines discrete and continuous dynamics in the form of an entangled mixture inherently present both in various natural phenomena, and in applications ranging from control theory to microbiology. The emergent behaviours…
This paper deals with an extended model of computations which uses the parameterized families of entities for data objects and reflects a preliminary outline of this problem. Some topics are selected out, briefly analyzed and arranged to…
In this article, we consider a simple representation for real numbers and propose top-down procedures to approximate various algebraic and transcendental operations with arbitrary precision. Detailed algorithms and proofs are provided to…
An event structure is a mathematical abstraction modeling concepts as causality, conflict and concurrency between events. While many other mathematical structures, including groups, topological spaces, rings, abound with algorithms and…
Computer simulations that demonstrate the valueof novel approaches are crucial to developing more flexibleand robust power systems operations with high penetrations ofrenewable energy at multiple geographic and temporal scales.However,…
The selection monad on a set consists of selection functions. These select an element from the set, based on a loss (dually, reward) function giving the loss resulting from a choice of an element. Abadi and Plotkin used the monad to model a…
An operad structure on certain bicoloured noncrossing configurations in regular polygons is studied. Motivated by this study, a general functorial construction of enveloping operad, with input a coloured operad and output an operad, is…
A data structure for finite bounded acyclic categories has been built, which is useful to encode and manipulate abstract orientable incidence structure. It can be represented as a directed acyclic multigraph with weighted edges, where the…
How can we perform computations over natural language representations to solve tasks that require symbolic and numeric reasoning? We propose natural language embedded programs (NLEP) as a unifying framework for addressing math/symbolic…
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,…