Related papers: Introducing the vfunc R package
Algebraic characterizations of the computational aspects of functions defined over the real numbers provide very effective tool to understand what computability and complexity over the reals, and generally over continuous spaces, mean. This…
We generalize signature Gr\"obner bases, previously studied in the free algebra over a field or polynomial rings over a ring, to ideals in the mixed algebra $R[x_1,...,x_k]\langle y_1,\dots,y_n \rangle$ where $R$ is a principal ideal…
I describe an approach to compiling common idioms in R code directly to native machine code and illustrate it with several examples. Not only can this yield significant performance gains, but it allows us to use new approaches to computing…
An F-system is a computational model that performs a folding operation on words of a given language, following directions coded on words of another given language. This paper considers the case in which both given languages are regular, and…
Logic can be made useful for programming and for databases independently of logic programming. To be useful in this way, logic has to provide a mechanism for the definition of new functions and new relations on the basis of those given in…
Given integers s,t, define a function phi_{s,t} on the space of all formal series expansions by phi_{s,t} (sum a_n x^n) = sum a_{sn+t} x^n. For each function phi_{s,t}, we determine the collection of all rational functions whose Taylor…
The aim of the paper is to provide solid foundations for a programming paradigm natively supporting the creation and manipulation of cyclic data structures. To this end, we describe coFJ, a Java-like calculus where objects can be infinite…
One of the basics of calculus is the following proposition: If $F$ and $G$ are antiderivatives of two real functions $f$ and $g$ resp., then an antiderivative of $\lambda f+g$ is $\lambda F + G$. It may be surprising that such systematic an…
The proposed system of integer functions is logically fully independent from the traditional mathematical analysis of the real functions, but there is a well-defined mutual correspondence between the two disciplines. The system of integer…
Modern software typically performs more than one functionality. These functionalities or features are not always organized in a way for modules representing these features to be used individually. Many software engineering approaches like…
A graph $G$ is called edge-magic if there is a bijective function $f$ from the set of vertices and edges to the set $\{1,2,\ldots,|V(G)|+|E(G)|\}$ such that the sum $f(x)+f(xy)+f(y)$ for any $xy$ in $E(G)$ is constant. Such a function is…
This paper reviews some programming techniques in R that have proved useful, particularly for substantial projects. These include several versions of object-oriented programming, used in a large number of R packages. The review tries to…
We consider the statistical problem of estimating constituent curves from observations of their aggregated curves, referred to as aggregated functional data, in models with additive errors. A typical model arises in chemometrics via the…
Grammatic is a tool for grammar definition and manipulation aimed to improve modularity and reuse of grammars and related development artifacts. It is independent from parsing technology and any other details of target system…
Incremental computation has recently been studied using the concepts of change structures and derivatives of programs, where the derivative of a function allows updating the output of the function based on a change to its input. We…
In the least-squares fitting framework, the Vandermonde with Arnoldi (V+A) method presented in [Brubeck, Nakatsukasa, and Trefethen, {SIAM Review}, 63 (2021), pp. 405-415] is an effective approach to compute a polynomial that approximates…
Given integers s and t, define a function phi_{s,t} on the space of all formal complex series expansions by phi_{s,t} (sum a_n x^n) = sum a_{sn+t} x^n. We define an integer r to be distinguished with respect to (s,t) if r and s are…
We present a tool, simplify-defun, that transforms the definition of a given function into a simplified definition of a new function, providing a proof checked by ACL2 that the old and new functions are equivalent. When appropriate it also…
Ultrafunctions are a particular class of generalized functions defined on a hyperreal field $\mathbb{R}^{*}\supset\mathbb{R}$ that allow to solve variational problems with no classical solutions. We recall the construction of ultrafunctions…
Functional data analysis has become a tool of interest in applied areas such as economics, medicine, and chemistry. Among the techniques developed in recent literature, functional semiparametric regression stands out for its balance between…