Related papers: Introducing the vfunc R package

Semantic analysis on visible (RGB) and infrared (IR) images has gained significant attention due to their enhanced accuracy and robustness under challenging conditions including low-illumination and adverse weather. However, due to the lack…

Let D\subseteq \mathbb{R} be closed and discrete and f:D^n \to \mathbb{R} be such that f(D^n) is somewhere dense. We show that (\mathbb{R},+,\cdot,f) defines the set of integers. As an application, we get that for every a,b \in \mathbb{R}…

For a function defined on an arbitrary subset of a Riemann surface, we give conditions which allow the function to be extended conformally. One folkloric consequence is that two common definitions of an analytic arc in ${\mathbb C}$ are…

A function $f$ on a topological space is sequentially continuous at a point $u$ if, given a sequence $(x_{n})$, $\lim x_{n}=u$ implies that $\lim f(x_{n})=f(u)$. This definition was modified by Connor and Grosse-Erdmann for real functions…

"Explain in Plain English" (EiPE) questions are widely used to assess code comprehension skills but are challenging to grade automatically. Recent approaches like Code Generation Based Grading (CGBG) leverage large language models (LLMs) to…

This article aims to explore the bridge between the algebraic structure of a linear code and the complete decoding process. To this end, we associate a specific binomial ideal $I_+(\mathcal C)$ to an arbitrary linear code. The binomials…

Matching logic is a logical framework for specifying and reasoning about programs using pattern matching semantics. A pattern is made up of a number of structural components and constraints. Structural components are syntactically matched,…

fgivenx is a Python package for functional posterior plotting, currently used in astronomy, but will be of use to scientists performing any Bayesian analysis which has predictive posteriors that are functions. The source code for fgivenx is…

Identifying the relationships among program elements is useful for program understanding, debugging, and analysis. One such relationship is synonymy. Function synonyms are functions that play a similar role in code, e.g. functions that…

Let $X$ and $Y$ be locally compact Hausdorff spaces. We denote by $C_0^+(X)$ the positive cone of all real-valued continuous functions on $X$ vanishing at infinity. In this paper, we consider a bijection $T\colon C_0^+(X) \to C_0^+(Y)$…

In this research summary we present our recent work on implementing functional patterns with inverse functions in the lazy functional-logic programming language Curry. Our goal is the synthesis of the inverse of any given function in Curry…

Here, we investigate the solutions to equation \[f(f(-x)+x)=f(-f(x))+f(x),\qquad x\in\mathbb{R}\] that are prescribed on the non-positive half-line. We will refer to this prescribed function as the generator of the corresponding solution.…

Given a graph $G$, an arithmetical structure on $G$ is a pair of positive integer vectors $({\bf d},{\bf r})$ such that $\mathrm{gcd}({\bf r}_v\, | \,v\in V(G))=1$ and \[ (\mathrm{diag}({\bf d})-A){\bf r}=0, \] where $A$ is the adjacency…

Fuzzy logic programming is a growing declarative paradigm aiming to integrate fuzzy logic into logic programming. One of the most difficult tasks when specifying a fuzzy logic program is determining the right weights for each rule, as well…

In previous work, we introduced the fundamentals and a supporting combinator library for \emph{strategic programming}. This an idiom for generic programming based on the notion of a \emph{functional strategy}: a first-class generic function…

We provide a computational definition of the notions of vector space and bilinear functions. We use this result to introduce a minimal language combining higher-order computation and linear algebra. This language extends the Lambda-calculus…

Functions of one or more variables are usually approximated with a basis: a complete, linearly-independent system of functions that spans a suitable function space. The topic of this paper is the numerical approximation of functions using…

Classical versions of Kolmogorov complexity are incomputable. Nevertheless, in 1975 Solovay showed that there are computable functions $f > K+O(1)$ such that for infinitely many strings $\sigma$, $f(\sigma)=K(\sigma)+O(1)$, where $K$…

The main result of the present paper is about the solutions of the functional equation \Eq{*}{ F\Big(\frac{x+y}2\Big)+f_1(x)+f_2(y)=G(g_1(x)+g_2(y)),\qquad x,y\in I, } derived originally, in a natural way, from the invariance problem of…

The notion of functional dependencies (FDs) can be used by data scientists and domain experts to confront background knowledge against data. To overcome the classical, too restrictive, satisfaction of FDs, it is possible to replace equality…