Related papers: Piecewise: Flexible piecewise functions for fast i…
MomentClosure.jl is a Julia package providing automated derivation of the time-evolution equations of the moments of molecule numbers for virtually any chemical reaction network using a wide range of moment closure approximations. It…
This book intends to deepen the study of the fractional calculus, giving special emphasis to variable-order operators. It is organized in two parts, as follows. In the first part, we review the basic concepts of fractional calculus (Chapter…
There has recently been considerable interest in using a nonstandard piecewise approximation to formulate fractional order differential equations as difference equations that describe the same dynamical behaviour and are more amenable to a…
Quantifying the complexity of systems consisting of many interacting parts has been an important challenge in the field of complex systems in both abstract and applied contexts. One approach, the complexity profile, is a measure of the…
A general piecewise (including pointwise) probability distribution with space-saving notation and its hierarchical particular cases are considered. The explicit closed-form normalization, expectation, and variance formulas along with the…
We present FrankWolfe.jl, an open-source implementation of several popular Frank-Wolfe and Conditional Gradients variants for first-order constrained optimization. The package is designed with flexibility and high-performance in mind,…
Wilson lines, being comparators that render non-local operator products gauge invariant, are extensively used in QCD calculations, especially in small-$x$ calculations, calculations concerning validation of factorisation schemes and in…
Random variables and their distributions are a central part in many areas of statistical methods. The Distributions.jl package provides Julia users and developers tools for working with probability distributions, leveraging Julia features…
Recently, we have proposed a new diffusive representation for fractional derivatives and, based on this representation, suggested an algorithm for their numerical computation. From the construction of the algorithm, it is immediately…
Criteria for piecewise linear circle homeomorphisms to be conjugate to a rigid rotation, $x\to x+\omega~({\rm mod}~1)$, with rational rotation number $\omega$ are given. The consequences of the existence of such maps in families of maps is…
Carlo is a Monte Carlo simulation framework written in Julia. It provides MPI-parallel scheduling, organized storage of input, checkpoint, and output files, as well as statistical postprocessing. With a minimalist design, it aims to aid the…
We introduce a fractional calculus on time scales using the theory of delta (or nabla) dynamic equations. The basic notions of fractional order integral and fractional order derivative on an arbitrary time scale are proposed, using the…
Hyperbolic Julia sets of complex polynomials are known to be computable in polynomial time due to pioneering work of Braverman in 2005 (10.1016/j.entcs.2004.06.031). In this paper, we present an alternative method for establishing poly-time…
We present an open source computational framework geared towards the efficient numerical investigation of open quantum systems written in the Julia programming language. Built exclusively in Julia and based on standard quantum optics…
We present in this paper a canonical form for the elements in the ring of continuous piecewise polynomial functions. This new representation is based on the use of a particular class of functions $$\{C_i(P):P\in\Q[x],i=0,\ldots,\deg(P)\}$$…
Slice-regular functions of a quaternionic variable have been studied extensively in the last 12 years, resulting, in many ways, quite close to classical holomorphic functions of a complex variable; indeed, there is a correspondence between…
We consider the problem of uncertainty quantification in change point regressions, where the signal can be piecewise polynomial of arbitrary but fixed degree. That is we seek disjoint intervals which, uniformly at a given confidence level,…
Our study is motivated by the solution of Mixed-Integer Non-Linear Programming (MINLP) problems with separable non-convex functions via the Sequential Convex MINLP technique, an iterative method whose main characteristic is that of solving,…
Variable selection, also known as feature selection in machine learning, plays an important role in modeling high dimensional data and is key to data-driven scientific discoveries. We consider here the problem of detecting influential…
Holderian functions have strong non-linearities, which result in singularities in the derivatives. This manuscript presents several fractional-order Taylor expansions of H\"olderian functions around points of non- differentiability. These…