Related papers: Piecewise: Flexible piecewise functions for fast i…
For many diseases it is reasonable to assume that the hazard rate is not constant across time, but also that it changes in different time intervals. To capture this, we work here with a piecewise survival model. One of the major problems in…
Increasing emphasis on data and quantitative methods in the biomedical sciences is making biological research more computational. Collecting, curating, processing, and analysing large genomic and imaging data sets poses major computational…
The modulating functions method has been used for the identification of linear and nonlinear systems. In this paper, we generalize this method to the on-line identification of fractional order systems based on the Riemann-Liouville…
Piecewise affine functions are widely used to approximate nonlinear and discontinuous functions. However, most, if not all existing models only deal with fitting continuous functions. In this paper, we investigate the problem of fitting a…
This paper describes Convex, a convex optimization modeling framework in Julia. Convex translates problems from a user-friendly functional language into an abstract syntax tree describing the problem. This concise representation of the…
We present a Julia package, DisjunctiveProgramming.jl, that extends the functionality in JuMP.jl to allow modeling problems via logical propositions and disjunctive constraints. Such models can then be reformulated into Mixed-Integer…
In this paper we develop a fractional Hamilton-Jacobi formulation for discrete systems in terms of fractional Caputo derivatives. The fractional action function is obtained and the solutions of the equations of motion are recovered. An…
A simple yet effective numerical method using orthogonal hybrid functions consisting of piecewise constant orthogonal sample-and-hold functions and piecewise linear orthogonal triangular functions is proposed to solve numerically fractional…
We study the fundamental problem of the calculus of variations with variable order fractional operators. Fractional integrals are considered in the sense of Riemann-Liouville while derivatives are of Caputo type.
This study investigates the use of fractional order differential models to simulate the dynamic response of non-homogeneous discrete systems and to achieve efficient and accurate model order reduction. The traditional integer order approach…
We consider stochastic volatility models using piecewise constant parameters. We suggest a hybrid optimization algorithm for fitting the models to a volatility surface and provide some numerical results. Finally, we provide an outlook on…
Marginal effects analysis is fundamental to interpreting statistical models, yet existing implementations face computational constraints that limit analysis at scale. We introduce two Julia packages that address this gap. Margins.jl…
We investigate the use of piecewise linear systems, whose coefficient matrix is a piecewise constant function of the solution itself. Such systems arise, for example, from the numerical solution of linear complementarity problems and in the…
Formulas for stable differentiation of piecewise-smooth functions are given. The data are noisy values of these functions. The locations of discontinuity points and the sizes of the jumps across these points are not assumed known, but found…
The study of dynamical systems involves analyzing how functions behave under iteration in different mathematical spaces. In the context of complex dynamics, tools such as Julia sets and filled Julia sets are used to understand the long-term…
In this paper the fractional-order Mandelbrot and Julia sets in the sense of $q$-th Caputo-like discrete fractional differences, for $q\in(0,1)$, are introduced and several properties are analytically and numerically studied. Some…
Recently, the place of the main programming language for scientific and engineering computations has been little by little taken by Julia. Some users want to work completely within the Julia framework as they work within the Python…
In probabilistic program analysis, quantitative analysis aims at deriving tight numerical bounds for probabilistic properties such as expectation and assertion probability. Most previous works consider numerical bounds over the whole…
We investigate the problem of reconstructing a 2D piecewise smooth function from its bandlimited Fourier measurements. This is a well known and well studied problem with many real world implications, in particular in medical imaging. While…
A generalization of the max-plus transformation, which is known as a method to derive cellular automata from integrable equations, is proposed for complex numbers. Operation rules for this transformation is also studied for general number…