Search results for "Iterated function"
showing 10 items of 62 documents
Resolution of singularities for multi-loop integrals
2007
We report on a program for the numerical evaluation of divergent multi-loop integrals. The program is based on iterated sector decomposition. We improve the original algorithm of Binoth and Heinrich such that the program is guaranteed to terminate. The program can be used to compute numerically the Laurent expansion of divergent multi-loop integrals regulated by dimensional regularisation. The symbolic and the numerical steps of the algorithm are combined into one program.
Radial growth of solutions to the poisson equation
2001
We establish a radial growth estimate of the type of the iterated law of the logarithm for solutions to the Poisson equation in the unit ball.
AMaLGaM IDEAs in noiseless black-box optimization benchmarking
2009
This paper describes the application of a Gaussian Estimation-of-Distribution (EDA) for real-valued optimization to the noiseless part of a benchmark introduced in 2009 called BBOB (Black-Box Optimization Benchmarking). Specifically, the EDA considered here is the recently introduced parameter-free version of the Adapted Maximum-Likelihood Gaussian Model Iterated Density-Estimation Evolutionary Algorithm (AMaLGaM-IDEA). Also the version with incremental model building (iAMaLGaM-IDEA) is considered.
Most Diverse Near-Shortest Paths
2021
Computing the shortest path in a road network is a fundamental problem that has attracted lots of attention. However, in many real-world scenarios, determining solely the shortest path is not enough as users want to have additional, alternative ways of reaching their destination. In this paper, we investigate a novel variant of alternative routing, termed the k-Most Diverse Near-Shortest Paths (kMDNSP). In contrast to previous work, kMDNSP aims at maximizing the diversity of the recommended paths, while bounding their length based on a user-defined constraint. Our theoretical analysis proves the NP-hardness of the problem at hand. To compute an exact solution to kMDNSP, we present an algori…
Metaheuristics for the linear ordering problem with cumulative costs
2012
The linear ordering problem with cumulative costs (LOPCC) is a variant of the well-known linear ordering problem, in which a cumulative propagation makes the objective function highly non-linear. The LOPCC has been recently introduced in the context of mobile-phone telecommunications. In this paper we propose two metaheuristic methods for this NP-hard problem. The first one is based on the GRASP methodology, while the second one implements an Iterated Greedy-Strategic Oscillation procedure. We also propose a post-processing based on Path Relinking to obtain improved outcomes. We compare our methods with the state-of-the-art procedures on a set of 218 previously reported instances. The compa…
NAUTILUS method: An interactive technique in multiobjective optimization based on the nadir point
2010
Most interactive methods developed for solving multiobjective optimization problems sequentially generate Pareto optimal or nondominated vectors and the decision maker must always allow impairment in at least one objective function to get a new solution. The NAUTILUS method proposed is based on the assumptions that past experiences affect decision makers’ hopes and that people do not react symmetrically to gains and losses. Therefore, some decision makers may prefer to start from the worst possible objective values and to improve every objective step by step according to their preferences. In NAUTILUS, starting from the nadir point, a solution is obtained at each iteration which dominates t…
Multi-layer canard cycles and translated power functions
2008
Abstract The paper deals with two-dimensional slow-fast systems and more specifically with multi-layer canard cycles. These are canard cycles passing through n layers of fast orbits, with n ⩾ 2 . The canard cycles are subject to n generic breaking mechanisms and we study the limit cycles that can be perturbed from the generic canard cycles of codimension n . We prove that this study can be reduced to the investigation of the fixed points of iterated translated power functions.
Pseudo-rotations of the closed annulus : variation on a theorem of J. Kwapisz
2003
Consider a homeomorphism h of the closed annulus S^1*[0,1], isotopic to the identity, such that the rotation set of h is reduced to a single irrational number alpha (we say that h is an irrational pseudo-rotation). For every positive integer n, we prove that there exists a simple arc gamma joining one of the boundary component of the annulus to the other one, such that gamma is disjoint from its n first iterates under h. As a corollary, we obtain that the rigid rotation of angle alpha can be approximated by homeomorphisms conjugate to h. The first result stated above is an analog of a theorem of J. Kwapisz dealing with diffeomorphisms of the two-torus; we give some new, purely two-dimension…
A normalized iterative Smoothed Particle Hydrodynamics method
2020
Abstract In this paper we investigate on a normalized iterative approach to improve the Smoothed Particle Hydrodynamics (SPH) estimate of a function. The method iterates on the residuals of an initial SPH approximation to obtain a more accurate solution. The iterative strategy preserves the matrix-free nature of the method, does not require changes on the kernel function and it is not affected by disordered data distribution. The iterative refinement is further improved by ensuring linear approximation order to the starting iterative values. We analyze the accuracy and the convergence of the method with the standard and normalized formulation giving evidence of the enhancements obtained wit…
On boundaries of attractors in dynamical systems
2021
Abstract Fractal geometry is one of the beautiful and challenging branches of mathematics. Self similarity is an important property, exhibited by most of the fractals. Several forms of self similarity have been discussed in the literature. Iterated Function System (IFS) is a mathematical scheme to generate fractals. There are several variants of IFSs such as condensation IFS, countable IFS, etc. In this paper, certain properties of self similar sets, using the concept of boundary are discussed. The notion of boundaries like similarity boundary and dynamical boundary are extended to condensation IFSs. The relationships and measure theoretic properties of boundaries in dynamical systems are a…