Search results for " approximation"
showing 10 items of 575 documents
Genetic algorithms for 3d reconstruction with supershapes
2009
Supershape model is a recent primitive that represents numerous 3D shapes with several symmetry axes. The main interest of this model is its capability to reconstruct more complex shape than superquadric model with only one implicit equation. In this paper we propose a genetic algorithms to re-construct a point cloud using those primitives. We used the pseudo-Euclidean distance to introduce a threshold to handle real data imperfection and speed up the process. Simulations using our proposed fitness functions and a fitness function based on inside-outside function show that our fitness function based on the pseudo-Euclidean distance performs better.
On the approximability of the range assignment problem on radio networks in presence of selfish agents
2005
AbstractWe consider the range assignment problem in ad-hoc wireless networks in the context of selfish agents: A network manager aims to assigning transmission ranges to the stations in order to achieve strong connectivity of the network within a minimal overall power consumption. Station is not directly controlled by the manager and may refuse to transmit with a certain transmission range because it might be costly in terms of power consumption.We investigate the existence of payment schemes which induce the stations to follow the decisions of a network manager in computing a range assignment, that is, truthful mechanisms for the range assignment problem. We provide both positive and negat…
Numerical Approximation of Elliptic Variational Problems
2003
This chapter is dedicated to the study of Elliptic Variational Inequalities (EVI). Different forms of such an EVI are considered. The Ritz—Galerkin discretization method is introduced, and methods to approximate the solution of an EVI are presented. The finite dimensional subspaces are built by use of the Finite Element Method. The discretized problems are solved using variants of the Successive OverRelaxation (SOR) method. The algorithms are tested on a typical example. The way to develop computer programs is carefully analysed.
Indirect Methods for Optimal Control Problems
2003
This chapter is dedicated to the numerical approximation of Optimal Control Problems. The algorithms are based on the necessary conditions for optimality which allow us to use a descent method for the minimization of the cost functional.
New analytical approach to analyze the nonlinear regime of stochastic resonance
2015
We propose some approximate methods to explore the nonlinear regime of the stochastic resonance phenomenon. These approximations correspond to different truncation schemes of cumulants. We compare the theoretical results for the signal power amplification, obtained by using ordinary cumulant truncation schemes, that is Gaussian and excess approximations, the modified two-state approximation with those obtained by numerical simulations of the Langevin equation describing the dynamics of the system.
A novel technique for stochastic root-finding: Enhancing the search with adaptive d-ary search
2017
The most fundamental problem encountered in the field of stochastic optimization, is the Stochastic Root Finding (SRF) problem where the task is to locate an unknown point x∗ for which g(x∗) = 0 for a given function g that can only be observed in the presence of noise [15]. The vast majority of the state-of-the-art solutions to the SRF problem involve the theory of stochastic approximation. The premise of the latter family of algorithms is to oper ate by means of so-called “small-step”processesthat explorethe search space in a conservative manner. Using this paradigm, the point investigated at any time instant is in the proximity of the point investigated at the previous time instant, render…
ε-Regularized two-level optimization problems: Approximation and existence results
2006
The purpose of this work is to improve some results given in [12], relating to approximate solutions for two-level optimization problems. By considering an e-regularized problem, we get new properties, under convexity assumptions in the lower level problems. In particular, we prove existence results for the solutions to the e-regularized problem, whereas the initial two-level optimization problem may fail to have a solution. Finally, as an example, we consider an approximation method with interior penalty functions.
Approximation by mappings with singular Hessian minors
2018
Let $\Omega\subset\mathbb R^n$ be a Lipschitz domain. Given $1\leq p<k\leq n$ and any $u\in W^{2,p}(\Omega)$ belonging to the little H\"older class $c^{1,\alpha}$, we construct a sequence $u_j$ in the same space with $\operatorname{rank}D^2u_j<k$ almost everywhere such that $u_j\to u$ in $C^{1,\alpha}$ and weakly in $W^{2,p}$. This result is in strong contrast with known regularity behavior of functions in $W^{2,p}$, $p\geq k$, satisfying the same rank inequality.
Computing continuous numerical solutions of matrix differential equations
1995
Abstract In this paper, we construct analytical approximate solutions of initial value problems for the matrix differential equation X ′( t ) = A ( t ) X ( t ) + X ( t ) B ( t ) + L ( t ), with twice continuously differentiable functions A ( t ), B ( t ), and L ( t ), continuous. We determine, in terms of the data, the existence interval of the problem. Given an admissible error e, we construct an approximate solution whose error is smaller than e uniformly, in all the domain.
Competing species system as a qualitative model of radiation therapy
2016
To examine complex features of tumor dynamics we analyze a competing-species lattice model that takes into account the competition for nutrients or space as well as interaction with therapeutic factors such as drugs or radiation. Our model might be interpreted as a certain prey–predator system having three trophic layers: (i) the basal species that might be interpreted as nutrients; (ii) normal and tumor cells that consume nutrients, and (iii) therapeutic factors that might kill either nutrient, normal or tumor cells. Using a wide spectrum of parameters we examined survival of our species and tried to identify the corresponding dynamical regimes. It was found that the radiotherapy influence…