Search results for "Mathematica"
showing 10 items of 7971 documents
Numerical decomposition of geometric constraints
2005
Geometric constraint solving is a key issue in CAD/CAM. Since Owen's seminal paper, solvers typically use graph based decomposition methods. However, these methods become difficult to implement in 3D and are misled by geometric theorems. We extend the Numerical Probabilistic Method (NPM), well known in rigidity theory, to more general kinds of constraints and show that NPM can also decompose a system into rigid subsystems. Classical NPM studies the structure of the Jacobian at a random (or generic) configuration. The variant we are proposing does not consider a random configuration, but a configuration similar to the unknown one. Similar means the configuration fulfills the same set of inci…
Using the Theory of Regular Functions to Formally Prove the ε-Optimality of Discretized Pursuit Learning Algorithms
2014
Learning Automata LA can be reckoned to be the founding algorithms on which the field of Reinforcement Learning has been built. Among the families of LA, Estimator Algorithms EAs are certainly the fastest, and of these, the family of Pursuit Algorithms PAs are the pioneering work. It has recently been reported that the previous proofs for e-optimality for all the reported algorithms in the family of PAs have been flawed. We applaud the researchers who discovered this flaw, and who further proceeded to rectify the proof for the Continuous Pursuit Algorithm CPA. The latter proof, though requires the learning parameter to be continuously changing, is, to the best of our knowledge, the current …
Constraint qualifications and Lagrange multipliers in nondifferentiable programming problems
1994
In this paper, we present several constraint qualifications, and we show that these conditions guarantee the nonvacuity and the boundedness of the Lagrange multiplier sets for general nondifferentiable programming problems. The relationships with various constraint qualifications are investigated.
An optimality test for semi-infinite linear programming
1992
In this paper we present a test to characterize the optimal solutions for the continuous semi-infinite linear programming problem. This optimality characterization is a condition of Kuhn–Tucker type. The resolution of a linear program permits to check the optimality of a feasible point,to detect the unboundedness of the problem and to find descent directions. We give some illustrative examples. We show that the local Mangasarian–Fromovitz constraint qualification is almost equivalent to Slater qualification for this problem. Furthermore, it follows from our study that this optimality condition is always necessary for a wide class of semi-infinite linear programming problems
Exact and Approximate Algorithms for Two–Criteria Topological Design Problem of WAN with Budget and Delay Constraints
2004
This paper studies the problem of designing wide area networks (WAN). In the paper the two-criteria topology assignment problem with two constraints is considered. The goal is select flow routes, channel capacities and network topology in order to minimize the total average delay per packet and the leasing cost of channels subject to the budget constraint and delay constraint. The problem is NP-complete. Then, the branch and bound method is used to construct the exact algorithm. Also the approximate algorithm is presented. Some computational results are reported. Based on computational experiments, several properties of the considered problem are formulated.
The Two-Criteria Topological Design Problem in WAN with Delay Constraint: An Algorithm and Computational Results
2003
The problem is concerned with designing of wide area networks (WAN). The problem consists in selection of flow routes, channel capacities and wide area network topology in order to minimize the total average delay per packet and the leasing cost of channels subject to delay constraint. The problem is NP complete. Then, the branch and bound method is used to construct the exact algorithm. Lower bound of the criterion function is proposed. Computational results are reported. Based on computational experiments, several properties of the considered problem are formulated.
New Geometric Constraint Solving Formulation: Application to the 3D Pentahedron
2014
Geometric Constraint Solving Problems (GCSP) are nowadays routinely investigated in geometric modeling. The 3D Pentahedron problem is a GCSP defined by the lengths of its edges and the planarity of its quadrilateral faces, yielding to an under-constrained system of twelve equations in eighteen unknowns. In this work, we focus on solving the 3D Pentahedron problem in a more robust and efficient way, through a new formulation that reduces the underlying algebraic formulation to a well-constrained system of three equations in three unknowns, and avoids at the same time the use of placement rules that resolve the under-constrained original formulation. We show that geometric constraints can be …
Solution isolation strategies for the Bernstein polytopes-based solver
2013
The Bernstein polytopes-based solver is a new method developed to solve systems of nonlinear equations, which often occur in Geometric Constraint Solving Problems. The principle of this solver is to linearize nonlinear monomials and then to solve the resulting linear programming problems, through linear programming. However, without any strategy for the isolation of the many solutions of multiple-solution systems, this solver is slow in practice. To overcome this problem, we propose in this work, a study of several strategies for solution isolation, through the split of solution boxes into several subboxes, according to three main steps answering the questions: when, where, and how to perfo…
Towards human cell simulation
2019
The faithful reproduction and accurate prediction of the phe-notypes and emergent behaviors of complex cellular systems are among the most challenging goals in Systems Biology. Although mathematical models that describe the interactions among all biochemical processes in a cell are theoretically feasible, their simulation is generally hard because of a variety of reasons. For instance, many quantitative data (e.g., kinetic rates) are usually not available, a problem that hinders the execution of simulation algorithms as long as some parameter estimation methods are used. Though, even with a candidate parameterization, the simulation of mechanistic models could be challenging due to the extr…
Sensitivity analysis of consumption cycles
2018
We study the special case of a nonlinear stochastic consumption model taking the form of a 2-dimensional, non-invertible map with an additive stochastic component. Applying the concept of the stochastic sensitivity function and the related technique of confidence domains, we establish the conditions under which the system's complex consumption attractor is likely to become observable. It is shown that the level of noise intensities beyond which the complex consumption attractor is likely to be observed depends on the weight given to past consumption in an individual's preference adjustment.