The capacitated minimum spanning tree problem (CMSTP), a well-known combinatorial optimiza- tion ... more The capacitated minimum spanning tree problem (CMSTP), a well-known combinatorial optimiza- tion problem, holds a central place in telecommunication network design. This problem is to fi nd a minimum cost spanning tree with an extra cardinality limitation on the orders of the subtrees incident to a certain root node. The balanced capacitated minimum spanning tree problem (BCMSTP) is a special case that aims to balance the orders of the subtrees. We show this problem is NP-hard and present two approximation algorithms, in this paper. Considering the maximum order of the subtrees Q, we provide a (3 - 1 /Q)-approximation algorithm to find a balanced solution. We improve this result to a (2:5 + epsilon)-approximation algorithm (for every given epsilon > 0), in the 2d-Euclidean spaces. Also, we present a polynomial time approximation scheme (PTAS) for CMSTP.
International Journal of Bifurcation and Chaos, 2016
Pancreatic beta-cells produce insulin to regularize the blood glucose level. Bursting is importan... more Pancreatic beta-cells produce insulin to regularize the blood glucose level. Bursting is important in beta cells due to its relation to the release of insulin. Pernarowski model is a simple polynomial model of beta-cell activities indicating bursting oscillations in these cells. This paper presents bursting behaviors of symmetric type in this model. In addition, it is shown that the current system exhibits the phenomenon of period doubling cascades of canards which is a route to chaos. Canards are also observed symmetrically near folds of slow manifold which results in a chaotic transition between [Formula: see text] and [Formula: see text] spikes symmetric bursting. Furthermore, mixed-mode oscillations (MMOs) and combination of symmetric bursting together with MMOs are illustrated during the transition between symmetric bursting and continuous spiking.
In the current paper we have investigated the capacitated distance constraint vehicle routing pro... more In the current paper we have investigated the capacitated distance constraint vehicle routing problem for the standard approximation algorithm. This problem consists of a number of different types of vehicles at the depot which differ at their capacity, cost and maximum distance bound. We have designed an approximation algorithm for this problem in the case that the tours are balanced.
In the current paper, we have investigated the generalized FitzHugh-Nagumo model. We have shown t... more In the current paper, we have investigated the generalized FitzHugh-Nagumo model. We have shown that symmetric bursting behaviors of different types could be observed in this model with an appropriate recovery term. A modified version of this system is used to construct bursting activities. Furthermore, we have shown some numerical examples of delayed Hopf bifurcation and canard phenomenon in the symmetric bursting of super-Hopf/homoclinic type near its super-Hopf and homoclinic bifurcations, respectively.
The capacitated minimum spanning tree problem (CMSTP), a well-known combinatorial optimiza- tion ... more The capacitated minimum spanning tree problem (CMSTP), a well-known combinatorial optimiza- tion problem, holds a central place in telecommunication network design. This problem is to fi nd a minimum cost spanning tree with an extra cardinality limitation on the orders of the subtrees incident to a certain root node. The balanced capacitated minimum spanning tree problem (BCMSTP) is a special case that aims to balance the orders of the subtrees. We show this problem is NP-hard and present two approximation algorithms, in this paper. Considering the maximum order of the subtrees Q, we provide a (3 - 1 /Q)-approximation algorithm to find a balanced solution. We improve this result to a (2:5 + epsilon)-approximation algorithm (for every given epsilon > 0), in the 2d-Euclidean spaces. Also, we present a polynomial time approximation scheme (PTAS) for CMSTP.
International Journal of Bifurcation and Chaos, 2016
Pancreatic beta-cells produce insulin to regularize the blood glucose level. Bursting is importan... more Pancreatic beta-cells produce insulin to regularize the blood glucose level. Bursting is important in beta cells due to its relation to the release of insulin. Pernarowski model is a simple polynomial model of beta-cell activities indicating bursting oscillations in these cells. This paper presents bursting behaviors of symmetric type in this model. In addition, it is shown that the current system exhibits the phenomenon of period doubling cascades of canards which is a route to chaos. Canards are also observed symmetrically near folds of slow manifold which results in a chaotic transition between [Formula: see text] and [Formula: see text] spikes symmetric bursting. Furthermore, mixed-mode oscillations (MMOs) and combination of symmetric bursting together with MMOs are illustrated during the transition between symmetric bursting and continuous spiking.
In the current paper we have investigated the capacitated distance constraint vehicle routing pro... more In the current paper we have investigated the capacitated distance constraint vehicle routing problem for the standard approximation algorithm. This problem consists of a number of different types of vehicles at the depot which differ at their capacity, cost and maximum distance bound. We have designed an approximation algorithm for this problem in the case that the tours are balanced.
In the current paper, we have investigated the generalized FitzHugh-Nagumo model. We have shown t... more In the current paper, we have investigated the generalized FitzHugh-Nagumo model. We have shown that symmetric bursting behaviors of different types could be observed in this model with an appropriate recovery term. A modified version of this system is used to construct bursting activities. Furthermore, we have shown some numerical examples of delayed Hopf bifurcation and canard phenomenon in the symmetric bursting of super-Hopf/homoclinic type near its super-Hopf and homoclinic bifurcations, respectively.
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