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377
Molecular Computation Of Solutions To Combinatorial Problems
, 1994
"... The tools of molecular biology are used to solve an instance of the directed Hamiltonian path problem. A small graph is encoded in molecules of DNA and the `operations' of the computation are performed with standard protocols and enzymes. This experiment demonstrates the feasibility of carrying ..."
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Cited by 773 (6 self)
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The tools of molecular biology are used to solve an instance of the directed Hamiltonian path problem. A small graph is encoded in molecules of DNA and the `operations' of the computation are performed with standard protocols and enzymes. This experiment demonstrates the feasibility
A Heuristic Approach for Hamiltonian Path Problem with Molecules
 Proceedings of the Second Annual Conference (GP97
, 1997
"... A new molecular solution of Hamiltonian Path Problem (HPP) is introduced. In this method, longer paths are generated by combining shorter paths and by eliminating paths containing duplicate vertices. For this purpose, we used two new experimental techniques for extending paths: PCR concatenation a ..."
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Cited by 13 (0 self)
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A new molecular solution of Hamiltonian Path Problem (HPP) is introduced. In this method, longer paths are generated by combining shorter paths and by eliminating paths containing duplicate vertices. For this purpose, we used two new experimental techniques for extending paths: PCR concatenation
Solid Phase DNA Solution to the Hamiltonian Path Problem
, 1997
"... . A solidphase method for solving the Hamiltonian path problem (HPP) is described. The method employs only fast and simple DNA operations amenable to full automation. Singlestranded DNA molecules representing paths with no city visited twice are synthesized citybycity from the start city on the ..."
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Cited by 16 (0 self)
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. A solidphase method for solving the Hamiltonian path problem (HPP) is described. The method employs only fast and simple DNA operations amenable to full automation. Singlestranded DNA molecules representing paths with no city visited twice are synthesized citybycity from the start city
Hamiltonian paths in Cayley graphs
, 2008
"... The classical question raised by Lovász asks whether every Cayley graph is Hamiltonian. We present a short survey of various results in that direction and make some additional observations. In particular, we prove that every finite group G has a generating set of size at most log 2 G, such that th ..."
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Cited by 21 (0 self)
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The classical question raised by Lovász asks whether every Cayley graph is Hamiltonian. We present a short survey of various results in that direction and make some additional observations. In particular, we prove that every finite group G has a generating set of size at most log 2 G
Hofer–Zehnder capacity and length minimizing Hamiltonian paths
 SG/0101085, Geom. Topol
"... We use the criteria of Lalonde and McDuff to show that a path that is generated by a generic autonomous Hamiltonian is length minimizing with respect to the Hofer norm among all homotopic paths provided that it induces no nonconstant closed trajectories in M. This generalizes a result of Hofer for ..."
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Cited by 38 (7 self)
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We use the criteria of Lalonde and McDuff to show that a path that is generated by a generic autonomous Hamiltonian is length minimizing with respect to the Hofer norm among all homotopic paths provided that it induces no nonconstant closed trajectories in M. This generalizes a result of Hofer
Hamiltonian Paths and Double Stranded DNA
, 1998
"... It is suggested that computations using DNA molecules as computing units may sometimes be simpler to carry out and less error prone if double stranded DNA molecules are used rather than the single stranded molecules currently being used. A detailed illustration is given of a biomolecular algorithm ..."
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Cited by 1 (0 self)
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algorithm that uses double stranded DNA for the solution of the directed Hamiltonian path problem. 1 Introduction Following the method used by Adleman [1] in his DNA solution of a seven vertex instance of the directed Hamiltonian path (DHP) problem, researchers continue to use the annealing of single
Length minimizing Hamiltonian paths for symplectically aspherical manifolds
, 2002
"... In this paper we consider the length minimizing properties of Hamiltonian paths generated by quasiautonomous Hamiltonians on symplectically aspherical manifolds. Motivated by the work of Schwarz in [Sc], we study the role of the fixed global extrema in the Floer complex of the generating Hamiltoni ..."
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Cited by 18 (6 self)
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In this paper we consider the length minimizing properties of Hamiltonian paths generated by quasiautonomous Hamiltonians on symplectically aspherical manifolds. Motivated by the work of Schwarz in [Sc], we study the role of the fixed global extrema in the Floer complex of the generating
The Number of Hamiltonian Paths in a Rectangular Grid
"... It is easy to find out which rectangular m vertex by n vertex grids have a Hamiltonian path from one corner to another using a checkerboard argument. However, it is quite difficult in general to count the total number of such paths. In this paper we give generating function answers for grids with fi ..."
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Cited by 6 (0 self)
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It is easy to find out which rectangular m vertex by n vertex grids have a Hamiltonian path from one corner to another using a checkerboard argument. However, it is quite difficult in general to count the total number of such paths. In this paper we give generating function answers for grids
Discrete variational Hamiltonian mechanics
 Journal of Physics A (Mathematical and General
"... The main contribution of this paper is to present a canonical choice of a Hamiltonian theory corresponding to the theory of discrete Lagrangian mechanics. We make use of Lagrange duality and follow a path parallel to that used for construction of the Pontryagin principle in optimal control theory. W ..."
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Cited by 25 (1 self)
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The main contribution of this paper is to present a canonical choice of a Hamiltonian theory corresponding to the theory of discrete Lagrangian mechanics. We make use of Lagrange duality and follow a path parallel to that used for construction of the Pontryagin principle in optimal control theory
Results 1  10
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377