Geometrical complexity of conformations of ring polymers under topological constraints

One measure of geometrical complexity of a spatial curve is the number of crossings in a planar projection of the curve. For $N$-noded ring polymers with a fixed knot type, we evaluate numerically the average of the crossing number over some directions. We find that the average crossing number under the topological constraint are less than that of no topological constraint for large $N$. The decrease of the geometrical complexity is significant when the thickness of polymers is small. The simulation with or without a topological constraint also shows that the average crossing number and the average size of ring polymers are independent measures of conformational complexity.Comment: 8 pages, 4figure

Gyration radius of a circular polymer under a topological constraint with excluded volume

It is nontrivial whether the average size of a ring polymer should become smaller or larger under a topological constraint. Making use of some knot invariants, we evaluate numerically the mean square radius of gyration for ring polymers having a fixed knot type, where the ring polymers are given by self-avoiding polygons consisting of freely-jointed hard cylinders. We obtain plots of the gyration radius versus the number of polygonal nodes for the trivial, trefoil and figure-eight knots. We discuss possible asymptotic behaviors of the gyration radius under the topological constraint. In the asymptotic limit, the size of a ring polymer with a given knot is larger than that of no topological constraint when the polymer is thin, and the effective expansion becomes weak when the polymer is thick enough.Comment: 12pages,3figure

Episodic future thinking: linking neuropsychological performance with episodic detail in young and old adults

Episodic future thinking (EFT) has been linked with our ability to remember past events. However, its specific neurocognitive subprocesses have remained elusive. In Experiment 1, a study of healthy older adults was conducted to investigate the candidate subprocesses of EFT. Participants completed a standard EFT cue word task, two memory measures (Verbal Paired Associates I, Source Memory), and two measures of executive function (Trail Making Test, Tower Test). In Experiment 2, healthy young adults also completed an EFT task and neuropsychological measures. The link between neurocognitive measures and five characteristics of EFT was investigated. Specifically, it was found that Source Memory and Trail Making Test performance predicted the episodic specificity of future events in older but not younger adults. Replicating previous findings, older adults produced future events with greater semantic but fewer episodic details than did young adults. These results extend the data and emphasize the importance of the multiple subprocesses underlying EFT