8,116 research outputs found
Pairs of Noncrossing Free Dyck Paths and Noncrossing Partitions
Using the bijection between partitions and vacillating tableaux, we establish
a correspondence between pairs of noncrossing free Dyck paths of length
and noncrossing partitions of with blocks. In terms of the
number of up steps at odd positions, we find a characterization of Dyck paths
constructed from pairs of noncrossing free Dyck paths by using the Labelle
merging algorithm.Comment: 9 pages, 5 figures, revised version, to appear in Discrete
Mathematic
Investigation of Settlements of a Trunk Road Embankment in Hong Kong
A 25 m high fill embankment was constructed as part of a Trunk Road scheme in Hong Kong. In June 1985, large settlements of the order of 250 mm were observed in the embankment. This was followed by a local slippage of surface material from the downstream slope face. To meet the schedule for opening the trunk road in late September, a number of emergency measures costing about HK0.13 M) were implemented to stabilize the embankment. An investigation was subsequently carried out to assess the cause of the movement and the long term stability of the embankment. This paper summarizes the sequence of events leading to the settlements and outlines the investigation carried out. The proposed hydrocompaction mechanism and the effects of grouting on the embankment are discussed
Preference of Small Molecules for Local Minimum Conformations when Binding to Proteins
It is well known that small molecules (ligands) do not necessarily adopt their lowest potential energy conformations when binding to proteins. Analyses of protein-bound ligand crystal structures have reportedly shown that many of them do not even adopt the conformations at local minima of their potential energy surfaces (local minimum conformations). The results of these analyses raise a concern regarding the validity of virtual screening methods that use ligands in local minimum conformations. Here we report a normal-mode-analysis (NMA) study of 100 crystal structures of protein-bound ligands. Our data show that the energy minimization of a ligand alone does not automatically stop at a local minimum conformation if the minimum of the potential energy surface is shallow, thus leading to the folding of the ligand. Furthermore, our data show that all 100 ligand conformations in their protein-bound ligand crystal structures are nearly identical to their local minimum conformations obtained from NMA-monitored energy minimization, suggesting that ligands prefer to adopt local minimum conformations when binding to proteins. These results both support virtual screening methods that use ligands in local minimum conformations and caution about possible adverse effect of excessive energy minimization when generating a database of ligand conformations for virtual screening
Normal-Mode-Analysis–Monitored Energy Minimization Procedure for Generating Small–Molecule Bound Conformations
The energy minimization of a small molecule alone does not automatically stop at a local minimum of the potential energy surface of the molecule if the minimum is shallow, thus leading to folding of the molecule and consequently hampering the generation of the bound conformation of a guest in the absence of its host. This questions the practicality of virtual screening methods that use conformations at local minima of their potential energy surfaces (local minimum conformations) as potential bound conformations. Here we report a normal-mode-analysis–monitored energy minimization (NEM) procedure that generates local minimum conformations as potential bound conformations. Of 22 selected guest–host complex crystal structures with guest structures possessing up to four rotatable bonds, all complexes were reproduced, with guest mass–weighted root mean square deviations of <1.0 Å, through docking with the NEM–generated guest local minimum conformations. An analysis of the potential energies of these local minimum conformations showed that 22 (100%), 18 (82%), 16 (73%), and 12 (55%) of the 22 guest bound conformations in the crystal structures had conformational strain energies of less than or equal to 3.8, 2.0, 0.6, and 0.0 kcal/mol, respectively. These results suggest that (1) the NEM procedure can generate small–molecule bound conformations, and (2) guests adopt low-strain–energy conformations for complexation, thus supporting the virtual screening methods that use local minimum conformations
Compensation for mutual coupling in transmit SENSE
Transmit SENSE has been developed to decrease the RF excitation duration by using a transmit coil array. In this work, mutual coupling between coils is
taken into account by introducing a coupling coefficient matrix into the central equation of transmit SENSE. Simulations demonstrate that this method is
effective to compensate for aliasing artifacts in transmit SENSE.published_or_final_versio
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