613,811 research outputs found
Folding kinetics of a polymer [corrigendum]
In our original article (Phys. Chem. Chem. Phys., 2012, 14, 60446053) a
convergence problem resulted in an averaging error in computing the entropy
from a set of Wang-Landau Monte-Carlo simulations. Here we report corrected
results for the freezing temperature of the homopolymer chain as a function of
the range of the non-bonded interaction. We find that the previously reported
forward-flux sampling (FFS) and brute-force (BF) simulation results are in
agreement with the revised Wang-Landau (WL) calculations. This confirms the
utility of FFS for computing crystallisation rates in systems of this kind.Comment: 2 pages, 4 figure
Cayley graphs generated by small degree polynomials over finite fields
We improve upper bounds of F. R. K. Chung and of M. Lu, D. Wan, L.-P. Wang,
X.-D. Zhang on the diameter of some Cayley graphs constructed from polynomials
over finite fields
Stochasticity of comet P/Slaughter-Burnham
Three comets are now known to be at or near the 1/1 resonance with Jupiter: P/Slaughter-Burnham, P/Boethin and the newly discovered P/Ge-Wang. Although details of the individual orbits differ, the three comets have very similar dynamical behavior: their orbits show many transitions between the different types of resonant motion (satellite libration, anti-satellite libration, and circulating motion). The stochastic character of such cometary orbits, mainly due to encounters with Jupiter is investigated using Lyapunov Characteristic Indicators. For each comet of the group, we study the influences on the stochasticity of initial eccentricity, inclination, longitude of node, and l-l(sub J) (mean longitude of comet minus mean longitude of Jupiter). We present here our first results for P/Slaughter-Burnham
Uniqueness of asymptotic cones of complete noncompact shrinking gradient Ricci solitons with Ricci curvature decay
We discuss an elementary consequence of the works of (1) Brett Kotschwar and
Lu Wang and (2) Ovidiu Munteanu and Jiaping Wang
Unitary Easy Quantum Groups: the free case and the group case
Easy quantum groups have been studied intensively since the time they were
introduced by Banica and Speicher in 2009. They arise as a subclass of
(-algebraic) compact matrix quantum groups in the sense of Woronowicz. Due
to some Tannaka-Krein type result, they are completely determined by the
combinatorics of categories of (set theoretical) partitions. So far, only
orthogonal easy quantum groups have been considered in order to understand
quantum subgroups of the free orthogonal quantum group .
We now give a definition of unitary easy quantum groups using colored
partitions to tackle the problem of finding quantum subgroups of . In
the free case (i.e. restricting to noncrossing partitions), the corresponding
categories of partitions have recently been classified by the authors by purely
combinatorial means. There are ten series showing up each indexed by one or two
discrete parameters, plus two additional quantum groups. We now present the
quantum group picture of it and investigate them in detail. We show how they
can be constructed from other known examples using generalizations of Banica's
free complexification. For doing so, we introduce new kinds of products between
quantum groups.
We also study the notion of easy groups.Comment: 39 page
A note on QUBO instances defined on Chimera graphs
McGeoch and Wang (2013) recently obtained optimal or near-optimal solutions
to some quadratic unconstrained boolean optimization (QUBO) problem instances
using a 439 qubit D-Wave Two quantum computing system in much less time than
with the IBM ILOG CPLEX mixed-integer quadratic programming (MIQP) solver. The
problems studied by McGeoch and Wang are defined on subgraphs -- with up to 439
nodes -- of Chimera graphs. We observe that after a standard reformulation of
the QUBO problem as a mixed-integer linear program (MILP), the specific
instances used by McGeoch and Wang can be solved to optimality with the CPLEX
MILP solver in much less time than the time reported in McGeoch and Wang for
the CPLEX MIQP solver. However, the solution time is still more than the time
taken by the D-Wave computer in the McGeoch-Wang tests.Comment: Version 1 discussed computational results with random QUBO instances.
McGeoch and Wang made an error in describing the instances they used; they
did not use random QUBO instances but rather random Ising Model instances
with fields (mapped to QUBO instances). The current version of the note
reports on tests with the precise instances used by McGeoch and Wan
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