6,015 research outputs found
Faster identification of optimal contraction sequences for tensor networks
The efficient evaluation of tensor expressions involving sums over multiple
indices is of significant importance to many fields of research, including
quantum many-body physics, loop quantum gravity, and quantum chemistry. The
computational cost of evaluating an expression may depend strongly upon the
order in which the index sums are evaluated, and determination of the
operation-minimising contraction sequence for a single tensor network (single
term, in quantum chemistry) is known to be NP-hard. The current preferred
solution is an exhaustive search, using either an iterative depth-first
approach with pruning or dynamic programming and memoisation, but these
approaches are impractical for many of the larger tensor network Ansaetze
encountered in quantum many-body physics. We present a modified search
algorithm with enhanced pruning which exhibits a performance increase of
several orders of magnitude while still guaranteeing identification of an
optimal operation-minimising contraction sequence for a single tensor network.
A reference implementation for MATLAB, compatible with the ncon() and
multienv() network contractors of arXiv:1402.0939 and arXiv:1310.8023
respectively, is supplied.Comment: 25 pages, 12 figs, 2 tables, includes reference implementation of
algorithm, v2.01. Update corrects the display of contraction sequences
involving single-tensor traces (i.e. where an index in the input appears
twice on the same tensor
Bends in the plane with variable curvature
Explicit formulae for planar variable curvature bends are constructed using Euler’s method of natural equations. The bend paths are expressed in terms of special functions. It is shown that the length of the different bend types varies linearly with increasing radius and that the curvature of variable curvature bends can be expressed as a multiple of the curvature of a circle
Immunoregulatory soluble CTLA-4 modifies effector T cell responses in systemic lupus erythematosus
Acknowledgments This work was supported by Arthritis Research UK (Grant no. 19282). We are grateful to Dr. Nick Fluck for his invaluable support in recruiting patients for the study, and Mrs. Vivien Vaughan for her invaluable expertise in recruiting study participants and maintaining ethical documentation.Peer reviewedPublisher PD
Inherent Structures for Soft Long-Range Interactions in Two-Dimensional Many-Particle Systems
We generate inherent structures, local potential-energy minima, of the
"-space overlap potential" in two-dimensional many-particle systems using a
cooling and quenching simulation technique. The ground states associated with
the -space overlap potential are stealthy ({\it i.e.,} completely suppress
single scattering of radiation for a range of wavelengths) and hyperuniform
({\it i.e.,} infinite wavelength density fluctuations vanish). However, we show
via quantitative metrics that the inherent structures exhibit a range of
stealthiness and hyperuniformity depending on the fraction of degrees of
freedom that are constrained. Inherent structures in two dimensions typically
contain five-particle rings, wavy grain boundaries, and vacancy-interstitial
defects. The structural and thermodynamic properties of inherent structures are
relatively insensitive to the temperature from which they are sampled,
signifying that the energy landscape is relatively flat and devoid of deep
wells. Using the nudged-elastic-band algorithm, we construct paths from
ground-state configurations to inherent structures and identify the transition
points between them. In addition, we use point patterns generated from a random
sequential addition (RSA) of hard disks, which are nearly stealthy, and examine
the particle rearrangements necessary to make the configurations absolutely
stealthy. We introduce a configurational proximity metric to show that only
small local, but collective, particle rearrangements are needed to drive
initial RSA configurations to stealthy disordered ground states. These results
lead to a more complete understanding of the unusual behaviors exhibited by the
family of "collective-coordinate" potentials to which the -space overlap
potential belongs.Comment: 36 pages, 16 figure
The effects of different additives on the dielectric relaxation and the dynamic mechanical properties of urethane dimethacrylate
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73548/1/j.1365-2842.2000.00491.x.pd
The effects of moisture on the dielectric relaxation of urethane dimethacrylate polymer and composites
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/75059/1/j.1365-2842.2001.00669.x.pd
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