14,556 research outputs found
Energy flow and fluctuations in non-equilibrium conformal field theory on star graphs
We consider non-equilibrium quantum steady states in conformal field theory
(CFT) on star-graph configurations, with a particular, simple connection
condition at the vertex of the graph. These steady states occur after a large
time as a result of initially thermalizing the legs of the graph at different
temperatures, and carry energy flows. Using purely Virasoro algebraic
calculations we evaluate the exact long-time cumulant generating function for
these flows. We show that this function satisfies a generalization of the usual
non-equilibrium fluctuation relations. This extends the results by two of the
authors (J. Phys. A 45: 362001, 2012; arXiv:1302.3125) to the cases of more
than two legs. It also provides an alternative derivation centered on Virasoro
algebra operators rather than local fields, hence an alternative regularization
scheme, thus confirming the validity and universality of the long-time cumulant
generating function. Our derivation shows how the usual Virasoro algebra leads,
in large volumes, to a continuous-index Virasoro algebra for which we develop
diagramatic principles, which may be of interest in other non-equilibrium
contexts as well. Finally, our results shed light on the Poisson process
interpretation of the long-time energy transfer in CFT.Comment: 26 pages, 2 figure
Maiter: An Asynchronous Graph Processing Framework for Delta-based Accumulative Iterative Computation
Myriad of graph-based algorithms in machine learning and data mining require
parsing relational data iteratively. These algorithms are implemented in a
large-scale distributed environment in order to scale to massive data sets. To
accelerate these large-scale graph-based iterative computations, we propose
delta-based accumulative iterative computation (DAIC). Different from
traditional iterative computations, which iteratively update the result based
on the result from the previous iteration, DAIC updates the result by
accumulating the "changes" between iterations. By DAIC, we can process only the
"changes" to avoid the negligible updates. Furthermore, we can perform DAIC
asynchronously to bypass the high-cost synchronous barriers in heterogeneous
distributed environments. Based on the DAIC model, we design and implement an
asynchronous graph processing framework, Maiter. We evaluate Maiter on local
cluster as well as on Amazon EC2 Cloud. The results show that Maiter achieves
as much as 60x speedup over Hadoop and outperforms other state-of-the-art
frameworks.Comment: ScienceCloud 2012, TKDE 201
Notes on Melonic Tensor Models
It has recently been demonstrated that the large N limit of a model of
fermions charged under the global/gauge symmetry group agrees with
the large limit of the SYK model. In these notes we investigate aspects of
the dynamics of the theories that differ from their SYK
counterparts. We argue that the spectrum of fluctuations about the finite
temperature saddle point in these theories has new light
modes in addition to the light Schwarzian mode that exists even in the SYK
model, suggesting that the bulk dual description of theories differ
significantly if they both exist. We also study the thermal partition function
of a mass deformed version of the SYK model. At large mass we show that the
effective entropy of this theory grows with energy like (i.e. faster
than Hagedorn) up to energies of order . The canonical partition function
of the model displays a deconfinement or Hawking Page type phase transition at
temperatures of order . We derive these results in the large mass
limit but argue that they are qualitatively robust to small corrections in
.Comment: 60 pages, 7 figure
A double coset ansatz for integrability in AdS/CFT
We give a proof that the expected counting of strings attached to giant
graviton branes in AdS_5 x S^5, as constrained by the Gauss Law, matches the
dimension spanned by the expected dual operators in the gauge theory. The
counting of string-brane configurations is formulated as a graph counting
problem, which can be expressed as the number of points on a double coset
involving permutation groups. Fourier transformation on the double coset
suggests an ansatz for the diagonalization of the one-loop dilatation operator
in this sector of strings attached to giant graviton branes. The ansatz agrees
with and extends recent results which have found the dynamics of open string
excitations of giants to be given by harmonic oscillators. We prove that it
provides the conjectured diagonalization leading to harmonic oscillators.Comment: 33 pages, 3 figures; v2: references adde
Gunrock: GPU Graph Analytics
For large-scale graph analytics on the GPU, the irregularity of data access
and control flow, and the complexity of programming GPUs, have presented two
significant challenges to developing a programmable high-performance graph
library. "Gunrock", our graph-processing system designed specifically for the
GPU, uses a high-level, bulk-synchronous, data-centric abstraction focused on
operations on a vertex or edge frontier. Gunrock achieves a balance between
performance and expressiveness by coupling high performance GPU computing
primitives and optimization strategies with a high-level programming model that
allows programmers to quickly develop new graph primitives with small code size
and minimal GPU programming knowledge. We characterize the performance of
various optimization strategies and evaluate Gunrock's overall performance on
different GPU architectures on a wide range of graph primitives that span from
traversal-based algorithms and ranking algorithms, to triangle counting and
bipartite-graph-based algorithms. The results show that on a single GPU,
Gunrock has on average at least an order of magnitude speedup over Boost and
PowerGraph, comparable performance to the fastest GPU hardwired primitives and
CPU shared-memory graph libraries such as Ligra and Galois, and better
performance than any other GPU high-level graph library.Comment: 52 pages, invited paper to ACM Transactions on Parallel Computing
(TOPC), an extended version of PPoPP'16 paper "Gunrock: A High-Performance
Graph Processing Library on the GPU
Multiresolution community detection for megascale networks by information-based replica correlations
We use a Potts model community detection algorithm to accurately and
quantitatively evaluate the hierarchical or multiresolution structure of a
graph. Our multiresolution algorithm calculates correlations among multiple
copies ("replicas") of the same graph over a range of resolutions. Significant
multiresolution structures are identified by strongly correlated replicas. The
average normalized mutual information, the variation of information, and other
measures in principle give a quantitative estimate of the "best" resolutions
and indicate the relative strength of the structures in the graph. Because the
method is based on information comparisons, it can in principle be used with
any community detection model that can examine multiple resolutions. Our
approach may be extended to other optimization problems. As a local measure,
our Potts model avoids the "resolution limit" that affects other popular
models. With this model, our community detection algorithm has an accuracy that
ranks among the best of currently available methods. Using it, we can examine
graphs over 40 million nodes and more than one billion edges. We further report
that the multiresolution variant of our algorithm can solve systems of at least
200000 nodes and 10 million edges on a single processor with exceptionally high
accuracy. For typical cases, we find a super-linear scaling, O(L^{1.3}) for
community detection and O(L^{1.3} log N) for the multiresolution algorithm
where L is the number of edges and N is the number of nodes in the system.Comment: 19 pages, 14 figures, published version with minor change
Anderson-like Transition for a Class of Random Sparse Models in d >= 2 Dimensions
We show that the Kronecker sum of d >= 2 copies of a random one-dimensional
sparse model displays a spectral transition of the type predicted by Anderson,
from absolutely continuous around the center of the band to pure point around
the boundaries. Possible applications to physics and open problems are
discussed briefly.Comment: 19 pages, 1 figure. New version corrects misprints and adds
pertaining reference
Approximating Holant problems by winding
We give an FPRAS for Holant problems with parity constraints and
not-all-equal constraints, a generalisation of the problem of counting
sink-free-orientations. The approach combines a sampler for near-assignments of
"windable" functions -- using the cycle-unwinding canonical paths technique of
Jerrum and Sinclair -- with a bound on the weight of near-assignments. The
proof generalises to a larger class of Holant problems; we characterise this
class and show that it cannot be extended by expressibility reductions.
We then ask whether windability is equivalent to expressibility by matchings
circuits (an analogue of matchgates), and give a positive answer for functions
of arity three
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