49,949 research outputs found
Decay of Correlations for the Hardcore Model on the -regular Random Graph
A key insight from statistical physics about spin systems on random graphs is
the central role played by Gibbs measures on trees. We determine the local weak
limit of the hardcore model on random regular graphs asymptotically until just
below its condensation threshold, showing that it converges in probability
locally in a strong sense to the free boundary condition Gibbs measure on the
tree. As a consequence we show that the reconstruction threshold on the random
graph, indicative of the onset of point to set spatial correlations, is equal
to the reconstruction threshold on the -regular tree for which we determine
precise asymptotics. We expect that our methods will generalize to a wide range
of spin systems for which the second moment method holds.Comment: 39 pages, 5 figures. arXiv admin note: text overlap with
arXiv:1004.353
Searching for a heavy Higgs boson via the H --> l nu jj decay mode at the CERN LHC
The discovery of a heavy Higgs boson with mass up to m_H = 1 TeV at the CERN
LHC is possible in the H--> W^+W^- --> l nu jj decay mode. The weak boson
scattering signal and backgrounds from t\bar tjj and from W+jets production are
analyzed with parton level Monte Carlo programs which are built on full tree
level amplitudes for all subprocesses. The use of double jet tagging and the
reconstruction of the W invariant mass reduce the combined backgrounds to the
same level as the Higgs signal. A central mini-jet veto, which distinguishes
the different gluon radiation patterns of the hard processes, further improves
the signal to background ratio to about 2.5:1, with a signal cross section of 1
fb. The jet energy asymmetry of the W --> jj decay will give a clear signature
of the longitudinal polarization of the W's in the final event sample.Comment: 23 pages (with 7 embedded figures), Revtex, uses epsf.sty.
Z-compressed postscript version also available at
http://phenom.physics.wisc.edu/pub/preprints/1997/madph-97-1017.ps.Z or at
ftp://phenom.physics.wisc.edu/pub/preprints/1997/madph-97-1017.ps.
Two are better than one: Fundamental parameters of frame coherence
This paper investigates two parameters that measure the coherence of a frame:
worst-case and average coherence. We first use worst-case and average coherence
to derive near-optimal probabilistic guarantees on both sparse signal detection
and reconstruction in the presence of noise. Next, we provide a catalog of
nearly tight frames with small worst-case and average coherence. Later, we find
a new lower bound on worst-case coherence; we compare it to the Welch bound and
use it to interpret recently reported signal reconstruction results. Finally,
we give an algorithm that transforms frames in a way that decreases average
coherence without changing the spectral norm or worst-case coherence
On a stronger reconstruction notion for monoids and clones
Motivated by reconstruction results by Rubin, we introduce a new
reconstruction notion for permutation groups, transformation monoids and
clones, called automatic action compatibility, which entails automatic
homeomorphicity. We further give a characterization of automatic
homeomorphicity for transformation monoids on arbitrary carriers with a dense
group of invertibles having automatic homeomorphicity. We then show how to lift
automatic action compatibility from groups to monoids and from monoids to
clones under fairly weak assumptions. We finally employ these theorems to get
automatic action compatibility results for monoids and clones over several
well-known countable structures, including the strictly ordered rationals, the
directed and undirected version of the random graph, the random tournament and
bipartite graph, the generic strictly ordered set, and the directed and
undirected versions of the universal homogeneous Henson graphs.Comment: 29 pp; Changes v1-->v2::typos corr.|L3.5+pf extended|Rem3.7 added|C.
Pech found out that arg of L5.3-v1 solved Probl2-v1|L5.3, C5.4, Probl2 of v1
removed|C5.2, R5.4 new, contain parts of pf of L5.3-v1|L5.2-v1 is now
L5.3,merged with concl of C5.4-v1,L5.3-v2 extends C5.4-v1|abstract, intro
updated|ref[24] added|part of L5.3-v1 is L2.1(e)-v2, another part merged with
pf of L5.2-v1 => L5.3-v
Hybrid approximate message passing
Gaussian and quadratic approximations of message passing algorithms on graphs have attracted considerable recent attention due to their computational simplicity, analytic tractability, and wide applicability in optimization and statistical inference problems. This paper presents a systematic framework for incorporating such approximate message passing (AMP) methods in general graphical models. The key concept is a partition of dependencies of a general graphical model into strong and weak edges, with the weak edges representing interactions through aggregates of small, linearizable couplings of variables. AMP approximations based on the Central Limit Theorem can be readily applied to aggregates of many weak edges and integrated with standard message passing updates on the strong edges. The resulting algorithm, which we call hybrid generalized approximate message passing (HyGAMP), can yield significantly simpler implementations of sum-product and max-sum loopy belief propagation. By varying the partition of strong and weak edges, a performance--complexity trade-off can be achieved. Group sparsity and multinomial logistic regression problems are studied as examples of the proposed methodology.The work of S. Rangan was supported in part by the National Science Foundation under Grants 1116589, 1302336, and 1547332, and in part by the industrial affiliates of NYU WIRELESS. The work of A. K. Fletcher was supported in part by the National Science Foundation under Grants 1254204 and 1738286 and in part by the Office of Naval Research under Grant N00014-15-1-2677. The work of V. K. Goyal was supported in part by the National Science Foundation under Grant 1422034. The work of E. Byrne and P. Schniter was supported in part by the National Science Foundation under Grant CCF-1527162. (1116589 - National Science Foundation; 1302336 - National Science Foundation; 1547332 - National Science Foundation; 1254204 - National Science Foundation; 1738286 - National Science Foundation; 1422034 - National Science Foundation; CCF-1527162 - National Science Foundation; NYU WIRELESS; N00014-15-1-2677 - Office of Naval Research
- …