311 research outputs found
On the Brauer groups of symmetries of abelian Dijkgraaf-Witten theories
Symmetries of three-dimensional topological field theories are naturally
defined in terms of invertible topological surface defects. Symmetry groups are
thus Brauer-Picard groups. We present a gauge theoretic realization of all
symmetries of abelian Dijkgraaf-Witten theories. The symmetry group for a
Dijkgraaf-Witten theory with gauge group a finite abelian group , and with
vanishing 3-cocycle, is generated by group automorphisms of , by
automorphisms of the trivial Chern-Simons 2-gerbe on the stack of -bundles,
and by partial e-m dualities.
We show that transmission functors naturally extracted from extended
topological field theories with surface defects give a physical realization of
the bijection between invertible bimodule categories of a fusion category and
braided auto-equivalences of its Drinfeld center. The latter provides the
labels for bulk Wilson lines; it follows that a symmetry is completely
characterized by its action on bulk Wilson lines.Comment: 21 pages, 9 figures. v2: Minor changes, typos corrected and
references added. v3: Typos correcte
Correlations between hidden units in multilayer neural networks and replica symmetry breaking
We consider feed-forward neural networks with one hidden layer, tree
architecture and a fixed hidden-to-output Boolean function. Focusing on the
saturation limit of the storage problem the influence of replica symmetry
breaking on the distribution of local fields at the hidden units is
investigated. These field distributions determine the probability for finding a
specific activation pattern of the hidden units as well as the corresponding
correlation coefficients and therefore quantify the division of labor among the
hidden units. We find that although modifying the storage capacity and the
distribution of local fields markedly replica symmetry breaking has only a
minor effect on the correlation coefficients. Detailed numerical results are
provided for the PARITY, COMMITTEE and AND machines with K=3 hidden units and
nonoverlapping receptive fields.Comment: 9 pages, 3 figures, RevTex, accepted for publication in Phys. Rev.
Storage capacity of correlated perceptrons
We consider an ensemble of single-layer perceptrons exposed to random
inputs and investigate the conditions under which the couplings of these
perceptrons can be chosen such that prescribed correlations between the outputs
occur. A general formalism is introduced using a multi-perceptron costfunction
that allows to determine the maximal number of random inputs as a function of
the desired values of the correlations. Replica-symmetric results for and
are compared with properties of two-layer networks of tree-structure and
fixed Boolean function between hidden units and output. The results show which
correlations in the hidden layer of multi-layer neural networks are crucial for
the value of the storage capacity.Comment: 16 pages, Latex2
Finite size scaling in neural networks
We demonstrate that the fraction of pattern sets that can be stored in
single- and hidden-layer perceptrons exhibits finite size scaling. This feature
allows to estimate the critical storage capacity \alpha_c from simulations of
relatively small systems. We illustrate this approach by determining \alpha_c,
together with the finite size scaling exponent \nu, for storing Gaussian
patterns in committee and parity machines with binary couplings and up to K=5
hidden units.Comment: 4 pages, RevTex, 5 figures, uses multicol.sty and psfig.st
Multilayer neural networks with extensively many hidden units
The information processing abilities of a multilayer neural network with a
number of hidden units scaling as the input dimension are studied using
statistical mechanics methods. The mapping from the input layer to the hidden
units is performed by general symmetric Boolean functions whereas the hidden
layer is connected to the output by either discrete or continuous couplings.
Introducing an overlap in the space of Boolean functions as order parameter the
storage capacity if found to scale with the logarithm of the number of
implementable Boolean functions. The generalization behaviour is smooth for
continuous couplings and shows a discontinuous transition to perfect
generalization for discrete ones.Comment: 4 pages, 2 figure
Chaos in neural networks with a nonmonotonic transfer function
Time evolution of diluted neural networks with a nonmonotonic transfer
function is analitically described by flow equations for macroscopic variables.
The macroscopic dynamics shows a rich variety of behaviours: fixed-point,
periodicity and chaos. We examine in detail the structure of the strange
attractor and in particular we study the main features of the stable and
unstable manifolds, the hyperbolicity of the attractor and the existence of
homoclinic intersections. We also discuss the problem of the robustness of the
chaos and we prove that in the present model chaotic behaviour is fragile
(chaotic regions are densely intercalated with periodicity windows), according
to a recently discussed conjecture. Finally we perform an analysis of the
microscopic behaviour and in particular we examine the occurrence of damage
spreading by studying the time evolution of two almost identical initial
configurations. We show that for any choice of the parameters the two initial
states remain microscopically distinct.Comment: 12 pages, 11 figures. Accepted for publication in Physical Review E.
Originally submitted to the neuro-sys archive which was never publicly
announced (was 9905001
Comment on "On the subtleties of searching for dark matter with liquid xenon detectors"
In a recent manuscript (arXiv:1208.5046) Peter Sorensen claims that
XENON100's upper limits on spin-independent WIMP-nucleon cross sections for
WIMP masses below 10 GeV "may be understated by one order of magnitude or
more". Having performed a similar, though more detailed analysis prior to the
submission of our new result (arXiv:1207.5988), we do not confirm these
findings. We point out the rationale for not considering the described effect
in our final analysis and list several potential problems with his study.Comment: 3 pages, no figure
A Hypermorphic Missense Mutation in PLCG2, Encoding Phospholipase Cγ2, Causes a Dominantly Inherited Autoinflammatory Disease with Immunodeficiency
Whole-exome sequencing was performed in a family affected by dominantly inherited inflammatory disease characterized by recurrent blistering skin lesions, bronchiolitis, arthralgia, ocular inflammation, enterocolitis, absence of autoantibodies, and mild immunodeficiency. Exome data from three samples, including the affected father and daughter and unaffected mother, were filtered for the exclusion of reported variants, along with benign variants, as determined by PolyPhen-2. A total of eight transcripts were identified as possible candidate genes. We confirmed a variant, c.2120C>A (p.Ser707Tyr), within PLCG2 as the only de novo variant that was present in two affected family members and not present in four unaffected members. PLCG2 encodes phospholipase Cγ2 (PLCγ2), an enzyme with a critical regulatory role in various immune and inflammatory pathways. The p.Ser707Tyr substitution is located in an autoinhibitory SH2 domain that is crucial for PLCγ2 activation. Overexpression of the altered p.Ser707Tyr protein and ex vivo experiments using affected individuals’ leukocytes showed clearly enhanced PLCγ2 activity, suggesting increased intracellular signaling in the PLCγ2-mediated pathway. Recently, our laboratory identified in individuals with cold-induced urticaria and immune dysregulation PLCG2 exon-skipping mutations resulting in protein products with constitutive phospholipase activity but with reduced intracellular signaling at physiological temperatures. In contrast, the p.Ser707Tyr substitution in PLCγ2 causes a distinct inflammatory phenotype that is not provoked by cold temperatures and that has different end-organ involvement and increased intracellular signaling at physiological temperatures. Our results highlight the utility of exome-sequencing technology in finding causal mutations in nuclear families with dominantly inherited traits otherwise intractable by linkage analysis
Search for Two-Neutrino Double Electron Capture of Xe with XENON100
Two-neutrino double electron capture is a rare nuclear decay where two
electrons are simultaneously captured from the atomic shell. For Xe
this process has not yet been observed and its detection would provide a new
reference for nuclear matrix element calculations. We have conducted a search
for two-neutrino double electron capture from the K-shell of Xe using
7636 kgd of data from the XENON100 dark matter detector. Using a
Bayesian analysis we observed no significant excess above background, leading
to a lower 90 % credibility limit on the half-life
yr. We also evaluated the sensitivity of the XENON1T experiment, which is
currently being commissioned, and find a sensitivity of
yr after an exposure of 2 tyr.Comment: 6 pages, 4 figure
Search for Event Rate Modulation in XENON100 Electronic Recoil Data
We have searched for periodic variations of the electronic recoil event rate
in the (2-6) keV energy range recorded between February 2011 and March 2012
with the XENON100 detector, adding up to 224.6 live days in total. Following a
detailed study to establish the stability of the detector and its background
contributions during this run, we performed an un-binned profile likelihood
analysis to identify any periodicity up to 500 days. We find a global
significance of less than 1 sigma for all periods suggesting no statistically
significant modulation in the data. While the local significance for an annual
modulation is 2.8 sigma, the analysis of a multiple-scatter control sample and
the phase of the modulation disfavor a dark matter interpretation. The
DAMA/LIBRA annual modulation interpreted as a dark matter signature with
axial-vector coupling of WIMPs to electrons is excluded at 4.8 sigma.Comment: 6 pages, 4 figure
- …