24,973 research outputs found
Distributed privacy-preserving network size computation: A system-identification based method
In this study, we propose an algorithm for computing the network size of
communicating agents. The algorithm is distributed: a) it does not require a
leader selection; b) it only requires local exchange of information, and; c)
its design can be implemented using local information only, without any global
information about the network. It is privacy-preserving, namely it does not
require to propagate identifying labels. This algorithm is based on system
identification, and more precisely on the identification of the order of a
suitably-constructed discrete-time linear time-invariant system over some
finite field. We provide a probabilistic guarantee for any randomly picked node
to correctly compute the number of nodes in the network. Moreover, numerical
implementation has been taken into account to make the algorithm applicable to
networks of hundreds of nodes, and therefore make the algorithm applicable in
real-world sensor or robotic networks. We finally illustrate our results in
simulation and conclude the paper with discussions on how our technique differs
from a previously-known strategy based on statistical inference.Comment: 52nd IEEE Conference on Decision and Control (CDC 2013) (2013
N-Point Tree-Level Scattering Amplitude in the New Berkovits' String
We give a proof by direct computation that at tree level, the twistor-like
superstring theory in the pure spinor formalism proposed very recently by
Berkovits describes ten-dimensional N=1 super Yang-Mills in its heterotic
version, and type II supergravity in its type II version. The Yang-Mills case
agrees with the result obtained by Mafra, Schlotterer, Stieberger and Tsimpis.
When restricting to gluon and graviton scattering, this new theory gives rise
to Cachazo-He-Yuan formula.Comment: two footnotes added; version submitted to JHE
Network Reconstruction from Intrinsic Noise
This paper considers the problem of inferring an unknown network of dynamical
systems driven by unknown, intrinsic, noise inputs. Equivalently we seek to
identify direct causal dependencies among manifest variables only from
observations of these variables. For linear, time-invariant systems of minimal
order, we characterise under what conditions this problem is well posed. We
first show that if the transfer matrix from the inputs to manifest states is
minimum phase, this problem has a unique solution irrespective of the network
topology. This is equivalent to there being only one valid spectral factor (up
to a choice of signs of the inputs) of the output spectral density.
If the assumption of phase-minimality is relaxed, we show that the problem is
characterised by a single Algebraic Riccati Equation (ARE), of dimension
determined by the number of latent states. The number of solutions to this ARE
is an upper bound on the number of solutions for the network. We give necessary
and sufficient conditions for any two dynamical networks to have equal output
spectral density, which can be used to construct all equivalent networks.
Extensive simulations quantify the number of solutions for a range of problem
sizes. For a slightly simpler case, we also provide an algorithm to construct
all equivalent networks from the output spectral density.Comment: 11 pages, submitted to IEEE Transactions on Automatic Contro
On minimal realisations of dynamical structure functions
Motivated by the fact that transfer functions do not contain structural
information about networks, dynamical structure functions were introduced to
capture causal relationships between measured nodes in networks. From the
dynamical structure functions, a) we show that the actual number of hidden
states can be larger than the number of hidden states estimated from the
corresponding transfer function; b) we can obtain partial information about the
true state-space equation, which cannot in general be obtained from the
transfer function. Based on these properties, this paper proposes algorithms to
find minimal realisations for a given dynamical structure function. This helps
to estimate the minimal number of hidden states, to better understand the
complexity of the network, and to identify potential targets for new
measurements
Progenitor delay-time distribution of short gamma-ray bursts: Constraints from observations
Context. The progenitors of short gamma-ray bursts (SGRBs) have not yet been
well identified. The most popular model is the merger of compact object
binaries (NS-NS/NS-BH). However, other progenitor models cannot be ruled out.
The delay-time distribution of SGRB progenitors, which is an important property
to constrain progenitor models, is still poorly understood. Aims. We aim to
better constrain the luminosity function of SGRBs and the delay-time
distribution of their progenitors with newly discovered SGRBs. Methods. We
present a low-contamination sample of 16 Swift SGRBs that is better defined by
a duration shorter than 0.8 s. By using this robust sample and by combining a
self-consistent star formation model with various models for the distribution
of time delays, the redshift distribution of SGRBs is calculated and then
compared to the observational data. Results. We find that the power-law delay
distribution model is disfavored and that only the lognormal delay distribution
model with the typical delay tau >= 3 Gyr is consistent with the data.
Comparing Swift SGRBs with T90 > 0.8 s to our robust sample (T90 < 0.8 s), we
find a significant difference in the time delays between these two samples.
Conclusions. Our results show that the progenitors of SGRBs are dominated by
relatively long-lived systems (tau >= 3 Gyr), which contrasts the results found
for Type Ia supernovae. We therefore conclude that primordial NS-NS systems are
not favored as the dominant SGRB progenitors. Alternatively, dynamically formed
NS-NS/BH and primordial NS-BH systems with average delays longer than 5 Gyr may
contribute a significant fraction to the overall SGRB progenitors.Comment: 8 pages, 6 figures, Astron. Astrophys. in pres
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