5,190 research outputs found
Comparing Mean Field and Euclidean Matching Problems
Combinatorial optimization is a fertile testing ground for statistical
physics methods developed in the context of disordered systems, allowing one to
confront theoretical mean field predictions with actual properties of finite
dimensional systems. Our focus here is on minimum matching problems, because
they are computationally tractable while both frustrated and disordered. We
first study a mean field model taking the link lengths between points to be
independent random variables. For this model we find perfect agreement with the
results of a replica calculation. Then we study the case where the points to be
matched are placed at random in a d-dimensional Euclidean space. Using the mean
field model as an approximation to the Euclidean case, we show numerically that
the mean field predictions are very accurate even at low dimension, and that
the error due to the approximation is O(1/d^2). Furthermore, it is possible to
improve upon this approximation by including the effects of Euclidean
correlations among k link lengths. Using k=3 (3-link correlations such as the
triangle inequality), the resulting errors in the energy density are already
less than 0.5% at d>=2. However, we argue that the Euclidean model's 1/d series
expansion is beyond all orders in k of the expansion in k-link correlations.Comment: 11 pages, 1 figur
Fitting heavy tailed distributions: the poweRlaw package
Over the last few years, the power law distribution has been used as the data
generating mechanism in many disparate fields. However, at times the techniques
used to fit the power law distribution have been inappropriate. This paper
describes the poweRlaw R package, which makes fitting power laws and other
heavy-tailed distributions straightforward. This package contains R functions
for fitting, comparing and visualising heavy tailed distributions. Overall, it
provides a principled approach to power law fitting.Comment: The code for this paper can be found at
https://github.com/csgillespie/poweRla
An Empirical Model for the Radio Emission from Pulsars
A model for slow radio pulsars is proposed which involves the entire
magnetosphere in the production of the observed radio emission. It is argued
that observations of pulsar profiles suggest that a feedback mechanism exists
between the star surface and the null charge surface, requiring particle flow
in both directions. In their flow to and from the surface the particles execute
an azimuthal drift around the magnetic pole, thereby creating a ring of
discrete `emission nodes' close to the surface. Motion of the nodes is observed
as the well-known subpulse `drift', but is interpreted here as a small residual
component of the real particle drift. The nodes can therefore move in either
direction, or even remain stationary. A precise fit is found for the pulsar
PSR0943+10. Azimuthal interactions between different regions of the
magnetosphere depend on the angle between the magnetic and rotation axes and
influence the conal type, as observed. The requirement of intermittent weak
pair-production in an outergap suggests a natural evolutionary link between
radio and gamma-ray pulsars.Comment: 17 pages 8 figure
Downlink Transmission of Short Packets: Framing and Control Information Revisited
Cellular wireless systems rely on frame-based transmissions. The frame design
is conventionally based on heuristics, consisting of a frame header and a data
part. The frame header contains control information that provides pointers to
the messages within the data part. In this paper, we revisit the principles of
frame design and show the impact of the new design in scenarios that feature
short data packets which are central to various 5G and Internet of Things
applications. We treat framing for downlink transmission in an AWGN broadcast
channel with K users, where the sizes of the messages to the users are random
variables. Using approximations from finite blocklength information theory, we
establish a framework in which a message to a given user is not necessarily
encoded as a single packet, but may be grouped with the messages to other users
and benefit from the improved efficiency of longer codes. This requires changes
in the way control information is sent, and it requires that the users need to
spend power decoding other messages, thereby increasing the average power
consumption. We show that the common heuristic design is only one point on a
curve that represents the trade-off between latency and power consumption.Comment: 10 page
Relaxation, closing probabilities and transition from oscillatory to chaotic attractors in asymmetric neural networks
Attractors in asymmetric neural networks with deterministic parallel dynamics
were shown to present a "chaotic" regime at symmetry eta < 0.5, where the
average length of the cycles increases exponentially with system size, and an
oscillatory regime at high symmetry, where the typical length of the cycles is
2. We show, both with analytic arguments and numerically, that there is a sharp
transition, at a critical symmetry \e_c=0.33, between a phase where the
typical cycles have length 2 and basins of attraction of vanishing weight and a
phase where the typical cycles are exponentially long with system size, and the
weights of their attraction basins are distributed as in a Random Map with
reversal symmetry. The time-scale after which cycles are reached grows
exponentially with system size , and the exponent vanishes in the symmetric
limit, where . The transition can be related to the dynamics
of the infinite system (where cycles are never reached), using the closing
probabilities as a tool.
We also study the relaxation of the function ,
where is the local field experienced by the neuron . In the symmetric
system, it plays the role of a Ljapunov function which drives the system
towards its minima through steepest descent. This interpretation survives, even
if only on the average, also for small asymmetry. This acts like an effective
temperature: the larger is the asymmetry, the faster is the relaxation of ,
and the higher is the asymptotic value reached. reachs very deep minima in
the fixed points of the dynamics, which are reached with vanishing probability,
and attains a larger value on the typical attractors, which are cycles of
length 2.Comment: 24 pages, 9 figures, accepted on Journal of Physics A: Math. Ge
Relaxation Behavior by Time-Salt and Time-Temperature Superpositions of Polyelectrolyte Complexes from Coacervate to Precipitate
Complexation between anionic and cationic polyelectrolytes results in
solid-like precipitates or liquid-like coacervate depending on the added salt
in the aqueous medium. However, the boundary between these polymer-rich phases
is quite broad and the associated changes in the polymer relaxation in the
complexes across the transition regime are poorly understood. In this work, the
relaxation dynamics of complexes across this transition is probed over a wide
timescale by measuring viscoelastic spectra and zero-shear viscosities at
varying temperatures and salt concentrations for two different salt types. We
find that the complexes exhibit time-temperature superposition (TTS) at all
salt concentrations, while the range of overlapped-frequencies for
time-temperature-salt superposition (TTSS) strongly depends on the salt
concentration (Cs) and gradually shifts to higher frequencies as Cs is
decreased. The sticky-Rouse model describes the relaxation behavior at all Cs.
However, collective relaxation of polyelectrolyte complexes gradually
approaches a rubbery regime and eventually exhibits a gel-like response as Cs
is decreased and limits the validity of TTSS.Comment: 12 pages, 5 figures, Follow Gels journal link for latest versio
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