253 research outputs found
Bit Error Rates for Ultrafast APD Based Optical Receivers: Exact and Large Deviation Based Asymptotic Approaches
Exact analysis as well as asymptotic analysis, based on large-deviation theory (LDT), are developed to compute the bit-error rate (BER) for ultrafast avalanche-photodiode (APD) based optical receivers assuming on-off keying and direct detection. The effects of intersymbol interference (ISI), resulting from the APD\u27s stochastic avalanche buildup time, as well as the APD\u27s dead space are both included in the analysis. ISI becomes a limiting factor as the transmission rate approaches the detector\u27s bandwidth, in which case the bit duration becomes comparable to APD\u27s avalanche buildup time. Further, the effect of dead space becomes significant in high-speed APDs that employ thin avalanche multiplication regions. While the exact BER analysis at the generality considered here has not been reported heretofore, the asymptotic analysis is a major generalization of that developed by Letaief and Sadowsky [IEEE Trans. Inform. Theory, vol. 38, 1992], in which the LDT was used to estimate the BER assuming APDs with an instantaneous response (negligible avalanche buildup time) and no dead space. These results are compared with those obtained using the common Gaussian approximation approach showing the inadequacy of the Guassian approximation when ISI noise has strong presence
Phase Diagram of a Two-Species Lattice Model with a Linear Instability
We review recent progress in understanding the full phase diagram of a
one-dimensional, driven, two-species lattice model [Lahiri and Ramaswamy, PRL
79 (1997) 1150] in which the mobility of each species depends on the density of
the other. The model shows three phases. The first is characterised by phase
separation of an exceptionally robust sort, termed Strong Phase Separation,
which survives at all temperature. The second phase has trivial static
correlations, but density fluctuations are transported by a pair of kinematic
waves involving both species. In the most interesting case, the two linearised
eigenmodes, although nonlinearly coupled, have different dynamic exponents. The
third ``phase'' arises at the phase boundary between the first two. Here, the
first species evolves autonomously, but its fluctuations influence the
evolution of the second, as in the passive scalar problem. The second species
then shows phase separation of a delicate sort, with density fluctuations
persisting even in the large-size limit. This fluctuation-dominated phase
ordering is associated with power law decays in cluster size distributions and
a breakdown of the Porod law.Comment: 9 pages, 1 postscript figure, added new reference
Epidemic Spreading with External Agents
We study epidemic spreading processes in large networks, when the spread is
assisted by a small number of external agents: infection sources with bounded
spreading power, but whose movement is unrestricted vis-\`a-vis the underlying
network topology. For networks which are `spatially constrained', we show that
the spread of infection can be significantly speeded up even by a few such
external agents infecting randomly. Moreover, for general networks, we derive
upper-bounds on the order of the spreading time achieved by certain simple
(random/greedy) external-spreading policies. Conversely, for certain common
classes of networks such as line graphs, grids and random geometric graphs, we
also derive lower bounds on the order of the spreading time over all
(potentially network-state aware and adversarial) external-spreading policies;
these adversarial lower bounds match (up to logarithmic factors) the spreading
time achieved by an external agent with a random spreading policy. This
demonstrates that random, state-oblivious infection-spreading by an external
agent is in fact order-wise optimal for spreading in such spatially constrained
networks
Precoding-Based Network Alignment For Three Unicast Sessions
We consider the problem of network coding across three unicast sessions over
a directed acyclic graph, where each sender and the receiver is connected to
the network via a single edge of unit capacity. We consider a network model in
which the middle of the network only performs random linear network coding, and
restrict our approaches to precoding-based linear schemes, where the senders
use precoding matrices to encode source symbols. We adapt a precoding-based
interference alignment technique, originally developed for the wireless
interference channel, to construct a precoding-based linear scheme, which we
refer to as as a {\em precoding-based network alignment scheme (PBNA)}. A
primary difference between this setting and the wireless interference channel
is that the network topology can introduce dependencies between elements of the
transfer matrix, which we refer to as coupling relations, and can potentially
affect the achievable rate of PBNA. We identify all possible such coupling
relations, and interpret these coupling relations in terms of network topology
and present polynomial-time algorithms to check the presence of these coupling
relations. Finally, we show that, depending on the coupling relations present
in the network, the optimal symmetric rate achieved by precoding-based linear
scheme can take only three possible values, all of which can be achieved by
PBNA.Comment: arXiv admin note: text overlap with arXiv:1202.340
Weak and strong dynamic scaling in a one-dimensional driven coupled-field model: Effects of kinematic waves
We study the coupled dynamics of the displacement fields in a one dimensional coupled-field model for drifting crystals, first proposed by Lahiri and Ramaswamy [Phys. Rev. Lett. 79, 1150 (1997)]. We present some exact results for the steady state and the current in the lattice version of the model for a special subspace in the parameter space, within the region where the model displays kinematic waves. We use these results to construct the effective continuum equations corresponding to the lattice model. These equations decouple at the linear level in terms of the eigenmodes. We examine the long-time, large-distance properties of the correlation functions of the eigenmodes by using symmetry arguments, Monte Carlo simulations, and self-consistent mode-coupling methods. For most parameter values, the scaling exponents of the Kardar-Parisi-Zhang equation are obtained. However, for certain symmetry-determined values of the coupling constants the two eigenmodes, although nonlinearly coupled, are characterized by two distinct dynamic exponents. We discuss the possible application of the dynamic renormalization group in this context
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Advantages of Bayesian monitoring methods in deciding whether and when to stop a clinical trial: an example of a neonatal cooling trial.
BackgroundDecisions to stop randomized trials are often based on traditional P value thresholds and are often unconvincing to clinicians. To familiarize clinical investigators with the application and advantages of Bayesian monitoring methods, we illustrate the steps of Bayesian interim analysis using a recent major trial that was stopped based on frequentist analysis of safety and futility.MethodsWe conducted Bayesian reanalysis of a factorial trial in newborn infants with hypoxic-ischemic encephalopathy that was designed to investigate whether outcomes would be improved by deeper (32 °C) or longer cooling (120 h), as compared with those achieved by standard whole body cooling (33.5 °C for 72 h). Using prior trial data, we developed neutral and enthusiastic prior probabilities for the effect on predischarge mortality, defined stopping guidelines for a clinically meaningful effect, and derived posterior probabilities for predischarge mortality.ResultsBayesian relative risk estimates for predischarge mortality were closer to 1.0 than were frequentist estimates. Posterior probabilities suggested increased predischarge mortality (relative risk > 1.0) for the three intervention groups; two crossed the Bayesian futility threshold.ConclusionsBayesian analysis incorporating previous trial results and different pre-existing opinions can help interpret accruing data and facilitate informed stopping decisions that are likely to be meaningful and convincing to clinicians, meta-analysts, and guideline developers.Trial registrationClinicalTrials.gov NCT01192776 . Registered on 31 August 2010
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