6,039 research outputs found
Weak Markovian Bisimulation Congruences and Exact CTMC-Level Aggregations for Concurrent Processes
We have recently defined a weak Markovian bisimulation equivalence in an
integrated-time setting, which reduces sequences of exponentially timed
internal actions to individual exponentially timed internal actions having the
same average duration and execution probability as the corresponding sequences.
This weak Markovian bisimulation equivalence is a congruence for sequential
processes with abstraction and turns out to induce an exact CTMC-level
aggregation at steady state for all the considered processes. However, it is
not a congruence with respect to parallel composition. In this paper, we show
how to generalize the equivalence in a way that a reasonable tradeoff among
abstraction, compositionality, and exactness is achieved for concurrent
processes. We will see that, by enhancing the abstraction capability in the
presence of concurrent computations, it is possible to retrieve the congruence
property with respect to parallel composition, with the resulting CTMC-level
aggregation being exact at steady state only for a certain subset of the
considered processes.Comment: In Proceedings QAPL 2012, arXiv:1207.055
Stochastic kinetics of viral capsid assembly based on detailed protein structures
We present a generic computational framework for the simulation of viral
capsid assembly which is quantitative and specific. Starting from PDB files
containing atomic coordinates, the algorithm builds a coarse grained
description of protein oligomers based on graph rigidity. These reduced protein
descriptions are used in an extended Gillespie algorithm to investigate the
stochastic kinetics of the assembly process. The association rates are obtained
from a diffusive Smoluchowski equation for rapid coagulation, modified to
account for water shielding and protein structure. The dissociation rates are
derived by interpreting the splitting of oligomers as a process of graph
partitioning akin to the escape from a multidimensional well. This modular
framework is quantitative yet computationally tractable, with a small number of
physically motivated parameters. The methodology is illustrated using two
different viruses which are shown to follow quantitatively different assembly
pathways. We also show how in this model the quasi-stationary kinetics of
assembly can be described as a Markovian cascading process in which only a few
intermediates and a small proportion of pathways are present. The observed
pathways and intermediates can be related a posteriori to structural and
energetic properties of the capsid oligomers
Bayesian Learning and Predictability in a Stochastic Nonlinear Dynamical Model
Bayesian inference methods are applied within a Bayesian hierarchical
modelling framework to the problems of joint state and parameter estimation,
and of state forecasting. We explore and demonstrate the ideas in the context
of a simple nonlinear marine biogeochemical model. A novel approach is proposed
to the formulation of the stochastic process model, in which ecophysiological
properties of plankton communities are represented by autoregressive stochastic
processes. This approach captures the effects of changes in plankton
communities over time, and it allows the incorporation of literature metadata
on individual species into prior distributions for process model parameters.
The approach is applied to a case study at Ocean Station Papa, using Particle
Markov chain Monte Carlo computational techniques. The results suggest that, by
drawing on objective prior information, it is possible to extract useful
information about model state and a subset of parameters, and even to make
useful long-term forecasts, based on sparse and noisy observations
Copulas in finance and insurance
Copulas provide a potential useful modeling tool to represent the dependence structure
among variables and to generate joint distributions by combining given marginal
distributions. Simulations play a relevant role in finance and insurance. They are used to
replicate efficient frontiers or extremal values, to price options, to estimate joint risks, and so
on. Using copulas, it is easy to construct and simulate from multivariate distributions based
on almost any choice of marginals and any type of dependence structure. In this paper we
outline recent contributions of statistical modeling using copulas in finance and insurance.
We review issues related to the notion of copulas, copula families, copula-based dynamic and
static dependence structure, copulas and latent factor models and simulation of copulas.
Finally, we outline hot topics in copulas with a special focus on model selection and
goodness-of-fit testing
Geographic Gossip: Efficient Averaging for Sensor Networks
Gossip algorithms for distributed computation are attractive due to their
simplicity, distributed nature, and robustness in noisy and uncertain
environments. However, using standard gossip algorithms can lead to a
significant waste in energy by repeatedly recirculating redundant information.
For realistic sensor network model topologies like grids and random geometric
graphs, the inefficiency of gossip schemes is related to the slow mixing times
of random walks on the communication graph. We propose and analyze an
alternative gossiping scheme that exploits geographic information. By utilizing
geographic routing combined with a simple resampling method, we demonstrate
substantial gains over previously proposed gossip protocols. For regular graphs
such as the ring or grid, our algorithm improves standard gossip by factors of
and respectively. For the more challenging case of random
geometric graphs, our algorithm computes the true average to accuracy
using radio
transmissions, which yields a factor improvement over
standard gossip algorithms. We illustrate these theoretical results with
experimental comparisons between our algorithm and standard methods as applied
to various classes of random fields.Comment: To appear, IEEE Transactions on Signal Processin
Towards a Collision-Free WLAN: Dynamic Parameter Adjustment in CSMA/E2CA
Carrier Sense Multiple Access with Enhanced Collision Avoidance (CSMA/ECA) is
a distributed MAC protocol that allows collision-free access to the medium in
WLAN. The only difference between CSMA/ECA and the well-known CSMA/CA is that
the former uses a deterministic backoff after successful transmissions.
Collision-free operation is reached after a transient state during which some
collisions may occur. This article shows that the duration of the transient
state can be shortened by appropriately setting the contention parameters.
Standard absorbing Markov Chain theory can be used to describe the behaviour of
the system in the transient state and to predict the expected number of slots
to reach the collision-free operation.
The article also introduces CSMA/E2CA, in which a deterministic backoff is
used two consecutive times after a successful transmission. CSMA/E2CA converges
quicker to collision-free operation and delivers higher performance than
CSMA/CA in harsh wireless scenarios with high frame error rates.
To achieve collision-free operations when the number of contenders is large,
it may be necessary to dynamically adjust the contention parameter. The last
part of the article suggests an approach for such parameter adjustment which is
validated by simulation results
FrogWild! -- Fast PageRank Approximations on Graph Engines
We propose FrogWild, a novel algorithm for fast approximation of high
PageRank vertices, geared towards reducing network costs of running traditional
PageRank algorithms. Our algorithm can be seen as a quantized version of power
iteration that performs multiple parallel random walks over a directed graph.
One important innovation is that we introduce a modification to the GraphLab
framework that only partially synchronizes mirror vertices. This partial
synchronization vastly reduces the network traffic generated by traditional
PageRank algorithms, thus greatly reducing the per-iteration cost of PageRank.
On the other hand, this partial synchronization also creates dependencies
between the random walks used to estimate PageRank. Our main theoretical
innovation is the analysis of the correlations introduced by this partial
synchronization process and a bound establishing that our approximation is
close to the true PageRank vector.
We implement our algorithm in GraphLab and compare it against the default
PageRank implementation. We show that our algorithm is very fast, performing
each iteration in less than one second on the Twitter graph and can be up to 7x
faster compared to the standard GraphLab PageRank implementation
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