65,319 research outputs found
Adiabatic reduction of a model of stochastic gene expression with jump Markov process
This paper considers adiabatic reduction in a model of stochastic gene
expression with bursting transcription considered as a jump Markov process. In
this model, the process of gene expression with auto-regulation is described by
fast/slow dynamics. The production of mRNA is assumed to follow a compound
Poisson process occurring at a rate depending on protein levels (the phenomena
called bursting in molecular biology) and the production of protein is a linear
function of mRNA numbers. When the dynamics of mRNA is assumed to be a fast
process (due to faster mRNA degradation than that of protein) we prove that,
with appropriate scalings in the burst rate, jump size or translational rate,
the bursting phenomena can be transmitted to the slow variable. We show that,
depending on the scaling, the reduced equation is either a stochastic
differential equation with a jump Poisson process or a deterministic ordinary
differential equation. These results are significant because adiabatic
reduction techniques seem to have not been rigorously justified for a
stochastic differential system containing a jump Markov process. We expect that
the results can be generalized to adiabatic methods in more general stochastic
hybrid systems.Comment: 17 page
Multi-channel Hybrid Access Femtocells: A Stochastic Geometric Analysis
For two-tier networks consisting of macrocells and femtocells, the channel
access mechanism can be configured to be open access, closed access, or hybrid
access. Hybrid access arises as a compromise between open and closed access
mechanisms, in which a fraction of available spectrum resource is shared to
nonsubscribers while the remaining reserved for subscribers. This paper focuses
on a hybrid access mechanism for multi-channel femtocells which employ
orthogonal spectrum access schemes. Considering a randomized channel assignment
strategy, we analyze the performance in the downlink. Using stochastic geometry
as technical tools, we model the distribution of femtocells as Poisson point
process or Neyman-Scott cluster process and derive the distributions of
signal-to-interference-plus-noise ratios, and mean achievable rates, of both
nonsubscribers and subscribers. The established expressions are amenable to
numerical evaluation, and shed key insights into the performance tradeoff
between subscribers and nonsubscribers. The analytical results are corroborated
by numerical simulations.Comment: This is the final version, which was accepted in IEEE Transactions on
Communication
Maximum Average Service Rate and Optimal Queue Scheduling of Delay-Constrained Hybrid Cognitive Radio in Nakagami Fading Channels
As a promising technique to improve achievable bandwidth efficiency, cognitive radio (CR) has attracted substantial research attention from both the academic and industrial communities. To improve the performance attained by the secondary user (SU), a novel hybrid CR system is proposed, which combines the conventional interweave and underlay paradigms to enhance the chance of the SU to access the spectrum. Queuing theory is invoked in this paper to analyze the impact of the primary user’s maximum tolerable delay on the performance of the SU. Multiple queues are assumed for the SU, which is engaged in video communication. Apart from the Poisson traffic generation,we also model the classic Nakagami-m fading channel as a Poisson service process by utilizing the outage probability in the presence of cochannel interference. We optimize both the hybrid interweave/underlay procedure to maximize the average service rate μ_S,max of the SU, as well as the queue’s scheduling scheme, for the sake of minimizing the overall average delay (OAD). As a result, the OAD of the SU is reduced by up to 27% and 20%, compared with the proportion and round-robin schemes, respectively
Hybrid marked point processes: characterisation, existence and uniqueness
We introduce a class of hybrid marked point processes, which encompasses and
extends continuous-time Markov chains and Hawkes processes. While this flexible
class amalgamates such existing processes, it also contains novel processes
with complex dynamics. These processes are defined implicitly via their
intensity and are endowed with a state process that interacts with
past-dependent events. The key example we entertain is an extension of a Hawkes
process, a state-dependent Hawkes process interacting with its state process.
We show the existence and uniqueness of hybrid marked point processes under
general assumptions, extending the results of Massouli\'e (1998) on interacting
point processes.Comment: v6: introduction updated with reference to application of
state-dependent Hawkes processe
A hybrid sampler for Poisson-Kingman mixture models
This paper concerns the introduction of a new Markov Chain Monte Carlo scheme
for posterior sampling in Bayesian nonparametric mixture models with priors
that belong to the general Poisson-Kingman class. We present a novel compact
way of representing the infinite dimensional component of the model such that
while explicitly representing this infinite component it has less memory and
storage requirements than previous MCMC schemes. We describe comparative
simulation results demonstrating the efficacy of the proposed MCMC algorithm
against existing marginal and conditional MCMC samplers
Poisson Multi-Bernoulli Mapping Using Gibbs Sampling
This paper addresses the mapping problem. Using a conjugate prior form, we
derive the exact theoretical batch multi-object posterior density of the map
given a set of measurements. The landmarks in the map are modeled as extended
objects, and the measurements are described as a Poisson process, conditioned
on the map. We use a Poisson process prior on the map and prove that the
posterior distribution is a hybrid Poisson, multi-Bernoulli mixture
distribution. We devise a Gibbs sampling algorithm to sample from the batch
multi-object posterior. The proposed method can handle uncertainties in the
data associations and the cardinality of the set of landmarks, and is
parallelizable, making it suitable for large-scale problems. The performance of
the proposed method is evaluated on synthetic data and is shown to outperform a
state-of-the-art method.Comment: 14 pages, 6 figure
Learning Hybrid System Models for Supervisory Decoding of Discrete State, with applications to the Parietal Reach Region
Based on Gibbs sampling, a novel method to identify mathematical models of neural activity in response to temporal changes of behavioral or cognitive state is presented. This work is motivated by the developing field of neural prosthetics, where a supervisory controller is required to classify activity of a brain region into suitable discrete modes. Here, neural activity in each discrete mode is modeled with nonstationary point processes, and transitions between modes are modeled as hidden Markov models. The effectiveness of this framework is first demonstrated on a simulated example. The identification algorithm is then applied to extracellular neural activity recorded from multi-electrode arrays in the parietal reach region of a rhesus monkey, and the results demonstrate the ability to decode discrete changes even from small data sets
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