17,148 research outputs found
The pseudo-compartment method for coupling PDE and compartment-based models of diffusion
Get PDFSpatial reaction-diffusion models have been employed to describe many
emergent phenomena in biological systems. The modelling technique most commonly
adopted in the literature implements systems of partial differential equations
(PDEs), which assumes there are sufficient densities of particles that a
continuum approximation is valid. However, due to recent advances in
computational power, the simulation, and therefore postulation, of
computationally intensive individual-based models has become a popular way to
investigate the effects of noise in reaction-diffusion systems in which regions
of low copy numbers exist.
The stochastic models with which we shall be concerned in this manuscript are
referred to as `compartment-based'. These models are characterised by a
discretisation of the computational domain into a grid/lattice of
`compartments'. Within each compartment particles are assumed to be well-mixed
and are permitted to react with other particles within their compartment or to
transfer between neighbouring compartments.
We develop two hybrid algorithms in which a PDE is coupled to a
compartment-based model. Rather than attempting to balance average fluxes, our
algorithms answer a more fundamental question: `how are individual particles
transported between the vastly different model descriptions?' First, we present
an algorithm derived by carefully re-defining the continuous PDE concentration
as a probability distribution. Whilst this first algorithm shows strong
convergence to analytic solutions of test problems, it can be cumbersome to
simulate. Our second algorithm is a simplified and more efficient
implementation of the first, it is derived in the continuum limit over the PDE
region alone. We test our hybrid methods for functionality and accuracy in a
variety of different scenarios by comparing the averaged simulations to
analytic solutions of PDEs for mean concentrations.Comment: MAIN - 24 pages, 10 figures, 1 supplementary file - 3 pages, 2
figure
Cellular Systems with Many Antennas: Large System Analysis under Pilot Contamination
Full text linkBase stations with a large number of transmit antennas have the potential to
serve a large number of users simultaneously at higher rates. They also promise
a lower power consumption due to coherent combining at the receiver. However,
the receiver processing in the uplink relies on the channel estimates which are
known to suffer from pilot interference. In this work, we perform an uplink
large system analysis of multi-cell multi-antenna system when the receiver
employs a matched filtering with a pilot contaminated estimate. We find the
asymptotic Signal to Interference plus Noise Ratio (SINR) as the number of
antennas and number of users per base station grow large while maintaining a
fixed ratio. To do this, we make use of the similarity of the uplink received
signal in a multi-antenna system to the representation of the received signal
in CDMA systems. The asymptotic SINR expression explicitly captures the effect
of pilot contamination and that of interference averaging. This also explains
the SINR performance of receiver processing schemes at different regimes such
as instances when the number of antennas are comparable to number of users as
well as when antennas exceed greatly the number of users. Finally, we also
propose that the adaptive MMSE symbol detection scheme, which does not require
the explicit channel knowledge, can be employed for cellular systems with large
number of antennas.Comment: 5 pages, 4 figure
Uplink Linear Receivers for Multi-cell Multiuser MIMO with Pilot Contamination: Large System Analysis
Full text linkBase stations with a large number of transmit antennas have the potential to
serve a large number of users at high rates. However, the receiver processing
in the uplink relies on channel estimates which are known to suffer from pilot
interference. In this work, making use of the similarity of the uplink received
signal in CDMA with that of a multi-cell multi-antenna system, we perform a
large system analysis when the receiver employs an MMSE filter with a pilot
contaminated estimate. We assume a Rayleigh fading channel with different
received powers from users. We find the asymptotic Signal to Interference plus
Noise Ratio (SINR) as the number of antennas and number of users per base
station grow large while maintaining a fixed ratio. Through the SINR expression
we explore the scenario where the number of users being served are comparable
to the number of antennas at the base station. The SINR explicitly captures the
effect of pilot contamination and is found to be the same as that employing a
matched filter with a pilot contaminated estimate. We also find the exact
expression for the interference suppression obtained using an MMSE filter which
is an important factor when there are significant number of users in the system
as compared to the number of antennas. In a typical set up, in terms of the
five percentile SINR, the MMSE filter is shown to provide significant gains
over matched filtering and is within 5 dB of MMSE filter with perfect channel
estimate. Simulation results for achievable rates are close to large system
limits for even a 10-antenna base station with 3 or more users per cell.Comment: Accepted for publication in IEEE Transactions on Wireless
Communication
An adaptive multi-level simulation algorithm for stochastic biological systems
Full text linkDiscrete-state, continuous-time Markov models are widely used in the modeling
of biochemical reaction networks. Their complexity often precludes analytic
solution, and we rely on stochastic simulation algorithms to estimate system
statistics. The Gillespie algorithm is exact, but computationally costly as it
simulates every single reaction. As such, approximate stochastic simulation
algorithms such as the tau-leap algorithm are often used. Potentially
computationally more efficient, the system statistics generated suffer from
significant bias unless tau is relatively small, in which case the
computational time can be comparable to that of the Gillespie algorithm. The
multi-level method (Anderson and Higham, Multiscale Model. Simul. 2012) tackles
this problem. A base estimator is computed using many (cheap) sample paths at
low accuracy. The bias inherent in this estimator is then reduced using a
number of corrections. Each correction term is estimated using a collection of
paired sample paths where one path of each pair is generated at a higher
accuracy compared to the other (and so more expensive). By sharing random
variables between these paired paths the variance of each correction estimator
can be reduced. This renders the multi-level method very efficient as only a
relatively small number of paired paths are required to calculate each
correction term. In the original multi-level method, each sample path is
simulated using the tau-leap algorithm with a fixed value of . This
approach can result in poor performance when the reaction activity of a system
changes substantially over the timescale of interest. By introducing a novel,
adaptive time-stepping approach where is chosen according to the
stochastic behaviour of each sample path we extend the applicability of the
multi-level method to such cases. We demonstrate the efficiency of our method
using a number of examples.Comment: 23 page
A study of compressible turbulent boundary layers using the method of invariant modeling
Get PDFModel equations for studying compressible turbulen boundary layer
Update or Wait: How to Keep Your Data Fresh
Full text linkIn this work, we study how to optimally manage the freshness of information
updates sent from a source node to a destination via a channel. A proper metric
for data freshness at the destination is the age-of-information, or simply age,
which is defined as how old the freshest received update is since the moment
that this update was generated at the source node (e.g., a sensor). A
reasonable update policy is the zero-wait policy, i.e., the source node submits
a fresh update once the previous update is delivered and the channel becomes
free, which achieves the maximum throughput and the minimum delay.
Surprisingly, this zero-wait policy does not always minimize the age. This
counter-intuitive phenomenon motivates us to study how to optimally control
information updates to keep the data fresh and to understand when the zero-wait
policy is optimal. We introduce a general age penalty function to characterize
the level of dissatisfaction on data staleness and formulate the average age
penalty minimization problem as a constrained semi-Markov decision problem
(SMDP) with an uncountable state space. We develop efficient algorithms to find
the optimal update policy among all causal policies, and establish sufficient
and necessary conditions for the optimality of the zero-wait policy. Our
investigation shows that the zero-wait policy is far from the optimum if (i)
the age penalty function grows quickly with respect to the age, (ii) the packet
transmission times over the channel are positively correlated over time, or
(iii) the packet transmission times are highly random (e.g., following a
heavy-tail distribution)
Women as Party Leaders: Are the Barriers Partisan?
Get PDFEven though women make up roughly 51% of the population of the United States, they are underrepresented in all branches of American government. Although there has been recent literature on women in politics and women and parties, very little has been done on women in party leadership. Research suggests that there are fewer women in elected office because of a lack of supply, or qualified and willing women, or a lack of demand, an electorate willing to vote for a woman. This study seeks to understand the levels of participation of women as party delegates in state party conventions and whether the barriers that they face are specific to each party Using a survey data set of over 5000 state party convention delegates, I analyze how women participate and the parties’ ideals on women’s role in politics. While I expected to find more Democratic women in leadership roles, this study has shown that perhaps the barriers are not specific to party as more Republican women delegates have held a party or government office than their Democratic women delegate counterparts. This paper suggests that the political culture of the Republican Party discourages women from joining, but once they join, they are equally as likely as Democratic women to hold leadership positions
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