13,377 research outputs found
Adaptive Delivery in Caching Networks
The problem of content delivery in caching networks is investigated for
scenarios where multiple users request identical files. Redundant user demands
are likely when the file popularity distribution is highly non-uniform or the
user demands are positively correlated. An adaptive method is proposed for the
delivery of redundant demands in caching networks. Based on the redundancy
pattern in the current demand vector, the proposed method decides between the
transmission of uncoded messages or the coded messages of [1] for delivery.
Moreover, a lower bound on the delivery rate of redundant requests is derived
based on a cutset bound argument. The performance of the adaptive method is
investigated through numerical examples of the delivery rate of several
specific demand vectors as well as the average delivery rate of a caching
network with correlated requests. The adaptive method is shown to considerably
reduce the gap between the non-adaptive delivery rate and the lower bound. In
some specific cases, using the adaptive method, this gap shrinks by almost 50%
for the average rate.Comment: 8 pages,8 figures. Submitted to IEEE transaction on Communications in
2015. A short version of this article was published as an IEEE Communications
Letter with DOI: 10.1109/LCOMM.2016.255814
On p-Robust Saturation for hp-AFEM
We consider the standard adaptive finite element loop SOLVE, ESTIMATE, MARK,
REFINE, with ESTIMATE being implemented using the -robust equilibrated flux
estimator, and MARK being D\"orfler marking. As a refinement strategy we employ
-refinement. We investigate the question by which amount the local
polynomial degree on any marked patch has to be increase in order to achieve a
-independent error reduction. The resulting adaptive method can be turned
into an instance optimal -adaptive method by the addition of a coarsening
routine
An automatic adaptive method to combine summary statistics in approximate Bayesian computation
To infer the parameters of mechanistic models with intractable likelihoods, techniques such as approximate Bayesian computation (ABC) are increasingly being adopted. One of the main disadvantages of ABC in practical situations, however, is that parameter inference must generally rely on summary statistics of the data. This is particularly the case for problems involving high-dimensional data, such as biological imaging experiments. However, some summary statistics contain more information about parameters of interest than others, and it is not always clear how to weight their contributions within the ABC framework. We address this problem by developing an automatic, adaptive algorithm that chooses weights for each summary statistic. Our algorithm aims to maximize the distance between the prior and the approximate posterior by automatically adapting the weights within the ABC distance function. Computationally, we use a nearest neighbour estimator of the distance between distributions. We justify the algorithm theoretically based on properties of the nearest neighbour distance estimator. To demonstrate the effectiveness of our algorithm, we apply it to a variety of test problems, including several stochastic models of biochemical reaction networks, and a spatial model of diffusion, and compare our results with existing algorithms
Numerical Methods for Singular Perturbation Problems
Consider the two-point boundary value problem for a stiff system of ordinary differential equations. An adaptive method to solve these problems even when turning points are present is discussed
An automatic adaptive method to combine summary statistics in approximate Bayesian computation
To infer the parameters of mechanistic models with intractable likelihoods,
techniques such as approximate Bayesian computation (ABC) are increasingly
being adopted. One of the main disadvantages of ABC in practical situations,
however, is that parameter inference must generally rely on summary statistics
of the data. This is particularly the case for problems involving
high-dimensional data, such as biological imaging experiments. However, some
summary statistics contain more information about parameters of interest than
others, and it is not always clear how to weight their contributions within the
ABC framework. We address this problem by developing an automatic, adaptive
algorithm that chooses weights for each summary statistic. Our algorithm aims
to maximize the distance between the prior and the approximate posterior by
automatically adapting the weights within the ABC distance function.
Computationally, we use a nearest neighbour estimator of the distance between
distributions. We justify the algorithm theoretically based on properties of
the nearest neighbour distance estimator. To demonstrate the effectiveness of
our algorithm, we apply it to a variety of test problems, including several
stochastic models of biochemical reaction networks, and a spatial model of
diffusion, and compare our results with existing algorithms
- …