55,769 research outputs found
Limiting search cost distribution for the move-to-front rule with random request probabilities
Consider a list of files whose popularities are random. These files are
updated according to the move-to-front rule and we consider the induced Markov
chain at equilibrium. We give the exact limiting distribution of the
search-cost per item as tends to infinity. Some examples are supplied.Comment: move-to-front, search cost, random discrete distribution, limiting
distribution, size biased permutatio
The limiting move-to-front search-cost in law of large numbers asymptotic regimes
We explicitly compute the limiting transient distribution of the search-cost
in the move-to-front Markov chain when the number of objects tends to infinity,
for general families of deterministic or random request rates. Our techniques
are based on a "law of large numbers for random partitions," a scaling limit
that allows us to exactly compute limiting expectation of empirical functionals
of the request probabilities of objects. In particular, we show that the
limiting search-cost can be split at an explicit deterministic threshold into
one random variable in equilibrium, and a second one related to the initial
ordering of the list. Our results ensure the stability of the limiting
search-cost under general perturbations of the request probabilities. We
provide the description of the limiting transient behavior in several examples
where only the stationary regime is known, and discuss the range of validity of
our scaling limit.Comment: Published in at http://dx.doi.org/10.1214/09-AAP635 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Stochastic ranking process with time dependent intensities
We consider the stochastic ranking process with the jump times of the
particles determined by Poisson random measures. We prove that the joint
empirical distribution of scaled position and intensity measure converges
almost surely in the infinite particle limit. We give an explicit formula for
the limit distribution and show that the limit distribution function is a
unique global classical solution to an initial value problem for a system of a
first order non-linear partial differential equations with time dependent
coefficients
Stochastic ranking process with space-time dependent intensities
We consider the stochastic ranking process with space-time dependent jump
rates for the particles. The process is a simplified model of the time
evolution of the rankings such as sales ranks at online bookstores. We prove
that the joint empirical distribution of jump rate and scaled position
converges almost surely to a deterministic distribution, and also the tagged
particle processes converge almost surely, in the infinite particle limit. The
limit distribution is characterized by a system of inviscid Burgers-like
integral-partial differential equations with evaporation terms, and the limit
process of a tagged particle is a motion along a characteristic curve of the
differential equations except at its Poisson times of jumps to the origin
Ant colony system-based applications to electrical distribution system optimization
Chapter 16, February 201
SuperSpike: Supervised learning in multi-layer spiking neural networks
A vast majority of computation in the brain is performed by spiking neural
networks. Despite the ubiquity of such spiking, we currently lack an
understanding of how biological spiking neural circuits learn and compute
in-vivo, as well as how we can instantiate such capabilities in artificial
spiking circuits in-silico. Here we revisit the problem of supervised learning
in temporally coding multi-layer spiking neural networks. First, by using a
surrogate gradient approach, we derive SuperSpike, a nonlinear voltage-based
three factor learning rule capable of training multi-layer networks of
deterministic integrate-and-fire neurons to perform nonlinear computations on
spatiotemporal spike patterns. Second, inspired by recent results on feedback
alignment, we compare the performance of our learning rule under different
credit assignment strategies for propagating output errors to hidden units.
Specifically, we test uniform, symmetric and random feedback, finding that
simpler tasks can be solved with any type of feedback, while more complex tasks
require symmetric feedback. In summary, our results open the door to obtaining
a better scientific understanding of learning and computation in spiking neural
networks by advancing our ability to train them to solve nonlinear problems
involving transformations between different spatiotemporal spike-time patterns
On Resource Pooling and Separation for LRU Caching
Caching systems using the Least Recently Used (LRU) principle have now become
ubiquitous. A fundamental question for these systems is whether the cache space
should be pooled together or divided to serve multiple flows of data item
requests in order to minimize the miss probabilities. In this paper, we show
that there is no straight yes or no answer to this question, depending on
complex combinations of critical factors, including, e.g., request rates,
overlapped data items across different request flows, data item popularities
and their sizes. Specifically, we characterize the asymptotic miss
probabilities for multiple competing request flows under resource pooling and
separation for LRU caching when the cache size is large.
Analytically, we show that it is asymptotically optimal to jointly serve
multiple flows if their data item sizes and popularity distributions are
similar and their arrival rates do not differ significantly; the
self-organizing property of LRU caching automatically optimizes the resource
allocation among them asymptotically. Otherwise, separating these flows could
be better, e.g., when data sizes vary significantly. We also quantify critical
points beyond which resource pooling is better than separation for each of the
flows when the overlapped data items exceed certain levels. Technically, we
generalize existing results on the asymptotic miss probability of LRU caching
for a broad class of heavy-tailed distributions and extend them to multiple
competing flows with varying data item sizes, which also validates the Che
approximation under certain conditions. These results provide new insights on
improving the performance of caching systems
Flower pollination algorithm: a novel approach for multiobjective optimization
Multiobjective design optimization problems require multiobjective optimization techniques to solve, and it is often very challenging to obtain high-quality Pareto fronts accurately. In this article, the recently developed flower pollination algorithm (FPA) is extended to solve multiobjective optimization problems. The proposed method is used to solve a set of multiobjective test functions and two bi-objective design benchmarks, and a comparison of the proposed algorithm with other algorithms has been made, which shows that the FPA is efficient with a good convergence rate. Finally, the importance for further parametric studies and theoretical analysis is highlighted and discussed
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