24,245 research outputs found
A Markovian event-based framework for stochastic spiking neural networks
In spiking neural networks, the information is conveyed by the spike times,
that depend on the intrinsic dynamics of each neuron, the input they receive
and on the connections between neurons. In this article we study the Markovian
nature of the sequence of spike times in stochastic neural networks, and in
particular the ability to deduce from a spike train the next spike time, and
therefore produce a description of the network activity only based on the spike
times regardless of the membrane potential process.
To study this question in a rigorous manner, we introduce and study an
event-based description of networks of noisy integrate-and-fire neurons, i.e.
that is based on the computation of the spike times. We show that the firing
times of the neurons in the networks constitute a Markov chain, whose
transition probability is related to the probability distribution of the
interspike interval of the neurons in the network. In the cases where the
Markovian model can be developed, the transition probability is explicitly
derived in such classical cases of neural networks as the linear
integrate-and-fire neuron models with excitatory and inhibitory interactions,
for different types of synapses, possibly featuring noisy synaptic integration,
transmission delays and absolute and relative refractory period. This covers
most of the cases that have been investigated in the event-based description of
spiking deterministic neural networks
Towards a general framework for an observation and knowledge based model of occupant behaviour in office buildings
This paper proposes a new general approach based on Bayesian networks to
model the human behaviour. This approach represents human behaviour
withprobabilistic cause-effect relations based not only on previous works, but
also with conditional probabilities coming either from expert knowledge or
deduced from observations. The approach has been used in the co-simulation of
building physics and human behaviour in order to assess the CO 2 concentration
in an office.Comment: IBPC 2015 Turin , Jun 2015, Turin, Italy. 201
Comparing hitting time behaviour of Markov jump processes and their diffusion approximations
Markov jump processes can provide accurate models in many applications, notably chemical and biochemical kinetics, and population dynamics. Stochastic differential equations offer a computationally efficient way to approximate these processes. It is therefore of interest to establish results that shed light on the extent to which the jump and diffusion models agree. In this work we focus on mean hitting time behavior in a thermodynamic limit. We study three simple types of reactions where analytical results can be derived, and we find that the match between mean hitting time behavior of the two models is vastly different in each case. In particular, for a degradation reaction we find that the relative discrepancy decays extremely slowly, namely, as the inverse of the logarithm of the system size. After giving some further computational results, we conclude by pointing out that studying hitting times allows the Markov jump and stochastic differential equation regimes to be compared in a manner that avoids pitfalls that may invalidate other approaches
Doeblin Trees
This paper is centered on the random graph generated by a Doeblin-type
coupling of discrete time processes on a countable state space whereby when two
paths meet, they merge. This random graph is studied through a novel subgraph,
called a bridge graph, generated by paths started in a fixed state at any time.
The bridge graph is made into a unimodular network by marking it and selecting
a root in a specified fashion. The unimodularity of this network is leveraged
to discern global properties of the larger Doeblin graph. Bi-recurrence, i.e.,
recurrence both forwards and backwards in time, is introduced and shown to be a
key property in uniquely distinguishing paths in the Doeblin graph, and also a
decisive property for Markov chains indexed by . Properties related
to simulating the bridge graph are also studied.Comment: 44 pages, 4 figure
Wind speed forecasting at different time scales: a non parametric approach
The prediction of wind speed is one of the most important aspects when
dealing with renewable energy. In this paper we show a new nonparametric model,
based on semi-Markov chains, to predict wind speed. Particularly we use an
indexed semi-Markov model, that reproduces accurately the statistical behavior
of wind speed, to forecast wind speed one step ahead for different time scales
and for very long time horizon maintaining the goodness of prediction. In order
to check the main features of the model we show, as indicator of goodness, the
root mean square error between real data and predicted ones and we compare our
forecasting results with those of a persistence model
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