31,013 research outputs found
On the Inability of Markov Models to Capture Criticality in Human Mobility
We examine the non-Markovian nature of human mobility by exposing the
inability of Markov models to capture criticality in human mobility. In
particular, the assumed Markovian nature of mobility was used to establish a
theoretical upper bound on the predictability of human mobility (expressed as a
minimum error probability limit), based on temporally correlated entropy. Since
its inception, this bound has been widely used and empirically validated using
Markov chains. We show that recurrent-neural architectures can achieve
significantly higher predictability, surpassing this widely used upper bound.
In order to explain this anomaly, we shed light on several underlying
assumptions in previous research works that has resulted in this bias. By
evaluating the mobility predictability on real-world datasets, we show that
human mobility exhibits scale-invariant long-range correlations, bearing
similarity to a power-law decay. This is in contrast to the initial assumption
that human mobility follows an exponential decay. This assumption of
exponential decay coupled with Lempel-Ziv compression in computing Fano's
inequality has led to an inaccurate estimation of the predictability upper
bound. We show that this approach inflates the entropy, consequently lowering
the upper bound on human mobility predictability. We finally highlight that
this approach tends to overlook long-range correlations in human mobility. This
explains why recurrent-neural architectures that are designed to handle
long-range structural correlations surpass the previously computed upper bound
on mobility predictability
Inferring Synaptic Structure in presence of Neural Interaction Time Scales
Biological networks display a variety of activity patterns reflecting a web
of interactions that is complex both in space and time. Yet inference methods
have mainly focused on reconstructing, from the network's activity, the spatial
structure, by assuming equilibrium conditions or, more recently, a
probabilistic dynamics with a single arbitrary time-step. Here we show that,
under this latter assumption, the inference procedure fails to reconstruct the
synaptic matrix of a network of integrate-and-fire neurons when the chosen time
scale of interaction does not closely match the synaptic delay or when no
single time scale for the interaction can be identified; such failure,
moreover, exposes a distinctive bias of the inference method that can lead to
infer as inhibitory the excitatory synapses with interaction time scales longer
than the model's time-step. We therefore introduce a new two-step method, that
first infers through cross-correlation profiles the delay-structure of the
network and then reconstructs the synaptic matrix, and successfully test it on
networks with different topologies and in different activity regimes. Although
step one is able to accurately recover the delay-structure of the network, thus
getting rid of any \textit{a priori} guess about the time scales of the
interaction, the inference method introduces nonetheless an arbitrary time
scale, the time-bin used to binarize the spike trains. We therefore
analytically and numerically study how the choice of affects the inference
in our network model, finding that the relationship between the inferred
couplings and the real synaptic efficacies, albeit being quadratic in both
cases, depends critically on for the excitatory synapses only, whilst
being basically independent of it for the inhibitory ones
On Timing Model Extraction and Hierarchical Statistical Timing Analysis
In this paper, we investigate the challenges to apply Statistical Static
Timing Analysis (SSTA) in hierarchical design flow, where modules supplied by
IP vendors are used to hide design details for IP protection and to reduce the
complexity of design and verification. For the three basic circuit types,
combinational, flip-flop-based and latch-controlled, we propose methods to
extract timing models which contain interfacing as well as compressed internal
constraints. Using these compact timing models the runtime of full-chip timing
analysis can be reduced, while circuit details from IP vendors are not exposed.
We also propose a method to reconstruct the correlation between modules during
full-chip timing analysis. This correlation can not be incorporated into timing
models because it depends on the layout of the corresponding modules in the
chip. In addition, we investigate how to apply the extracted timing models with
the reconstructed correlation to evaluate the performance of the complete
design. Experiments demonstrate that using the extracted timing models and
reconstructed correlation full-chip timing analysis can be several times faster
than applying the flattened circuit directly, while the accuracy of statistical
timing analysis is still well maintained
Linear response for spiking neuronal networks with unbounded memory
We establish a general linear response relation for spiking neuronal
networks, based on chains with unbounded memory. This relation allows us to
predict the influence of a weak amplitude time-dependent external stimuli on
spatio-temporal spike correlations, from the spontaneous statistics (without
stimulus) in a general context where the memory in spike dynamics can extend
arbitrarily far in the past. Using this approach, we show how linear response
is explicitly related to neuronal dynamics with an example, the gIF model,
introduced by M. Rudolph and A. Destexhe. This example illustrates the
collective effect of the stimuli, intrinsic neuronal dynamics, and network
connectivity on spike statistics. We illustrate our results with numerical
simulations.Comment: 60 pages, 8 figure
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