3,328 research outputs found
Cascades of Dynamical Transitions in an Adaptive Population
In an adaptive population which models financial markets and distributed
control, we consider how the dynamics depends on the diversity of the agents'
initial preferences of strategies. When the diversity decreases, more agents
tend to adapt their strategies together. This change in the environment results
in dynamical transitions from vanishing to non-vanishing step sizes. When the
diversity decreases further, we find a cascade of dynamical transitions for the
different signal dimensions, supported by good agreement between simulations
and theory. Besides, the signal of the largest step size at the steady state is
likely to be the initial signal.Comment: 4 pages, 8 figure
Minimizing Unsatisfaction in Colourful Neighbourhoods
Colouring sparse graphs under various restrictions is a theoretical problem
of significant practical relevance. Here we consider the problem of maximizing
the number of different colours available at the nodes and their
neighbourhoods, given a predetermined number of colours. In the analytical
framework of a tree approximation, carried out at both zero and finite
temperatures, solutions obtained by population dynamics give rise to estimates
of the threshold connectivity for the incomplete to complete transition, which
are consistent with those of existing algorithms. The nature of the transition
as well as the validity of the tree approximation are investigated.Comment: 28 pages, 12 figures, substantially revised with additional
explanatio
Dynamical Synapses Enhance Neural Information Processing: Gracefulness, Accuracy and Mobility
Experimental data have revealed that neuronal connection efficacy exhibits
two forms of short-term plasticity, namely, short-term depression (STD) and
short-term facilitation (STF). They have time constants residing between fast
neural signaling and rapid learning, and may serve as substrates for neural
systems manipulating temporal information on relevant time scales. The present
study investigates the impact of STD and STF on the dynamics of continuous
attractor neural networks (CANNs) and their potential roles in neural
information processing. We find that STD endows the network with slow-decaying
plateau behaviors-the network that is initially being stimulated to an active
state decays to a silent state very slowly on the time scale of STD rather than
on the time scale of neural signaling. This provides a mechanism for neural
systems to hold sensory memory easily and shut off persistent activities
gracefully. With STF, we find that the network can hold a memory trace of
external inputs in the facilitated neuronal interactions, which provides a way
to stabilize the network response to noisy inputs, leading to improved accuracy
in population decoding. Furthermore, we find that STD increases the mobility of
the network states. The increased mobility enhances the tracking performance of
the network in response to time-varying stimuli, leading to anticipative neural
responses. In general, we find that STD and STP tend to have opposite effects
on network dynamics and complementary computational advantages, suggesting that
the brain may employ a strategy of weighting them differentially depending on
the computational purpose.Comment: 40 pages, 17 figure
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