923 research outputs found
Complexity without chaos: Plasticity within random recurrent networks generates robust timing and motor control
It is widely accepted that the complex dynamics characteristic of recurrent
neural circuits contributes in a fundamental manner to brain function. Progress
has been slow in understanding and exploiting the computational power of
recurrent dynamics for two main reasons: nonlinear recurrent networks often
exhibit chaotic behavior and most known learning rules do not work in robust
fashion in recurrent networks. Here we address both these problems by
demonstrating how random recurrent networks (RRN) that initially exhibit
chaotic dynamics can be tuned through a supervised learning rule to generate
locally stable neural patterns of activity that are both complex and robust to
noise. The outcome is a novel neural network regime that exhibits both
transiently stable and chaotic trajectories. We further show that the recurrent
learning rule dramatically increases the ability of RRNs to generate complex
spatiotemporal motor patterns, and accounts for recent experimental data
showing a decrease in neural variability in response to stimulus onset
Synchronizing noisy nonidentical oscillators by transient uncoupling
Synchronization is the process of achieving identical dynamics among coupled
identical units. If the units are different from each other, their dynamics
cannot become identical; yet, after transients, there may emerge a functional
relationship between them -- a phenomenon termed "generalized synchronization."
Here, we show that the concept of transient uncoupling, recently introduced for
synchronizing identical units, also supports generalized synchronization among
nonidentical chaotic units. Generalized synchronization can be achieved by
transient uncoupling even when it is impossible by regular coupling. We
furthermore demonstrate that transient uncoupling stabilizes synchronization in
the presence of common noise. Transient uncoupling works best if the units stay
uncoupled whenever the driven orbit visits regions that are locally diverging
in its phase space. Thus, to select a favorable uncoupling region, we propose
an intuitive method that measures the local divergence at the phase points of
the driven unit's trajectory by linearizing the flow and subsequently
suppresses the divergence by uncoupling
Traveling Salesman Problem
The idea behind TSP was conceived by Austrian mathematician Karl Menger in mid 1930s who invited the research community to consider a problem from the everyday life from a mathematical point of view. A traveling salesman has to visit exactly once each one of a list of m cities and then return to the home city. He knows the cost of traveling from any city i to any other city j. Thus, which is the tour of least possible cost the salesman can take? In this book the problem of finding algorithmic technique leading to good/optimal solutions for TSP (or for some other strictly related problems) is considered. TSP is a very attractive problem for the research community because it arises as a natural subproblem in many applications concerning the every day life. Indeed, each application, in which an optimal ordering of a number of items has to be chosen in a way that the total cost of a solution is determined by adding up the costs arising from two successively items, can be modelled as a TSP instance. Thus, studying TSP can never be considered as an abstract research with no real importance
The evolution of cell formation problem methodologies based on recent studies (1997-2008): review and directions for future research
This paper presents a literature review of the cell formation (CF) problem concentrating on formulations
proposed in the last decade. It refers to a number of solution approaches that have been employed for CF
such as mathematical programming, heuristic and metaheuristic methodologies and artificial intelligence
strategies. A comparison and evaluation of all methodologies is attempted and some shortcomings are
highlighted. Finally, suggestions for future research are proposed useful for CF researchers
Recurrences reveal shared causal drivers of complex time series
Many experimental time series measurements share unobserved causal drivers.
Examples include genes targeted by transcription factors, ocean flows
influenced by large-scale atmospheric currents, and motor circuits steered by
descending neurons. Reliably inferring this unseen driving force is necessary
to understand the intermittent nature of top-down control schemes in diverse
biological and engineered systems. Here, we introduce a new unsupervised
learning algorithm that uses recurrences in time series measurements to
gradually reconstruct an unobserved driving signal. Drawing on the mathematical
theory of skew-product dynamical systems, we identify recurrence events shared
across response time series, which implicitly define a recurrence graph with
glass-like structure. As the amount or quality of observed data improves, this
recurrence graph undergoes a percolation transition manifesting as weak
ergodicity breaking for random walks on the induced landscape -- revealing the
shared driver's dynamics, even in the presence of strongly corrupted or noisy
measurements. Across several thousand random dynamical systems, we empirically
quantify the dependence of reconstruction accuracy on the rate of information
transfer from a chaotic driver to the response systems, and we find that
effective reconstruction proceeds through gradual approximation of the driver's
dominant orbit topology. Through extensive benchmarks against classical and
neural-network-based signal processing techniques, we demonstrate our method's
strong ability to extract causal driving signals from diverse real-world
datasets spanning ecology, genomics, fluid dynamics, and physiology.Comment: 8 pages, 5 figure
Evolving higher-order synergies reveals a trade-off between stability and information integration capacity in complex systems
There has recently been an explosion of interest in how "higher-order"
structures emerge in complex systems. This "emergent" organization has been
found in a variety of natural and artificial systems, although at present the
field lacks a unified understanding of what the consequences of higher-order
synergies and redundancies are for systems. Typical research treat the presence
(or absence) of synergistic information as a dependent variable and report
changes in the level of synergy in response to some change in the system. Here,
we attempt to flip the script: rather than treating higher-order information as
a dependent variable, we use evolutionary optimization to evolve boolean
networks with significant higher-order redundancies, synergies, or statistical
complexity. We then analyse these evolved populations of networks using
established tools for characterizing discrete dynamics: the number of
attractors, average transient length, and Derrida coefficient. We also assess
the capacity of the systems to integrate information. We find that high-synergy
systems are unstable and chaotic, but with a high capacity to integrate
information. In contrast, evolved redundant systems are extremely stable, but
have negligible capacity to integrate information. Finally, the complex systems
that balance integration and segregation (known as Tononi-Sporns-Edelman
complexity) show features of both chaosticity and stability, with a greater
capacity to integrate information than the redundant systems while being more
stable than the random and synergistic systems. We conclude that there may be a
fundamental trade-off between the robustness of a systems dynamics and its
capacity to integrate information (which inherently requires flexibility and
sensitivity), and that certain kinds of complexity naturally balance this
trade-off
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