Professor of Electrical Engineering
Professor of Mathematics
Affiliated Professor of Physics
Arizona State University
Tempe, AZ 85287
Phone: (480) 965-6668
Fax: (480) 965-8325
Research Highlights
We developed a general method to detect hidden nodes in complex networks,
using only time series from nodes that are accessible to external
observation. Our method is based on compressive sensing and we
formulate a general framework encompassing continuous and discrete-time,
and evolutionary-game type of dynamical systems as well. For
concrete demonstration, we present an example of detecting hidden
nodes from an experimental social network.
Our paradigm for detecting hidden nodes is expected
to find applications in a variety of fields where identifying
hidden or black-boxed objects based on limited amount of data
is of interest.
R.-Q. Su, W.-X. Wang, and Y.-C. Lai,
``Detecting hidden nodes in complex networks from time series,''
Physical Review E 85, 065201(R) (2012).
We solved the Dirac equation in two spatial dimensions in the setting of
resonant tunneling, where the system consists of two symmetric cavities
connected by a finite potential barrier. The shape of the cavities can be
chosen to yield both regular and chaotic dynamics in the classical limit. We
find that certain pointer states about classical periodic orbits can exist,
which suppress quantum tunneling, and the effect becomes less severe as the
underlying classical dynamics in the cavity is chaotic, leading to
regularization of tunneling dynamics even in the relativistic quantum regime.
Similar phenomena have been observed in graphene. A physical theory is
developed to explain the phenomenon based on the spectrum of complex
eigenenergies of the non-Hermitian Hamiltonian describing the effectively open
cavity system.
X. Ni, L. Huang, Y.-C. Lai and L. M. Pecora,
``Effect of chaos on relativistic quantum tunneling,''
Europhysics Letters 98, 50007 (2012).
(2012) Controlling complex networks: how much energy is needed?
The outstanding problem of controlling complex networks is relevant to many
areas of science and engineering, and has the potential to generate technological
breakthroughs as well. We addressed the physically important issue of the
energy required for achieving control by deriving and validating scaling
laws for the lower and upper energy bounds. These bounds represent a
reasonable estimate of the energy cost associated with control, and provide
a step forward from the current research on controllability toward ultimate
control of complex networked dynamical systems.
G. Yan, J. Ren, Y.-C. Lai, C. H. Lai, and B. Li,
``Controlling complex networks: How much energy is needed?''
Physical Review Letters 108, 218703 (2012).
(2004) A Trick to Remember: Capacity of oscillatory associative-memory networks
with error-free retrieval
Networks of coupled periodic oscillators (similar to the Kuramoto model) have been proposed as
models of associative memory. However, error-free retrieval states of such oscillatory networks are
typically \emph{unstable}, resulting in a near zero capacity. This puts the networks at disadvantage
as compared with the classical Hopfield network. We recently proposed a simple remedy for this
undesirable property and show rigorously that the error-free capacity of our oscillatory,
associative-memory networks can be made as high as that of the Hopfield network. They can thus not
only provide insights into the origin of biological memory, but can also be potentially useful for
applications in information science and engineering.
T. Nishikawa, Y.-C. Lai, and F. C. Hoppensteadt,
``Capacity of oscillatory associative-memory networks with error-free retrieval,''
Physical Review Letters92, 108101(1-4) (2004).
PDF file
This research was featured in
Physical Review Focus (March 12, 2004).
(2004) Strange nonchaotic attractors in random dynamical systems
Whether strange nonchaotic attractors (SNAs) can occur typically in
dynamical systems other than quasiperiodically driven systems has long
been an open question. We have recently shown, based on a physical analysis and
numerical evidence, that robust SNAs can be induced by small noise in
autonomous discrete-time maps and in periodically driven continuous-time
systems. These attractors, which are relevant to physical and biological
applications, can thus be expected to occur more commonly in dynamical
systems than previously thought.
X. Wang, M. Zhan, C.-H. Lai, and Y.-C. Lai,
``Strange nonchaotic attractors in random dynamical systems,''
Physical Review Letters 92, 074102(1-4) (2004).
PDF file
Superpersistent chaotic transients are characterized by an exponential-like
scaling law for their lifetimes where the exponent in the exponential
dependence diverges as a parameter approaches a critical value. So far this type
of transient chaos has been illustrated exclusively in the phase space of dynamical
systems. Here we report the phenomenon of noise-induced superpersistent transients
in the physical space and explain the associated scaling law based on the solutions
to a class of stochastic differential equations. The context of our study is
advective dynamics of inertial particles in
open chaotic flows. Our finding makes direct experimental observation of
superpersistent chaotic transients feasible and it also
has implications to problems of current concern
such as the transport and trapping of chemically or biologically active particles
in large scale flows.
Y. Do and Y.-C. Lai, ``Superpersistent chaotic transients in physical space -
advective dynamics of inertial particles in open chaotic flows under noise,''
Physical Review Letters 91, 224101(1-4) (2003).
PDF file
(2003) Inability of Lyapunov exponents to predict epileptic seizures
Concepts from nonlinear dynamics such as Lyapunov exponents and fractal
dimensions have been increasingly applied to significant biomedical
time series for detection, prediction, or control of diseases. In the
area of epilepsy, a great deal of effort has been devoted to monitoring
the evolution of Lyapunov exponents for early seizure prediction, with
claims that seizures can be predicted minutes or even tens of minutes
in advance of their clinical onset. Our central concern is that
there has been no systematic analysis about the predictive power of
Lyapunov exponents from nonstationary time series such as ECoG
in the existing literature. Without such analysis, any claim of
prediction can be misleading. We have recently investigated
the predictive power of the Lyapunov exponents computed
from time series. Our analysis and computations indicate that there are
two major factors that can prevent the exponents from being effective
tools to predict characteristic system changes: statistical fluctuations
and noise. The basic message is that for low-dimensional, deterministic
chaotic systems, the predictive power of Lyapunov exponents holds only
in noiseless or extremely low-noise situations. In reality where an
appreciable but reasonable amount of noise is present, especially in a
system as high-dimensional and noisy as the brain, it is unlikely
that the Lyapunov exponents, or related quantities from nonlinear
dynamics, can be used to predict or even to detect epileptic seizures.
We feel that this is an important point to keep in mind in light
of repeated claims in the literature of seizure prediction with Lyapunov
exponents. It is also clear that our result is relevant to many other
applications where the temporal evolutions of the Lyapunov exponents
estimated from time series are intended for prediction or detection.
Y.-C. Lai, M. A. F. Harrison, M. G. Frei, and I. Osorio,
``Inability of Lyapunov exponents to predict epileptic seizures,''
Physical Review Letters 91, 068102 (2003).
PDF file
This work was selected by
the Virtual Journal of Biological Physics Research for the August 15, 2003 issue
See here
(2003) Heterogeneity in oscillator networks: Are smaller worlds easier to synchronize?
Small-world networks are known to be more easily synchronized than
regular lattices, which is usually attributed to the smaller network
distance between oscillators. Surprisingly, we show that networks
with a homogeneous distribution of connectivity are more synchronizable
than heterogeneous ones (e.g., scale-free networks), even though
the average network distance is larger. Some degree of homogeneity is
then expected in naturally evolved structures, such as neural
networks, where synchronizability is desirable.
T. Nishikawa, A. E. Motter, Y.-C. Lai, and F. Hoppensteadt,
``Heterogeneity in oscillator networks: Are smaller worlds easier to synchronize?''
Physical Review Letters 91, 014101 (2003).
PDF file
We live in a modern world supported by large, complex networks.
Examples range from financial markets to
communication and transportation systems.
In many realistic situations the flow
of physical quantities in the network, as characterized by the loads on nodes,
is important.
We show that for such networks where loads can redistribute among the nodes,
intentional attacks can lead to a cascade of overload failures,
which can in turn cause the entire or a substantial part of the network to collapse.
This is relevant for
real-world networks that possess a highly heterogeneous distribution of {\it loads},
such as the Internet and power grids.
We demonstrate that
the heterogeneity of these networks makes them particularly vulnerable to attacks
in that a large-scale cascade can be triggered by disabling a single key node.
This brings obvious concerns on the security of such systems.
A. E. Motter and Y.-C. Lai,
``Cascade-based attacks on complex networks,''
Physical Review E (Rapid Communications) 66, 065102 (2002).
PDF file
This research was featured in NewsFactor Network
(February 6, 2003)
PS file
(2002) Can statistical averages of chaotic systems be
computed or measured reliably?
Computing or measuring statistical averages is a common practice in
science and engineering. A fundamental question concerns the reliability of
such computations or measurements. The question, which is of paramount importance
for quantitative sciences such as physics and biology, is
particularly relevant when the system under investigation exhibits chaos,
as characterized by a sensitive dependence on initial conditions.
For chaotic systems, numerical trajectories
are not always shadowable by true trajectories. However, for statistical averages,
it is naturally assumed that they can be computed or measured reliably because,
the effect of computational errors or noise would be
averaged out due to ergodicity. Is this intuition always true?
We have recently shown that there are common situations
in chaotic dynamics where statistical averages of physical quantities
depend on the level of computational error or noise.
We have derived a universal scaling law governing this noisy dependence
obtained experimental evidence with a
chaotic electronic circuit. The implication can be quite intriguing. For example,
in computational science, if a different precision or a different computer
is used, the computed values of statistical averages may be different.
In a laboratory experiment, measurements performed under nonidentical
circumstances may yield different results.
Y.-C. Lai, Z. Liu, W.-G. Wei, and C.-H. Lai, ``Shadowability of
statistical averages in chaotic systems,'' Physical Review Letters
89, 184101 (2002).
PDF file
Any language is composed of many thousands of words linked together in an
apparently fairly sophisticated way. A language can thus be regarded as a
network, in the following sense: (1) the words correspond to nodes of the
network, and (2) a link exists between two words if they express similar
concepts. Clearly, the underlying network of a language is necessarily sparse
in the sense that the average number of links per node is typically much
smaller than the total number of nodes.
Identifying and understanding the common network topology of languages
is of great importance, not only for the study of languages themselves, but
also for cognitive science where one of the most fundmental issues concerns
associative memory that is intimately related to the network topology.
The network of connections among the many thousands
of words that make up a language is important not only
for the study of the structure and evolution of languages, but also
for cognitive science. We have studied this issue quantitatively by mapping out
the conceptual network of the English language, with the connections being
defined by the entries in a Thesaurus dictionary. We find that this network
presents a small-world structure, with an amazingly small average shortest path,
and appears to exhibit an asymptotic scale-free feature with algebraic
connectivity distribution.
From the standpoint of
retrieval of information in an associative memory, the small-world
property of the network represents a maximization of efficiency: on
the one hand, similar pieces of information are stored together, due
to the high clustering, which makes searching by association possible;
on the other hand, even very different pieces of information are never
separated by more than a few links, or associations, which guarantees a
fast search. We thus speculate that associative memory has arisen
partly because of a maximization of efficiency in the retrieval by
natural selection. This issue may be related to the fact that the neural
network is probably a small-world network as well
which is probably necessary for the brain to be able to hold a conceptual network
which is needed for associative memory.
A. E. Motter, A. P. S. de Moura, Y.-C. Lai, and P. Dasgupta,
``Language, small-worlds, and cognition,'' Physical Review E
(Rapid Communications) 65, 065102(1-4) (2002).
PDF file
This research was recently featured in New Scientists
(July 13, page 22)
PS file
AND Nature Science Update
See here
or
PS file
AND Wissenschaft in German
See here
or
English Translation
AND in newspapers in Europe, Brazil, and China.
This work was also selected by
the Virtual Journal of Biological Physics Research for the July 1, 2002 issue
See here
(2002) Noise-induced enhancement of chemical reactions in nonlinear
flows
The interplay between noise and nonlinear dynamics has long been a
topic of tremendous interest in statistical physics. While noise can
be detrimental in many situations, it can also be beneficial through,
for example, the mechanisms of stochastic and coherence resonances.
Recently, a new area of interdisciplinary science emerges: active
processes in nonlinear flows. Such processes can be chemical or biological,
and are believed to be relevant to a large number of important problems
in a variety of areas. Our work focuses on the role of noise in
active nonlinear processes. In particular,
motivated by the problem of ozone production in atmospheres of urban
areas, we investigate how noise
influence a general type of chemical reaction, supported on a chaotic
flow. To be as realistic as possible, we take into consideration
important physical effects such as particle inertia and finite size.
Our finding is that noise can enhance the rate of chemical
reaction, in a manner similar to that of stochastic resonance. We
provide numerical results and also a physical theory, suggesting that
at a fundamental level, the resonant behavior is due to the interaction
between noise and nonlinearity of the particle (Lagrangian) dynamics.
Z. Liu, Y.-C. Lai, and J. M. Lopez, ``Noise-induced enhancement of chemical
reactions in chaotic flows,'' Chaos 12, 417-425 (2002).
PDF file
This research recently appeared in Physics News Updates of American Institute
of Physics
See here
The problem of noise-induced chaos is fundamental to understanding the
interplay between stochasticity and nonlinearity, which is important
for a variety of fields. We consider
situations where in a continuous-time dynamical system, a nonchaotic
attractor coexists with a nonattracting chaotic saddle, as in a periodic window.
Under the influence of noise, chaos can arise.
We investigate the fundamental dynamical mechanism responsible
for the transition and obtain a general scaling law for the largest Lyapunov exponent.
A striking finding is that the topology of the flow is fundamentally disturbed
after the onset of noisy chaos, and we point out that such a disturbance is due to
changes in the number of unstable eigendirections along a continuous
trajectory under the influence of noise.
Z. Liu, Y.-C. Lai, L. Billings, and I. B. Schwartz, ``Transition
to chaos in continuous-time random dynamical systems,''
Physical Review Letters 88, 124101 (2002).
PDF file
B. Xu, Y.-C. Lai, L. Zhu, and Y. Do, ``Experimental
characterization of transition to chaos in random dynamical
systems,'' Physical Review Letters 90, 164101 (2003).
PDF file
Electronic transport in semiconductor nanostructures is a frontier
problem in condensed matter physics and nonlinear science. On
sub-micron scales, quantum interference gives
rise to phenomena as conductance fluctuations and the
Aharonov-Bohm effect. We have recently reported
our finding concerning the fundamental role played by
dynamical tunneling in conductance fluctuations
in realistic quantum dots. We
present strong evidence that dynamical
tunneling through regular phase-space structures, such as
Kolmogorov-Arnold-Moser (KAM) islands, fundamentally determines the
characteristics of conductance fluctuations in typical quantum dots.
Theoretical analysis based on the tunneling mechanism gives
quantitative predictions (the average frequency of the
fluctuations) in excellent agreement with experimental
measurements. To our knowledge, this is the first time that the
major characteristics of experimentally observable conductance fluctuations
in quantum dots are explained in a quantitative way, indicating
the fundamental importance of dynamical tunneling in the transport
dynamics of electrons in semiconductor nanostructures.
A. P. S. de Moura, Y.-C. Lai, R. Akis, J. Bird, and D. K. Ferry,
``Tunneling and nonhyperbolicity in quantum dots,''
Physical Review Letters 88, 236804(1-4) (2002).
PDF file
An outstanding problem in biomedical sciences is to devise techniques
to understand and, more importantly, to predict in advance of clinical
onset, epileptic seizures which
affect about $1\%$ of the population in industrialized
countries. Epileptic
seizures are characterized electrographically by sudden simultaneous
changes in power spectral density and
increases in wave rhythmicity.
These changes in brain activity, whether local or global, can be
monitored via electrodes on the scalp (EEG),
or intracranially (ECoG).
These recordings provide a window, perhaps
the only practically accessible window at present, through which
the dynamics of epilepsy can be investigated.
Analysis of EEG/ECoG has thus become
the subject of renewed interest in this field.
We focus on an anomalous scaling region in correlation-integral analysis
of electrocorticogram (ECoG) in epilepsy patients.
We find that epileptic seizures
typically are accompanied by wide fluctuations in the slope
of this scaling region. An explanation, based on analyzing
the interplay between the autocorrelation and $C(\epsilon)$,
is provided for these fluctuations. This
anomalous slope appears to be a sensitive measure for
tracking (but not predicting) seizures.
Our study suggests that
the underlying dynamical process contains a significant stochastic
component. Though epileptic seizures
are characterized by fluctuations in the value of the anomalous slope,
the fluctuations correspond to those of the autocorrelation, a more
computationally efficient measure for seizure tracking.
Thus, it is questionable whether any correlation-integral based
techniques can be more effective at predicting seizures than traditional
signal processing methods. This
is apparently in sharp contrast to the recent claims that such techniques
are powerful for prediction of seizures.
Y.-C. Lai, I. Oserio, M. A. Harrison, and M. Frei,
``Correlation-dimension and autocorrelation fluctuations in seizure dynamics,''
Physical Review E 65, 031921(1-5) (2002).
PDF file
This work was selected by
the Virtual Journal of Biological Physics Research for the March 15, 2002 issue
See here
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