Comparison of gene regulatory networks to identify pathogenic genes for lymphoma.

Lymphoma is the most complicated cancer that can be divided into several tens of subtypes. It may occur in any part of body that has lymphocytes, and is closely correlated with diverse environmental factors such as the ionizing radiation, chemocarcinogenesis, and virus infection. All the environmental factors affect the lymphoma through genes.

Mapping topological characteristics of dynamical systems into neural networks: A reservoir computing approach.

Significant advances have recently been made in modeling chaotic systems with the reservoir computing approach, especially for prediction. We find that although state prediction of the trained reservoir computer will gradually deviate from the actual trajectory of the original system, the associated geometric features remain invariant. Specifically, we show that the typical geometric metrics including the correlation dimension, the multiscale entropy, and the memory effect are nearly identical between the trained reservoir computer and its learned chaotic systems.

Excited state of spiral waves in oscillatory reaction-diffusion systems caused by a pulse.

Previous studies claim that the dynamic behaviors of spiral waves are uniquely determined by the nature of the medium, which can be determined by control parameters. In this article, the authors break from the previous view and present an alternate stable state of spiral waves, named the excited state. The authors find that two states of the spiral wave switch to each other after a one-off pulse is applied to the medium.

Disassortative Network Structure Improves the Synchronization between Neurons in the Suprachiasmatic Nucleus.

In mammals, an endogenous clock located in the suprachiasmatic nucleus (SCN) of the brain regulates the circadian rhythms of physiological and behavioral activities. The SCN is composed of about 20,000 neurons that are autonomous oscillators with nonidentical intrinsic periods ranging from 22 h to 28 h. These neurons are coupled through neurotransmitters and synchronized to form a network, which produces a robust circadian rhythm of a uniform period.

Synchronization of chaotic systems and their machine-learning models.

Recent advances have demonstrated the effectiveness of a machine-learning approach known as "reservoir computing" for model-free prediction of chaotic systems. We find that a well-trained reservoir computer can synchronize with its learned chaotic systems by linking them with a common signal. A necessary condition for achieving this synchronization is the negative values of the sub-Lyapunov exponents.

Sampling frequency dependent visibility graphlet approach to time series.

Recent years have witnessed special attention on complex network based time series analysis. To extract evolutionary behaviors of a complex system, an interesting strategy is to separate the time series into successive segments, map them further to graphlets as representatives of states, and extract from the state (graphlet) chain transition properties, called graphlet based time series analysis. Generally speaking, properties of time series depend on the time scale.

Predicting search time when hunting for multiple moving targets: A recursive harmonic law.

We investigate searching for multiple mobile objects on networks and introduce the concept of mean random search time (MRST) to quantify the expected time a searcher takes to capture moving targets specified in advance. We consider this quantity averaged over all initial conditions for a searcher and multiple targets called the global MRST. We find that the growth of global MRST follows a recursive harmonic law with respect to that of stalking the individuals.

A Patient Suffering From Neurodegenerative Disease May Have a Strengthened Fractal Gait Rhythm.

Scale invariance in stride series, namely, the series shows similar patterns across multiple time scales, is used widely as a non-invasive identifier of health assessment. Detailed calculations in the literature with standard tools, such as de-trended fluctuation analysis and wavelet transform modulus maxima seem to lead a conclusion that patients suffering from neurodegenerative diseases have weakened fractal gait rhythm compared with healthy persons. These variance-based methods are dynamical mechanism dependent, namely, for some dynamical process the scale invariance cannot be detected qualitatively, while for some others the scale invariance can be detected correctly, but the estimated value of scaling exponent is not correct.

Universal principles governing multiple random searchers on complex networks: The logarithmic growth pattern and the harmonic law.

We propose a unified framework to evaluate and quantify the search time of multiple random searchers traversing independently and concurrently on complex networks. We find that the intriguing behaviors of multiple random searchers are governed by two basic principles-the logarithmic growth pattern and the harmonic law. Specifically, the logarithmic growth pattern characterizes how the search time increases with the number of targets, while the harmonic law explores how the search time of multiple random searchers varies relative to that needed by individual searchers.

Multitarget search on complex networks: A logarithmic growth of global mean random cover time.

We investigate multitarget search on complex networks and derive an exact expression for the mean random cover time that quantifies the expected time a walker needs to visit multiple targets. Based on this, we recover and extend some interesting results of multitarget search on networks. Specifically, we observe the logarithmic increase of the global mean random cover time with the target number for a broad range of random search processes, including generic random walks, biased random walks, and maximal entropy random walks.

Multiple random walks on complex networks: A harmonic law predicts search time.

We investigate multiple random walks traversing independently and concurrently on complex networks and introduce the concept of mean first parallel passage time (MFPPT) to quantify their search efficiency. The mean first parallel passage time represents the expected time required to find a given target by one or some of the multiple walkers. We develop a general theory that allows us to calculate the MFPPT analytically.

Memory and betweenness preference in temporal networks induced from time series.

We construct temporal networks from time series via unfolding the temporal information into an additional topological dimension of the networks. Thus, we are able to introduce memory entropy analysis to unravel the memory effect within the considered signal. We find distinct patterns in the entropy growth rate of the aggregate network at different memory scales for time series with different dynamics ranging from white noise, 1/f noise, autoregressive process, periodic to chaotic dynamics.

Navigation by anomalous random walks on complex networks.

Anomalous random walks having long-range jumps are a critical branch of dynamical processes on networks, which can model a number of search and transport processes. However, traditional measurements based on mean first passage time are not useful as they fail to characterize the cost associated with each jump. Here we introduce a new concept of mean first traverse distance (MFTD) to characterize anomalous random walks that represents the expected traverse distance taken by walkers searching from source node to target node, and we provide a procedure for calculating the MFTD between two nodes.

Lévy Walk Navigation in Complex Networks: A Distinct Relation between Optimal Transport Exponent and Network Dimension.

We investigate, for the first time, navigation on networks with a Lévy walk strategy such that the step probability scales as pij ~ dij(-α), where dij is the Manhattan distance between nodes i and j, and α is the transport exponent. We find that the optimal transport exponent α(opt) of such a diffusion process is determined by the fractal dimension df of the underlying network. Specially, we theoretically derive the relation α(opt) = df + 2 for synthetic networks and we demonstrate that this holds for a number of real-world networks.

Time-series analysis of networks: exploring the structure with random walks.

We generate time series from scale-free networks based on a finite-memory random walk traversing the network. These time series reveal topological and functional properties of networks via their temporal correlations. Remarkably, networks with different node-degree mixing patterns exhibit distinct self-similar characteristics.

Geometrical invariability of transformation between a time series and a complex network.

We present a dynamically equivalent transformation between time series and complex networks based on coarse geometry theory. In terms of quasi-isometric maps, we characterize how the underlying geometrical characters of complex systems are preserved during transformations. Fractal dimensions are shown to be the same for time series (or complex network) and its transformed counterpart.