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Register a new userInferring a network from dynamical signals at its nodes
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We give an approximate solution to the difficult inverse problem of inferring the topology of an unknown network from given time-dependent signals at the nodes. For example, we measure signals from individual neurons in the brain, and infer how they are inter-connected. We use Maximum Caliber as an inference principle. The combinatorial challenge of high-dimensional data is handled using two different approximations to the pairwise couplings. We show two proofs of principle: in a nonlinear genetic toggle switch circuit, and in a toy neural network.
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Cycles, which can be found in many different kinds of networks, make the problems more intractable, especially when dealing with dynamical processes on networks. On the contrary, tree networks in which no cycle exists, are simplifications and usually allow for analyticity. There lacks a quantity, however, to tell the ratio of cycles which determines the extent of network being close to tree networks. Therefore we introduce the term Cycle Nodes Ratio (CNR) to describe the ratio of number of nodes belonging to cycles to the number of total nodes, and provide an algorithm to calculate CNR. CNR is studied in both network models and real networks. The CNR remains unchanged in different sized Erdos Renyi (ER) networks with the same average degree, and increases with the average degree, which yields a critical turning point. The approximate analytical solutions of CNR in ER networks are given, which fits the simulations well. Furthermore, the difference between CNR and two-core ratio (TCR) is analyzed. The critical phenomenon is explored by analysing the giant component of networks. We compare the CNR in network models and real networks, and find the latter is generally smaller. Combining the coarse-graining method can distinguish the CNR structure of networks with high average degree. The CNR is also applied to four different kinds of transportation networks and fungal networks, which give rise to different zones of effect. It is interesting to see that CNR is very useful in network recognition of machine learning.
We analyze the synchronous firings of the salamander ganglion cells from the perspective of the complex network viewpoint where the networks links reflect the correlated behavior of firings. We study the time-aggregated properties of the resulting network focusing on its topological features. The behavior of pairwise correlations has been inspected in order to construct an appropriate measure that will serve as a weight of network connection.
We analyze the complex networks associated with brain electrical activity. Multichannel EEG measurements are first processed to obtain 3D voxel activations using the tomographic algorithm LORETA. Then, the correlation of the current intensity activation between voxel pairs is computed to produce a voxel cross-correlation coefficient matrix. Using several correlation thresholds, the cross-correlation matrix is then transformed into a network connectivity matrix and analyzed. To study a specific example, we selected data from an earlier experiment focusing on the MMN brain wave. The resulting analysis highlights significant differences between the spatial activations associated with Standard and Deviant tones, with interesting physiological implications. When compared to random data networks, physiological networks are more connected, with longer links and shorter path lengths. Furthermore, as compared to the Deviant case, Standard data networks are more connected, with longer links and shorter path lengths--i.e., with a stronger ``small worlds character. The comparison between both networks shows that areas known to be activated in the MMN wave are connected. In particular, the analysis supports the idea that supra-temporal and inferior frontal data work together in the processing of the differences between sounds by highlighting an increased connectivity in the response to a novel sound.
In order to model volatile real-world network behavior, we analyze phase-flipping dynamical scale-free network in which nodes and links fail and recover. We investigate how stochasticity in a parameter governing the recovery process affects phase-flipping dynamics, and find the probability that no more than q% of nodes and links fail. We derive higher moments of the fractions of active nodes and active links, $f_n(t)$ and $f_{ell}(t)$, and define two estimators to quantify the level of risk in a network. We find hysteresis in the correlations of $f_n(t)$ due to failures at the node level, and derive conditional probabilities for phase-flipping in networks. We apply our model to economic and traffic networks.
The totally asymmetric simple exclusion process (TASEP), which describes the stochastic dynamics of interacting particles on a lattice, has been actively studied over the past several decades and applied to model important biological transport processes. Here we present a software package, called EGGTART (Extensive GUI gives TASEP-realization in real time), which quantifies and visualizes the dynamics associated with a generalized version of the TASEP with an extended particle size and heterogeneous jump rates. This computational tool is based on analytic formulas obtained from deriving and solving the hydrodynamic limit of the process. It allows an immediate quantification of the particle density, flux, and phase diagram, as a function of a few key parameters associated with the system, which would be difficult to achieve via conventional stochastic simulations. Our software should therefore be of interest to biophysicists studying general transport processes, and can in particular be used in the context of gene expression to model and quantify mRNA translation of different coding sequences.
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