Causal connectivity measures for pulse-output network reconstruction: Analysis and applications.

The causal connectivity of a network is often inferred to understand network function. It is arguably acknowledged that the inferred causal connectivity relies on the causality measure one applies, and it may differ from the network's underlying structural connectivity. However, the interpretation of causal connectivity remains to be fully clarified, in particular, how causal connectivity depends on causality measures and how causal connectivity relates to structural connectivity. Here, we focus on nonlinear networks with pulse signals as measured output, e.g., neural networks with spike output, and address the above issues based on four commonly utilized causality measures, i.e., time-delayed correlation coefficient, time-delayed mutual information, Granger causality, and transfer entropy. We theoretically show how these causality measures are related to one another when applied to pulse signals. Taking a simulated Hodgkin-Huxley network and a real mouse brain network as two illustrative examples, we further verify the quantitative relations among the four causality measures and demonstrate that the causal connectivity inferred by any of the four well coincides with the underlying network structural connectivity, therefore illustrating a direct link between the causal and structural connectivity. We stress that the structural connectivity of pulse-output networks can be reconstructed pairwise without conditioning on the global information of all other nodes in a network, thus circumventing the curse of dimensionality. Our framework provides a practical and effective approach for pulse-output network reconstruction.

Exponential Time Differencing Algorithm for Pulse-Coupled Hodgkin-Huxley Neural Networks.

The exponential time differencing (ETD) method allows using a large time step to efficiently evolve stiff systems such as Hodgkin-Huxley (HH) neural networks. For pulse-coupled HH networks, the synaptic spike times cannot be predetermined and are convoluted with neuron's trajectory itself. This presents a challenging issue for the design of an efficient numerical simulation algorithm. The stiffness in the HH equations are quite different, for example, between the spike and non-spike regions. Here, we design a second-order adaptive exponential time differencing algorithm (AETD2) for the numerical evolution of HH neural networks. Compared with the regular second-order Runge-Kutta method (RK2), our AETD2 method can use time steps one order of magnitude larger and improve computational efficiency more than ten times while excellently capturing accurate traces of membrane potentials of HH neurons. This high accuracy and efficiency can be robustly obtained and do not depend on the dynamical regimes, connectivity structure or the network size.

Expression of MIF, Beclin1, and LC3 in human salivary gland adenoid cystic carcinoma and its prognostic value.

Adenoid cystic carcinoma (ACC) is an uncommon salivary gland malignancy with a poor long-term prognosis. Clinical reports show the high rates of local recurrences and distant metastases. This study aimed to investigate the expression of MIF, Beclin1, and light-chain 3 (LC3) in salivary adenoid cystic carcinoma (SACC).Tissue specimens were obtained from 48 salivary glands adenoid cystic carcinoma (SACC) patients and 15 oral squamous cell carcinoma (OSCC) patients. Immunohistochemical staining was performed to estimate the level of LC3, Beclin1, and MIF. All SACC patients were followed up. The Kaplan-Meier method was used to compare the prognosis of patients after treatment.The 3-year, 5 year-, and 10 year-survival rates of the SACC patients were 83.9%, 69.9%, and 46.6%, respectively. MIF, LC3, and Beclin1 in SACC were all obviously over-expressed. MIF showed an increased tendency in cases with advanced TNM stages, and at the same time, there was an inversely proportional relationship between MIF and LC3, Beclin1.The long-term survival of SACC patients is poor. MIF might be a risk factor for SACC patients, whereas, LC3 and Beclin1 might be an effective strategy for treatment of SACC.

The Dynamics of Balanced Spiking Neuronal Networks Under Poisson Drive Is Not Chaotic.

Some previous studies have shown that chaotic dynamics in the balanced state, i.e., one with balanced excitatory and inhibitory inputs into cortical neurons, is the underlying mechanism for the irregularity of neural activity. In this work, we focus on networks of current-based integrate-and-fire neurons with delta-pulse coupling. While we show that the balanced state robustly persists in this system within a broad range of parameters, we mathematically prove that the largest Lyapunov exponent of this type of neuronal networks is negative. Therefore, the irregular firing activity can exist in the system without the chaotic dynamics. That is the irregularity of balanced neuronal networks need not arise from chaos.