Contour plot of <i>R</i> in the <i>A—p</i> plane.

<p>Other parameters for bounded noise are set to <i>σ</i> = 1 and <i>f</i> = 80.</p

Impact of Bounded Noise and Rewiring on the Formation and Instability of Spiral Waves in a Small-World Network of Hodgkin-Huxley Neurons

<div><p>Spiral waves are observed in the chemical, physical and biological systems, and the emergence of spiral waves in cardiac tissue is linked to some diseases such as heart ventricular fibrillation and epilepsy; thus it has importance in theoretical studies and potential medical applications. Noise is inevitable in neuronal systems and can change the electrical activities of neuron in different ways. Many previous theoretical studies about the impacts of noise on spiral waves focus an unbounded Gaussian noise and even colored noise. In this paper, the impacts of bounded noise and rewiring of network on the formation and instability of spiral waves are discussed in small-world (SW) network of Hodgkin-Huxley (HH) neurons through numerical simulations, and possible statistical analysis will be carried out. Firstly, we present SW network of HH neurons subjected to bounded noise. Then, it is numerically demonstrated that bounded noise with proper intensity <i>σ</i>, amplitude <i>A</i>, or frequency <i>f</i> can facilitate the formation of spiral waves when rewiring probability <i>p</i> is below certain thresholds. In other words, bounded noise-induced resonant behavior can occur in the SW network of neurons. In addition, rewiring probability <i>p</i> always impairs spiral waves, while spiral waves are confirmed to be robust for small <i>p</i>, thus shortcut-induced phase transition of spiral wave with the increase of <i>p</i> is induced. Furthermore, statistical factors of synchronization are calculated to discern the phase transition of spatial pattern, and it is confirmed that larger factor of synchronization is approached with increasing of rewiring probability <i>p</i>, and the stability of spiral wave is destroyed.</p></div

Developed patterns in the SW network at <i>t</i> = 500 time units, which are obtained by fixing <i>A</i> = 10, <i>f</i> = 80 and adjusting <i>p</i> and <i>σ</i>, respectively.

<p><i>σ</i> = 1 is adopted in top panel. <i>p</i> = 0.02 is adopted in bottom panel.</p

Additional file 2: of Diverse effects of distance cutoff and residue interval on the performance of distance-dependent atom-pair potential in protein structure prediction

The list of the 1762 non-redundant PDB chains and the detailed information for the filtered CASP11 and CASP12 decoys. (XLSX 339 kb

The synchronization factor <i>R</i> as a function of rewiring probability <i>p</i> for the different intensity <i>σ</i>.

<p>And <i>A</i> = 10 and <i>f</i> = 80 are adopted.</p

Contour plot of <i>R</i> in the <i>f—p</i> plane.

<p>Other parameters for bounded noise are set to <i>A</i> = 10 and <i>σ</i> = 1.</p

Developed patterns in the SW network at <i>t</i> = 500 time units, which are obtained by fixing <i>f</i> = 80, <i>σ</i> = 1, <i>p</i> = 0.02 and adjusting amplitude <i>A</i>.

<p>Developed patterns in the SW network at <i>t</i> = 500 time units, which are obtained by fixing <i>f</i> = 80, <i>σ</i> = 1, <i>p</i> = 0.02 and adjusting amplitude <i>A</i>.</p

Additional file 1: Figure S1. of Diverse effects of distance cutoff and residue interval on the performance of distance-dependent atom-pair potential in protein structure prediction

The occurrence frequency of 27,889 atom pairs on the structural dataset of 1762 proteins. Figure S2. The variation of Z-score with the distance cutoff and residue interval for potentials based on different reference states. Figure S3. The numbers of residue outlier (in native structures and in decoys with the lowest value) for each decoy set from the I-TASSER and CASP11 decoy sets. Figure S4. The variation of average PCC between energy score and TM-score (over all 16 residue intervals) with distance cutoff for the 6 bunches of decoy sets. Figure S5. The variation of average PCC between energy score and TM-score (over all 18 distance cutoff) with residue interval for the 6 bunches of decoy sets. (DOCX 1096 kb