This picture is a hand-made illustration.

<p>Squares are filled as to create an image of a stochastic process whose points spread according to the given Lyapunov exponents. (A) A small box representing a set of initial conditions. After one iteration of the system, the points that leave the initial box in (A) go to 4 boxes along the diagonal line [filled squares in (B)] and 8 boxes off-diagonal (along the transverse direction) [filled circles in (B)]. At the second iteration, the points occupy other neighbouring boxes as illustrated in (C) and after an interval of time the points do not spread any longer (D).</p

Results for experimental networks of Double-Scroll circuits.

<p>On the left-side upper corner pictograms represent how the circuits (filled circles) are bidirectionally coupled. as (green online) filled circles, as the (red online) thick line, and as the (blue online) squares, for a varying coupling resistance . The unit of these quantities shown in these figures is (kbits/s). (A) Topology I, (B) Topology II, (C) Topology III, and (D) Topology IV. In all figures, increases smoothly from 1.25 to 1.95 as varies from 0.1k to 5k. The line on the top of the figure represents the interval of resistance values responsible to induce almost synchronisation (AS) and phase synchronisation (PS).</p

Black filled circles represent a Chua’s circuit and the numbers identify each circuit in the networks.

<p>Coupling is diffusive. We consider 4 topologies: 2 coupled Chua’s circuit (A), an array of 3 coupled circuits, an array of 4 coupled circuits, and a ring formed by 4 coupled circuits.</p

Results for a network of Hindmarsh-Rose neurons.

<p>(a) Expected value of the local mean field of the node against the node degree . The error bar indicates the variance () of . (b) Black points indicate the value of and for <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0048118#pone.0048118.e248" target="_blank">Eq. (13)</a> to present a stable periodic orbit (no positive Lyapunov exponents). The maximal values of the periodic orbits obtained from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0048118#pone.0048118.e248" target="_blank">Eq. (13)</a> is shown in the bifurcation diagram in (c) considering and . (d) The CAS pattern for a neuron with degree  = 25 (with and ). In the inset, the same CAS pattern of the neuron and some sampled points of the trajectory for the neuron and another neuron with degree . (e) The difference between the first coordinates of the trajectories of neurons and , with a time-lag of . (f) Phase difference between the phases of the trajectories for neurons and .</p

Results for a network of coupled maps.

<p>(a) Expected value of the local mean field of the node against the node degree . The error bar indicates the variance () of . (b) A bifurcation diagram of the CAS pattern [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0048118#pone.0048118.e060" target="_blank">Eq. (6)</a>] considering . (c) Probability density function of the trajectory of a node with degree  = 80 (therefore, , ). (d) A return plot considering two nodes ( and ) with the same degree 80.</p

Results for two coupled maps. [Eq. (3)] as (green online) filled circles, [Eq. (5)] as the (red online) thick line, and [Eq. (7)] as the (blue online) crosses.

<p>In (A) and in (B) . The units of , , and are [bits/iteration].</p

Assessing the role of two key mechanisms responsible for the cell adaptation to osmotic stress during the G1 phase.

<p>The x-axis represents the time point of application of stress, whereas the y-axis illustrates the corresponding arrest duration. Blocking the interaction of Sic1 with Hog1PP, reduces the arrest duration significantly along the G1 phase (red crosses).</p

The HOG MAPK network rescues the mitotic exit defect of MEN mutants.

<p>(A) A <i>cdc15</i> cell is arrested in M phase and cannot divide. (B) Application of 0.4 M NaCl stimulates the <i>cdc15</i> cell to go through cell division. (C) The <i>cdc14</i> cell can go through the cell division in the presence of 0.4 M NaCl. (D) Removing the interaction of Hog1PP with <i>CLB2</i> does not cancel the cell division of the <i>cdc15</i> cell in the presence of osmotic stress. Note that the <i>cdc15</i> cell upon osmotic stress is able to finish its current cell cycle but gets arrested in the next G2/M phase. (E) The <i>cdc15</i> cell, in which the interaction of Sic1 with Hog1PP is blocked, cannot finish its cell cycle and is arrested in M phase.</p

Application of osmotic stress during late S phase or early G2/M phase causes DNA re-replication.

<p>(A) Time course activity of the cell cycle components for the wild type untreated cell. (B) 1 M NaCl applied at minute 76. Activity of Hog1PP causes downregulation of Cdc28-Clb5. In addition, the level of Cdc6 slightly increases when Cdc28-Clb5 activity is reduced by Hog1PP (see inset). Then, after Hog1PP returns to its basal level, Clb5 starts increasing again. The downregulation, following by an upregulation of Cdc28-Clb5 can lead to DNA re-replication. (C) Overexpression of <i>CLB5</i>, by simulating induction of <i>CLB5</i> transcription from the GAL1 promoter, inhibits the DNA re-replication. (D) Blocking the interaction of Sic1 with Hog1PP also hinders the DNA re-replication in the presence of 1 M NaCl.</p

Time course activity of cell cycle components upon application of 1 M NaCl at early S phase.

<p>The left vertical axis refers to the concentrations of total Sic1, SBF/MBF, Swe1, Cdc28-Clb2, Cdc28-Clb5, and Hog1PP and the right vertical axis refers to the concentration of the Hsl1-Hsl7 complex. (A) A wild type untreated cell, (B) 1 M NaCl applied during early S phase (at t = 45 min) to a wild type cell causes the cell cycle to last about 76 minutes longer compared to the wild type untreated cell. (C) 1 M NaCl applied to a Δ<i>swe1</i> cell; in this case the cell cycle duration is 62 minutes longer than in an untreated Δ<i>swe1</i> cell. (D) The deletion of Sic1 does not cancel the delay caused by Hog1PP activity. 1 M NaCl applied to a Δ<i>sic1</i> cell prolongs the cell cycle around 52 minutes compared to a Δ<i>sic1</i> untreated cell.</p