Mutual information rate and bounds for it

The amount of information exchanged per unit of time between two nodes in a dynamical network or between two data sets is a powerful concept for analysing complex systems. This quantity, known as the mutual information rate (MIR), is calculated from the mutual information, which is rigorously defined only for random systems. Moreover, the definition of mutual information is based on probabilities of significant events. This work offers a simple alternative way to calculate the MIR in dynamical (deterministic) networks or between two data sets (not fully deterministic), and to calculate its upper and lower bounds without having to calculate probabilities, but rather in terms of well known and well defined quantities in dynamical systems. As possible applications of our bounds, we study the relationship between synchronisation and the exchange of information in a system of two coupled maps and in experimental networks of coupled oscillators

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

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 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

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

Substrate and Mg doping effects in GaAs nanowires

Mg doping of GaAs nanowires has been established as a viable alternative to Be doping in order to achieve p-type electrical conductivity. Although reports on the optical properties are available, few reports exist about the physical properties of intermediate-to-high Mg doping in GaAs nanowires grown by molecular beam epitaxy (MBE) on GaAs(111)B and Si(111) substrates. In this work, we address this topic and present further understanding on the fundamental aspects. As the Mg doping was increased, structural and optical investigations revealed: i) a lower influence of the polytypic nature of the GaAs nanowires on their electronic structure; ii) a considerable reduction of the density of vertical nanowires, which is almost null for growth on Si(111); iii) the occurrence of a higher WZ phase fraction, in particular for growth on Si(111); iv) an increase of the activation energy to release the less bound carrier in the radiative state from nanowires grown on GaAs(111)B; and v) a higher influence of defects on the activation of nonradiative de-excitation channels in the case of nanowires only grown on Si(111). Back-gate field effect transistors were fabricated with individual nanowires and the p-type electrical conductivity was measured with free hole concentration ranging from 2.7 × 1016 cm−3 to 1.4 × 1017 cm−3. The estimated electrical mobility was in the range ≈0.3–39 cm2/Vs and the dominant scattering mechanism is ascribed to the WZ/ZB interfaces. Electrical and optical measurements showed a lower influence of the polytypic structure of the nanowires on their electronic structure. The involvement of Mg in one of the radiative transitions observed for growth on the Si(111) substrate is suggested

Promoting a significant increase in the photoluminescence quantum yield of terbium(III) complexes by ligand modification

Two discrete mononuclear complexes, [Tb(bbpen)(NO3)] (I) and [Tb(bbppn)(NO3)] (II), for which H 2 bbpen = N,N'-bis(2-hydroxybenzyl)-N,N'-bis(pyridin-2-ylmethyl)ethylenediamine and H 2 bbppn = N,N'-bis(2-hydroxylbenzyl)-N,N'-bis(pyridin-2-ylmethyl)-1,2-propanediamine, were synthesized and characterized by FTIR, Raman, and photoluminescence (PL, steady-state and time-resolved modes) spectroscopy. The attachment of a methyl group to the ethylenediamine portion of the ligand backbone differentiates II from I and acts as a determining feature to both the structural and optical properties of the former. The single-crystal X-ray structure of H 2 bbppn is described here for the first time, while that of complex II has been redetermined in the monoclinic C2 space group in light of new diffraction data. In II, selective crystallization leads to spontaneous resolution of enantiomeric molecules in different crystals. Absolute emission quantum yields (ϕ) and luminescence excited-state lifetimes (at room temperature and 11 K) were measured for both complexes. Despite their similar molecular structures, I and II exhibit remarkably different ϕ values of 21 ± 2% and 67 ± 7%, respectively, under UV excitation at room temperature. Results of quantum-mechanical (DFT and TD-DFT) calculations and experimental PL measurements also performed for H 2 bbpen and H 2 bbppn confirmed that both ligands are suitable to work as "antennas" for TbIII. Considering the 5D4 lifetime profiles and the significantly higher absolute quantum yield of II, it appears that thermally active nonradiative pathways present in I are minimized in II due to differences in the conformation of the ethylenediamine bridge