Emergence and Growth of Complex Networks in Adaptive Systems

We consider the population dynamics of a set of species whose network of catalytic interactions is described by a directed graph. The relationship between the attractors of this dynamics and the underlying graph theoretic structures like cycles and autocatalytic sets is discussed. It is shown that when the population dynamics is suitably coupled to a slow dynamics of the graph itself, the network evolves towards increasing complexity driven by autocatalytic sets. Some quantitative measures of network complexity are described.Comment: 10 pages (including figures), 3 Postscript figure

Autocatalytic Sets and the Growth of Complexity in an Evolutionary Model

A model of $s$ interacting species is considered with two types of dynamical variables. The fast variables are the populations of the species and slow variables the links of a directed graph that defines the catalytic interactions among them. The graph evolves via mutations of the least fit species. Starting from a sparse random graph, we find that an autocatalytic set (ACS) inevitably appears and triggers a cascade of exponentially increasing connectivity until it spans the whole graph. The connectivity subsequently saturates in a statistical steady state. The time scales for the appearance of an ACS in the graph and its growth have a power law dependence on $s$ and the catalytic probability. At the end of the growth period the network is highly non-random, being localized on an exponentially small region of graph space for large $s$.Comment: 13 pages REVTEX (including figures), 4 Postscript figure

Shift Estimation Algorithm for Dynamic Sensors With Frame-to-Frame Variation in Their Spectral Response

This study is motivated by the emergence of a new class of tunable infrared spectral-imaging sensors that offer the ability to dynamically vary the sensor\u27s intrinsic spectral response from frame to frame in an electronically controlled fashion. A manifestation of this is when a sequence of dissimilar spectral responses is periodically realized, whereby in every period of acquired imagery, each frame is associated with a distinct spectral band. Traditional scene-based global shift estimation algorithms are not applicable to such spectrally heterogeneous video sequences, as a pixel value may change from frame to frame as a result of both global motion and varying spectral response. In this paper, a novel algorithm is proposed and examined to fuse a series of coarse global shift estimates between periodically sampled pairs of nonadjacent frames to estimate motion between consecutive frames; each pair corresponds to two nonadjacent frames of the same spectral band. The proposed algorithm outperforms three alternative methods, with the average error being one half of that obtained by using an equal weights version of the proposed algorithm, one-fourth of that obtained by using a simple linear interpolation method, and one-twentieth of that obtained by using a nai¿ve correlation-based direct method

Carrier lifetimes in green emitting InGaN/GaN disks‐in‐nanowire and characteristics of green light emitting diodes

Improvement in the internal quantum efficiency (IQE) of InGaN/GaN disks‐in‐nanowires by surface passivation is demonstrated. The highest IQE achieved through surface passivation for green emitting (λ=540 nm) InGaN/GaN disks‐in‐nanowires is ∼53%. Radiative and nonradiative carrier lifetimes are calculated for as‐grown and surface passivated green emitting disks‐in‐nanowires. Passivated green sample exhibits a room temperature radiative lifetime of ∼748 ps, which is much smaller than that of equivalent quantum wells. Electroluminescence measurements on passivated green light emitting diodes containing InGaN disks demonstrate no roll over or efficiency droop up to 375 A/cm 2 , and exhibit a blue‐shift of 7 nm in peak wavelength. An enhancement in the light output due to surface passivation is observable in the relative external quantum efficiency of the surface passivated devices as compared with the as‐grown samples. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/98222/1/812_ftp.pd

Role of bias conditions in the hot carrier degradation of AlGaN/GaN high electron mobility transistors

The impacts of gate bias and device temperature on carrier energy distributions are reported for AlGaN/GaN High Electron Mobility Transistors. The lateral electric field and the average carrier energy are the highest at the end of gate on the gate‐drain access side. The number of high energy carriers is the greatest in the semi‐ON operating condition, with maximum energies exceeding the activation energy of defects in the AlGaN. There is a significant decrease in the number of very high energy carriers (greater than 2 eV) as the device temperature increases whereas the number of moderately energetic carriers (between 1 to 2 eV) is higher at elevated temperatures.(© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/98280/1/794_ftp.pd

Crashes, recoveries, and "core shifts" in a model of evolving networks

A model of an evolving network of interacting molecular species is shown to exhibit repeated rounds of crashes in which several species get rapidly depopulated, followed by recoveries. The network inevitably self- organizes into an autocatalytic structure, which consists of an irreducible "core" surrounded by a parasitic "periphery." Crashes typically occur when the existing autocatalytic set becomes fragile and suffers a "core shift," defined graph theoretically. The nature of the recovery after a crash, in particular, the time of recovery, depends upon the organizational structure that survives the crash. The largest eigenvalue of the adjacency matrix of the graph is an important signal of network fragility or robustness

Cavity Q, mode volume, and lasing threshold in small diameter AlGaAs microdisks with embedded quantum dots

The quality factor (Q), mode volume (Veff), and room-temperature lasing threshold of microdisk cavities with embedded quantum dots (QDs) are investigated. Finite element method simulations of standing wave modes within the microdisk reveal that Veff can be as small as 2(lambda/n)^3 while maintaining radiation-limited Qs in excess of 10^5. Microdisks of diameter D=2 microns are fabricated in an AlGaAs material containing a single layer of InAs QDs with peak emission at lambda = 1317 nm. For devices with Veff ~2 (lambda/n)^3, Qs as high as 1.2 x 10^5 are measured passively in the 1.4 micron band, using an optical fiber taper waveguide. Optical pumping yields laser emission in the 1.3 micron band, with room temperature, continuous-wave thresholds as low as 1 microWatt of absorbed pump power. Out-coupling of the laser emission is also shown to be significantly enhanced through the use of optical fiber tapers, with laser differential efficiency as high as xi~16% and out-coupling efficiency in excess of 28%.Comment: 6 figure