Predicting collapse of adaptive networked systems without knowing the network

The collapse of ecosystems, the extinction of species, and the breakdown of economic and financial networks usually hinges on topological properties of the underlying networks, such as the existence of self-sustaining (or autocatalytic) feedback cycles. Such collapses can be understood as a massive change of network topology, usually accompanied by the extinction of a macroscopic fraction of nodes and links. It is often related to the breakdown of the last relevant directed catalytic cycle within a dynamical system. Without detailed structural information it seems impossible to state, whether a network is robust or if it is likely to collapse in the near future. Here we show that it is nevertheless possible to predict collapse for a large class of systems that are governed by a linear (or linearized) dynamics. To compute the corresponding early warning signal, we require only non-structural information about the nodes’ states such as species abundances in ecosystems, or company revenues in economic networks. It is shown that the existence of a single directed cycle in the network can be detected by a “quantization effect” of node states, that exists as a direct consequence of a corollary of the Perron–Frobenius theorem. The proposed early warning signal for the collapse of networked systems captures their structural instability without relying on structural information. We illustrate the validity of the approach in a transparent model of co-evolutionary ecosystems and show this quantization in systems of species evolution, epidemiology, and population dynamics

Analysis and modeling of an ultrasound-modulated guide star to increase the depth of focusing in a turbid medium

The effects of strong scattering in tissue limit the depth to which light may be focused. However, it has been shown that scattering may be reduced utilizing adaptive optics with a focused ultrasound (US) beam guidestar. The optical signal traveling through the US beam waist is frequency shifted and may be isolated with demodulation. This paper utilizes a multiphysics simulation to model the optical and US interactions in both synthetic tissue and random scattering media. The results illustrate that optical energy may be focused within a turbid medium utilizing a US guidestar. The results also suggest that optical energy travels preferentially along optical channels within a turbid medium

Diffusion model for ultrasound-modulated light

Researchers use ultrasound (US) to modulate diffusive light in a highly scattering medium like tissue. This paper analyzes the US–optical interaction in the scattering medium and derives an expression for the US-modulated optical radiance. The diffusion approximation to the radiative transport equation is employed to develop a Green’s function for US-modulated light. The predicted modulated fluence and flux are verified using finite-difference time-domain simulations. The Green’s function is then utilized to illustrate the modulated reflectance as the US–optical interaction increases in depth. The intent of this paper is to focus on high US frequencies necessary for high-resolution imaging because they are of interest for applications such as phase conjugation

A model for ultrasound modulated light in a turbid medium

The ability to focus light in most tissue degrades quickly with depth due to high optical scattering. Researchers have investigated using both ultrasound (US) and light synergistically to overcome this difficulty. Ultrasound has been utilized to modulated light within tissue to create a diffusive wave at that is modulated at the US frequency. Recently, there has been interest in the modulated sidebands which reside at optical frequency plus or minus the US frequency. This paper will discuss a model for US-light interactions in a scattering medium. We will use this model to relate the radiance in the probe beam to the radiance in the diffusive wave. We will then employ the P-1 approximation to the radiative transport equation to find the fluence and flux of the modulated wave. We will use these parameters to write a diffusion equation for the modulated wave that can be described in terms of the incoming optical power, and the US intensity and geometry

Characterization of exact lumpability for vector fields on smooth manifolds

We characterize the exact lumpability of smooth vector fields on smooth manifolds. We derive necessary and sufficient conditions for lumpability and express them from four different perspectives, thus simplifying and generalizing various results from the literature that exist for Euclidean spaces. We introduce a partial connection on the pullback bundle that is related to the Bott connection and behaves like a Lie derivative. The lumping conditions are formulated in terms of the differential of the lumping map, its covariant derivative with respect to the connection and their respective kernels. Some examples are discussed to illustrate the theory. © 2016 Published by Elsevier B.V

Network topology near criticality in adaptive epidemics

We study structural changes of adaptive networks in the coevolutionary susceptible-infected-susceptible (SIS) network model along its phase transition. We clarify to what extent these changes can be used as early-warning signs for the transition at the critical infection rate λc at which the network collapses and the system disintegrates. We analyze the interplay between topology and node-state dynamics near criticality. Several network measures exhibit clear maxima or minima close to the critical threshold and could potentially serve as early-warning signs. These measures include the SI link density, triplet densities, clustering, assortativity, and the eigenvalue gap. For the SI link density and triplet densities the maximum is found to originate from the coexistence of two power laws. Other network quantities, such as the degree, the branching ratio, or the harmonic mean distance, show scaling with a singularity at λ=0 (not at λc), which means that they are incapable of detecting the transition. © 2018 American Physical Society

12^{12}C/13^{13}C ratio in planetary nebulae from the IUE archives

We investigated the abundance ratio of $^{12}$C/$^{13}$C in planetary nebulae by examining emission lines arising from \ion{C}{3} 2s2p ^3P_{2,1,0} \to 2s^2 ^1S_0. Spectra were retrieved from the International Ultraviolet Explorer archives, and multiple spectra of the same object were coadded to achieve improved signal-to-noise. The $^{13}$C hyperfine structure line at 1909.6 \AA was detected in NGC 2440. The $^{12}$C/$^{13}$C ratio was found to be $\sim4.4\pm$1.2. In all other objects, we provide an upper limit for the flux of the 1910 \AA line. For 23 of these sources, a lower limit for the $^{12}$C/$^{13}$C ratio was established. The impact on our current understanding of stellar evolution is discussed. The resulting high signal-to-noise \ion{C}{3} spectrum helps constrain the atomic physics of the line formation process. Some objects have the measured 1907/1909 flux ratio outside the low-electron density theoretical limit for $^{12}$C. A mixture of $^{13}$C with $^{12}$C helps to close the gap somewhat. Nevertheless, some observed 1907/1909 flux ratios still appear too high to conform to the presently predicted limits. It is shown that this limit, as well as the 1910/1909 flux ratio, are predominantly influenced by using the standard partitioning among the collision strengths for the multiplet $^1S_0$--$^3P_J$ according to the statistical weights. A detailed calculation for the fine structure collision strengths between these individual levels would be valuable.Comment: ApJ accepted: 19 pages, 3 Figures, 2 Table

A model for ultrasound modulated light in a turbid medium

The ability to focus light in most tissue degrades quickly with depth due to high optical scattering. Researchers have investigated using both ultrasound (US) and light synergistically to overcome this difficulty. Ultrasound has been utilized to modulated light within tissue to create a diffusive wave at that is modulated at the US frequency. Recently, there has been interest in the modulated sidebands which reside at optical frequency plus or minus the US frequency. This paper will discuss a model for US-light interactions in a scattering medium. We will use this model to relate the radiance in the probe beam to the radiance in the diffusive wave. We will then employ the P-1 approximation to the radiative transport equation to find the fluence and flux of the modulated wave. We will use these parameters to write a diffusion equation for the modulated wave that can be described in terms of the incoming optical power, and the US intensity and geometry