Regulatory Dynamics on Random Networks: Asymptotic Periodicity and Modularity

We study the dynamics of discrete-time regulatory networks on random digraphs. For this we define ensembles of deterministic orbits of random regulatory networks, and introduce some statistical indicators related to the long-term dynamics of the system. We prove that, in a random regulatory network, initial conditions converge almost surely to a periodic attractor. We study the subnetworks, which we call modules, where the periodic asymptotic oscillations are concentrated. We proof that those modules are dynamically equivalent to independent regulatory networks.Comment: 23 pages, 3 figure

Noise Effects on the Complex Patterns of Abnormal Heartbeats

Patients at high risk for sudden death often exhibit complex heart rhythms in which abnormal heartbeats are interspersed with normal heartbeats. We analyze such a complex rhythm in a single patient over a 12-hour period and show that the rhythm can be described by a theoretical model consisting of two interacting oscillators with stochastic elements. By varying the magnitude of the noise, we show that for an intermediate level of noise, the model gives best agreement with key statistical features of the dynamics.Comment: 4 pages, 4 figures, RevTe

Schwarzschild Atmospheric Processes: A Classical Path to the Quantum

We develop some classical descriptions for processes in the Schwarzschild string atmosphere. These processes suggest relationships between macroscopic and microscopic scales. The classical descriptions developed in this essay highlight the fundamental quantum nature of the Schwarzschild atmospheric processes.Comment: to appear in Gen. Rel. Gra

Morphology of the 12-micron Seyfert Galaxies: II. Optical and Near-Infrared Image Atlas

We present 263 optical and near-infrared (NIR) images for 42 Seyfert 1s and 48 Seyfert 2s, selected from the Extended 12-micron Galaxy Sample. Elliptically-averaged profiles are derived from the images, and isophotal radii and magnitudes are calculated from these. We also report virtual aperture photometry, that judging from comparison with previous work, is accurate to roughly 0.05mag in the optical, and 0.07mag in the NIR. Our B-band isophotal magnitude and radii, obtained from ellipse fitting, are in good agreement with those of RC3. When compared with the B band, V, I, J, and K isophotal diameters show that the colors in the outer regions of Seyferts are consistent with the colors of normal spirals. Differences in the integrated isophotal colors and comparison with a simple model show that the active nucleus+bulge is stronger and redder in the NIR than in the optical. Finally, roughly estimated Seyfert disk surface brightnesses are significantly brighter in B and K than those in normal spirals of similar morphological type.Comment: 17 pgs including figures; Table 2 is a separate file. Complete Figure 1 is available by contacting the authors. Accepted for publication in ApJ

Collective dynamics of two-mode stochastic oscillators

We study a system of two-mode stochastic oscillators coupled through their collective output. As a function of a relevant parameter four qualitatively distinct regimes of collective behavior are observed. In an extended region of the parameter space the periodicity of the collective output is enhanced by the considered coupling. This system can be used as a new model to describe synchronization-like phenomena in systems of units with two or more oscillation modes. The model can also explain how periodic dynamics can be generated by coupling largely stochastic units. Similar systems could be responsible for the emergence of rhythmic behavior in complex biological or sociological systems.Comment: 4 pages, RevTex, 5 figure

Synchronization in a neuronal feedback loop through asymmetric temporal delays

We consider the effect of asymmetric temporal delays in a system of two coupled Hopfield neurons. For couplings of opposite signs, a limit cycle emerges via a supercritical Hopf bifurcation when the sum of the delays reaches a critical value. We show that the angular frequency of the limit cycle is independent of an asymmetry in the delays. However, the delay asymmetry determines the phase difference between the periodic activities of the two components. Specifically, when the connection with negative coupling has a delay much larger than the delay for the positive coupling, the system approaches in-phase synchrony between the two components. Employing variational perturbation theory (VPT), we achieve an approximate analytical evaluation of the phase shift, in good agreement with numerical results.Comment: 5 pages, 4 figure

Debris disks around Sun-like stars

We have observed nearly 200 FGK stars at 24 and 70 microns with the Spitzer Space Telescope. We identify excess infrared emission, including a number of cases where the observed flux is more than 10 times brighter than the predicted photospheric flux, and interpret these signatures as evidence of debris disks in those systems. We combine this sample of FGK stars with similar published results to produce a sample of more than 350 main sequence AFGKM stars. The incidence of debris disks is 4.2% (+2.0/-1.1) at 24 microns for a sample of 213 Sun-like (FG) stars and 16.4% (+2.8/-2.9) at 70 microns for 225 Sun-like (FG) stars. We find that the excess rates for A, F, G, and K stars are statistically indistinguishable, but with a suggestion of decreasing excess rate toward the later spectral types; this may be an age effect. The lack of strong trend among FGK stars of comparable ages is surprising, given the factor of 50 change in stellar luminosity across this spectral range. We also find that the incidence of debris disks declines very slowly beyond ages of 1 billion years.Comment: ApJ, in pres

Gravitational Collapse of Null Radiation and a String fluid

We consider the end state of collapsing null radiation with a string fluid. It is shown that, if diffusive transport is assumed for the string, that a naked singularity can form (at least locally). The model has the advantage of not being asymptotically flat. We also analyse the case of a radiation-string two-fluid and show that a locally naked singularity can result in the collapse of such matter. We contrast this model with that of strange quark matter.Comment: RevTeX 4.0 (8 pages - no figures). submitted to Phys Rev D. Some changes to abstract, introduction and conclusion - references update

The neurointensive nursery: concept, development, and insights gained.

PURPOSE OF REVIEW: With the advent of therapeutic hypothermia for treatment of hypoxic ischemic encephalopathy, and improvements in neuroimaging and bedside neuromonitoring, a new era of neonatal brain-focused care has emerged in recent years. We describe the development of the first neurointensive care nursery (NICN) as a model for comanagement of neonates with identified neurologic risk factors by a multidisciplinary team constituted of neurologists, neonatologists, specialized nurses, and others with the goal of optimizing management, preventing secondary injury and maximizing long-term outcomes. RECENT FINDINGS: Optimizing brain metabolic environment and perfusion and preventing secondary brain injury are key to neurocritical care. This includes close management of temperature, blood pressure, oxygenation, carbon dioxide, and glucose levels. Early developmental interventions and involvement of physical and occupational therapy provide additional assessment information. Finally, long-term follow-up is essential for any neurocritical care program. SUMMARY: The NICN model aims to optimize evidence-based care of infants at risk for neurologic injury. Results from ongoing hypothermia and neuroprotective trials are likely to yield additional treatments. New technologies, such as functional MRI, continuous neurophysiological assessment, and whole genomic approaches to rapid diagnosis may further enhance clinical protocols and neonatal precision medicine. Importantly, advances in neurocritical care improve our ability to provide comprehensive information when counseling families. Long-term follow-up data will determine if the NICN/Neuro-NICU provides enduring benefit to infants at risk for neurologic injury

Euler configurations and quasi-polynomial systems

In the Newtonian 3-body problem, for any choice of the three masses, there are exactly three Euler configurations (also known as the three Euler points). In Helmholtz' problem of 3 point vortices in the plane, there are at most three collinear relative equilibria. The "at most three" part is common to both statements, but the respective arguments for it are usually so different that one could think of a casual coincidence. By proving a statement on a quasi-polynomial system, we show that the "at most three" holds in a general context which includes both cases. We indicate some hard conjectures about the configurations of relative equilibrium and suggest they could be attacked within the quasi-polynomial framework.Comment: 21 pages, 6 figure