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

Dimension in a Radiative Stellar Atmosphere

Dimensional scales are examined in an extended 3+1 Vaidya atmosphere surrounding a Schwarzschild source. At one scale, the Vaidya null fluid vanishes and the spacetime contains only a single spherical 2-surface. Both of these behaviors can be addressed by including higher dimensions in the spacetime metric.Comment: to appear in Gen. Rel. Gra

A core genetic module : the Mixed Feedback Loop

The so-called Mixed Feedback Loop (MFL) is a small two-gene network where protein A regulates the transcription of protein B and the two proteins form a heterodimer. It has been found to be statistically over-represented in statistical analyses of gene and protein interaction databases and to lie at the core of several computer-generated genetic networks. Here, we propose and mathematically study a model of the MFL and show that, by itself, it can serve both as a bistable switch and as a clock (an oscillator) depending on kinetic parameters. The MFL phase diagram as well as a detailed description of the nonlinear oscillation regime are presented and some biological examples are discussed. The results emphasize the role of protein interactions in the function of genetic modules and the usefulness of modelling RNA dynamics explicitly.Comment: To be published in Physical Review

Metabolite Fingerprinting in Transgenic Nicotiana tabacum Altered by the Escherichia coli Glutamate Dehydrogenase Gene

With about 200 000 phytochemicals in existence, identifying those of biomedical significance is a mammoth task. In the postgenomic era, relating metabolite fingerprints, abundances, and profiles to genotype is also a large task. Ion analysis using Fourier transformed ion cyclotron resonance mass spectrometry (FT-ICR-MS) may provide a high-throughput approach to measure genotype dependency of the inferred metabolome if reproducible techniques can be established. Ion profile inferred metabolite fingerprints are coproducts. We used FT-ICR-MS-derived ion analysis to examine gdhA (glutamate dehydrogenase (GDH; EC 1.4.1.1)) transgenic Nicotiana tabacum (tobacco) carrying out altered glutamate, amino acid, and carbon metabolisms, that fundamentally alter plant productivity. Cause and effect between gdhA expression, glutamate metabolism, and plant phenotypes was analyzed by [Formula: see text] labeling of amino acid fractions, and by FT-ICR-MS analysis of metabolites. The gdhA transgenic plants increased (13)N labeling of glutamate and glutamine significantly. FT-ICR-MS detected 2 012 ions reproducible in 2 to 4 ionization protocols. There were 283 ions in roots and 98 ions in leaves that appeared to significantly change abundance due to the measured GDH activity. About 58% percent of ions could not be used to infer a corresponding metabolite. From the 42% of ions that inferred known metabolites we found that certain amino acids, organic acids, and sugars increased and some fatty acids decreased. The transgene caused increased ammonium assimilation and detectable ion variation. Thirty-two compounds with biomedical significance were altered in abundance by GDH including 9 known carcinogens and 14 potential drugs. Therefore, the GDH transgene may lead to new uses for crops like tobacco

Icebreaker-3 Drill Integration and Testing at Two Mars-Analog Sites

A decade of evolutionary development of integrated automated drilling and sample handling at analog sites and in test chambers has made it possible to go 1 meter through hard rocks and ice layers on Mars. The latest Icebreaker-3 drill has been field tested in 2014 at the Haughton Crater Marsanalog site in the Arctic and in 2015 with a Mars lander mockup in Rio Tinto, Spain, (with sample transfer arm and with a prototype life-detection instrument). Tests in Rio Tinto in 2015 successfully demonstrated that the drill sample (cuttings) was handed-off from the drill to the sample transfer arm and thence to the on-deck instrument inlet where it was taken in and analyzed ("dirt-to-data")

Ideal MHD theory of low-frequency Alfven waves in the H-1 Heliac

A part analytical, part numerical ideal MHD analysis of low-frequency Alfven wave physics in the H-1 stellarator is given. The three-dimensional, compressible ideal spectrum for H-1 is presented and it is found that despite the low beta (approx. 10^-4) of H-1 plasmas, significant Alfven-acoustic interactions occur at low frequencies. Several quasi-discrete modes are found with the three-dimensional linearised ideal MHD eigenmode solver CAS3D, including beta-induced Alfven eigenmode (BAE)- type modes in beta-induced gaps. The strongly shaped, low-aspect ratio magnetic geometry of H-1 causes CAS3D convergence difficulties requiring the inclusion of many Fourier harmonics for the parallel component of the fluid displacement eigenvector even for shear wave motions. The highest beta-induced gap reproduces large parts of the observed configurational frequency dependencies in the presence of hollow temperature profiles

Fractal Scales in a Schwarzschild Atmosphere

Recently, Glass and Krisch have extended the Vaidya radiating metric to include both a radiation fluid and a string fluid [1999 Class. Quantum Grav. vol 16, 1175]. Mass diffusion in the extended Schwarzschild atmosphere was studied. The continuous solutions of classical diffusive transport are believed to describe the envelope of underlying fractal behavior. In this work we examine the classical picture at scales on which fractal behavior might be evident.Comment: to appear in Class. Quantum Gra

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

Collapsing Layers on Schwarzschild-Lemaitre Geodesics

We discuss Israel layers collapsing inward from rest at infinity along Schwarzschild-Lemaitre geodesics. The dynamics of the collapsing layer and its equation of state are developed. There is a general equation of state which is approximately polytropic in the limit of very low pressure. The equation of state establishes a new limit on the stress-density ratio.Comment: To appear in Phys. Rev. D 1