Modelling Holling type II functional response in deterministic and stochastic food chain models with mass conservation

The Rosenzweig-MacArthur predator-prey model is the building block in modeling food chain, food webs and ecosystems. There are a number of hidden assumptions involved in the derivation. For instance the prey population growth is logistic without predation but also with predation. In order to reveal these we will start with modelling a resource-predator-prey system in a closed spatially homogeneous environment. This allows us to keep track of the nutrient flow. With an instantaneous remineralisation of the products excreted in the environment by the populations and dead body mass there is conservation of mass. This allows for a model dimension reduction and yields the mass balance predator-prey model. When furthermore the searching and handling processes are much faster that the population changing rates, the trophic interaction is described by a Holling type II functional response, also assumed in the Rosenzweig-MacArthur model. The derivation uses an extended deterministic model with number of searching and handling predators as model variables where the ratio of the predator/prey body masses is used as a mechanistic time-scale parameter. This extended model is also used as a starting point for the derivation of a stochastic model. We will investigate the stochastic effects of random switching between searching and handling of the predators and predator dying. Prey growth by consumption of ambient resources is still deterministic and therefore the stochastic model is hybrid. The transient dynamics is studied by numerical Monte Carlo simulations and also the quasi-equilibrium distribution for the population quantities is calculated. The body mass of the prey individual is the scaling parameter in the stochastic model formulation. This allows for a quantification of the mean-field approximation criterion for the justification of replacement of the stochastic by a deterministic model.Marie Skłodowska-Curie grant agreement No. 79249

Cheryl's Birthday

We present four logic puzzles and after that their solutions. Joseph Yeo designed 'Cheryl's Birthday'. Mike Hartley came up with a novel solution for 'One Hundred Prisoners and a Light Bulb'. Jonathan Welton designed 'A Blind Guess' and 'Abby's Birthday'. Hans van Ditmarsch and Barteld Kooi authored the puzzlebook 'One Hundred Prisoners and a Light Bulb' that contains other knowledge puzzles, and that can also be found on the webpage http://personal.us.es/hvd/lightbulb.html dedicated to the book.Comment: In Proceedings TARK 2017, arXiv:1707.0825

Playing cards with Hintikka An introduction to dynamic epistemic logic

This contribution is a gentle introduction to so-called dynamic epistemic logics, that can describe how agents change their knowledge and beliefs. We start with a concise introduction to epistemic logic, through the example of one, two and finally three players holding cards; and, mainly for the purpose of motivating the dynamics, we also very summarily introduce the concepts of general and common knowledge. We then pay ample attention to the logic of public announcements, wherein agents change their knowledge as the result of public announcements. One crucial topic in that setting is that of unsuccessful updates: formulas that become false when announced. The Moore-sentences that were already extensively discussed at the conception of epistemic logic in Hintikka’s ‘Knowledge and Belief ’ (1962) give rise to such unsuccessful updates. After that, we present a few examples of more complex epistemic updates

Continuation of connecting orbits in 3D-ODEs: (I) Point-to-cycle connections

We propose new methods for the numerical continuation of point-to-cycle connecting orbits in 3-dimensional autonomous ODE's using projection boundary conditions. In our approach, the projection boundary conditions near the cycle are formulated using an eigenfunction of the associated adjoint variational equation, avoiding costly and numerically unstable computations of the monodromy matrix. The equations for the eigenfunction are included in the defining boundary-value problem, allowing a straightforward implementation in AUTO, in which only the standard features of the software are employed. Homotopy methods to find connecting orbits are discussed in general and illustrated with several examples, including the Lorenz equations. Complete AUTO demos, which can be easily adapted to any autonomous 3-dimensional ODE system, are freely available.Comment: 18 pages, 10 figure

Mg/Ti multilayers: structural, optical and hydrogen absorption properties

Mg-Ti alloys have uncommon optical and hydrogen absorbing properties, originating from a "spinodal-like" microstructure with a small degree of chemical short-range order in the atoms distribution. In the present study we artificially engineer short-range order by depositing Pd-capped Mg/Ti multilayers with different periodicities and characterize them both structurally and optically. Notwithstanding the large lattice parameter mismatch between Mg and Ti, the as-deposited metallic multilayers show good structural coherence. Upon exposure to H2 gas a two-step hydrogenation process occurs, with the Ti layers forming the hydride before Mg. From in-situ measurements of the bilayer thickness L at different hydrogen pressures, we observe large out-of-plane expansions of the Mg and Ti layers upon hydrogenation, indicating strong plastic deformations in the films and a consequent shortening of the coherence length. Upon unloading at room temperature in air, hydrogen atoms remain trapped in the Ti layers due to kinetic constraints. Such loading/unloading sequence can be explained in terms of the different thermodynamic properties of hydrogen in Mg and Ti, as shown by diffusion calculations on a model multilayered systems. Absorption isotherms measured by hydrogenography can be interpreted as a result of the elastic clamping arising from strongly bonded Mg/Pd and broken Mg/Ti interfaces

Herschel observations of ortho- and para-oxidaniumyl (H_2O^+) in spiral arm clouds toward Sagittarius B2(M)

H_2O^+ has been observed in its ortho- and para- states toward the massive star forming core Sgr B2(M), located close to the Galactic center. The observations show absorption in all spiral arm clouds between the Sun and Sgr B2. The average o/p ratio of H_2O^+ in most velocity intervals is 4.8, which corresponds to a nuclear spin temperature of 21 K. The relationship of this spin temperature to the formation temperature and current physical temperature of the gas hosting H_2O^+ is discussed, but no firm conclusion is reached. In the velocity interval 0–60 km s^(−1), an ortho/para ratio of below unity is found, but if this is due to an artifact of contamination by other species or real is not clear

The Amplitude of Non-Equilibrium Quantum Interference in Metallic Mesoscopic Systems

We study the influence of a DC bias voltage V on quantum interference corrections to the measured differential conductance in metallic mesoscopic wires and rings. The amplitude of both universal conductance fluctuations (UCF) and Aharonov-Bohm effect (ABE) is enhanced several times for voltages larger than the Thouless energy. The enhancement persists even in the presence of inelastic electron-electron scattering up to V ~ 1 mV. For larger voltages electron-phonon collisions lead to the amplitude decaying as a power law for the UCF and exponentially for the ABE. We obtain good agreement of the experimental data with a model which takes into account the decrease of the electron phase-coherence length due to electron-electron and electron-phonon scattering.Comment: New title, refined analysis. 7 pages, 3 figures, to be published in Europhysics Letter

Technology Development for the Caltech Submillimeter Observatory Balanced Receivers

The Caltech Submillimeter Observatory (CSO) is located on top of Mauna Kea, Hawaii, at an altitude of 4.2 km. The existing suite of facility heterodyne receivers covering the submillimeter band is rapidly aging and in need of replacement. To facilitate deep integrations and automated spectral line surveys, a family of remote programmable, synthesized, dual-frequency balanced receivers covering the astronomical important 180 - 720 GHz atmospheric windows is in an advanced stage of development. Installation of the first set of receivers is expected in the spring of 2012. Dual-frequency observation will be an important mode of operation offered by the new facility instrumentation. Two band observations are accomplished by separating the H and V polarizations of the incoming signal and routing them via folded optics to the appropriate polarization sensitive balanced mixer. Scientifically this observation mode facilitates pointing for the higher receiver band under mediocre weather conditions and a doubling of scientific throughput (2 x 4 GHz) under good weather conditions.Comment: 12 pages, 17 figures; IEEE Terahertz Science & Technology, January 2012, Volume 2, Issue

Near-infrared spectroscopy as a diagnostic tool for necrotizing enterocolitis in preterm infants

BACKGROUND: We aimed to investigate whether splanchnic tissue oxygen saturation (rsSO2) measured by near-infrared spectroscopy (NIRS) could contribute to the early diagnosis of necrotizing enterocolitis (NEC). METHODS: We retrospectively included infants with suspected NEC, gestational age <32 weeks and/or birth weight <1200 g in the first 3 weeks after birth. We calculated mean rsSO2, cerebral tissue oxygen saturation (rcSO2), variability of rsSO2 (coefficients of variation [rsCoVAR] = SD/mean), and splanchnic-cerebral oxygenation ratio ([SCOR] = rsSO2/rcSO2) in the period around the abdominal radiograph to confirm or reject NEC. RESULTS: Of the 75 infants, 21 (28%) had NEC (Bell's stage ≥2). Characteristics of infants with and without NEC differed only on mechanical ventilation and nil-per-os status. RsSO2 tended to be higher and rcSO2 lower in infants with NEC. RsCoVAR (median [range]) was lower (0.11 [0.03-0.34]) vs. 0.20 [0.01-0.52], P = 0.002) and SCOR higher (0.64 [0.37-1.36]) vs. 0.47 [0.16-1.09], P = 0.004) in NEC infants. Adjusted for postnatal age, mechanical ventilation, and nil-per-os status, a 0.1 higher rsCoVAR decreased the likelihood of NEC diagnosis with likelihood ratio (LR) 0.38 (95% CI 0.18-0.78) and a 0.1 higher SCOR increased it with LR 1.28 (1.02-1.61). CONCLUSIONS: Using NIRS, high SCOR may confirm NEC and high variability of rsSO2 may rule out NEC, when suspicion arises. IMPACT: Near-infrared spectroscopy may contribute to the diagnosis of necrotizing enterocolitis.When clinical signs are present a high splanchnic-cerebral oxygenation may indicate necrotizing enterocolitis.A low splanchnic-cerebral oxygenation ratio and high variability of splanchnic tissue oxygen saturation may rule out necrotizing enterocolitis.Whether a bedside real-time availability of the splanchnic-cerebral oxygenation ratio and variability of splanchnic tissue oxygen saturation improves NEC diagnosis needs to be further investigated

Detection of OH+ and H_2O+ towards Orion KL

We report observations of the reactive molecular ions OH+, H_(2)O+, and H_(3)O+ towards Orion KL with Herschel/HIFI. All three N = 1-0 fine-structure transitions of OH+ at 909, 971, and 1033 GHz and both fine-structure components of the doublet ortho-H_(2)O+ 1_(11)–0_(00) transition at 1115 and 1139 GHz were detected; an upper limit was obtained for H_(3)O+. OH+ and H_(2)O+ are observed purely in absorption, showing a narrow component at the source velocity of 9 km s^(-1), and a broad blueshifted absorption similar to that reported recently for HF and para-H_(2)^(18)O, and attributed to the low velocity outflow of Orion KL. We estimate column densities of OH+ and H_(2)O+ for the 9 km s^(-1) component of 9 ± 3 × 10^(12) cm^(-2) and 7 ± 2 × 10^(12) cm^(-2), and those in the outflow of 1.9 ± 0.7 × 10^(13) cm^(-2) and 1.0 ± 0.3 × 10^(13) cm^(-2). Upper limits of 2.4 × 10^(12) cm^(-2) and 8.7 × 10^(12) cm^(-2) were derived for the column densities of ortho and para-H_(3)O+ from transitions near 985 and 1657 GHz. The column densities of the three ions are up to an order of magnitude lower than those obtained from recent observations of W31C and W49N. The comparatively low column densities may be explained by a higher gas density despite the assumption of a very high ionization rate