Dynamics of a combined Medea-underdominant population transformation system

Background: Transgenic constructs intended to be stably established at high frequencies in wild populations have been demonstrated to “drive” from low frequencies in experimental insect populations. Linking such population transformation constructs to genes which render them unable to transmit pathogens could eventually be used to stop the spread of vector-borne diseases like malaria and dengue. Results: Generally, population transformation constructs with only a single transgenic drive mechanism have been envisioned. Using a theoretical modelling approach we describe the predicted properties of a construct combining autosomal Medea and underdominant population transformation systems. We show that when combined they can exhibit synergistic properties which in broad circumstances surpass those of the single systems. Conclusion: With combined systems, intentional population transformation and its reversal can be achieved readily. Combined constructs also enhance the capacity to geographically restrict transgenic constructs to targeted populations. It is anticipated that these properties are likely to be of particular value in attracting regulatory approval and public acceptance of this novel technology

On the master equation approach to kinetic theory: linear and nonlinear Fokker--Planck equations

We discuss the relationship between kinetic equations of the Fokker-Planck type (two linear and one non-linear) and the Kolmogorov (a.k.a. master) equations of certain N-body diffusion processes, in the context of Kac's "propagation of chaos" limit. The linear Fokker-Planck equations are well-known, but here they are derived as a limit N->infty of a simple linear diffusion equation on (3N-C)-dimensional N-velocity spheres of radius sqrt(N) (with C=1 or 4 depending on whether the system conserves energy only or energy and momentum). In this case, a spectral gap separating the zero eigenvalue from the positive spectrum of the Laplacian remains as N->infty,so that the exponential approach to equilibrium of the master evolution is passed on to the limiting Fokker-Planck evolution in R^3. The non-linear Fokker-Planck equation is known as Landau's equation in the plasma physics literature. Its N-particle master equation, originally introduced (in the 1950s) by Balescu and Prigogine (BP), is studied here on the (3N-4)-dimensional N-velocity sphere. It is shown that the BP master equation represents a superposition of diffusion processes on certain two-dimensional sub-manifolds of R^{3N} determined by the conservation laws for two-particle collisions. The initial value problem for the BP master equation is proved to be well-posed and its solutions are shown to decay exponentially fast to equilibrium. However, the first non-zero eigenvalue of the BP operator is shown to vanish in the limit N->infty. This indicates that the exponentially fast approach to equilibrium may not be passed from the finite-N master equation on to Landau's nonlinear kinetic equation.Comment: 20 pages; based on talk at the 18th ICTT Conference. Some typos and a few minor technical fixes. Modified title slightl

Remote sensing techniques for mapping range sites and estimating range yield

Image interpretation procedures for determining range yield and for extrapolating range information were investigated for an area of the Pine Ridge Indian Reservation in southwestern South Dakota. Soil and vegetative data collected in the field utilizing a grid sampling design and digital film data from color infrared film and black and white films were analyzed statistically using correlation and regression techniques. The pattern recognition techniques used were K-class, mode seeking, and thresholding. The herbage yield equation derived for the detailed test site was used to predict yield for an adjacent similar field. The herbage yield estimate for the adjacent field was 1744 lbs. of dry matter per acre and was favorably compared to the mean yield of 1830 lbs. of dry matter per acre based upon ground observations. Also an inverse relationship was observed between vegetative cover and the ratio of MSS 5 to MSS 7 of ERTS-1 imagery

Local energy decay of massive Dirac fields in the 5D Myers-Perry metric

We consider massive Dirac fields evolving in the exterior region of a 5-dimensional Myers-Perry black hole and study their propagation properties. Our main result states that the local energy of such fields decays in a weak sense at late times. We obtain this result in two steps: first, using the separability of the Dirac equation, we prove the absence of a pure point spectrum for the corresponding Dirac operator; second, using a new form of the equation adapted to the local rotations of the black hole, we show by a Mourre theory argument that the spectrum is absolutely continuous. This leads directly to our main result.Comment: 40 page

Using surgical sustainability principles to improve planetary health and optimise surgical services following the COVID-19 pandemic

As the world faces crises instigated by environmental disruption, demands on healthcare require sustainable solutions. In this article, we outline the principles of sustainable surgery, how these can be used to optimise surgical services in light of healthcare crises, and how long-term adoption of these principles can help to reduce the carbon and plastic footprint of surgery in the UK and internationally. We describe how planetary and human health are closely related, including the relationship between environmental disruption and emerging infectious diseases

Correlated defects, metal-insulator transition, and magnetic order in ferromagnetic semiconductors

The effect of disorder on transport and magnetization in ferromagnetic III-V semiconductors, in particular (Ga,Mn)As, is studied theoretically. We show that Coulomb-induced correlations of the defect positions are crucial for the transport and magnetic properties of these highly compensated materials. We employ Monte Carlo simulations to obtain the correlated defect distributions. Exact diagonalization gives reasonable results for the spectrum of valence-band holes and the metal-insulator transition only for correlated disorder. Finally, we show that the mean-field magnetization also depends crucially on defect correlations.Comment: 4 pages RevTeX4, 5 figures include

Using scenarios to explore UK upland futures

Uplands around the world are facing significant social, economic and environmental changes, and decision-makers need to better understand what the future may hold if they are to adapt and maintain upland goods and services. This paper draws together all major research comprising eight studies that have used scenarios to describe possible futures for UK uplands. The paper evaluates which scenarios are perceived by stakeholders to be most likely and desirable, and assesses the benefits and drawbacks of the scenario methods used in UK uplands to date. Stakeholders agreed that the most desirable and likely scenario would be a continuation of hill farming (albeit at reduced levels) based on cross-compliance with environmental measures. The least desirable scenario is a withdrawal of government financial support for hill farming. Although this was deemed by stakeholders to be the least likely scenario, the loss of government support warrants close attention due to its potential implications for the local economy. Stakeholders noted that the environmental implications of this scenario are much less clear-cut. As such, there is an urgent need to understand the full implications of this scenario, so that upland stakeholders can adequately prepare, and policy-makers can better evaluate the likely implications of different policy options. The paper concludes that in future, upland scenario research needs to: (1) better integrate in-depth and representative participation from stakeholders during both scenario development and evaluation; and (2) make more effective use of visualisation techniques and simulation models

Where can we really find the First Stars' Remnants today?

A number of recent numerical investigations concluded that the remnants of rare structures formed at very high redshift, such as the very first stars and bright redshift z~6 QSOs, are preferentially located at the center of the most massive galaxy clusters at redshift z=0. In this paper we readdress this question using a combination of cosmological simulations of structure formation and extended Press-Schechter formalism and we show that the typical remnants of Population III stars are instead more likely to be found in a group environment, that is in dark matter halos of mass ~2x10^{13} h^{-1}M_sun. Similarly, the descendants of the brightest z~6 QSOs are expected to be in medium-sized clusters (mass of a few 10^{14} h^{-1}M_sun), rather than in the most massive superclusters (M>10^{15} h^{-1}M_sun) found within the typical 1 Gpc^3 cosmic volume where a bright z~6 QSO lives. The origin of past claims that the most massive clusters preferentially host these remnants is rooted in the numerical method used to initialize their numerical simulations: Only a small region of the cosmological volume of interest was simulated with sufficient resolution to identify low-mass halos at early times, and this region was chosen to host the most massive halo in the cosmological volume at late times. The conclusion that the earliest structures formed in the entire cosmological volume evolve into the most massive halo at late times was thus arrived at by construction. We demonstrate that, to the contrary, the first structures to form in a cosmological region evolve into relatively typical objects at later times. We propose alternative numerical methods for simulating the earliest structures in cosmological volumes.Comment: 18 pages, 5 figures, ApJ accepted, high resolution version of the paper available at http://www.stsci.edu/~trenti/papers/halo_evolution.pd

Scaling Limits for the System of Semi-Relativistic Particles Coupled to a Scalar Bose Field

In this paper the Hamiltonian for the system of semi-relativistic particles interacting with a scalar bose field is investigated. A scaled total Hamiltonian of the system is defined and its scaling limit is considered. Then the semi-relativistic Schrodinger operator with an effective potential is derived

Connection Conditions and the Spectral Family under Singular Potentials

To describe a quantum system whose potential is divergent at one point, one must provide proper connection conditions for the wave functions at the singularity. Generalizing the scheme used for point interactions in one dimension, we present a set of connection conditions which are well-defined even if the wave functions and/or their derivatives are divergent at the singularity. Our generalized scheme covers the entire U(2) family of quantizations (self-adjoint Hamiltonians) admitted for the singular system. We use this scheme to examine the spectra of the Coulomb potential $V(x) = - e^2 / | x |$ and the harmonic oscillator with square inverse potential $V(x) = (m \omega^2 / 2) x^2 + g/x^2$, and thereby provide a general perspective for these models which have previously been treated with restrictive connection conditions resulting in conflicting spectra. We further show that, for any parity invariant singular potentials $V(-x) = V(x)$, the spectrum is determined solely by the eigenvalues of the characteristic matrix $U \in U(2)$.Comment: TeX, 18 page