Amortised resource analysis with separation logic

Type-based amortised resource analysis following Hofmann and Jost—where resources are associated with individual elements of data structures and doled out to the programmer under a linear typing discipline—have been successful in providing concrete resource bounds for functional programs, with good support for inference. In this work we translate the idea of amortised resource analysis to imperative languages by embedding a logic of resources, based on Bunched Implications, within Separation Logic. The Separation Logic component allows us to assert the presence and shape of mutable data structures on the heap, while the resource component allows us to state the resources associated with each member of the structure. We present the logic on a small imperative language with procedures and mutable heap, based on Java bytecode. We have formalised the logic within the Coq proof assistant and extracted a certified verification condition generator. We demonstrate the logic on some examples, including proving termination of in-place list reversal on lists with cyclic tails

Landscape phage, phage display, stripped phage, biosensors, detection, affinity reagent, nanotechnology, Salmonella typhimurium, Bacillus anthracis

Filamentous phage, such as fd used in this study, are thread-shaped bacterial viruses. Their outer coat is a tube formed by thousands equal copies of the major coat protein pVIII. We constructed libraries of random peptides fused to all pVIII domains and selected phages that act as probes specific for a panel of test antigens and biological threat agents. Because the viral carrier is infective, phage borne bio-selective probes can be cloned individually and propagated indefinitely without needs of their chemical synthesis or reconstructing. We demonstrated the feasibility of using landscape phages and their stripped fusion proteins as new bioselective materials that combine unique characteristics of affinity reagents and self assembling membrane proteins. Biorecognition layers fabricated from phage-derived probes bind biological agents and generate detectable signals. The performance of phage-derived materials as biorecognition films was illustrated by detection of streptavidin-coated beads, Bacillus anthracis spores and Salmonella typhimurium cells. With further refinement, the phage-derived analytical platforms for detecting and monitoring of numerous threat agents may be developed, since the biodetector films may be obtained from landscape phages selected against any bacteria, virus or toxin. As elements of field-use detectors, they are superior to antibodies, since they are inexpensive, highly specific and strong binders, resistant to high temperatures and environmental stresses.Comment: Submitted on behalf of TIMA Editions (http://irevues.inist.fr/tima-editions

Doppler cooling of gallium atoms: 2. Simulation in complex multilevel systems

This paper derives a general procedure for the numerical solution of the Lindblad equations that govern the coherences arising from multicoloured light interacting with a multilevel system. A systematic approach to finding the conservative and dissipative terms is derived and applied to the laser cooling of gallium. An improved numerical method is developed to solve the time-dependent master equation and results are presented for transient cooling processes. The method is significantly more robust, efficient and accurate than the standard method and can be applied to a broad range of atomic and molecular systems. Radiation pressure forces and the formation of dynamic dark-states are studied in the gallium isotope 66Ga.Comment: 15 pages, 8 figure

Trapping effects on inflation

We develop a Lagrangian approach based on the influence functional method so as to derive self-consistently the Langevin equation for the inflaton field in the presence of trapping points along the inflaton trajectory. The Langevin equation exhibits the backreaction and the fluctuation-dissipation relation of the trapping. The fluctuation is induced by a multiplicative colored noise that can be identified as the the particle number density fluctuations and the dissipation is a new effect that may play a role in the trapping with a strong coupling. In the weak coupling regime, we calculate the power spectrum of the noise-driven inflaton fluctuations for a single trapping point and studied its variation with the trapping location. We also consider a case with closely spaced trapping points and find that the resulting power spectrum is blue.Comment: 13 pages, 2 figure

Tree growth and management in Ugandan agroforestry systems: effects of root pruning on tree growth and crop yield

Tree root pruning is a potential tool for managing below-ground competition when trees and crops are grown together in agroforestry systems. This study investigates its effects on growth and root distribution of Alnus acuminata (HB & K), Casuarina equisetifolia (L), Grevillea robusta (A. Cunn. ex R. Br), Maesopsis eminii (Engl.), and Markhamia lutea (Benth.) K. Schum. and on yield of adjacent crops in sub-humid Uganda. The trees were 3 years old at the commencement of the study, and most species were competing strongly with crops. Tree roots were pruned 41 months after planting by cutting and back-filling a trench to a depth of 0.3 m, at a distance of 0.3 m from the trees, on one side of the tree row. The trench was re-opened and roots re-cut at 50 and 62 months after planting. Effects on tree growth and root distribution were assessed over a 3 year period, and crop yield after the third root pruning at 62 months is reported here. Overall, root pruning had only a slight effect on tree growth: height growth was unaffected and diameter growth was reduced by only 4 %. A substantial amount of root re-growth was observed by 11 months after pruning. Tree species varied in the number and distribution of their roots, and Casuarina and Markhamia had considerably more roots per unit of trunk volume than the other tree species, especially in the surface soil layers. Casuarina and Maesopsis were the most competitive tree species with crops and Grevillea and Markhamia the least. Crop yield data provides strong evidence of the redistribution of root activity following root pruning, so that competition increased on the unpruned side of tree rows. Thus, one-sided root pruning will only be of use to farmers in a few circumstances. Key words: Alnus acuminata, Casuarina equisetifolia, Grevillea robusta, Maesopsis eminii, Markhamia lutea, root distribution, root functio

Higher-order splitting algorithms for solving the nonlinear Schr\"odinger equation and their instabilities

Since the kinetic and the potential energy term of the real time nonlinear Schr\"odinger equation can each be solved exactly, the entire equation can be solved to any order via splitting algorithms. We verified the fourth-order convergence of some well known algorithms by solving the Gross-Pitaevskii equation numerically. All such splitting algorithms suffer from a latent numerical instability even when the total energy is very well conserved. A detail error analysis reveals that the noise, or elementary excitations of the nonlinear Schr\"odinger, obeys the Bogoliubov spectrum and the instability is due to the exponential growth of high wave number noises caused by the splitting process. For a continuum wave function, this instability is unavoidable no matter how small the time step. For a discrete wave function, the instability can be avoided only for \dt k_{max}^2{<\atop\sim}2 \pi, where $k_{max}=\pi/\Delta x$.Comment: 10 pages, 8 figures, submitted to Phys. Rev.

High-Contrast Interference in a Thermal Cloud of Atoms

The coherence properties of a gas of bosonic atoms above the BEC transition temperature were studied. Bragg diffraction was used to create two spatially separated wave packets, which interfere during expansion. Given sufficient expansion time, high fringe contrast could be observed in a cloud of arbitrary temperature. Fringe visibility greater than 90% was observed, which decreased with increasing temperature, in agreement with a simple model. When the sample was "filtered" in momentum space using long, velocity-selective Bragg pulses, the contrast was significantly enhanced in contrast to predictions

Quantum Statistical Calculations and Symplectic Corrector Algorithms

The quantum partition function at finite temperature requires computing the trace of the imaginary time propagator. For numerical and Monte Carlo calculations, the propagator is usually split into its kinetic and potential parts. A higher order splitting will result in a higher order convergent algorithm. At imaginary time, the kinetic energy propagator is usually the diffusion Greens function. Since diffusion cannot be simulated backward in time, the splitting must maintain the positivity of all intermediate time steps. However, since the trace is invariant under similarity transformations of the propagator, one can use this freedom to "correct" the split propagator to higher order. This use of similarity transforms classically give rises to symplectic corrector algorithms. The split propagator is the symplectic kernel and the similarity transformation is the corrector. This work proves a generalization of the Sheng-Suzuki theorem: no positive time step propagators with only kinetic and potential operators can be corrected beyond second order. Second order forward propagators can have fourth order traces only with the inclusion of an additional commutator. We give detailed derivations of four forward correctable second order propagators and their minimal correctors.Comment: 9 pages, no figure, corrected typos, mostly missing right bracket

Forward Symplectic Integrators and the Long Time Phase Error in Periodic Motions

We show that when time-reversible symplectic algorithms are used to solve periodic motions, the energy error after one period is generally two orders higher than that of the algorithm. By use of correctable algorithms, we show that the phase error can also be eliminated two orders higher than that of the integrator. The use of fourth order forward time step integrators can result in sixth order accuracy for the phase error and eighth accuracy in the periodic energy. We study the 1-D harmonic oscillator and the 2-D Kepler problem in great details, and compare the effectiveness of some recent fourth order algorithms.Comment: Submitted to Phys. Rev. E, 29 Page

On the construction of high-order force gradient algorithms for integration of motion in classical and quantum systems

A consequent approach is proposed to construct symplectic force-gradient algorithms of arbitrarily high orders in the time step for precise integration of motion in classical and quantum mechanics simulations. Within this approach the basic algorithms are first derived up to the eighth order by direct decompositions of exponential propagators and further collected using an advanced composition scheme to obtain the algorithms of higher orders. Contrary to the scheme by Chin and Kidwell [Phys. Rev. E 62, 8746 (2000)], where high-order algorithms are introduced by standard iterations of a force-gradient integrator of order four, the present method allows to reduce the total number of expensive force and its gradient evaluations to a minimum. At the same time, the precision of the integration increases significantly, especially with increasing the order of the generated schemes. The algorithms are tested in molecular dynamics and celestial mechanics simulations. It is shown, in particular, that the efficiency of the new fourth-order-based algorithms is better approximately in factors 5 to 1000 for orders 4 to 12, respectively. The results corresponding to sixth- and eighth-order-based composition schemes are also presented up to the sixteenth order. For orders 14 and 16, such highly precise schemes, at considerably smaller computational costs, allow to reduce unphysical deviations in the total energy up in 100 000 times with respect to those of the standard fourth-order-based iteration approach.Comment: 23 pages, 2 figures; submitted to Phys. Rev.