On the convergence of the no response test

The no response test is a new scheme in inverse problems for partial differential equations which was recently proposed in [D. R. Luke and R. Potthast, SIAM J. Appl. Math., 63 (2003), pp. 1292–1312] in the framework of inverse acoustic scattering problems. The main idea of the scheme is to construct special probing waves which are small on some test domain. Then the response for these waves is constructed. If the response is small, the unknown object is assumed to be a subset of the test domain. The response is constructed from one, several, or many particular solutions of the problem under consideration. In this paper, we investigate the convergence of the no response test for the reconstruction information about inclusions D from the Cauchy values of solutions to the Helmholtz equation on an outer surface $\partial\Omega$ with $\overline{D} \subset \Omega$. We show that the one‐wave no response test provides a criterion to test the analytic extensibility of a field. In particular, we investigate the construction of approximations for the set of singular points $N(u)$ of the total fields u from one given pair of Cauchy data. Thus, the no response test solves a particular version of the classical Cauchy problem. Also, if an infinite number of fields is given, we prove that a multifield version of the no response test reconstructs the unknown inclusion D. This is the first convergence analysis which could be achieved for the no response test.

Unification of the probe and singular sources methods for the inverse boundary value problem by the no-response test

In this article, we use the no-response test idea, introduced in Luke and Potthast (2003) and Potthast (Preprint) and the inverse obstacle problem, to identify the interface of the discontinuity of the coefficient gamma of the equation del (.) gamma(x)del + c(x) with piecewise regular gamma and bounded function c(x). We use infinitely many Cauchy data as measurement and give a reconstructive method to localize the interface. We will base this multiwave version of the no-response test on two different proofs. The first one contains a pointwise estimate as used by the singular sources method. The second one is built on an energy (or an integral) estimate which is the basis of the probe method. As a conclusion of this, the probe and the singular sources methods are equivalent regarding their convergence and the no-response test can be seen as a unified framework for these methods. As a further contribution, we provide a formula to reconstruct the values of the jump of gamma(x), x is an element of partial derivative D at the boundary. A second consequence of this formula is that the blow-up rate of the indicator functions of the probe and singular sources methods at the interface is given by the order of the singularity of the fundamental solution.

Krakatoa lives: The effect of volcanic eruptions on ocean heat content and thermal expansion

A suite of climate model experiments indicates that 20th Century increases in ocean heat content and sea-level ( via thermal expansion) were substantially reduced by the 1883 eruption of Krakatoa. The volcanically-induced cooling of the ocean surface is subducted into deeper ocean layers, where it persists for decades. Temporary reductions in ocean heat content associated with the comparable eruptions of El Chichon ( 1982) and Pinatubo ( 1991) were much shorter lived because they occurred relative to a non-stationary background of large, anthropogenically-forced ocean warming. Our results suggest that inclusion of the effects of Krakatoa ( and perhaps even earlier eruptions) is important for reliable simulation of 20th century ocean heat uptake and thermal expansion. Inter-model differences in the oceanic thermal response to Krakatoa are large and arise from differences in external forcing, model physics, and experimental design. Systematic experimentation is required to quantify the relative importance of these factors. The next generation of historical forcing experiments may require more careful treatment of pre-industrial volcanic aerosol loadings.

Blood-clotting response tests for resistance to diphacinone and chlorophacinone in the Norway rat (Rattus norvegicus Berk.)

Resistance baselines were obtained for the first generation anticoagulant rodenticides chlorophacinone and diphacinone using laboratory, caesarian-derived Norway rats (Rattus norvegicus) as the susceptible strain and the blood clotting response test method. The ED99 estimates for a quantal response were: chlorophacinone, males 0.86 mg kg−1, females 1.03 mg kg−1; diphacinone, males 1.26 mg kg−1, females 1.60 mg kg−1. The dose-response data also showed that chlorophacinone was significantly (p<0.0001) more potent than diphacinone for both male and female rats, and that male rats were more susceptible than females to both compounds (p<0.002). The ED99 doses were then given to groups of five male and five female rats of the Welsh and Hampshire warfarin-resistant strains. Twenty-four hours later, prothrombin times were slightly elevated in both strains but all the animals were classified as resistant to the two compounds, indicating cross-resistance from warfarin to diphacinone and chlorophacinone. When rats of the two resistant strains were fed for six consecutive days on baits containing either diphacinone or chlorophacinone, many animals survived, indicating that their resistance might enable them to survive treatments with these compounds in the field.

A survey on sampling and probe methods for inverse problems

The goal of the review is to provide a state-of-the-art survey on sampling and probe methods for the solution of inverse problems. Further, a configuration approach to some of the problems will be presented. We study the concepts and analytical results for several recent sampling and probe methods. We will give an introduction to the basic idea behind each method using a simple model problem and then provide some general formulation in terms of particular configurations to study the range of the arguments which are used to set up the method. This provides a novel way to present the algorithms and the analytic arguments for their investigation in a variety of different settings. In detail we investigate the probe method (Ikehata), linear sampling method (Colton-Kirsch) and the factorization method (Kirsch), singular sources Method (Potthast), no response test (Luke-Potthast), range test (Kusiak, Potthast and Sylvester) and the enclosure method (Ikehata) for the solution of inverse acoustic and electromagnetic scattering problems. The main ideas, approaches and convergence results of the methods are presented. For each method, we provide a historical survey about applications to different situations.

Relationship between resistance factors and treatment efficacy when bromadiolone was used against anticoagulant-resistant Norway rats (Rattus norvegicus Berk.) in Wales

We investigated the relationship between the severity and incidence of resistance among Norway rats (Rattus norvegicus) on a farm in Wales and the subsequent outcome of a practical rodent control operation. Bromadiolone resistance factors were estimated for rats trapped on the farm using the blood clotting response test, and were found to be 2 to 3 for male rats and approximately 6 for females. The incidence of resistance in the rat population was high. Infestation size was estimated by census baiting and tracking, and was found to be substantial, with a maximum of 6.5 kg of bait being eaten on a single night. A proprietary rodenticide (Deadline (TM)), containing 0.005% bromadiolone, was used to control the infestation. The duration of baiting was 35 days and, according to the two methods of assessment used, treatment success was in the region of 87 and 93%. No evidence was observed of a significant impact of resistance on the rat control operation, and the remaining rats of this very heavy infestation would probably have been controlled if baiting had continued for longer.

Susceptibility to the anticoagulants bromadiolone and coumatetralyl in wild Norway rats (Rattus norvegicus) from the UK and Germany

A new blood clotting response test was used to determine the susceptibility, to coumatetralyl and bromadiolone, of laboratory strains of Norway rat from Germany and the UK (Hampshire), and wild rats trapped on farms in Wales (UK) and Westphalia (Germany). Resistance factors were calculated in relation to the CD strain of Norway rat. An outbred strain of wild rats, raised from rats trapped in Germany, was found to be more susceptible to coumatetralyl by a factor of 0.5-0.6 compared to the CD strain. Homozygous and heterozygous animals of a strain of resistant rats from Westphalia were cross-resistant to coumatetralyl and bromadiolone, with a higher resistance factor for bromadiolone than that found in both UK strains. Our results show that the degree of altered susceptibility and resistance varies between strains of wild rat and between resistance foci. Some wild rat strains may be more susceptible than laboratory rat strains. Even in a well-established resistance area, it may be difficult to find infestations with resistance high enough to suspect control problems with bromadiolone, even after decades of use of this compound.

A reappraisal of blood clotting response tests for anticoagulant resistance and a proposal for a standardised BCR test methodology

Blood clotting response (BCR) resistance tests are available for a number of anticoagulant rodenticides. However, during the development of these tests many of the test parameters have been changed, making meaningful comparisons between results difficult. It was recognised that a standard methodology was urgently required for future BCR resistance tests and, accordingly, this document presents a reappraisal of published tests, and proposes a standard protocol for future use (see Appendix). The protocol can be used to provide information on the incidence and degree of resistance in a particular rodent population; to provide a simple comparison of resistance factors between active ingredients, thus giving clear information about cross-resistance for any given strain; and to provide comparisons of susceptibility or resistance between different populations. The methodology has a sound statistical basis in being based on the ED50 response, and requires many fewer animals than the resistance tests in current use. Most importantly, tests can be used to give a clear indication of the likely practical impact of the resistance on field efficacy. The present study was commissioned and funded by the Rodenticide Resistance Action Committee (RRAC) of CropLife International.

Can Rachman’s indirect pathways be used to un-learn fear? A prospective paradigm to test whether children’s fears can be reduced using positive information and modelling a non-anxious response

This study investigated whether children’s fears could be un-learned using Rachman’s indirect pathways for learning fear. We hypothesised that positive information and modelling a non-anxious response are effective methods of un-learning fears acquired through verbal information. One hundred and seven children aged 6–8 years received negative information about one animal and no information about another. Fear beliefs and behavioural avoidance were measured. Children were randomised to receive positive verbal information, modelling, or a control task. Fear beliefs and behavioural avoidance were measured again. Positive information and modelling led to lower fear beliefs and behavioural avoidance than the control condition. Positive information was more effective than modelling in reducing fear beliefs and both methods significantly reduced behavioural avoidance. The results support Rachman’s indirect pathways as viable fear un-learning pathways and supports associative learning theories.

The importance of surface pressure changes in the response of the atmosphere to zonally-symmetric thermal and mechanical forcing

he classical problem of the response of a balanced, axisymmetric vortex to thermal and mechanical forcing is re-examined, paying special attention to the lower boundary condition. The correct condition is DΦ/Dt = 0, where Φ is the geopotential and D/Dt the material derivative, which explicitly accounts for a mass redistribution as part of the mean-flow response. This redistribution is neglected when using the boundary condition Dp/Dt = 0, which has conventionally been applied in this problem. It is shown that applying the incorrect boundary condition, and thereby ignoring the surface pressure change, leads to a zonal wind acceleration δū/δt that is too strong, especially near the surface. The effect is significant for planetary-scale forcing even when applied at tropopause level. A comparison is made between the mean-flow evolution in a baroclinic life-cycle, as simulated in a fully nonlinear, primitive-equation model, and that predicted by using the simulated eddy fluxes in the zonally-symmetric response problem. Use of the correct lower boundary condition is shown to lead to improved agreement.

An experimental test of response consistency in contingent valuation

We compare hypothetical and observed (experimental) willingness to pay (WTP) for a gradual improvement in the environmental performance of a marketed good (an office table). First, following usual practices in marketing research, subjects’ stated WTP for the improvement is obtained. Second, the same subjects participate in a real reward experiment designed to replicate the scenario valued in the hypothetical question. Our results show that, independently of the degree of the improvement, there are no significant median differences between stated and experimental data. However, subjects reporting extreme values of WTP (low or high) exhibit a more moderate behavior in the experiment.

A genome-wide test of the differential susceptibility hypothesis reveals a genetic predictor of differential response to psychological treatments for child anxiety disorders

Background: The differential susceptibly hypothesis suggests that certain genetic variants moderate the effects of both negative and positive environments on mental health and may therefore be important predictors of response to psychological treatments. Nevertheless, the identification of such variants has so far been limited to preselected candidate genes. In this study we extended the differential susceptibility hypothesis from a candidate gene to a genome-wide approach to test whether a polygenic score of environmental sensitivity predicted response to Cognitive Behavioural Therapy (CBT) in children with anxiety disorders. Methods: We identified variants associated with environmental sensitivity using a novel method in which within-pair variability in emotional problems in 1026 monozygotic (MZ) twin pairs was examined as a function of the pairs’ genotype. We created a polygenic score of environmental sensitivity based on the whole-genome findings and tested the score as a moderator of parenting on emotional problems in 1,406 children and response to individual, group and brief parent-led CBT in 973 children with anxiety disorders. Results: The polygenic score significantly moderated the effects of parenting on emotional problems and the effects of treatment. Individuals with a high score responded significantly better to individual CBT than group CBT or brief parent-led CBT (remission rates: 70.9%, 55.5% and 41.6% respectively). Conclusions: Pending successful replication, our results should be considered exploratory. Nevertheless, if replicated, they suggest that individuals with the greatest environmental sensitivity may be more likely to develop emotional problems in adverse environments, but also benefit more from the most intensive types of treatment.

On the climate response of the low-latitude Pacific Ocean to changes in the global freshwater cycle

Under global warming, the predicted intensification of the global freshwater cycle will modify the net freshwater flux at the ocean surface. Since the freshwater flux maintains ocean salinity structures, changes to the density-driven ocean circulation are likely. A modified ocean circulation could further alter the climate, potentially allowing rapid changes, as seen in the past. The relevant feedback mechanisms and timescales are poorly understood in detail, however, especially at low latitudes where the effects of salinity are relatively subtle. In an attempt to resolve some of these outstanding issues, we present an investigation of the climate response of the low-latitude Pacific region to changes in freshwater forcing. Initiated from the present-day thermohaline structure, a control run of a coupled ocean-atmosphere general circulation model is compared with a perturbation run in which the net freshwater flux is prescribed to be zero over the ocean. Such an extreme experiment helps to elucidate the general adjustment mechanisms and their timescales. The atmospheric greenhouse gas concentrations are held constant, and we restrict our attention to the adjustment of the upper 1,000 m of the Pacific Ocean between 40°N and 40°S, over 100 years. In the perturbation run, changes to the surface buoyancy, near-surface vertical mixing and mixed-layer depth are established within 1 year. Subsequently, relative to the control run, the surface of the low-latitude Pacific Ocean in the perturbation run warms by an average of 0.6°C, and the interior cools by up to 1.1°C, after a few decades. This vertical re-arrangement of the ocean heat content is shown to be achieved by a gradual shutdown of the heat flux due to isopycnal (i.e. along surfaces of constant density) mixing, the vertical component of which is downwards at low latitudes. This heat transfer depends crucially upon the existence of density-compensating temperature and salinity gradients on isopycnal surfaces. The timescale of the thermal changes in the perturbation run is therefore set by the timescale for the decay of isopycnal salinity gradients in response to the eliminated freshwater forcing, which we demonstrate to be around 10-20 years. Such isopycnal heat flux changes may play a role in the response of the low-latitude climate to a future accelerated freshwater cycle. Specifically, the mechanism appears to represent a weak negative sea surface temperature feedback, which we speculate might partially shield from view the anthropogenically-forced global warming signal at low latitudes. Furthermore, since the surface freshwater flux is shown to play a role in determining the ocean's thermal structure, it follows that evaporation and/or precipitation biases in general circulation models are likely to cause sea surface temperature biases.

The soil-dwelling earthworm Allolobophora chlorotica modifies its burrowing behaviour in response to carbendazim applications

Carbendazim-amended soil was placed above or below unamended soil. Control tests comprised two layers of unamended soil. Allolobophora chlorotica earthworms were added to either the upper or the unamended soil. After 72 h vertical distributions of earthworms were compared between control and carbendazim-amended experiments. Earthworm distributions in the carbendazim-amended test containers differed significantly from the ‘normal’ distribution observed in the control tests. In the majority of the experiments, earthworms significantly altered their burrowing behaviour to avoid carbendazim. However, when earthworms were added to an upper layer of carbendazim-amended soil they remained in this layer. This non-avoidance is attributed to (1) the earthworms’ inability to sense the lower layer of unamended soil and (2) the toxic effect of carbendazim inhibiting burrowing. Earthworms modified their burrowing behaviour in response to carbendazim in the soil. This may explain anomalous results observed in pesticide field trials when carbendazim is used as a control substance.

Plants growing on contaminated and brownfield sites appropriate for use in Organisation for Economic Co-operation and Development terrestrial plant growth test

The Organisation for Economic Co-operation and Development (OECD) Terrestrial plant test is often used for the ecological risk assessment of contaminated land. However, its origins in plant protection product testing mean that the species recommended in the OECD guidelines are unlikely to occur on contaminated land. Six alternative species were tested on contaminated soils from a former Zn smelter and a metal fragmentizer with elevated concentrations of Cd, Cu, Pb, and Zn. The response of the alternative species was compared to two species recommended by the OECD; Lolium perenne (perennial ryegrass) and Trifolium pratense (red clover). Urtica dioica (stinging nettle) and Poa annua (annual meadow-grass) had low emergence rates in the control soil so may be considered unsuitable. Festuca rubra (chewings fescue), Holcus lanatus (Yorkshire fog), Senecio vulgaris (common groundsel), and Verbascum thapsus (great mullein) offer good alternatives to the OECD species. In particular, H. lanatus and S. vulgaris were more sensitive to the soils with moderate concentrations of Cd, Cu, Pb, and Zn than the OECD species.