Response theory for equilibrium and non-equilibrium statistical mechanics: causality and generalized Kramers-Kronig relations

We consider the general response theory recently proposed by Ruelle for describing the impact of small perturbations to the non-equilibrium steady states resulting from Axiom A dynamical systems. We show that the causality of the response functions entails the possibility of writing a set of Kramers-Kronig (K-K) relations for the corresponding susceptibilities at all orders of nonlinearity. Nonetheless, only a special class of directly observable susceptibilities obey K-K relations. Specific results are provided for the case of arbitrary order harmonic response, which allows for a very comprehensive K-K analysis and the establishment of sum rules connecting the asymptotic behavior of the harmonic generation susceptibility to the short-time response of the perturbed system. These results set in a more general theoretical framework previous findings obtained for optical systems and simple mechanical models, and shed light on the very general impact of considering the principle of causality for testing self-consistency: the described dispersion relations constitute unavoidable benchmarks that any experimental and model generated dataset must obey. The theory exposed in the present paper is dual to the time-dependent theory of perturbations to equilibrium states and to non-equilibrium steady states, and has in principle similar range of applicability and limitations. In order to connect the equilibrium and the non equilibrium steady state case, we show how to rewrite the classical response theory by Kubo so that response functions formally identical to those proposed by Ruelle, apart from the measure involved in the phase space integration, are obtained. These results, taking into account the chaotic hypothesis by Gallavotti and Cohen, might be relevant in several fields, including climate research. In particular, whereas the fluctuation-dissipation theorem does not work for non-equilibrium systems, because of the non-equivalence between internal and external fluctuations, K-K relations might be robust tools for the definition of a self-consistent theory of climate change.

Steady state and dynamic modelling of nitrogen in the River Kennet: impacts of land use change since the 1930s

Steady state and dynamic models have been developed and applied to the River Kennet system. Annual nitrogen exports from the land surface to the river have been estimated based on land use from the 1930s and the 1990s. Long term modelled trends indicate that there has been a large increase in nitrogen transport into the river system driven by increased fertiliser application associated with increased cereal production, increased population and increased livestock levels. The dynamic model INCA Integrated Nitrogen in Catchments. has been applied to simulate the day-to-day transport of N from the terrestrial ecosystem to the riverine environment. This process-based model generates spatial and temporal data and reproduces the observed instream concentrations. Applying the model to current land use and 1930s land use indicates that there has been a major shift in the short term dynamics since the 1930s, with increased river and groundwater concentrations caused by both non-point source pollution from agriculture and point source discharges. �

A rare case of solution and solid state inter-conversion of two copper(II) dimers and a copper(II) chain

Three Cu(II)-azido complexes of formula [Cu2L2(N-3)(2)] (1), [Cu2L2(N-3)(2)]center dot H2O (2) and [CuL(N-3)](n) (3) have been synthesized using the same tridentate Schiff base ligand HL (2-[(3-methylaminopropylimino)-methyl]-phenol), the condensation product of N-methyl-1,3-propanediamine and salicyldehyde). Compounds 1 and 2 are basal-apical mu-1,1 double azido bridged dimers. The dimeric structure of 1 is centro-symmetric but that of 2 is non-centrommetric. Compound 3 is a mu-1,1 single azido bridged 1D chain. The three complexes interconvert in solution and can be obtained in pure form by carefully controlling the synthetic conditions. Compound 2 undergoes an irreversible transformation to 1 upon dehydration in the solid state. The magnetic properties of compounds 1 and 2 show the presence of weak antiferromagnetic exchange interactions mediated by the double 1,1-N-3 azido bridges (J = -2.59(4) and -0.10(1) cm-(1), respectively). The single 1,1-N-3 bridge in compound 3 mediates a negligible exchange interaction.

A police state? The Nyasaland emergency and colonial intelligence.

The Nyasaland Emergency in 1959 proved a decisive turning point in the history of the Federation of Rhodesia and Nyasaland, which from 1953 to 1963 brought together the territories of Northern Rhodesia (Zambia), Southern Rhodesia (Zambia) and Nyasaland (Malawi) under a settler-dominated federal government. The British and Nyasaland governments defended the emergency by claiming to have gathered intelligence which showed that the Nyasaland African Congress was preparing a campaign of sabotage and murder. The Devlin Commission, appointed to investigate the emergency, dismissed the evidence of a ‘murder plot’, criticised the Nyasaland government's handling of the Emergency and, notoriously, described Nyasaland as a ‘police state’. This article has two principal aims. First, using the recently declassified papers of the Intelligence and Security Department (ISD) of the Colonial Office, it seeks to provide the first detailed account of what the British government knew of the intelligence relating to the ‘murder plot’ and how they assessed it, prior to the outbreak of the emergency. It demonstrates that officials in the ISD and members of the Security Service adopted a far more cautious attitude towards the intelligence than did Conservative ministers, and had greater qualms about allowing it into the public domain to justify government policy. Second, the article examines the implications of Devlin's use of the phrase ‘police state’ for Nyasaland and for the late colonial state in general. It contrasts Devlin's use of the term with that of security experts in the ISD, who routinely applied it to policing systems that diverged from their own preferred model. Hence, whereas Devlin compared policing in Nyasaland unfavourably with that in Southern Rhodesia, implying, ironically, that Nyasaland was ‘under-policed’ (because there were fewer police per head of population in Nyasaland than in Southern Rhodesia), the ISD regarded the intensive system of policing operated by the British South Africa Police in Southern Rhodesia as characteristic of a ‘police state’. The article suggests that the frequent use of the term ‘police state’ was indicative of broader anxieties about what Britain's legacy would be for the post-independence African state.

Present state of global wetland extent and wetland methane modelling: conclusions from a model inter-comparison project (WETCHIMP)

Global wetlands are believed to be climate sensitive, and are the largest natural emitters of methane (CH4). Increased wetland CH4 emissions could act as a positive feedback to future warming. The Wetland and Wetland CH4 Inter-comparison of Models Project (WETCHIMP) investigated our present ability to simulate large-scale wetland characteristics and corresponding CH4 emissions. To ensure inter-comparability, we used a common experimental protocol driving all models with the same climate and carbon dioxide (CO2) forcing datasets. The WETCHIMP experiments were conducted for model equilibrium states as well as transient simulations covering the last century. Sensitivity experiments investigated model response to changes in selected forcing inputs (precipitation, temperature, and atmospheric CO2 concentration). Ten models participated, covering the spectrum from simple to relatively complex, including models tailored either for regional or global simulations. The models also varied in methods to calculate wetland size and location, with some models simulating wetland area prognostically, while other models relied on remotely sensed inundation datasets, or an approach intermediate between the two. Four major conclusions emerged from the project. First, the suite of models demonstrate extensive disagreement in their simulations of wetland areal extent and CH4 emissions, in both space and time. Simple metrics of wetland area, such as the latitudinal gradient, show large variability, principally between models that use inundation dataset information and those that independently determine wetland area. Agreement between the models improves for zonally summed CH4 emissions, but large variation between the models remains. For annual global CH4 emissions, the models vary by ±40% of the all-model mean (190 Tg CH4 yr−1). Second, all models show a strong positive response to increased atmospheric CO2 concentrations (857 ppm) in both CH4 emissions and wetland area. In response to increasing global temperatures (+3.4 °C globally spatially uniform), on average, the models decreased wetland area and CH4 fluxes, primarily in the tropics, but the magnitude and sign of the response varied greatly. Models were least sensitive to increased global precipitation (+3.9 % globally spatially uniform) with a consistent small positive response in CH4 fluxes and wetland area. Results from the 20th century transient simulation show that interactions between climate forcings could have strong non-linear effects. Third, we presently do not have sufficient wetland methane observation datasets adequate to evaluate model fluxes at a spatial scale comparable to model grid cells (commonly 0.5°). This limitation severely restricts our ability to model global wetland CH4 emissions with confidence. Our simulated wetland extents are also difficult to evaluate due to extensive disagreements between wetland mapping and remotely sensed inundation datasets. Fourth, the large range in predicted CH4 emission rates leads to the conclusion that there is both substantial parameter and structural uncertainty in large-scale CH4 emission models, even after uncertainties in wetland areas are accounted for.

Forecasting economic and financial time series with non-linear models

In this paper we discuss the current state-of-the-art in estimating, evaluating, and selecting among non-linear forecasting models for economic and financial time series. We review theoretical and empirical issues, including predictive density, interval and point evaluation and model selection, loss functions, data-mining, and aggregation. In addition, we argue that although the evidence in favor of constructing forecasts using non-linear models is rather sparse, there is reason to be optimistic. However, much remains to be done. Finally, we outline a variety of topics for future research, and discuss a number of areas which have received considerable attention in the recent literature, but where many questions remain.

Non-Refoulement between 'Common Article 1' and 'Common Article 3'

This article considers whether, in the context of armed conflicts, certain non-refoulement obligations of non-belligerent States can be derived from the 1949 Geneva Conventions. According to Common Article 1 (CA1) thereof, all High Contracting Parties (HCPs) undertake to ‘respect and to ensure respect’ for the four conventions ‘in all circumstances’. It is contended that CA1 applies both in international armed conflicts (IACs) and in non-international armed conflicts (NIACs). In turn, it is suggested that Common Article 3 (CA3) which regulates conduct in NIACs serves as a ‘minimum yardstick’ also applicable in IACs. It is widely (though not uniformly) acknowledged that the undertaking to ‘ensure respect’ in a given armed conflict extends to HCPs that are not parties to it; nevertheless, the precise scope of this undertaking is subject to scholarly debate. This article concerns situations where, in the course of an (international or non-international) armed conflict, persons ’taking no active part in hostilities’ flee from States where violations of CA3 are (likely to be) occurring to a non-belligerent State. Based on the undertaking in CA1, the central claim of this article is that, as long as risk of exposure to these violations persists, persons should not be refouled notwithstanding possible assessment of whether they qualify as refugees based on the 1951 Refugee Convention definition, or could be eligible for complementary or subsidiary forms of protection that are regulated in regional arrangements. The analysis does not affect the explicit protection from refoulement that the Fourth Geneva Convention accords to ‘protected persons’ (as defined in Article 4 thereof). It is submitted that CA1 should be read in tandem with other obligations of non-belligerent States under the 1949 Geneva Conventions. Most pertinently, all HCPs are required to take specific measures to repress ‘grave breaches’ and to take measures necessary for the suppression of all acts contrary to the 1949 Geneva Conventions other than the grave breaches. A HCP that is capable of protecting displaced persons from exposure to risks of violations of CA3 and nonetheless refoules them to face such risks is arguably failing to take lawful measures at its disposal in order to suppress acts contrary to the conventions and, consequently, fails to ‘ensure respect’ for the conventions. KEYWORDS Non-refoulement; International Armed Conflict; Non-International Armed Conflict; Common Article 1; Common Article 3

Fractional order and non-linear system identification algorithms for biomedical applications

We discuss the modelling of dielectric responses of amorphous biological samples. Such samples are commonly encountered in impedance spectroscopy studies as well as in UV, IR, optical and THz transient spectroscopy experiments and in pump-probe studies. In many occasions, the samples may display quenched absorption bands. A systems identification framework may be developed to provide parsimonious representations of such responses. To achieve this, it is appropriate to augment the standard models found in the identification literature to incorporate fractional order dynamics. Extensions of models using the forward shift operator, state space models as well as their non-linear Hammerstein-Wiener counterpart models are highlighted. We also discuss the need to extend the theory of electromagnetically excited networks which can account for fractional order behaviour in the non-linear regime by incorporating nonlinear elements to account for the observed non-linearities. The proposed approach leads to the development of a range of new chemometrics tools for biomedical data analysis and classification.

The modelled occurrence of non-thermal plasma in the ionospheric F-region and the possible consequences for ion outflows into the magnetosphere

A global, time-dependent, three-dimensional, coupled ionosphere-thermosphere model is used to predict the spatial distribution of non-thermal plasma in the F-layer. It is shown that, even for steady-state conditions with Kp as low as 3, the difference between the ion and neutral velocities often exceeds the neutral thermal speed by a factor, D', which can be as large as 4. Theoretically, highly non-Maxwellian, and probably toroidal, ion velocity distributions are expected when D' exceeds about 1.5. The lack of response of the neutral winds to sunward ion drifts in the dawn sector of the auroral oval cause this to be the region most likely to contain toroidal distributions. The maximum in D' is found in the throat region of the convection pattern, where the strong neutral winds of the afternoon sector meet the eastward ion flows of the morning sector. These predictions are of interest, not only to radar scientists searching for non-thermal ionospheric plasma, but also as one possible explanation of the initial heating and upward flows of ions in the cleft ion fountain and nightside auroral oval, both of which are a major source of plasma for the magnetosphere.

Autonomic arousal in childhood anxiety disorders: associations with state anxiety and social anxiety disorder

Background Psychophysiological theories suggest that individuals with anxiety disorders may evidence inflexibility in their autonomic activity at rest and when responding to stressors. In addition, theories of social anxiety disorder, in particular, highlight the importance of physical symptoms. Research on autonomic activity in childhood (social) anxiety disorders, however, is scarce and has produced inconsistent findings, possibly because of methodological limitations. Method The present study aimed to account for limitations of previous studies and measured respiratory sinus arrhythmia (RSA) and heart rate (HR) using Actiheart heart rate monitors and software (Version 4) during rest and in response to a social and a non-social stressor in 60 anxious (30 socially anxious and 30 ‘other’ anxious), and 30 nonanxious sex-and age-matched 7–12 year olds. In addition, the effect of state anxiety during the tasks was explored. Results No group differences at rest or in response to stress were found. Importantly, however, with increases in state anxiety, all children, regardless of their anxiety diagnoses showed less autonomic responding (i.e., less change in HR and RSA from baseline in response to task) and took longer to recover once the stressor had passed. Limitations This study focused primarily on parasympathetic arousal and lacked measures of sympathetic arousal. Conclusion The findings suggest that childhood anxiety disorders may not be characterized by inflexible autonomic responding, and that previous findings to the contrary may have been the result of differences in subjective anxiety between anxious and nonanxious groups during the tasks, rather than a function of chronic autonomic dysregulation.

The slowly evolving background state of the atmosphere

The theory of wave–mean flow interaction requires a partition of the atmospheric flow into a notional background state and perturbations to it. Here, a background state, known as the Modified Lagrangian Mean (MLM), is defined as the zonally symmetric state obtained by requiring that every potential vorticity (PV) contour lying within an isentropic layer encloses the same mass and circulation as in the full flow. For adiabatic and frictionless flow, these two integral properties are time-invariant and the MLM state is a steady solution of the primitive equations. The time dependence in the adiabatic flow is put into the perturbations, which can be described by a wave-activity conservation law that is exact even at large amplitude. Furthermore, the effects of non-conservative processes on wave activity can be calculated from the conservation law. A new method to calculate the MLM state is introduced, where the position of the lower boundary is obtained as part of the solution. The results are illustrated using Northern Hemisphere ERA-Interim data. The MLM state evolves slowly, implying that the net non-conservative effects are weak. Although ‘adiabatic eddy fluxes’ cannot affect the MLM state, the effects of Rossby-wave breaking, PV filamentation and subsequent dissipation result in sharpening of the polar vortex edge and meridional shifts in the MLM zonal flow, both at tropopause level and on the winter stratospheric vortex. The rate of downward migration of wave activity during stratospheric sudden warmings is shown to be given by the vertical scale associated with polar vortex tilt divided by the time-scale for wave dissipation estimated from the wave-activity conservation law. Aspects of troposphere–stratosphere interaction are discussed. The new framework is suitable to examine the climate and its interactions with disturbances, such as midlatitude storm tracks, and makes a clean partition between adiabatic and non-conservative processes.

Preferred response of the East Asian summer monsoon to local and non-local anthropogenic sulphur dioxide emissions

In this study, the atmospheric component of a state-of-the-art climate model (HadGEM2-ES) that includes earth system components such as interactive chemistry and eight species of tropospheric aerosols considering aerosol direct, indirect, and semi-direct effects, has been used to investigate the impacts of local and non-local emissions of anthropogenic sulphur dioxide on the East Asian summer monsoon (EASM). The study focuses on the fast responses (including land surface feedbacks, but without sea surface temperature feedbacks) to sudden changes in emissions from Asia and Europe. The initial responses, over days 1–40, to Asian and European emissions show large differences. The response to Asian emissions involves a direct impact on the sulphate burden over Asia, with immediate consequences for the shortwave energy budget through aerosol–radiation and aerosol–cloud interactions. These changes lead to cooling of East Asia and a weakening of the EASM. In contrast, European emissions have no significant impact on the sulphate burden over Asia, but they induce mid-tropospheric cooling and drying over the European sector. Subsequently, however, this cold and dry anomaly is advected into Asia, where it induces atmospheric and surface feedbacks over Asia and the Western North Pacific (WNP), which also weaken the EASM. In spite of very different perturbations to the local aerosol burden in response to Asian and European sulphur dioxide emissions, the large scale pattern of changes in land–sea thermal contrast, atmospheric circulation and local precipitation over East Asia from days 40 onward exhibits similar structures, indicating a preferred response, and suggesting that emissions from both regions likely contributed to the observed weakening of the EASM. Cooling and drying of the troposphere over Asia, together with warming and moistening over the WNP, reduces the land–sea thermal contrast between the Asian continent and surrounding oceans. This leads to high sea level pressure (SLP) anomalies over Asia and low SLP anomalies over the WNP, associated with a weakened EASM. In response to emissions from both regions warming and moistening over the WNP plays an important role and determines the time scale of the response.

Non-visual and multisensory BCI systems: present and future

During the past decade, brain–computer interfaces (BCIs) have rapidly developed, both in technological and application domains. However, most of these interfaces rely on the visual modality. Only some research groups have been studying non-visual BCIs, primarily based on auditory and, sometimes, on somatosensory signals. These non-visual BCI approaches are especially useful for severely disabled patients with poor vision. From a broader perspective, multisensory BCIs may offer more versatile and user-friendly paradigms for control and feedback. This chapter describes current systems that are used within auditory and somatosensory BCI research. Four categories of noninvasive BCI paradigms are employed: (1) P300 evoked potentials, (2) steady-state evoked potentials, (3) slow cortical potentials, and (4) mental tasks. Comparing visual and non-visual BCIs, we propose and discuss different possible multisensory combinations, as well as their pros and cons. We conclude by discussing potential future research directions of multisensory BCIs and related research questions

Can a native rodent species limit the invasive potential of a non-native rodent species in tropical agroforest habitats?

BACKGROUND Little is known about native and non-native rodent species interactions in complex tropical agro-ecosystems. We hypothesised that the native non-pest rodent Rattus everetti may be competitively dominant over the invasive pest rodent Rattus tanezumi within agroforests. We tested this experimentally by using pulse removal for three consecutive months to reduce populations of R. everetti in agroforest habitat and assessed over 6-months the response of R. tanezumi and other rodent species. RESULTS Following removal, R. everetti individuals rapidly immigrated into removal sites. At the end of the study period, R. tanezumi were larger and there was a significant shift in their microhabitat use with respect to the use of ground vegetation cover following the perturbation of R. everetti. Irrespective of treatment, R. tanezumi selected microhabitat with less tree canopy cover, indicative of severely disturbed habitat, whereas, R. everetti selected microhabitat with a dense canopy. CONCLUSION Our results suggest that sustained habitat disturbance in agroforests favours R. tanezumi, whilst the regeneration of agroforests towards a more natural state would favour native species and may reduce pest pressure in adjacent crops. In addition, the rapid recolonisation of R. everetti suggests this species would be able to recover from non-target impacts of short-term rodent pest control.

Conditioning and preconditioning of the optimal state estimation problem

Optimal state estimation is a method that requires minimising a weighted, nonlinear, least-squares objective function in order to obtain the best estimate of the current state of a dynamical system. Often the minimisation is non-trivial due to the large scale of the problem, the relative sparsity of the observations and the nonlinearity of the objective function. To simplify the problem the solution is often found via a sequence of linearised objective functions. The condition number of the Hessian of the linearised problem is an important indicator of the convergence rate of the minimisation and the expected accuracy of the solution. In the standard formulation the convergence is slow, indicating an ill-conditioned objective function. A transformation to different variables is often used to ameliorate the conditioning of the Hessian by changing, or preconditioning, the Hessian. There is only sparse information in the literature for describing the causes of ill-conditioning of the optimal state estimation problem and explaining the effect of preconditioning on the condition number. This paper derives descriptive theoretical bounds on the condition number of both the unpreconditioned and preconditioned system in order to better understand the conditioning of the problem. We use these bounds to explain why the standard objective function is often ill-conditioned and why a standard preconditioning reduces the condition number. We also use the bounds on the preconditioned Hessian to understand the main factors that affect the conditioning of the system. We illustrate the results with simple numerical experiments.