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.

Evidence of dispersion relations for the nonlinear response of the Lorenz 63 system

Along the lines of the nonlinear response theory developed by Ruelle, in a previous paper we have proved under rather general conditions that Kramers-Kronig dispersion relations and sum rules apply for a class of susceptibilities describing at any order of perturbation the response of Axiom A non equilibrium steady state systems to weak monochromatic forcings. We present here the first evidence of the validity of these integral relations for the linear and the second harmonic response for the perturbed Lorenz 63 system, by showing that numerical simulations agree up to high degree of accuracy with the theoretical predictions. Some new theoretical results, showing how to derive asymptotic behaviors and how to obtain recursively harmonic generation susceptibilities for general observables, are also presented. Our findings confirm the conceptual validity of the nonlinear response theory, suggest that the theory can be extended for more general non equilibrium steady state systems, and shed new light on the applicability of very general tools, based only upon the principle of causality, for diagnosing the behavior of perturbed chaotic systems and reconstructing their output signals, in situations where the fluctuation-dissipation relation is not of great help.

Inequality, intergenerational mobility and redistributive policies under endogenous information

This paper presents a dynamic model to study how different levels of information about the root determinants of wealth (luck versus effort) can impact inequality and intergenerational mobility through societal beliefs, individual choices and redistributive policies. To my knowledge, the model presented is the first dynamicmodel in which skills are stochastic and both beliefs and voted redistribution are determined endogenously. The model is able to explain a number of empirical facts. Large empirical evidence shows that the difference in the political support for redistribution appears to reflect differences in the social perceptions regarding the determinants of individual wealth and the underlying sources of income inequality. Moreover the beliefs about the determinants of wealth impact individual choices of effort and therefore the beliefs about the determinants of wealth impact inequality and mobility both through choices of effort and redistributive policies. The model generates multiple equilibria (US versus Europe-type) which may account for the observed features not only in terms of societal beliefs and redistribution but also in terms of perceived versus real mobility and inequality.

Intergenerational persistence in health in developing countries : the penalty of gender inequality?

This paper is motivated to investigate the often neglected payoff to investments in the health of girls and women in terms of next generation outcomes. This paper investigates the intergenerational persistence of health across time and region as well as across the distribution of maternal health. It uses comparable microdata on as many as 2.24 million children born of about 0.6 million mothers in 38 developing countries in the 31 year period, 1970–2000. Mother's health is indicated by her height, BMI and anemia status. Child health is indicated by mortality risk and anthropometric failure. We find a positive relationship between maternal and child health across indicators and highlight non-linearities in these relationships. The results suggest that both contemporary and childhood health of the mother matter and that the benefits to the next generation are likely to be persistent. Averaging across the sample, persistence shows a considerable decline over time. Disaggregation shows that the decline is only significant in Latin America. Persistence has remained largely constant in Asia and has risen in Africa. The paper provides the first cross-country estimates of the intergenerational persistence in health and the first estimates of trends.

Gradients of the intergenerational transmission of health in developing countries

This paper investigates sensitivity of the intergenerational transmission of health to changes in the socioeconomic and public health environment into which children are born using individual survey data on 2.24 million children born to 600000 mothers during 1970-2000 in 38 developing countries merged by country and cohort with macroeconomic data. We find that children are more likely to bear the penalty exerted by poor maternal health if they are conceived or born in adverse socioeconomic conditions. Equivalently, shocks to the child’s birth environment are more damaging of children born to women with a weaker stock of health at birth.

Intergenerational wealth mobility in rural Bangladesh

Unique residential history data with retrospective information on parental assets are used to study household wealth mobility in 141 villages in rural Bangladesh. Regression estimates of father–son correlations and analyses of intergenerational transition matrices show substantial persistence in wealth even when we correct for measurement errors in parental wealth. We do not find wealth mobility to be higher between periods of a person's life than between generations. We find that the process of household division plays an important role: sons who splinter off from the father's household experience greater (albeit downward) mobility in wealth. Despite significant occupational mobility across generations, its contribution to wealth mobility, net of human capital attainment of individuals, appears insignificant. Low wealth mobility in our data is primarily explained by intergenerational persistence in educational attainment.

Conductance of amyloid β based peptide filaments: structure–function relations.

Controlling the morphology of self-assembled peptide nanostructures, particularly those based on amyloid peptides, has been the focus of intense research. In order to exploit these structures in electronic applications, further understanding of their electronic behavior is required. In this work, the role of peptide morphology in determining electronic conduction along self-assembled peptide nanofilament networks is demonstrated. The peptides used in this work were based on the sequence AAKLVFF, which is an extension of a core sequence from the amyloid b peptide. We show that the incorporation of a non-natural amino acid, 2-thienylalanine, instead of phenylalanine improves the obtained conductance with respect to that obtained for a similar structure based on the native sequence, which was not the case for the incorporation of 3-thienylalanine. Furthermore, we demonstrate that the morphology of the self-assembled structures, which can be controlled by the solvent used in the assembly process, strongly affects the conductance, with larger conduction obtained for a morphology of long, straight filaments. Our results demonstrate that, similar to natural systems, the assembly and folding of peptides could be of great importance for optimizing their function as components of electronic devices. Hence, sequence design and assembly conditions can be used to control the performance of peptide based structures in such electronic applications.

Young people’s caring relations and transitions within families affected by HIV

This chapter provides insight into young people’s caring relations and transitions within what is often considered a particularly ‘troubling’ familial context in both the global North and South: living with HIV. I analyse the findings from two qualitative studies of young people’s caring roles in families affected by HIV in the UK, Tanzania and Uganda from the perspective of a feminist ethics of care, emotion work and life course transitions.

Transatlantic Relations: Sharing Ideals and Costs

A study of European relations with the USA and Canada after the end of the Cold War

Haunted by History: Myths in International Relations

A series of studies on interpretations of history and their use in political debates. Includes: Beatrice Heuser & Cyril Buffet: ‘Michel and Marianne’ Beatrice Heuser & Cyril Buffet: ‘Of Myths and Men’, Beatrice Heuser & Cyril Buffet: ‘Historical Myths and the Denial of Change’, Beatrice Heuser: ‘Dunkirk, Dien Bien Phu, and Suez, or why France doesn't trust allies and has learned to love the bomb’.

International relations theory and peacebuilding

The chapter examines the contribution that International Relations theory has made to the reading and practice of peacebuilding.

Whole-brain functional connectivity during emotional word classification in medication-free Major Depressive Disorder: abnormal salience circuitry and relations to positive emotionality

Major Depressive Disorder (MDD) has been associated with biased processing and abnormal regulation of negative and positive information, which may result from compromised coordinated activity of prefrontal and subcortical brain regions involved in evaluating emotional information. We tested whether patients with MDD show distributed changes in functional connectivity with a set of independently derived brain networks that have shown high correspondence with different task demands, including stimulus salience and emotional processing. We further explored if connectivity during emotional word processing related to the tendency to engage in positive or negative emotional states. In this study, 25 medication-free MDD patients without current or past comorbidity and matched controls (n=25) performed an emotional word-evaluation task during functional MRI. Using a dual regression approach, individual spatial connectivity maps representing each subject’s connectivity with each standard network were used to evaluate between-group differences and effects of positive and negative emotionality (extraversion and neuroticism, respectively, as measured with the NEO-FFI). Results showed decreased functional connectivity of the medial prefrontal cortex, ventrolateral prefrontal cortex, and ventral striatum with the fronto-opercular salience network in MDD patients compared to controls. In patients, abnormal connectivity was related to extraversion, but not neuroticism. These results confirm the hypothesis of a relative (para)limbic-cortical decoupling that may explain dysregulated affect in MDD. As connectivity of these regions with the salience network was related to extraversion, but not to general depression severity or negative emotionality, dysfunction of this network may be responsible for the failure to sustain engagement in rewarding behavior.

The heuristic application of explanatory theories in international relations

Explanatory theorists increasingly insist that their theories are useful even though they cannot be deductively applied. But if so, then how do such theories contribute to our understanding of international relations? I argue that explanatory theories are typically heuristically applied: theorists’ accounts of specific empirical episodes are shaped by their theories’ thematic content, but are not inferred from putative causal generalizations or covering laws. These accounts therefore gain no weight from their purely rhetorical association with theories’ quasi-deductive arguments: they must be judged on the plausibility of their empirical claims. Moreover, the quasi-deductive form in which explanatory theories are typically presented obscures their actual explanatory role, which is to indicate what sort of explanation may be required, to provide conceptual categories, and to suggest an empirical focus. This account of how theoretical explanations are constructed subverts the nomothetic–idiographic distinction that is often used to distinguish International Relations from History.

Regulating vertical relations in the presence of retailer differentiation costs

We discuss public policy towards vertical relations, comparing different types of contracts between a manufacturer and a maximum of two retailers. Together with (potential) price competition between the retailers, we study the role of a (sunk) differentiation cost paid by them in order to relax competition in the retail market and broaden the market potential of the distributed product. This non-price competition element in the downstream market is responsible for our conclusion that, unlike in standard policy guidelines and previous theoretical analysis, restrictions in intra-brand competition may deserve a permissive treatment even in the absence of inter-brand competition, if retailer differentiation is costly.