Probability density adjoint for sensitivity analysis of the Mean of Chaos

Sensitivity analysis, especially adjoint based sensitivity analysis, is a powerful tool for engineering design which allows for the efficient computation of sensitivities with respect to many parameters. However, these methods break down when used to compute sensitivities of long-time averaged quantities in chaotic dynamical systems. The following paper presents a new method for sensitivity analysis of {\em ergodic} chaotic dynamical systems, the density adjoint method. The method involves solving the governing equations for the system's invariant measure and its adjoint on the system's attractor manifold rather than in phase-space. This new approach is derived for and demonstrated on one-dimensional chaotic maps and the three-dimensional Lorenz system. It is found that the density adjoint computes very finely detailed adjoint distributions and accurate sensitivities, but suffers from large computational costs.Comment: 29 pages, 27 figure

Transport and diffusion in the embedding map

We study the transport properties of passive inertial particles in a $2-d$ incompressible flows. Here the particle dynamics is represented by the $4-d$ dissipative embedding map of $2-d$ area-preserving standard map which models the incompressible flow. The system is a model for impurity dynamics in a fluid and is characterized by two parameters, the inertia parameter $\alpha$, and the dissipation parameter $\gamma$. We obtain the statistical characterisers of transport for this system in these dynamical regimes. These are, the recurrence time statistics, the diffusion constant, and the distribution of jump lengths. The recurrence time distribution shows a power law tail in the dynamical regimes where there is preferential concentration of particles in sticky regions of the phase space, and an exponential decay in mixing regimes. The diffusion constant shows behaviour of three types - normal, subdiffusive and superdiffusive, depending on the parameter regimes. Phase diagrams of the system are constructed to differentiate different types of diffusion behaviour, as well as the behaviour of the absolute drift. We correlate the dynamical regimes seen for the system at different parameter values with the transport properties observed at these regimes, and in the behaviour of the transients. This system also shows the existence of a crisis and unstable dimension variability at certain parameter values. The signature of the unstable dimension variability is seen in the statistical characterisers of transport. We discuss the implications of our results for realistic systems.Comment: 28 pages, 14 figures, To Appear in Phys. Rev. E; Vol. 79 (2009

An Assessment of Weather-Related Risks in Europe: Maps of Flood and Drought Risks

This technical report describes the adopted methodology and the outputs produced during the first 18 months of life of the 'ADAM' project. ADAM (Adaptation and Mitigation Strategies: Supporting European Climate Policy) is an Integrated Project financed under thematic priority 'Global Change and Ecosystems' of the 6th framework programme (for further information, see www.adam.info) The task 'A2.1 - An assessment of weather-related risks in Europe' has the following main objective: 'Quantify and map weather-related extreme-event risks to public and private capital assets, human lives, and agriculture/forestry/tourism, and identify high-risk areas (hot spots) on which to focus more detailed analysis.' The key innovative aspects of the work herein presented are manifold: - the quantification of the probabilistic monetary impact of extreme events; - the combined use of modelling techniques and of observed data to supply the lack of information at the various scales of relevance of the study; - the estimation of uncertainty arising from limitations in data availability and modelling assumptions; - the geographical scale (continental) of the exercise. The key outputs of task A2.1 are digital maps of risks from natural extremes at European scale identifying monetary/economic losses. The maps are furnished as input to other tasks of package A2 for successive modelling exercises and analysis. As defined in the project work-plan, task A.21 has duration of 24 months. The 18-month deliverables are maps of flood and drought risks. The report focuses on inland river flood damage to properties and infrastructures and on climatic stresses (drought and heat waves) in agriculture. Population exposure has only been addressed in a partial study and it's therefore not included in the final monetary losses assessment. The work on floods has been carried out by the Institute for Environment and Sustainability of the Joint Research Centre; the work on droughts and heat waves by the Department of Agronomy and Land Management - University of Florence. The methodology is centred on the risk paradigm of the research community. The risk is defined as a product of hazard, exposure and vulnerability where: - Hazard is the threatening natural event including its probability/magnitude of occurrence; - Exposure is the values/humans that are present at the location related to a given event; - Vulnerability is the lack of resistance to damaging/destructive forces (damage function). This definition has been applied to extreme events such as floods and heat/water stresses, with the due adjustments required by data availability and specific modelling techniques.JRC.H.7-Land management and natural hazard

Satellite remote sensing for ice sheet research

Potential research applications of satellite data over the terrestrial ice sheets of Greenland and Antarctica are assessed and actions required to ensure acquisition of relevant data and appropriate processing to a form suitable for research purposes are recommended. Relevant data include high-resolution visible and SAR imagery, infrared, passive-microwave and scatterometer measurements, and surface topography information from laser and radar altimeters

Individual and population-level responses of the Alabama beach mouse (Peromyscus polionotus ammobates) to environmental variation in space and time

In Chapter two, I show that the giving up density of P. p. ammobates is related to nocturnal light intensity, temperature, and an interaction between light intensity and temperature. This is interpreted in terms of the intensity of perceived predation risk by snakes versus owls, as mediated by temperature-regulated physiological state of the mice. In Chapter three, I consider a source-sink system where disturbance momentarily reverses the dependency structure of these two areas. Specifically, I show how a sink can rescue a source, thereby increasing persistence of both. I further show that decelerating the rate of population decline in the putative sink population can result in large improvement in persistence relative to increasing the rate of post-disturbance carrying capacity in the putative source. The magnitude of this result depends on disturbances frequency. In Chapter four, I show the degree of spatial segregation of P. p. ammobates and the Hispid cotton rat (Sigmodon hispidus) at the scale of tens of meters. After removing S. hispdus from some locations, the distribution of P. p. ammobates appears to respond. This suggests that the realized niche of P. p. ammobates is influenced by a species 10 times its size, and I suggest the possibility that this interspecific competition could be a proximate cause of extinction of P. p. ammobates if hurricanes force both species into a few remaining habitat remnants. In Chapter five, I present an analysis of data on the detection/nondetection of P. p. ammobates collected over a four-year period immediately following Hurricane Katrina. I estimate the rate of post-hurricane recovery and show the effects of various remotely-sensed environmental covariates on rates of colonization and survival. In Chapter six, I use results from Chapter five to parameterize a spatially-explicit simulation of P. p. ammobates occupancy dynamics. The model suggests that the probability of extinction over 100 years increases very abruptly at a threshold level of habitat loss and hurricane frequency. The implications of the combined effects of global warming and human development on the future of P. p. ammobates is then discussed

Recommendations for the quantitative analysis of landslide risk

This paper presents recommended methodologies for the quantitative analysis of landslide hazard, vulnerability and risk at different spatial scales (site-specific, local, regional and national), as well as for the verification and validation of the results. The methodologies described focus on the evaluation of the probabilities of occurrence of different landslide types with certain characteristics. Methods used to determine the spatial distribution of landslide intensity, the characterisation of the elements at risk, the assessment of the potential degree of damage and the quantification of the vulnerability of the elements at risk, and those used to perform the quantitative risk analysis are also described. The paper is intended for use by scientists and practising engineers, geologists and other landslide experts.JRC.H.5-Land Resources Managemen

Corticonic models of brain mechanisms underlying cognition and intelligence

The concern of this review is brain theory or more specifically, in its first part, a model of the cerebral cortex and the way it:(a) interacts with subcortical regions like the thalamus and the hippocampus to provide higher-level-brain functions that underlie cognition and intelligence, (b) handles and represents dynamical sensory patterns imposed by a constantly changing environment, (c) copes with the enormous number of such patterns encountered in a lifetime bymeans of dynamic memory that offers an immense number of stimulus-specific attractors for input patterns (stimuli) to select from, (d) selects an attractor through a process of “conjugation” of the input pattern with the dynamics of the thalamo–cortical loop, (e) distinguishes between redundant (structured)and non-redundant (random) inputs that are void of information, (f) can do categorical perception when there is access to vast associative memory laid out in the association cortex with the help of the hippocampus, and (g) makes use of “computation” at the edge of chaos and information driven annealing to achieve all this. Other features and implications of the concepts presented for the design of computational algorithms and machines with brain-like intelligence are also discussed. The material and results presented suggest, that a Parametrically Coupled Logistic Map network (PCLMN) is a minimal model of the thalamo–cortical complex and that marrying such a network to a suitable associative memory with re-entry or feedback forms a useful, albeit, abstract model of a cortical module of the brain that could facilitate building a simple artificial brain. In the second part of the review, the results of numerical simulations and drawn conclusions in the first part are linked to the most directly relevant works and views of other workers. What emerges is a picture of brain dynamics on the mesoscopic and macroscopic scales that gives a glimpse of the nature of the long sought after brain code underlying intelligence and other higher level brain functions. Physics of Life Reviews 4 (2007) 223–252 © 2007 Elsevier B.V. All rights reserved

The effect of noise on dynamics and the influence of biochemical systems

Understanding a complex system requires integration and collective analysis of data from many levels of organisation. Predictive modelling of biochemical systems is particularly challenging because of the nature of data being plagued by noise operating at each and every level. Inevitably we have to decide whether we can reliably infer the structure and dynamics of biochemical systems from present data. Here we approach this problem from many fronts by analysing the interplay between deterministic and stochastic dynamics in a broad collection of biochemical models. In a classical mathematical model we first illustrate how this interplay can be described in surprisingly simple terms; we furthermore demonstrate the advantages of a statistical point of view also for more complex systems. We then investigate strategies for the integrated analysis of models characterised by different organisational levels, and trace the propagation of noise through such systems. We use this approach to uncover, for the first time, the dynamics of metabolic adaptation of a plant pathogen throughout its life cycle and discuss the ecological implications. Finally, we investigate how reliably we can infer model parameters of biochemical models. We develop a novel sensitivity/inferability analysis framework that is generally applicable to a large fraction of current mathematical models of biochemical systems. By using this framework to quantify the effect of parametric variation on system dynamics, we provide practical guidelines as to when and why certain parameters are easily estimated while others are much harder to infer. We highlight the limitations on parameter inference due to model structure and qualitative dynamical behaviour, and identify candidate elements of control in biochemical pathways most likely of being subjected to regulation