Dynamical indicators for the prediction of bursting phenomena in high-dimensional systems

Drawing upon the bursting mechanism in slow-fast systems, we propose indicators for the prediction of such rare extreme events which do not require a priori known slow and fast coordinates. The indicators are associated with functionals defined in terms of Optimally Time Dependent (OTD) modes. One such functional has the form of the largest eigenvalue of the symmetric part of the linearized dynamics reduced to these modes. In contrast to other choices of subspaces, the proposed modes are flow invariant and therefore a projection onto them is dynamically meaningful. We illustrate the application of these indicators on three examples: a prototype low-dimensional model, a body forced turbulent fluid flow, and a unidirectional model of nonlinear water waves. We use Bayesian statistics to quantify the predictive power of the proposed indicators

"Last-Mile" preparation for a potential disaster

Extreme natural events, like e.g. tsunamis or earthquakes, regularly lead to catastrophes with dramatic consequences. In recent years natural disasters caused hundreds of thousands of deaths, destruction of infrastructure, disruption of economic activity and loss of billions of dollars worth of property and thus revealed considerable deficits hindering their effective management: Needs for stakeholders, decision-makers as well as for persons concerned include systematic risk identification and evaluation, a way to assess countermeasures, awareness raising and decision support systems to be employed before, during and after crisis situations. The overall goal of this study focuses on interdisciplinary integration of various scientific disciplines to contribute to a tsunami early warning information system. In comparison to most studies our focus is on high-end geometric and thematic analysis to meet the requirements of small-scale, heterogeneous and complex coastal urban systems. Data, methods and results from engineering, remote sensing and social sciences are interlinked and provide comprehensive information for disaster risk assessment, management and reduction. In detail, we combine inundation modeling, urban morphology analysis, population assessment, socio-economic analysis of the population and evacuation modeling. The interdisciplinary results eventually lead to recommendations for mitigation strategies in the fields of spatial planning or coping capacity

Co-Localization of Audio Sources in Images Using Binaural Features and Locally-Linear Regression

This paper addresses the problem of localizing audio sources using binaural measurements. We propose a supervised formulation that simultaneously localizes multiple sources at different locations. The approach is intrinsically efficient because, contrary to prior work, it relies neither on source separation, nor on monaural segregation. The method starts with a training stage that establishes a locally-linear Gaussian regression model between the directional coordinates of all the sources and the auditory features extracted from binaural measurements. While fixed-length wide-spectrum sounds (white noise) are used for training to reliably estimate the model parameters, we show that the testing (localization) can be extended to variable-length sparse-spectrum sounds (such as speech), thus enabling a wide range of realistic applications. Indeed, we demonstrate that the method can be used for audio-visual fusion, namely to map speech signals onto images and hence to spatially align the audio and visual modalities, thus enabling to discriminate between speaking and non-speaking faces. We release a novel corpus of real-room recordings that allow quantitative evaluation of the co-localization method in the presence of one or two sound sources. Experiments demonstrate increased accuracy and speed relative to several state-of-the-art methods.Comment: 15 pages, 8 figure

Refraction of a Gaussian Seaway

Refraction of a Longuet-Higgins Gaussian sea by random ocean currents creates persistent local variations in average energy and wave action. These variations take the form of lumps or streaks, and they explicitly survive dispersion over wavelength and incoming wave propagation direction. Thus, the uniform sampling assumed in the venerable Longuet-Higgins theory does not apply following refraction by random currents. Proper handling of the non-uniform sampling results in greatly increased probability of freak wave formation. The present theory represents a synthesis of Longuet-Higgins Gaussian seas and the refraction model of White and Fornberg, which considered the effect of currents on a plane wave incident seaway. Using the linearized equations for deep ocean waves, we obtain quantitative predictions for the increased probability of freak wave formation when the refractive effects are taken into account. The crest height or wave height distribution depends primarily on the ``freak index", gamma, which measures the strength of refraction relative to the angular spread of the incoming sea. Dramatic effects are obtained in the tail of this distribution even for the modest values of the freak index that are expected to occur commonly in nature. Extensive comparisons are made between the analytical description and numerical simulations.Comment: 18 pages, 10 figure

Modeling Non-Stationary Processes Through Dimension Expansion

In this paper, we propose a novel approach to modeling nonstationary spatial fields. The proposed method works by expanding the geographic plane over which these processes evolve into higher dimensional spaces, transforming and clarifying complex patterns in the physical plane. By combining aspects of multi-dimensional scaling, group lasso, and latent variables models, a dimensionally sparse projection is found in which the originally nonstationary field exhibits stationarity. Following a comparison with existing methods in a simulated environment, dimension expansion is studied on a classic test-bed data set historically used to study nonstationary models. Following this, we explore the use of dimension expansion in modeling air pollution in the United Kingdom, a process known to be strongly influenced by rural/urban effects, amongst others, which gives rise to a nonstationary field