Observing extreme events in incomplete state spaces with application to rainfall estimation from satellite images

International audienceReconstructing the dynamics of nonlinear systems from observations requires the complete knowledge of its state space. In most cases, this is either impossible or at best very difficult. Here, by using a toy model, we investigate the possibility of deriving useful insights about the variability of the system from only a part of the complete state vector. We show that while some of the details of the variability might be lost, other details, especially extreme events, are successfully recovered. We then apply these ideas to the problem of rainfall estimation from satellite imagery. We show that, while reducing the number of observables reduces the correlation between actual and inferred precipitation amounts, good estimates for extreme events are still recoverable

Unique expression patterns of the retinoblastoma (Rb) gene in intact and lens regeneration-undergoing newt eyes. Anat. Rec. A

ABSTRACT Based on the role of retinoblastoma (Rb) in lens development and in the cell cycle reentry of muscle cells during limb regeneration, we have analyzed expression or Rb patterns in intact and lens regeneration-undergoing newt eyes. We find that in intact newt eye Rb is expressed in the retina as a gradient with higher levels in the photoreceptor layer and virtually no expression in the ganglion layer. In addition, a second gradient was detected within the photoreceptor layer with expression diminishing at the dorsal and ventral regions. In the intact lens, Rb is expressed in the lens epithelium and in the differentiating lens fibers at the bow region. During lens regeneration, Rb is expressed very strongly in the differentiating lens fibers, but not in the lens epithelium. Using an antibody specific to the hyperphosphorylated form of Rb, we detected the inactive protein only in the pigment epithelial cells of the iris. These distinct patterns might be related to the regenerative potential of the lens in the newt. Anat Rec Par

Node-weighted measures for complex networks with spatially embedded, sampled, or differently sized nodes

When network and graph theory are used in the study of complex systems, a typically finite set of nodes of the network under consideration is frequently either explicitly or implicitly considered representative of a much larger finite or infinite region or set of objects of interest. The selection procedure, e.g., formation of a subset or some kind of discretization or aggregation, typically results in individual nodes of the studied network representing quite differently sized parts of the domain of interest. This heterogeneity may induce substantial bias and artifacts in derived network statistics. To avoid this bias, we propose an axiomatic scheme based on the idea of node splitting invariance to derive consistently weighted variants of various commonly used statistical network measures. The practical relevance and applicability of our approach is demonstrated for a number of example networks from different fields of research, and is shown to be of fundamental importance in particular in the study of spatially embedded functional networks derived from time series as studied in, e.g., neuroscience and climatology.Comment: 21 pages, 13 figure

Climate Dynamics: A Network-Based Approach for the Analysis of Global Precipitation

Precipitation is one of the most important meteorological variables for defining the climate dynamics, but the spatial patterns of precipitation have not been fully investigated yet. The complex network theory, which provides a robust tool to investigate the statistical interdependence of many interacting elements, is used here to analyze the spatial dynamics of annual precipitation over seventy years (1941-2010). The precipitation network is built associating a node to a geographical region, which has a temporal distribution of precipitation, and identifying possible links among nodes through the correlation function. The precipitation network reveals significant spatial variability with barely connected regions, as Eastern China and Japan, and highly connected regions, such as the African Sahel, Eastern Australia and, to a lesser extent, Northern Europe. Sahel and Eastern Australia are remarkably dry regions, where low amounts of rainfall are uniformly distributed on continental scales and small-scale extreme events are rare. As a consequence, the precipitation gradient is low, making these regions well connected on a large spatial scale. On the contrary, the Asiatic South-East is often reached by extreme events such as monsoons, tropical cyclones and heat waves, which can all contribute to reduce the correlation to the short-range scale only. Some patterns emerging between mid-latitude and tropical regions suggest a possible impact of the propagation of planetary waves on precipitation at a global scale. Other links can be qualitatively associated to the atmospheric and oceanic circulation. To analyze the sensitivity of the network to the physical closeness of the nodes, short-term connections are broken. The African Sahel, Eastern Australia and Northern Europe regions again appear as the supernodes of the network, confirming furthermore their long-range connection structure. Almost all North-American and Asian nodes vanish, revealing that extreme events can enhance high precipitation gradients, leading to a systematic absence of long-range patterns

Investigating the topology of interacting networks - Theory and application to coupled climate subnetworks

Network theory provides various tools for investigating the structural or functional topology of many complex systems found in nature, technology and society. Nevertheless, it has recently been realised that a considerable number of systems of interest should be treated, more appropriately, as interacting networks or networks of networks. Here we introduce a novel graph-theoretical framework for studying the interaction structure between subnetworks embedded within a complex network of networks. This framework allows us to quantify the structural role of single vertices or whole subnetworks with respect to the interaction of a pair of subnetworks on local, mesoscopic and global topological scales. Climate networks have recently been shown to be a powerful tool for the analysis of climatological data. Applying the general framework for studying interacting networks, we introduce coupled climate subnetworks to represent and investigate the topology of statistical relationships between the fields of distinct climatological variables. Using coupled climate subnetworks to investigate the terrestrial atmosphere's three-dimensional geopotential height field uncovers known as well as interesting novel features of the atmosphere's vertical stratification and general circulation. Specifically, the new measure "cross-betweenness" identifies regions which are particularly important for mediating vertical wind field interactions. The promising results obtained by following the coupled climate subnetwork approach present a first step towards an improved understanding of the Earth system and its complex interacting components from a network perspective

Estimating the Fractal Dimension, K_2-entropy, and the Predictability of the Atmosphere

The series of mean daily temperature of air recorded over a period of 215 years is used for analysing the dimensionality and the predictability of the atmospheric system. The total number of data points of the series is 78527. Other 37 versions of the original series are generated, including ``seasonally adjusted'' data, a smoothed series, series without annual course, etc. Modified methods of Grassberger and Procaccia are applied. A procedure for selection of the ``meaningful'' scaling region is proposed. Several scaling regions are revealed in the ln C(r) versus ln r diagram. The first one in the range of larger ln r has a gradual slope and the second one in the range of intermediate ln r has a fast slope. Other two regions are settled in the range of small ln r. The results lead us to claim that the series arises from the activity of at least two subsystems. The first subsystem is low-dimensional (d_f=1.6) and it possesses the potential predictability of several weeks. We suggest that this subsystem is connected with seasonal variability of weather. The second subsystem is high-dimensional (d_f>17) and its error-doubling time is about 4-7 days. It is found that the predictability differs in dependence on season. The predictability time for summer, winter and the entire year (T_2 approx. 4.7 days) is longer than for transition-seasons (T_2 approx. 4.0 days for spring, T_2 approx. 3.6 days for autumn). The role of random noise and the number of data points are discussed. It is shown that a 15-year-long daily temperature series is not sufficient for reliable estimations based on Grassberger and Procaccia algorithms.Comment: 27 pages (LaTex version 2.09) and 15 figures as .ps files, e-mail: [email protected]

Hydrological cycle in the Danube basin in present-day and XXII century simulations by IPCCAR4 global climate models

We present an intercomparison and verification analysis of 20 GCMs (Global Circulation Models) included in the 4th IPCC assessment report regarding their representation of the hydrological cycle on the Danube river basin for 1961–2000 and for the 2161–2200 SRESA1B scenario runs. The basin-scale properties of the hydrological cycle are computed by spatially integrating the precipitation, evaporation, and runoff fields using the Voronoi-Thiessen tessellation formalism. The span of the model- simulated mean annual water balances is of the same order of magnitude of the observed Danube discharge of the Delta; the true value is within the range simulated by the models. Some land components seem to have deficiencies since there are cases of violation of water conservation when annual means are considered. The overall performance and the degree of agreement of the GCMs are comparable to those of the RCMs (Regional Climate Models) analyzed in a previous work, in spite of the much higher resolution and common nesting of the RCMs. The reanalyses are shown to feature several inconsistencies and cannot be used as a verification benchmark for the hydrological cycle in the Danubian region. In the scenario runs, for basically all models the water balance decreases, whereas its interannual variability increases. Changes in the strength of the hydrological cycle are not consistent among models: it is confirmed that capturing the impact of climate change on the hydrological cycle is not an easy task over land areas. Moreover, in several cases we find that qualitatively different behaviors emerge among the models: the ensemble mean does not represent any sort of average model, and often it falls between the models’ clusters

miRNAs in Newt Lens Regeneration: Specific Control of Proliferation and Evidence for miRNA Networking

Background: Lens regeneration in adult newts occurs via transdifferentiation of the pigment epithelial cells (PECs) of the dorsal iris. The same source of cells from the ventral iris is not able to undergo this process. In an attempt to understand this restriction we have studied in the past expression patterns of miRNAs. Among several miRNAs we have found that mir-148 shows an up-regulation in the ventral iris, while members of the let-7 family showed down-regulation in dorsal iris during dedifferentiation. Methodology/Principal Findings: We have performed gain- and loss-of–function experiments of mir-148 and let-7b in an attempt to delineate their function. We find that up-regulation of mir-148 caused significant decrease in the proliferation rates of ventral PECs only, while up-regulation of let-7b affected proliferation of both dorsal and ventral PECs. Neither miRNA was able to affect lens morphogenesis or induction. To further understand how this effect of miRNA up-regulation is mediated we examined global expression of miRNAs after up-regulation of mir148 and let-7b. Interestingly, we identified a novel level of mirRNA regulation, which might indicate that miRNAs are regulated as a network. Conclusion/Significance: The major conclusion is that different miRNAs can control proliferation in the dorsal or ventral iris possibly by a different mechanism. Of interest is that down-regulation of the let-7 family members has also been documented in other systems undergoing reprogramming, such as in stem cells or oocytes. This might indicate tha