Hausdorff dimension of non-hyperbolic repellers. I: Maps with holes

This is the first paper in a two-part series devoted to studying the Hausdorff dimension of invariant sets of non-uniformly hyperbolic, non-conformal maps. Here we consider a general abstract model, that we call piecewise smooth maps with holes. We show that the Hausdorff dimension of the repeller is strictly less than the dimension of the ambient manifold. Our approach also provides information on escape rates and dynamical dimension of the repeller.

Long term economic relationships from cointegration maps

We employ the Bayesian framework to define a cointegration measure aimed to represent long term relationships between time series. For visualization of these relationships we introduce a dissimilarity matrix and a map based on the sorting points into neighborhoods (SPIN) technique, which has been previously used to analyze large data sets from DNA arrays. We exemplify the technique in three data sets: US interest rates (USIR), monthly inflation rates and gross domestic product (GDP) growth rates. (c) 2007 Elsevier B.V. All rights reserved.

A Bayesian approach for constructing genetic maps when markers are miscoded

The advent of molecular markers has created opportunities for a better understanding of quantitative inheritance and for developing novel strategies for genetic improvement of agricultural species, using information on quantitative trait loci (QTL). A QTL analysis relies on accurate genetic marker maps. At present, most statistical methods used for map construction ignore the fact that molecular data may be read with error. Often, however, there is ambiguity about some marker genotypes. A Bayesian MCMC approach for inferences about a genetic marker map when random miscoding of genotypes occurs is presented, and simulated and real data sets are analyzed. The results suggest that unless there is strong reason to believe that genotypes are ascertained without error, the proposed approach provides more reliable inference on the genetic map.

Chains of Infinite Order, Chains with Memory of Variable Length, and Maps of the Interval

We show how to construct a topological Markov map of the interval whose invariant probability measure is the stationary law of a given stochastic chain of infinite order. In particular we characterize the maps corresponding to stochastic chains with memory of variable length. The problem treated here is the converse of the classical construction of the Gibbs formalism for Markov expanding maps of the interval.

Scalp field maps and their characterization

The present chapter gives a comprehensive introduction into the display and quantitative characterization of scalp field data. After introducing the construction of scalp field maps, different interpolation methods, the effect of the recording reference and the computation of spatial derivatives are discussed. The arguments raised in this first part have important implications for resolving a potential ambiguity in the interpretation of differences of scalp field data. In the second part of the chapter different approaches for comparing scalp field data are described. All of these comparisons can be interpreted in terms of differences of intracerebral sources either in strength, or in location and orientation in a nonambiguous way. In the present chapter we only refer to scalp field potentials, but mapping also can be used to display other features, such as power or statistical values. However, the rules for comparing and interpreting scalp field potentials might not apply to such data. Generic form of scalp field data Electroencephalogram (EEG) and event-related potential (ERP) recordings consist of one value for each sample in time and for each electrode. The recorded EEG and ERP data thus represent a two-dimensional array, with one dimension corresponding to the variable “time” and the other dimension corresponding to the variable “space” or electrode. Table 2.1 shows ERP measurements over a brief time period. The ERP data (averaged over a group of healthy subjects) were recorded with 19 electrodes during a visual paradigm. The parietal midline Pz electrode has been used as the reference electrode.

Environmental variables and multivariate seabed classification maps via k means clustering of Potter Cove, Antarctica, link to input and result files in GeoTIFF format

This study subdivides the Potter Cove, King George Island, Antarctica, into seafloor regions using multivariate statistical methods. These regions are categories used for comparing, contrasting and quantifying biogeochemical processes and biodiversity between ocean regions geographically but also regions under development within the scope of global change. The division obtained is characterized by the dominating components and interpreted in terms of ruling environmental conditions. The analysis includes in total 42 different environmental variables, interpolated based on samples taken during Australian summer seasons 2010/2011 and 2011/2012. The statistical errors of several interpolation methods (e.g. IDW, Indicator, Ordinary and Co-Kriging) with changing settings have been compared and the most reasonable method has been applied. The multivariate mathematical procedures used are regionalized classification via k means cluster analysis, canonical-correlation analysis and multidimensional scaling. Canonical-correlation analysis identifies the influencing factors in the different parts of the cove. Several methods for the identification of the optimum number of clusters have been tested and 4, 7, 10 as well as 12 were identified as reasonable numbers for clustering the Potter Cove. Especially the results of 10 and 12 clusters identify marine-influenced regions which can be clearly separated from those determined by the geological catchment area and the ones dominated by river discharge.

Residual delay maps unveil global patterns of atmospheric nonlinearity and produce improved local forecasts

We use residual-delay maps of observational field data for barometric pressure to demonstrate the structure of latitudinal gradients in nonlinearity in the atmosphere. Nonlinearity is weak and largely lacking in tropical and subtropical sites and increases rapidly into the temperate regions where the time series also appear to be much noisier. The degree of nonlinearity closely follows the meridional variation of midlatitude storm track frequency. We extract the specific functional form of this nonlinearity, a V shape in the lagged residuals that appears to be a basic feature of midlatitude synoptic weather systems associated with frontal passages. We present evidence that this form arises from the relative time scales of high-pressure versus low-pressure events. Finally, we show that this nonlinear feature is weaker in a well regarded numerical forecast model (European Centre for Medium-Range Forecasts) because small-scale temporal and spatial variation is smoothed out in the grided inputs. This is significant, in that it allows us to demonstrate how application of statistical corrections based on the residual-delay map may provide marked increases in local forecast accuracy, especially for severe weather systems.

Ensemble prediction distribution maps of macroalgae for current conditions and four climate change scenarios and high resultion bathymetry for Potter Cove, WAP, Antarctica

Species distribution models (SDM) predict species occurrence based on statistical relationships with environmental conditions. The R-package biomod2 which includes 10 different SDM techniques and 10 different evaluation methods was used in this study. Macroalgae are the main biomass producers in Potter Cove, King George Island (Isla 25 de Mayo), Antarctica, and they are sensitive to climate change factors such as suspended particulate matter (SPM). Macroalgae presence and absence data were used to test SDMs suitability and, simultaneously, to assess the environmental response of macroalgae as well as to model four scenarios of distribution shifts by varying SPM conditions due to climate change. According to the averaged evaluation scores of Relative Operating Characteristics (ROC) and True scale statistics (TSS) by models, those methods based on a multitude of decision trees such as Random Forest and Classification Tree Analysis, reached the highest predictive power followed by generalized boosted models (GBM) and maximum-entropy approaches (Maxent). The final ensemble model used 135 of 200 calculated models (TSS > 0.7) and identified hard substrate and SPM as the most influencing parameters followed by distance to glacier, total organic carbon (TOC), bathymetry and slope. The climate change scenarios show an invasive reaction of the macroalgae in case of less SPM and a retreat of the macroalgae in case of higher assumed SPM values.

Canada, past, present and future : being a historical, geographical, geological and statistical account of Canada West /

"Business directory of Canada West": v.1, 184 p. at end.

Modelling pre-clearing vegetation distribution using GIS-integrated statistical, ecological and data models: A case study from the wet tropics of Northeastern Australia

Traditional vegetation mapping methods use high cost, labour-intensive aerial photography interpretation. This approach can be subjective and is limited by factors such as the extent of remnant vegetation, and the differing scale and quality of aerial photography over time. An alternative approach is proposed which integrates a data model, a statistical model and an ecological model using sophisticated Geographic Information Systems (GIS) techniques and rule-based systems to support fine-scale vegetation community modelling. This approach is based on a more realistic representation of vegetation patterns with transitional gradients from one vegetation community to another. Arbitrary, though often unrealistic, sharp boundaries can be imposed on the model by the application of statistical methods. This GIS-integrated multivariate approach is applied to the problem of vegetation mapping in the complex vegetation communities of the Innisfail Lowlands in the Wet Tropics bioregion of Northeastern Australia. The paper presents the full cycle of this vegetation modelling approach including sampling sites, variable selection, model selection, model implementation, internal model assessment, model prediction assessments, models integration of discrete vegetation community models to generate a composite pre-clearing vegetation map, independent data set model validation and model prediction's scale assessments. An accurate pre-clearing vegetation map of the Innisfail Lowlands was generated (0.83r(2)) through GIS integration of 28 separate statistical models. This modelling approach has good potential for wider application, including provision of. vital information for conservation planning and management; a scientific basis for rehabilitation of disturbed and cleared areas; a viable method for the production of adequate vegetation maps for conservation and forestry planning of poorly-studied areas. (c) 2006 Elsevier B.V. All rights reserved.

Semi-supervised learning of statistical models for natural language understanding

Natural language understanding is to specify a computational model that maps sentences to their semantic mean representation. In this paper, we propose a novel framework to train the statistical models without using expensive fully annotated data. In particular, the input of our framework is a set of sentences labeled with abstract semantic annotations. These annotations encode the underlying embedded semantic structural relations without explicit word/semantic tag alignment. The proposed framework can automatically induce derivation rules that map sentences to their semantic meaning representations. The learning framework is applied on two statistical models, the conditional random fields (CRFs) and the hidden Markov support vector machines (HM-SVMs). Our experimental results on the DARPA communicator data show that both CRFs and HM-SVMs outperform the baseline approach, previously proposed hidden vector state (HVS) model which is also trained on abstract semantic annotations. In addition, the proposed framework shows superior performance than two other baseline approaches, a hybrid framework combining HVS and HM-SVMs and discriminative training of HVS, with a relative error reduction rate of about 25% and 15% being achieved in F-measure.

Statue of Liberty National Monument, maps /

In text: In 1986 the Statue will be 100 years old.

Statistical Analysis of the heavy neutral Atoms measured by IBEX

We investigate the directional distribution of heavy neutral atoms in the heliosphere by using heavy neutral maps generated with the IBEX-Lo instrument over three years from 2009 to 2011. The interstellar neutral (ISN) O&Ne gas flow was found in the first-year heavy neutral map at 601 keV and its flow direction and temperature were studied. However, due to the low counting statistics, researchers have not treated the full sky maps in detail. The main goal of this study is to evaluate the statistical significance of each pixel in the heavy neutral maps to get a better understanding of the directional distribution of heavy neutral atoms in the heliosphere. Here, we examine three statistical analysis methods: the signal-to-noise filter, the confidence limit method, and the cluster analysis method. These methods allow us to exclude background from areas where the heavy neutral signal is statistically significant. These methods also allow the consistent detection of heavy neutral atom structures. The main emission feature expands toward lower longitude and higher latitude from the observational peak of the ISN O&Ne gas flow. We call this emission the extended tail. It may be an imprint of the secondary oxygen atoms generated by charge exchange between ISN hydrogen atoms and oxygen ions in the outer heliosheath.