Applicability of Statistical Learning Algorithms for Spatial Variability of Rock Depth

Two algorithms are outlined, each of which has interesting features for modeling of spatial variability of rock depth. In this paper, reduced level of rock at Bangalore, India, is arrived from the 652 boreholes data in the area covering 220 sqa <.km. Support vector machine (SVM) and relevance vector machine (RVM) have been utilized to predict the reduced level of rock in the subsurface of Bangalore and to study the spatial variability of the rock depth. The support vector machine (SVM) that is firmly based on the theory of statistical learning theory uses regression technique by introducing epsilon-insensitive loss function has been adopted. RVM is a probabilistic model similar to the widespread SVM, but where the training takes place in a Bayesian framework. Prediction results show the ability of learning machine to build accurate models for spatial variability of rock depth with strong predictive capabilities. The paper also highlights the capability ofRVM over the SVM model.

Spatial ecology of food webs : herbivore-parasitoid communities on the pedunculate oak

Herbivorous insects, their host plants and natural enemies form the largest and most species-rich communities on earth. But what forces structure such communities? Do they represent random collections of species, or are they assembled by given rules? To address these questions, food webs offer excellent tools. As a result of their versatile information content, such webs have become the focus of intensive research over the last few decades. In this thesis, I study herbivore-parasitoid food webs from a new perspective: I construct multiple, quantitative food webs in a spatially explicit setting, at two different scales. Focusing on food webs consisting of specialist herbivores and their natural enemies on the pedunculate oak, Quercus robur, I examine consistency in food web structure across space and time, and how landscape context affects this structure. As an important methodological development, I use DNA barcoding to resolve potential cryptic species in the food webs, and to examine their effect on food web structure. I find that DNA barcoding changes our perception of species identity for as many as a third of the individuals, by reducing misidentifications and by resolving several cryptic species. In terms of the variation detected in food web structure, I find surprising consistency in both space and time. From a spatial perspective, landscape context leaves no detectable imprint on food web structure, while species richness declines significantly with decreasing connectivity. From a temporal perspective, food web structure remains predictable from year to year, despite considerable species turnover in local communities. The rate of such turnover varies between guilds and species within guilds. The factors best explaining these observations are abundant and common species, which have a quantitatively dominant imprint on overall structure, and suffer the lowest turnover. By contrast, rare species with little impact on food web structure exhibit the highest turnover rates. These patterns reveal important limitations of modern metrics of quantitative food web structure. While they accurately describe the overall topology of the web and its most significant interactions, they are disproportionately affected by species with given traits, and insensitive to the specific identity of species. As rare species have been shown to be important for food web stability, metrics depicting quantitative food web structure should then not be used as the sole descriptors of communities in a changing world. To detect and resolve the versatile imprint of global environmental change, one should rather use these metrics as one tool among several.

Topics in Spatial Econometrics - With Applications to House Prices

Topics in Spatial Econometrics — With Applications to House Prices Spatial effects in data occur when geographical closeness of observations influences the relation between the observations. When two points on a map are close to each other, the observed values on a variable at those points tend to be similar. The further away the two points are from each other, the less similar the observed values tend to be. Recent technical developments, geographical information systems (GIS) and global positioning systems (GPS) have brought about a renewed interest in spatial matters. For instance, it is possible to observe the exact location of an observation and combine it with other characteristics. Spatial econometrics integrates spatial aspects into econometric models and analysis. The thesis concentrates mainly on methodological issues, but the findings are illustrated by empirical studies on house price data. The thesis consists of an introductory chapter and four essays. The introductory chapter presents an overview of topics and problems in spatial econometrics. It discusses spatial effects, spatial weights matrices, especially k-nearest neighbours weights matrices, and various spatial econometric models, as well as estimation methods and inference. Further, the problem of omitted variables, a few computational and empirical aspects, the bootstrap procedure and the spatial J-test are presented. In addition, a discussion on hedonic house price models is included. In the first essay a comparison is made between spatial econometrics and time series analysis. By restricting the attention to unilateral spatial autoregressive processes, it is shown that a unilateral spatial autoregression, which enjoys similar properties as an autoregression with time series, can be defined. By an empirical study on house price data the second essay shows that it is possible to form coordinate-based, spatially autoregressive variables, which are at least to some extent able to replace the spatial structure in a spatial econometric model. In the third essay a strategy for specifying a k-nearest neighbours weights matrix by applying the spatial J-test is suggested, studied and demonstrated. In the final fourth essay the properties of the asymptotic spatial J-test are further examined. A simulation study shows that the spatial J-test can be used for distinguishing between general spatial models with different k-nearest neighbours weights matrices. A bootstrap spatial J-test is suggested to correct the size of the asymptotic test in small samples.

Analysis of Dynamic Heterogeneity in a Glass Former from the Spatial Correlations of Mobility

The growth of characteristic length scales associated with dynamic heterogeneity in glass-forming liquids is investigated in an extensive computational study of a four-point, time-dependent structure factor defined from spatial correlations of mobility, for a model liquid for system sizes extending up to 351 232 particles, in constant-energy and constant-temperature ensembles. Our estimates for dynamic correlation lengths and susceptibilities are consistent with previous results from finite size scaling. We find scaling exponents that are inconsistent with predictions from inhomogeneous mode coupling theory and a recent simulation confirmation of these predictions.

Spatial survival probability for one-dimensional fluctuating interfaces in the steady state

We report numerical and analytic results for the spatial survival probability for fluctuating one-dimensional interfaces with Edwards-Wilkinson or Kardar-Parisi-Zhang dynamics in the steady state. Our numerical results are obtained from analysis of steady-state profiles generated by integrating a spatially discretized form of the Edwards-Wilkinson equation to long times. We show that the survival probability exhibits scaling behavior in its dependence on the system size and the "sampling interval" used in the measurement for both "steady-state" and "finite" initial conditions. Analytic results for the scaling functions are obtained from a path-integral treatment of a formulation of the problem in terms of one-dimensional Brownian motion. A "deterministic approximation" is used to obtain closed-form expressions for survival probabilities from the formally exact analytic treatment. The resulting approximate analytic results provide a fairly good description of the numerical data.

Markov random fields and spatial smoothing in improving of forest inventory estimates

Markov random fields (MRF) are popular in image processing applications to describe spatial dependencies between image units. Here, we take a look at the theory and the models of MRFs with an application to improve forest inventory estimates. Typically, autocorrelation between study units is a nuisance in statistical inference, but we take an advantage of the dependencies to smooth noisy measurements by borrowing information from the neighbouring units. We build a stochastic spatial model, which we estimate with a Markov chain Monte Carlo simulation method. The smooth values are validated against another data set increasing our confidence that the estimates are more accurate than the originals.

Role of spatial coherence on the rotation sensitivity of Lau fringes: an experimental study

A simple technique involving the use of a rotating and a stationary diffuser has been developed to vary the spatial coherence of light from a He-Ne laser. Using this technique an experimental investigation of the dependence of rotation sensitivity of Lau fringes on the spatial coherence of the illuminating wavefield has been carried out. It is observed that (i) the rotation sensitivity of Lau fringes varies in a well-defined manner as a function of the spatial coherence of the light used; (ii) the extremely good rotation sensitivity of Lau fringes can be used to great advantage (compared to the conventional double slit method) in the measurement of the spatial coherence of a wavefield; (iii) Lau fringes are formed at various levels of spatial coherence and as such it appears that the Lau effect need not be associated with an incoherent optical field

Microsite occupancy and spatial structure of regeneration in three late-successional Norway spruce forests in northern Europe

A comparison of microsite occupancy and the spatial structure of regeneration in three areas of late-successional Norway spruce dominated forest. Pallas-Ylläs is understood to have been influenced only by small-scale disturbance; Dvina-Pinega has had sporadic larger-scale disturbances; Kazkim has been affected by fire. All spruce and birch trees with diameter at breast height (DBH) ?10 cm were mapped in five stands on 40 m x 400 m transects, and those with DBH < 10 cm on 2 or 4 m x 400 m subplots. Microsite type was inventoried at 1m intervals along the centre line and for each tree with DBH < 10 cm. At all study areas small seedlings (h < 0.3 m, DBH < 10 cm) preferentially occupied disturbed microsites. In contrast, spruce saplings (h ? 1.3 m, DBH <10 cm) at all study areas showed less, or no, preference. At Pallas-Ylläs spruce seedlings (h < 1.3 m, DBH < 10 cm) and saplings (h ? 1.3 m, DBH < 10 cm) exhibited spatial correlation at scales from 32-52 m. At Dvina-Pinega saplings of both spruce and birch exhibited spatial correlation at scales from 32-81 m. At Kazkim spatial correlation of seedlings and saplings of both species was exhibited over variable distances. No spatial cross-correlation was found between overstorey basal area (DBH ? 10 cm) and regeneration (h ? 1.3 m, DBH < 10 cm) at any study area. The results confirm the importance of disturbed microsites for seedling establishment, but suggest that undisturbed microsites may sometimes be more advantageous for long-term tree survival. The regeneration gap concept may not be useful in describing the regeneration dynamics of late-successional boreal forests.

Field-tunable stochasticity in the magnetization reversal of a cylindrical nanomagnet

The nature of magnetization reversal in an isolated cylindrical nanomagnet has been studied employing time-resolved magnetoresistance measurement. We find that the reversal mode is highly stochastic, occurring either by multimode or single-step switching. Intriguingly, the stochasticity was found to depend on the alignment of the driving magnetic field to the long axis of the nanowires, where predominantly multimode switching gives way to single-step switching behavior as the field direction is rotated from parallel to transverse with respect to the nanowire axis.

Paleoseismological evidence of surface faulting along the northeastern Himalayan front, India: Timing, size, and spatial extent of great earthquakes

The similar to 2500 km long Himalayan arc has experienced three large to great earthquakes of M-w 7.8 to 8.4 during the past century, but none produced surface rupture. Paleoseismic studies have been conducted during the last decade to begin understanding the timing, size, rupture extent, return period, and mechanics of the faulting associated with the occurrence of large surface rupturing earthquakes along the similar to 2500 km long Himalayan Frontal Thrust (HFT) system of India and Nepal. The previous studies have been limited to about nine sites along the western two-thirds of the HFT extending through northwest India and along the southern border of Nepal. We present here the results of paleoseismic investigations at three additional sites further to the northeast along the HFT within the Indian states of West Bengal and Assam. The three sites reside between the meizoseismal areas of the 1934 Bihar-Nepal and 1950 Assam earthquakes. The two westernmost of the sites, near the village of Chalsa and near the Nameri Tiger Preserve, show that offsets during the last surface rupture event were at minimum of about 14 m and 12 m, respectively. Limits on the ages of surface rupture at Chalsa (site A) and Nameri (site B), though broad, allow the possibility that the two sites record the same great historical rupture reported in Nepal around A.D. 1100. The correlation between the two sites is supported by the observation that the large displacements as recorded at Chalsa and Nameri would most likely be associated with rupture lengths of hundreds of kilometers or more and are on the same order as reported for a surface rupture earthquake reported in Nepal around A.D. 1100. Assuming the offsets observed at Chalsa and Nameri occurred synchronously with reported offsets in Nepal, the rupture length of the event would approach 700 to 800 km. The easternmost site is located within Harmutty Tea Estate (site C) at the edges of the 1950 Assam earthquake meizoseismal area. Here the most recent event offset is relatively much smaller (<2.5 m), and radiocarbon dating shows it to have occurred after A.D. 1100 (after about A.D. 1270). The location of the site near the edge of the meizoseismal region of the 1950 Assam earthquake and the relatively lesser offset allows speculation that the displacement records the 1950 M-w 8.4 Assam earthquake. Scatter in radiocarbon ages on detrital charcoal has not resulted in a firm bracket on the timing of events observed in the trenches. Nonetheless, the observations collected here, when taken together, suggest that the largest of thrust earthquakes along the Himalayan arc have rupture lengths and displacements of similar scale to the largest that have occurred historically along the world's subduction zones.

Weighted subspace methods and spatial smoothing: analysis and comparison

The effect of using a spatially smoothed forward-backward covariance matrix on the performance of weighted eigen-based state space methods/ESPRIT, and weighted MUSIC for direction-of-arrival (DOA) estimation is analyzed. Expressions for the mean-squared error in the estimates of the signal zeros and the DOA estimates, along with some general properties of the estimates and optimal weighting matrices, are derived. A key result is that optimally weighted MUSIC and weighted state-space methods/ESPRIT have identical asymptotic performance. Moreover, by properly choosing the number of subarrays, the performance of unweighted state space methods can be significantly improved. It is also shown that the mean-squared error in the DOA estimates is independent of the exact distribution of the source amplitudes. This results in a unified framework for dealing with DOA estimation using a uniformly spaced linear sensor array and the time series frequency estimation problems.

Further results in spatial smoothing

The paper analyses the effect of spatial smoothing on the performance of MUSIC algorithm. In particular, an attempt is made to bring out two effects of the smoothing: (i) reduction of effective correlation between the impinging signals and (ii) reduction of the noise perturbations due to finite data. For the case of a two-source scenario with widely spaced sources, simplified expressions for improvement with smoothing have been obtained which provide more insight into the impact of smoothing. Specifically, a pessimistic estimate of the minimum value of source correlation beyond which the smoothing is beneficial is brought out by these expressions. Computer simulations are used to demonstrate the usefulness of the analytical results.