Characteristics and Fertility Status of Soils and Minesoils in Selected Areas of Usibelli Coal Mine, Healy, Alaska

Alaska has been proven to contain not only bountiful oil and gas reserves. but also vast coal fields occurring from the southcentral coastline to the Interior and the Arctic zone to the north. Because of concerns for stable sources of energy, particularly by the energy-short, industrial nations of the Orient, more exploration and stripmining for coal can be expected in the near future. Therefore, it is important to know the consequences of large-area soil disturbances tn the subarctic and bow the effects of man's reclamation efforts and natural processes combine in reestablishing vegetative community. The culmination or synthesis of these processes is soil development and is of great importance in successful stripmine reclamation. The Usibelli Coal Mine Company in the Healy coal field, located in Interior Alaska. commenced stripmining in 1943. Its operation has been continuous, moving from area to area, for the last 40 years. Stripmining requires the excavation of overburden and subsequent redeposition, therefore the Healy operation has exposed minespoils from different strata on various topography. In 1972, the Usibelli Coal Mine company initiated a reclamation program and, over the ensuing l0 years, has seeded and fertilized over 2000 acres. Nevertheless, there remain barren areas and areas undergoing natural revegetation. Additionally, experimental trials in seeding and fertilization were started in 1980. Large areas of intact native plant communities adjoin the mined areas. The company property provides opportunities to study the processes of soil formation under different sets of conditions. The objectives of this study were to (1) characterize the soils on the mine lease area for baseline data, (2) to characterize the mine soils with various history, (3) to study the process of soil formation under different sets of conditions, and (4) to evaluate the nutrient levels of both soil and minesoils to form a basis for establishing soil-handling requirements to promote reclamation practices.This study was supported by funds from the U.S. Department of Energy (AM06-76RL02229) and the U.S. Department of Agriculture Hatch project. Our appreciation to Drs. W.M. Mitchell. G.A. Mitchell. and F. Wooding of the Agricultural and Forestry Experiment Station. and Mr. J.P. Moore of USDA Son Conservation Service for reviewing the manuscript and offering many useful suggestions. Our appreciation also to Dr. Milton A. Wiltse of Division of Geological and Geophysical Surveys. Department of Natural Resources for access to the X-ray diffractometer and technical advice. Special thanks to the Usibelli Coal Mine Inc. for logistic and technical assistance tn carrying out this study

Boolean algebras and Lubell functions

Let $2^{[n]}$ denote the power set of $[n]:=\{1,2,..., n\}$. A collection \B\subset 2^{[n]} forms a $d$-dimensional {\em Boolean algebra} if there exist pairwise disjoint sets $X_0, X_1,..., X_d \subseteq [n]$, all non-empty with perhaps the exception of $X_0$, so that \B={X_0\cup \bigcup_{i\in I} X_i\colon I\subseteq [d]}. Let $b(n,d)$ be the maximum cardinality of a family \F\subset 2^X that does not contain a $d$-dimensional Boolean algebra. Gunderson, R\"odl, and Sidorenko proved that $b(n,d) \leq c_d n^{-1/2^d} \cdot 2^n$ where $c_d= 10^d 2^{-2^{1-d}}d^{d-2^{-d}}$. In this paper, we use the Lubell function as a new measurement for large families instead of cardinality. The Lubell value of a family of sets \F with \F\subseteq \tsupn is defined by h_n(\F):=\sum_{F\in \F}1/{{n\choose |F|}}. We prove the following Tur\'an type theorem. If \F\subseteq 2^{[n]} contains no $d$-dimensional Boolean algebra, then h_n(\F)\leq 2(n+1)^{1-2^{1-d}} for sufficiently large $n$. This results implies $b(n,d) \leq C n^{-1/2^d} \cdot 2^n$, where $C$ is an absolute constant independent of $n$ and $d$. As a consequence, we improve several Ramsey-type bounds on Boolean algebras. We also prove a canonical Ramsey theorem for Boolean algebras.Comment: 10 page

Data-based stochastic model reduction for the Kuramoto--Sivashinsky equation

The problem of constructing data-based, predictive, reduced models for the Kuramoto-Sivashinsky equation is considered, under circumstances where one has observation data only for a small subset of the dynamical variables. Accurate prediction is achieved by developing a discrete-time stochastic reduced system, based on a NARMAX (Nonlinear Autoregressive Moving Average with eXogenous input) representation. The practical issue, with the NARMAX representation as with any other, is to identify an efficient structure, i.e., one with a small number of terms and coefficients. This is accomplished here by estimating coefficients for an approximate inertial form. The broader significance of the results is discussed.Comment: 23 page, 7 figure

Selfdecomposability of Weak Variance Generalised Gamma Convolutions

Weak variance generalised gamma convolution processes are multivariate Brownian motions weakly subordinated by multivariate Thorin subordinators. Within this class, we extend a result from strong to weak subordination that a driftless Brownian motion gives rise to a self-decomposable process. Under moment conditions on the underlying Thorin measure, we show that this condition is also necessary. We apply our results to some prominent processes such as the weak variance alpha-gamma process, and illustrate the necessity of our moment conditions in some cases

A Study of All-Convolutional Encoders for Connectionist Temporal Classification

Connectionist temporal classification (CTC) is a popular sequence prediction approach for automatic speech recognition that is typically used with models based on recurrent neural networks (RNNs). We explore whether deep convolutional neural networks (CNNs) can be used effectively instead of RNNs as the "encoder" in CTC. CNNs lack an explicit representation of the entire sequence, but have the advantage that they are much faster to train. We present an exploration of CNNs as encoders for CTC models, in the context of character-based (lexicon-free) automatic speech recognition. In particular, we explore a range of one-dimensional convolutional layers, which are particularly efficient. We compare the performance of our CNN-based models against typical RNNbased models in terms of training time, decoding time, model size and word error rate (WER) on the Switchboard Eval2000 corpus. We find that our CNN-based models are close in performance to LSTMs, while not matching them, and are much faster to train and decode.Comment: Accepted to ICASSP-201

Weak Subordination of Multivariate Lévy Processes

Based on the idea of constructing a time-changed process, strong subordination is the operation that evaluates a multivariate Lévy process at a multivariate subordinator. This produces a Lévy process again when the subordinate has independent components or the subordinator has indistinguishable components, otherwise we prove that it does not in a wide range of cases. A new operation known as weak subordination is introduced, acting on multivariate Lévy processes and multivariate subordinators, to extend this idea in a way that always produces a Lévy process, even when the subordinate has dependent components. We show that weak subordination matches strong subordination in law in the previously mentioned cases where the latter produces a Lévy process. In addition, we give the characteristics of weak subordination, and prove sample path properties, moment formulas and marginal component consistency. We also give distributional representations for weak subordination with ray subordinators, a superposition of independent subordinators, subordinators having independent components and subordinators having monotonic components. The variance generalised gamma convolution class, formed by strongly subordinating Brownian motion with Thorin subordinators, is further extended using weak subordination. For these weak variance generalised gamma convolutions, we derive characteristics, including a formula for their Lévy measure in terms of that of a variance-gamma process, and prove sample path properties. As an example of a weak variance generalised gamma convolution, we construct a weak subordination counterpart to the variance-alpha-gamma process of Semeraro. For these weak variance-alpha-gamma processes, we derive characteristics, show that they are a superposition of independent variance-gamma processes and compare three calibration methods: method of moments, maximum likelihood and digital moment estimation. As the density function is not explicitly known for maximum likelihood, we derive a Fourier invertibility condition. We show in simulations that maximum likelihood produces a better fit when this condition holds, while digital moment estimation is better when it does not. Also, weak variance-alpha-gamma processes exhibit a wider range of dependence structures and produces a significantly better fit than variance-alpha-gamma processes for the log returns of an S&P500-FTSE100 data set, and digital moment estimation has the best fit in this situation. Lastly, we study the self-decomposability of weak variance generalised gamma convolutions. Specifically, we prove that a driftless Brownian motion gives rise to a self-decomposable process, and when some technical conditions on the underlying Thorin measure are satisfied, that this is also necessary. Our conditions improve and generalise an earlier result of Grigelionis. These conditions are applied to a variety of weakly subordinated processes, including the weak variance-alpha-gamma process, and in the previous fit, a likelihood ratio test fails to reject the self-decomposability of the log returns