Data-adaptive harmonic spectra and multilayer Stuart-Landau models

Harmonic decompositions of multivariate time series are considered for which we adopt an integral operator approach with periodic semigroup kernels. Spectral decomposition theorems are derived that cover the important cases of two-time statistics drawn from a mixing invariant measure. The corresponding eigenvalues can be grouped per Fourier frequency, and are actually given, at each frequency, as the singular values of a cross-spectral matrix depending on the data. These eigenvalues obey furthermore a variational principle that allows us to define naturally a multidimensional power spectrum. The eigenmodes, as far as they are concerned, exhibit a data-adaptive character manifested in their phase which allows us in turn to define a multidimensional phase spectrum. The resulting data-adaptive harmonic (DAH) modes allow for reducing the data-driven modeling effort to elemental models stacked per frequency, only coupled at different frequencies by the same noise realization. In particular, the DAH decomposition extracts time-dependent coefficients stacked by Fourier frequency which can be efficiently modeled---provided the decay of temporal correlations is sufficiently well-resolved---within a class of multilayer stochastic models (MSMs) tailored here on stochastic Stuart-Landau oscillators. Applications to the Lorenz 96 model and to a stochastic heat equation driven by a space-time white noise, are considered. In both cases, the DAH decomposition allows for an extraction of spatio-temporal modes revealing key features of the dynamics in the embedded phase space. The multilayer Stuart-Landau models (MSLMs) are shown to successfully model the typical patterns of the corresponding time-evolving fields, as well as their statistics of occurrence.Comment: 26 pages, double columns; 15 figure

Contrasting carbonate depositional systems for Pliocene cool-water limestones cropping out in central Hawke's Bay, New Zealand

Pliocene limestone formations in central Hawke's Bay (eastern North Island, New Zealand) accumulated on and near the margins of a narrow forearc basin seaway within the convergent Australia/Pacific plate boundary zone. The active tectonic setting and varied paleogeographic features of the limestone units investigated, in association with probable glacioeustatic sea-level fluctuations, resulted in complex stratigraphic architectures and contrasting types of carbonate accumulation on either side of the seaway. Here, we recognise recurring patterns of sedimentary facies, and sequences and systems tracts bounded by key physical surfaces within the limestone sheets. The facies types range from Bioclastic (B) to Siliciclastic (S) end-members via Mixed (M) carbonate-siliciclastic deposits. Skeletal components are typical cool-water associations dominated by epifaunal calcitic bivalves, bryozoans, and especially barnacles. Siliciclastic contents vary from one formation to another, and highlight siliciclastic-rich limestone units in the western ranges versus siliciclastic-poor limestone units in the eastern coastal hills. Heterogeneities in facies types, stratal patterns, and also in diagenetic pathways between eastern and western limestone units are considered to originate in the coeval occurrence in different parts of the forearc basin of two main morphodynamic carbonate systems over time

Quantum Ballistic Evolution in Quantum Mechanics: Application to Quantum Computers

Quantum computers are important examples of processes whose evolution can be described in terms of iterations of single step operators or their adjoints. Based on this, Hamiltonian evolution of processes with associated step operators $T$ is investigated here. The main limitation of this paper is to processes which evolve quantum ballistically, i.e. motion restricted to a collection of nonintersecting or distinct paths on an arbitrary basis. The main goal of this paper is proof of a theorem which gives necessary and sufficient conditions that T must satisfy so that there exists a Hamiltonian description of quantum ballistic evolution for the process, namely, that T is a partial isometry and is orthogonality preserving and stable on some basis. Simple examples of quantum ballistic evolution for quantum Turing machines with one and with more than one type of elementary step are discussed. It is seen that for nondeterministic machines the basis set can be quite complex with much entanglement present. It is also proved that, given a step operator T for an arbitrary deterministic quantum Turing machine, it is decidable if T is stable and orthogonality preserving, and if quantum ballistic evolution is possible. The proof fails if T is a step operator for a nondeterministic machine. It is an open question if such a decision procedure exists for nondeterministic machines. This problem does not occur in classical mechanics.Comment: 37 pages Latexwith 2 postscript figures tar+gzip+uuencoded, to be published in Phys. Rev.

On Unbounded Composition Operators in L2L^2-Spaces

Fundamental properties of unbounded composition operators in $L^2$-spaces are studied. Characterizations of normal and quasinormal composition operators are provided. Formally normal composition operators are shown to be normal. Composition operators generating Stieltjes moment sequences are completely characterized. The unbounded counterparts of the celebrated Lambert's characterizations of subnormality of bounded composition operators are shown to be false. Various illustrative examples are supplied

Diethylstilbestrol for Wintering, Pasturing and Fattening Beef Cattle

Since the approval of stilbestrol for cattle feeding, numerous experiments have been conducted to determine its value with various rations and feeding systems. Several questions have been raised. What are the effects of stilbestrol over a long period of time? What effects will stilbestrol administration during the pasture season have on later feed-lot performance when stilbestrol is given again? How long are implants effective? What are the comparative effects of implants and feeding stilbestrol under various feeding systems and the effects of the two methods of administration on carcass grade and carcass characteristics? These are important questions and present research in these areas is limited or not conclusive. The trial reported here was conducted to obtain more specific information on these problems

Processing of Oats in Limited Grain Rations for Wintering Calves

Hay fed to appetite along with 5 to 6 lb. of grain is a common ration for growing calves for herd replacements or later feedlot finishing. Feeding could be simplified and costs reduced by feeding grain in the whole form. Studies with corn have often shown some improvement in weight gain and feed efficiency from processing the grain for cattle where the roughage level exceeds about 20% of the dry ration. Sorghum grain, wheat and barley appear to benefit more from processing than does corn grain

Dry and High-Moisture Grain Fed Whole or Rolled With Hay or Haylage in Cattle Finishing Diets

In a previous experiment (A.S. Series 70-20 ) , steers were fed dry or reconstituted high-moisture corn grain , whole or rolled , at 1 lb . per 100 lb . of body weight with alfalfa-brome hay or reconstituted haylage to appetite from weights of about 500 to 825 lb . Higher rates of gain with lower feed requirements were obtained with high-moisture corn and haylage than from dry corn and hay. The greatest benefits from the moist feeds resulted when high-moisture corn and haylage were fed together. There appeared to be a slight advantage for rolling the corn under these conditions of limited grain and full-fed roughage. The cattle were also used in a finishing experiment where diet treatments were the same as during the growing experiment, except the roughage portion of the diet was limited to low levels with corn grain full-fed. This finishing experiment is reported herein

Dry and High-Moisture Corn as Affected by Processing and Type of Diet

High-moisture grains have received considerable emphasis in cattle feeding research and by feedlot operators during recent years. Large quantities of grain are harvested at high-moisture contents because of harvesting and other advantages associated with the high-moisture content or because of unfavorable natural drying conditions. Drying grain is expensive, and it would appear that first consideration should be given to storing and using the grain in the high-moisture form if it is to be fed livestock

Dry and High-Moisture Corn Fed Whole or Rolled With Corn Silage in Cattle Growing-Finishing Diets

One area of research in beef cattle feeding that is receiving major emphasis at this station is the comparative value of dry and high-moisture grain under various conditions of use and the benefits of processing in comparison to feeding as whole grain. Previous research has involved levels of roughage and moisture content of the roughage (hay or haylage). In this experiment, dry or high-moisture corn grain was fed whole and rolled with a limited feed of corn silage with urea or soybean meal furnishing the supplemental protein

Nitrate and Vitamin A Interrelationship in Sheep

Several researchers have demonstrated that dietary nitrate reduced liver stores of vitamin A in ruminants. However, it has not been shown whether the effect is due to a more rapid depletion of existing vitamin A stores or to a lowered depatic deposition of the vitamin. Two experiments were conducted to determine the effect of nitrate on plasma vitamin A, hepatic vitamin A and performance of lambs during a growing period (experiment 1) and vitamin A depletion and repletion periods (experiment 2)