Linear Exponential Models Research Articles

Estimates of calf starter energy affected by consumption of nutrients. 1. Evaluation of models to predict changing digestion on energy content in calf starters

Apparent total-tract digestibility data from 3 published studies with calves from 0 to 4 mo of age were used to evaluate National Research Council (2001) estimates of metabolizable energy (ME) in calf starters (CS). Calves (n = 83) or pens of calves (n = 24) were used in model development. In each study, 48 Holstein bull calves (2 to 3 d of age at initiation of each study) were fed varying amounts of milk replacer with CS and water for ad libitum consumption. Calf starters varied in nutrient content and form (pelleted, texturized, or mixed with 5% grass hay and fed as a total mixed ration). Apparent total-tract digestibility was measured at various ages from 3 to 16 wk. Feed and feces were collected from 20 calves per trial during 5-d collection periods during the first 56 d of each trial. In 2 studies, calves were grouped in pens (4 calves/pen) for a second 56-d measurement period. Fecal collections were repeated occasionally during the second period. Total-tract digestibilities (n = 207) of neutral detergent fiber, nonfiber carbohydrates, crude protein, and fat were used to calculate digestible energy (DE) and ME in CS using equations from the 2001 Dairy National Research Council. Three modeling approaches were constructed to evaluate changing digestion of nutrients, DE, and ME in CS, including linear mixed models, broken-line regression, and exponential models. Linear mixed models provided best model fit statistics for digestion of crude protein, ether extract, neutral detergent fiber, and ME. Exponential models were optimal for digestion of dry matter and nonfiber carbohydrates. Linear mixed models were selected for evaluation of effects of intake on changing nutrient digestion from CS and amount of DE and ME available at various ages.

Effects of different nitrogen supply levels on the yield of Orychophragmus violaceus, soil residual inorganic nitrogen, and nitrogen balance.

Understanding the responses of winter green manure February orchid (Orychophragmus violaceus) to different levels of nitrogen (N) supply in Northern China and determining the optimal soil N supply level to meet N demands of green manure production with high yield and efficiency, could provide a theoretical foundation and practice reference for maximizing ecological effects of green manure and optimizing N management for spring maize-green manure rotation system in intensive farmland in Northern China. We carried out a field experiment in a site which had received no fertilizer for many years. The aboveground biomass accumulation, N uptake of February orchid and soil residual inorganic N before green manure incorporation, as well as the N balance during the green manure growing season were determined under different levels of N supply. The results showed that N fertilizer application significantly increased the biomass and N uptake of February orchid under low soil inorganic N content (15 kg·hm-2 in 0-90 cm soil layer). At the application rate of 90 kg·hm-2, the biomass (dry mass) and N uptake reached the maximum, being 2031 and 42 kg·hm-2, respectively. The soil residual inorganic N amount rose with the increases of N fertilizer application before sowing, growing very rapidly once the application rate was over 60 kg·hm-2. With the increases of N application rate, the calculated apparent N balance changed from deficit to surplus in the growing season of February orchid. The inputs and outputs of N reached a balance at the application rates of 60 to 90 kg·hm-2. The relationships between February orchid biomass, N uptake, soil inorganic N before green manure incorporation, and soil N supply amount (0-90 cm preplant soil inorganic N content plus N application rate) could be fitted by the quadratic, linear plus plateau and exponential models respectively. Based on the simulation, we calculated the preplant soil N supply and soil residual inorganic N content before green manure incorporation would be 136 and 78 kg·hm-2 individually, as the biomass of February orchid reached the maximum (2010 kg·hm-2). While N uptake was at the highest level of 40 kg·hm-2, the biomass of February orchid was 95% of the maximum biomass mentioned above (1919 kg·hm-2) and the soil residual inorganic N before green manure incorporation decreased to 57 kg·hm-2 whose corresponding minimum soil N supply amount was 105 kg·hm-2. This value was quite near to the recommended soil residual inorganic N (100 kg·hm-2) after maize harvest under optimized N management in Nor-thern China. Taken together, our results showed that the level of soil N supply should be at approximately 100 to 105 kg·hm-2 in spring maize-winter green manure system for improving tradeoffs between agronomic and environmental impacts.

Spatial distribution of LAI and its relationship with throughfall kinetic energy of common tree species in a Chinese subtropical forest plantation

The hilly red soil region in southern China is still facing serious soil erosion, even after long-term afforestation projects. This might result from structural shortcomings of the tree species chosen for afforestation. Within the Biodiversity and Ecosystem Functioning China project (BEF China), we used point cloud data from terrestrial laser scanners (TLS) and splash cups to analyze spatial leaf area index (LAI) and to predict the potential of splash erosion in subtropical forests. High LAI of Lithocarpus glaber and Schima superba was measured mainly at the middle and lower parts of the trees while for Sapindus saponaria it was found at the upper parts. LAI was decreasing from the tree stems to the edges of the canopy. Lognormal and exponential linear models were suitable to describe the vertical and horizontal LAI distribution of selected tree species, respectively. Sapindus saponaria generally had the highest values of throughfall kinetic energy (TKE) among the analyzed tree species and measured rainfall events. In the radial direction, higher LAI tended to produce lower TKE, whereas in the vertical direction, higher skewness of LAI distribution had higher TKE. LAI and its spatial distribution both were important for TKE. These findings can help to understand mechanisms of splash erosion in forest plantations related to unsuitable spatial LAI of tree species planted. It might further improve our knowledge how tree diversity may influence splash erosion by enriching the canopy layers in an early successional stage of subtropical forest plantations.

Szanse realizacji strategii Europa 2020 w aspekcie poziomu edukacji w Polsce

The paper presents the state of the strategy Europe 2020 of the range of implementation in Poland the educational objectives. Based on data from the years 2001–2015, the trend models and linear exponential smoothing models were constructed. Based on these models the forecasts relating to the education sector were constructed. The aim of this article is to assess opportunities and to identify the time frame of the strategy Europe 2020, in the aspect of achieving the adopted “educational goals”. On the basis of the proposed models, it has been demonstrated, that the designated limits in the field of higher education in general in Poland will be realized already in 2016. This situation is more preferably in a group of women. In the case of index persons who prematurely ending the process of education, there is little chance of achieving the threshold of 4.5% in the target year of 2020, for both the total population as well as among men. Required values of indicators have already been achieved in women’s group.

A hybrid ETS–ANN model for time series forecasting

Over the past few decades, a large literature has evolved to forecast time series using various linear, nonlinear and hybrid linear–nonlinear models. Recently, hybrid models by suitably combining linear models like autoregressive integrated moving average (ARIMA) with nonlinear models like artificial neural network (ANN) have become popular due to superior performance than individual models. These models assume the time series to be a sum of a linear and a nonlinear component. However, a real world time series may be purely linear or purely nonlinear or often contains a combination of linear and nonlinear patterns. Motivated by this need, a new hybrid methodology is developed by combining linear and nonlinear exponential smoothing models from innovation state space (ETS) with ANN. The proposed hybrid ETS–ANN model glorifies the chances of capturing different combination of linear and/or nonlinear patterns in time series. This is because both ETS and ANN models have linear as well as nonlinear modeling capability. However, ANN cannot handle linear patterns equally well as nonlinear patterns. Therefore, in the proposed method, first ETS is applied to the given time series and predictions are obtained. This enhances the chances of capturing existing linear patterns (if any) well using linear ETS models. Then residual error sequence is calculated by subtracting the ETS-predictions from the original series. The residual error sequence obtained is modeled by ANN. Then final prediction is obtained by combining the ETS-predictions with ANN-predictions. Sixteen time series datasets are used for comparative performance analysis of the proposed methodology with ARIMA, ETS, multilayer perceptron(MLP) and some existing hybrid ARIMA–ANN models. Experimental results show that the proposed hybrid model shows statistically promising result for the datasets used.

Infection‐related and ‐unrelated malignancies, HIV and the aging population

HIV-positive people have increased risk of infection-related malignancies (IRMs) and infection-unrelated malignancies (IURMs). The aim of the study was to determine the impact of aging on future IRM and IURM incidence. People enrolled in EuroSIDA and followed from the latest of the first visit or 1 January 2001 until the last visit or death were included in the study. Poisson regression was used to investigate the impact of aging on the incidence of IRMs and IURMs, adjusting for demographic, clinical and laboratory confounders. Linear exponential smoothing models forecasted future incidence. A total of 15 648 people contributed 95 033 person-years of follow-up, of whom 610 developed 643 malignancies [IRMs: 388 (60%); IURMs: 255 (40%)]. After adjustment, a higher IRM incidence was associated with a lower CD4 count [adjusted incidence rate ratio (aIRR) CD4 count < 200 cells/μL: 3.77; 95% confidence interval (CI) 2.59, 5.51; compared with ≥ 500 cells/μL], independent of age, while a CD4 count < 200 cells/μL was associated with IURMs in people aged < 50 years only (aIRR: 2.51; 95% CI 1.40-4.54). Smoking was associated with IURMs (aIRR: 1.75; 95% CI 1.23, 2.49) compared with never smokers in people aged ≥ 50 years only, and not with IRMs. The incidences of both IURMs and IRMs increased with older age. It was projected that the incidence of IRMs would decrease by 29% over a 5-year period from 3.1 (95% CI 1.5-5.9) per 1000 person-years in 2011, whereas the IURM incidence would increase by 44% from 4.1 (95% CI 2.2-7.2) per 1000 person-years over the same period. Demographic and HIV-related risk factors for IURMs (aging and smoking) and IRMs (immunodeficiency and ongoing viral replication) differ markedly and the contribution from IURMs relative to IRMs will continue to increase as a result of aging of the HIV-infected population, high smoking and lung cancer prevalence and a low prevalence of untreated HIV infection. These findings suggest the need for targeted preventive measures and evaluation of the cost-benefit of screening for IURMs in HIV-infected populations.

Changes in middle cerebral artery velocimetry of fetuses diagnosed postnatally with mild or moderate hemolytic disease.

To determine the longitudinal trends of middle cerebral artery peak systolic velocity (MCA PSV) in fetuses with mild or moderate hemolytic disease according to the need for postnatal therapy. Prospective cohort study. University referral center. Twenty-three fetuses from singleton alloimmunized pregnancies. Serial measurements of MCA PSV were performed. After delivery, newborns were grouped by the need for postnatal management into mild hemolytic disease, which required no or only phototherapy (n = 14, group 1), and moderate hemolytic disease, where postnatal top-up or exchange transfusions were required (n = 9, group 2). Serial Doppler MCA PSV data transformed to multiples of the median, analyzed with linear regression and exponential models. We performed 83 measurements in group 1: 3-8 per fetus; mean GA at inclusion, 23 weeks and 65 measurements in group 2: 4-15 per fetus; mean GA at inclusion, 22 weeks. The estimated mean slopes of the MCA PSVs increased with the degree of postnatal therapy required (group 1: MCA PSV = 0.003 GA + 1.298; group 2: MCA PSV = 0.035 GA + 0.436). The relative average increments (RAI) were 4.7% and 7.1%, respectively. The two groups exhibited significant differences in mean slope and RAI (p<0.05). Fetuses that required postnatal transfusions due to hemolytic disease showed an enhanced progressive increase in MCA PSVs compared to those without transfusion requirement. This information might enable their identification during pregnancy.

Classical mathematical models for description and prediction of experimental tumor growth.

Despite internal complexity, tumor growth kinetics follow relatively simple laws that can be expressed as mathematical models. To explore this further, quantitative analysis of the most classical of these were performed. The models were assessed against data from two in vivo experimental systems: an ectopic syngeneic tumor (Lewis lung carcinoma) and an orthotopically xenografted human breast carcinoma. The goals were threefold: 1) to determine a statistical model for description of the measurement error, 2) to establish the descriptive power of each model, using several goodness-of-fit metrics and a study of parametric identifiability, and 3) to assess the models' ability to forecast future tumor growth. The models included in the study comprised the exponential, exponential-linear, power law, Gompertz, logistic, generalized logistic, von Bertalanffy and a model with dynamic carrying capacity. For the breast data, the dynamics were best captured by the Gompertz and exponential-linear models. The latter also exhibited the highest predictive power, with excellent prediction scores (≥80%) extending out as far as 12 days in the future. For the lung data, the Gompertz and power law models provided the most parsimonious and parametrically identifiable description. However, not one of the models was able to achieve a substantial prediction rate (≥70%) beyond the next day data point. In this context, adjunction of a priori information on the parameter distribution led to considerable improvement. For instance, forecast success rates went from 14.9% to 62.7% when using the power law model to predict the full future tumor growth curves, using just three data points. These results not only have important implications for biological theories of tumor growth and the use of mathematical modeling in preclinical anti-cancer drug investigations, but also may assist in defining how mathematical models could serve as potential prognostic tools in the clinic.

Comparative analysis of insect succession data from Victoria (Australia) using summary statistics versus preceding mean ambient temperature models.

Minimum postmortem interval (mPMI) can be estimated with preceding mean ambient temperature models that predict carrion taxon pre-appearance interval. But accuracy has not been compared with using summary statistics (mean ± SD of taxon arrival/departure day, range, 95% CI). This study collected succession data from ten experimental and five control (infrequently sampled) pig carcasses over two summers (n = 2 experimental, n = 1 control per placement date). Linear and exponential preceding mean ambient temperature models for appearance and departure times were constructed for 17 taxa/developmental stages. There was minimal difference in linear or exponential model success, although arrival models were more often significant: 65% of linear arrival (r2 = 0.09–0.79) and exponential arrival models (r2 = 0.05–81.0) were significant, and 35% of linear departure (r2 = 0.0–0.71) and exponential departure models (r2 = 0.0–0.72) were significant. Performance of models and summary statistics for estimating mPMI was compared in two forensic cases. Only summary statistics produced accurate mPMI estimates.

Geospatial Strategy for Tropical Forest-Wildlife Reserve Biomass Estimation

This study focus on the biomass estimation of Sariska Wildlife Reserve using forest inventory and geospatial approaches to develop a model based on the statistical correlation between biomass measured at plot level and the associated spectral characteristics. The multistage statistical technique with incorporated the satellite data of IRS P-6 LISS III gives a precise estimation of biomass. Forest cover, forest stratum, and biomass maps were generated in the study. Spectral signatures along with tonal and textural variations were used to classify different forest types validated with GPS and ground truth data. Altitude dependent vegetation and contour information from toposheets were also considered while classifying imagery during interpretation. Sample plots were laid in study area with 0.1 ha area at intersect of the diagonals of the plots. DBH and height of all the trees inside the plot were measured and converted to biomass using volumetric equations depending upon specific gravity. The specific gravity of each tree species differ from each other and sometimes unique in different regions and varies from forest type of different regions. Estimation of tree biomass can serve as useful benchmark for future studies in related areas. Linear equation obtained was used as the model to generate final biomass map where predicted and estimated biomass were compared for each band of the satellite imageries. Linear, logarithm and power exponential models were compared to each other for correlation coefficient. Correlation between estimated and predicted AGB is 0.835 and coefficient of determination (r <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) value is 0.698.

The Influence of Air Temperature on Water Temperature and the Concentration of Dissolved Oxygen in Newfoundland Rivers

In this paper regression models are developed for predicting water temperature and the concentration of dissolved oxygen in rivers monitored by the Newfoundland and Labrador Real-Time Water Quality Monitoring (RTWQM) network. The developed models can be used to predict mean, maximum and minimum water temperatures and dissolved oxygen at the monthly, weekly and daily time scales. A nonlinear logistic model is found to best represent the S-shaped relationship between water temperature at the real-time stations and air temperature collected from meteorological stations 5-50 kilometers away. There is a clear tendency for monthly and weekly models to be more accurate for prediction than the daily models. Both linear and nonlinear exponential decay models were found to best represent the relationship between water temperature and dissolved oxygen at the real-time stations. A novel graphical method of linking air temperature to water temperature and dissolved oxygen has been developed and may prove to be a valuable simple tool in the assessment of the health of the rivers in the real-time network.

Diving decompression models and bubble metrics: Modern computer syntheses

A quantitative summary of computer models in diving applications is presented, underscoring dual phase dynamics and quantifying metrics in tissue and blood. Algorithms covered include the multitissue, diffusion, split phase gradient, linear-exponential, asymmetric tissue, thermodynamic, varying permeability, reduced gradient bubble, tissue bubble diffusion, and linear-exponential phase models. Defining relationships are listed, and diver staging regimens are underscored. Implementations, diving sectors, and correlations are indicated for models with a history of widespread acceptance, utilization, and safe application across recreational, scientific, military, research, and technical communities. Presently, all models are incomplete, but many (included above) are useful, having resulted in diving tables, underwater meters, and dive planning software. Those herein employ varying degrees of calibration and data tuning. We discuss bubble metrics in tissue and blood as a backdrop against computer models. The past 15 years, or so, have witnessed changes and additions to diving protocols and table procedures, such as shorter nonstop time limits, slower ascent rates, shallow safety stops, ascending repetitive profiles, deep decompression stops, helium based breathing mixtures, permissible reverse profiles, multilevel techniques, both faster and slower controlling repetitive tissue halftimes, smaller critical tensions, longer flying-after-diving surface intervals, and others. Stimulated by Doppler and imaging technology, table and decompression meter development, theory, statistics, chamber and animal testing, or safer diving consensus, these modifications affect a gamut of activity, spanning bounce to decompression, single to multiday, and air to mixed gas diving. As it turns out, there is growing support for many protocols on operational, experimental, and theoretical grounds, with bubble models addressing many concerns on plausible bases, but with further testing or profile data analyses requisite.

Temporal and Quantitative Analyses of Stem Lesion Development and Foliar Disease Progression of Peach Rust in California

ABSTRACT The development of rust epidemics caused by Tranzschelia discolor on leaves and stems of cling peach was studied in California orchards. Sporulating stems lesions were only detected from late March until July in 1997 and 1998. When rust was present in the fall, the quadratic equation Y = -82.51 + 1.97JD - 0.01JD(2) using Julian day (JD) described the incidence of sporulating lesions on stems of cv. Andross (R(2) = 0.73; P </= 0.001) in the following spring season. Late-season rust epidemics occurred in 1996 and 1997. Incidence of rust on leaves of cvs. Andross and Ross was <10% from April through July and 80 to 100% by October/November. In 1998, early-season epidemics developed with disease incidence at 28 to 56% by July/August in two cv. Andross orchards. No disease was observed during the 1999 growing season. Using linear regression analysis, logistic and exponential models best described the development of disease in 1996 and 1997, respectively. In contrast, the monomolecular model best described the disease in 1998. In an analysis of variance comparing disease progress curves on cv. Andross from 1996 to 1998, no significant differences in area under the disease progress curve and rho were observed, whereas y(max) was significantly different (P < 0.001). A repeated measures analysis indicated that in a cv. Andross orchard the year of the disease progress curve, time of sampling, and their interaction were highly significant (P < 0.01). This indicated a distinct difference between early- and late-season epidemics. Earlyseason development of rust on leaves occurred in years with >/=117.3 mm of total precipitation and maximum temperatures of </=30.2 degrees C in April to June.

A Study of High-Precision CNC Lathe Thermal Errors and Compensation

This study is addressed at the thermal deformation errors resulting from temperature rise that contribute to 40%-70% of the precision errors in machining at a turning centre, and proposes an economic, accurate, and quick measurement method. It also investigates the thermal error differentials between static idle turning and in the actual cutting environment. The temperature measurement units are intelligent IC temperature sensors with correction circuits. The AID card extracts and transforms data and saves data in the computer files, and the displacement sensor measures the displacement deviation online during cutting. The temperatures and the deviation of thermal drifts so obtained are used to establish the relationship function using multivariable linear regression and nonlinear exponential regression models, respectively. Finally, this paper compares software compensation methods for the thermal-drift relationship. As proven by experiments, the software compensation method can limit the thermal error of a turning centre to within 5 μm. Moreover, the software compensation for the thermal error relationship using a single variable nonlinear exponent regression model can reduce the error by 40% to 60%.

Theory &amp; Methods: Detection of influential observations in nonlinear reproductive dispersion models

A robust case‐deletion diagnostic which could avoid masking is presented for nonlinear reproductive dispersion models (NRDM) (Jorgensen, 1997) that include generalized linear models and exponential family nonlinear models as special cases. Based on the second‐order approximation of log‐likelihood displacement and Poon &amp; Poon’s (1999) conformal normal curvature, a measure of local influence ranging from 0 to 1 is constructed. An example illustrates application of the techniques.

Discrete time filters for doubly stochastic poisson processes and other exponential noise models

The well-known Kalman filter is the optimal filter for a linear Gaussian state-space model. Furthermore, the Kalman filter is one of the few known finite-dimensional filters. In search of other discrete-time finite-dimensional filters, this paper derives filters for general linear exponential state-space models, of which the Kalman filter is a special case. One particularly interesting model for which a finite-dimensional filter is found to exist is a doubly stochastic discrete-time Poisson process whose rate evolves as the square of the state of a linear Gaussian dynamical system. Such a model has wide applications in communications systems and queueing theory. Another filter, also with applications in communications systems, is derived for estimating the arrival times of a Poisson process based on negative exponentially delayed observations. Copyright © 1999 John Wiley & Sons, Ltd.

Quality-Adjusted Life Years (QALY) Utility Models under Expected Utility and Rank Dependent Utility Assumptions

Quality-adjusted life years (QALY) utility models are multiattribute utility models of survival duration and health quality. This paper formulates six classes of QALY utility models and axiomatizes these models under expected utility (EU) and rank-dependent utility (RDU) assumptions. The QALY models investigated in this paper include the standard linear QALY model, the power and exponential multiplicative models, and the general multiplicative model. Emphasis is placed on a preference assumption, the zero condition, that greatly simplifies the axiomatizations under EU and RDU assumptions. The RDU axiomatizations of QALY models are generally similar to their EU counterparts, but in some cases, they require modification because linearity in probability is no longer assumed, and rank dependence introduces asymmetries between the domains of better-than-death health states and worse-than-death health states.

Temperature-Dependent Developmental Models for Predicting the Phenology of Maladera matrida (Coleoptera: Scarabaeidae)

Maladera matrida Argaman is a key pest of peanuts ( Arachis hypogaea L.) in Israel. The ability to predict accurately the occurrence of different developmental stages of this beetle may facilitate and improve the control of population of this pest. Thus, 4 non linear (logistic, exponential, sigmoid, and biophysical) models and 1 linear model were tested to fit the relationship between the developmental rate of M. matrida and temperature in a wide range of constant temperatures (20–31 ± 1°C). The required degree-days and the developmental threshold were estimated from the linear portion of the biophysical model, which provided the best fit to the developmental rate data generated in the laboratory. A linear phenological model using the parameters derived from the biophysical model accurately predicted the developmental time of the early generation of M. matrida in peanut fields but failed to predict developmental time of later generations. Predictive extension timing estimation (PETE), a time varying distribution delay model, accurately predicted the occurrence of both early and late generations. It is critical for growers to be able to predict the occurrence of 1st instars in the soil of germinating peanut fields following the emergence of the pest after overwintering. This information allows peanut growers to be prepared with monitoring and control devices to reduce the damage caused by M. matrida to peanuts.

On statistical models for regression diagnostics

In regression diagnostics, the case deletion model (CDM) and the mean shift outlier model (MSOM) are commonly used in practice. In this paper we show that the estimates of CDM and MSOM are equal in a wide class of statistical models, which include LSE, MLE, Bayesian estimate andM-estimate in linear and nonlinear regression models; MLE in generalized linear models and exponential family nonlinear models; MLEs of transformation parameters of explanatory variables in a Box-Cox regression models and so on. Furthermore, we study some models, in which, the estimates are not exactly equal but are approximately equal for CDM and MSOM.

Exponential mixtures and quadratic exponential families

SUMMARY Conditions are derived under which quadratic and polynomial exponential models can be generated as mixtures of linear exponential models. The conditions are highly restrictive for continuous sample spaces, but less restrictive in the discrete case. Some properties of binary quadratic exponential models are explored with a view towards finding models that have properties suitable for epidemiological applications.