Values Of Independent Variables Research Articles

Using Functional Trajectories to Track Constructed Salt Marsh Development in the Great Bay Estuary, Maine/New Hampshire, U.S.A.

AbstractA growing number of studies have assessed the functional equivalency of restored and natural salt marshes. Several of these have explored the use of functional trajectories to track the increase in restored marsh function over time; however, these studies have disagreed as to the usefulness of such models in long‐term predictions of restored marsh development. We compared indicators of four marsh functions (primary production, soil organic matter accumulation, sediment trapping, and maintenance of plant communities) in 6 restored and 11 reference (matched to restored marshes using principal components analysis) salt marshes in the Great Bay Estuary. The restored marshes were all constructed and planted on imported substrate and ranged in age from 1 to 14 years. We used marsh age in a space‐for‐time substitution to track constructed salt marsh development and explore the use of trajectories. A high degree of variability was observed among natural salt marsh sites, displaying the importance of carefully chosen reference sites. As expected, mean values for constructed site (n = 6) and reference site (n = 11) functions were significantly different. Using constructed marsh age as the independent variable and functional indicator values as dependent variables, nonlinear regression analyses produced several ecologically meaningful trajectories (r 2> 0.9), demonstrating that the use of different‐aged marshes can be a viable approach to developing functional trajectories. The trajectories illustrated that although indicators of some functions (primary production, sediment deposition, and plant species richness) may reach natural site values relatively quickly (<10 years), others (soil organic matter content) will take longer.

Reduced Functions, Gradients and Hessians from Fixed-Point Iterations for State Equations

In design optimization and parameter identification, the objective, or response function(s) are typically linked to the actually independent variables through equality constraints, which we will refer to as state equations. Our key assumption is that it is impossible to form and factor the corresponding constraint Jacobian, but one has instead some fixed-point algorithm for computing a feasible state, given any reasonable value of the independent variables. Assuming that this iteration is eventually contractive, we will show how reduced gradients (Jacobians) and Hessians (in other words, the total derivatives) of the response(s) with respect to the independent variables can be obtained via algorithmic, or automatic, differentiation (AD). In our approach the actual application of the so-called reverse, or adjoint differentiation mode is kept local to each iteration step. Consequently, the memory requirement is typically not unduly enlarged. The resulting approximating Lagrange multipliers are used to compute estimates of the reduced function values that can be shown to converge twice as fast as the underlying state space iteration. By a combination with the forward mode of AD, one can also obtain extra-accurate directional derivatives of the reduced functions as well as feasible state space directions and the corresponding reduced or projected Hessians of the Lagrangian. Our approach is verified by test calculations on an aircraft wing with two responses, namely, the lift and drag coefficient, and two variables, namely, the angle of attack and the Mach number. The state is a 2-dimensional flow field defined as solution of the discretized Euler equation under transonic conditions.

The Design and Implementation of Usable ODE Software

In the last decade it has become standard for students and researchers to be introduced to state-of-the-art numerical software through a problem solving environment (PSE) rather than through the use of scientific libraries callable from a high level language such as Fortran or C. In this paper we will identify the constraints and implications that this imposes on the ODE software we investigate and develop. In particular, the way a ‘numerical solution’ is displayed and viewed by a user dictates that new measures of performance and quality must be adopted. We will use the MATLAB environment and ODE software for initial value problems, boundary value problems and delay problems to illustrate the issues that arise and the progress that has been made. One of the major implications is the expectation that accurate approximations at ‘off-mesh’ points must be provided. Traditional numerical methods for ODEs have produced approximations to the underlying solution on an associated discrete, adaptively chosen mesh. In recent years it has become common for the ODE software to also deliver approximations at off-mesh values of the independent variable. Such a feature can be extremely valuable in applications and leads to new measures of quality and performance which are more meaningful to users and more consistently interpreted and implemented in contemporary ODE software. Numerical examples of the robust and reliable behaviour of such software will be presented and the cost/reliability trade-offs that arise will be quantified.

Determination of optimum hazelnut roasting conditions

The objective of this study was to test the hypothesis that the roasting conditions used for hazelnuts, such as the air temperature, air velocity and roasting time (independent variables), could be optimized by using Response Surface Methodology. Effects of independent variables on sensory and physical characteristics were determined. A consumer test was used to determine the acceptable samples. Very dark and very light roasted samples, corresponding to 165 °C, 3 m/s, 25 min and 125 °C, 1 m/s, 15 min process conditions, respectively, were unacceptable. Superimposed contour plots were used to determine the values of independent variables and these showed the process conditions where all product characteristics were acceptable to consumers. At low velocity (0.3 m/s), acceptable products were produced at about 165–179 °C for 20–25 min. When air velocity increased, air temperature shifted to lower temperatures. Samples roasted at 145 °C, 2 m/s, 28 min, 165 °C, 1 m/s, 25 min and 145 °C, 3.7 m/s, 20 min produced the most acceptable products. The sample roasted at 165 °C, 1 m/s, 25 min required the least air velocity and was the most economical in terms of energy consumed among the samples rated most acceptable by consumers.

Can one ever be too wealthy or too chaste? Searching for nonlinearities in mate judgment.

In 3 studies, the authors searched for nonlinearities as possible clues to context-sensitive mechanisms involved in mating decisions. Participants judged targets' sexual desirability, marital desirability, or social status on the basis of information about income or number of past sexual partners. Because one cannot know in advance where nonlinearities occur or measure all values of independent variables, a "zoom and focus" method was used. The authors began by sampling a wide range of values, followed by successively more focused examination of potentially interesting regions. Across studies, income and desirability were linked exponentially, particularly for male targets and marriage partners. Sexual partners and desirability were sometimes linked nonmonotonically, with more partners first increasing, then decreasing, desirability. The authors discuss how nonmonotonic functions may suggest competing underlying processes.

Predicting Future Forestland Area: A Comparison of Econometric Approaches

Abstract . Predictions of future forestland area are an important component of forest policy analyses. In this article, we test the ability of econometric land use models to accurately forecast forest area. We construct a panel data set for Alabama consisting of county and time-series observation for the period 1964 to 1992. We estimate models using restricted data sets—namely, data from early periods—and use out-of-sample values of dependent and independent variables to construct precise tests of the model's forecasting accuracy. Three model specifications are examined: ordinary least squares, dummy variables (fixed effects), and error components (random effects). We find that the dummy variables model produces more accurate forecasts at the county and state level than the other model specifications. This result is related to the ability of the dummy variables model to more completely control for cross-sectional variation in the dependent variables. This suggests that the estimated model parameters better capture the temporal relationship between forest area and economic variables. FOR. SCI. 46(3): 363–376.

Optimization of thin-film thermoelectric radiation sensor with separate disposition of absorbing layer and comb thermoelectric transducer

An analytical optimization of the structure of the thin-film thermoelectric radiation sensor with the separate disposition of the absorbing layer and the comb thermoelectric transducer is presented. A problem of the optimization of this sensor is solved by the method of Lagrange multipliers. The specific total volt–watt sensitivity has been chosen as a goal function and expression of the thermal time constant has been used as a constraint. The length of the absorbing layer of the radiation sensor and the distance between the boundary of this layer and the line of the disposition of cold thermojunctions of the thermoelectric transducer have been chosen as independent variables. The obtained system of equations for components of the gradient of Lagrange function in extremum point is solved by numerical method. Dependencies of optimum values of the specific total volt–watt sensitivity and corresponding values of independent variables on the thermal time constant, the thickness of the substrate layer, the thermal conductivity of the material of the substrate layer and the convection coefficient of the structure have been determined. The present analytical model of the optimization of the thermoelectric radiation sensor can be used in order to obtain the maximum value of the specific total volt–watt sensitivity under the given value of the thermal time constant.

Extending the Scope of Wavelet Regression Methods by Coefficient-Dependent Thresholding

Various aspects of the wavelet approach to nonparametric regression are considered, with the overall aim of extending the scope of wavelet techniques, to irregularlyspaced data, to regularly-spaced data sets of arbitrary size, to heteroscedastic and correlated data, and to data some of which may be downweighted or omitted as outliers. At the core of the methodology discussed is the following problem: if a sequence has a given covariance structure, what is the variance and covariance structure of its discrete wavelet transform? For sequences whose length is a power of 2, an algorithm for finding all the variances and within-level covariances in the wavelet table is developed and investigated in detail. In particular, it is shown that if the original sequence has band-limited covariance matrix, then the time required by the algorithm is linear in the length of the sequence. Up to now, most statistical work on wavelet methods presumes that the number of observations is a power of 2 and that the independent variable takes values on a regular grid. The variance-calculation algorithm allows data on any set of independent variable values to be treated, by first interpolating to a fine regular grid of suitable length, and then constructing a wavelet expansion of the gridded data. The gridded data will, in general, have a band-limited covariance matrix, and the algorithm therefore allows the elements of the wavelet transform to be thresholded individually using thresholds proportional to their standard deviation. Various thresholding methods are discussed and investigated. Exact risk formulae for the mean square error of the methodology for given design are derived and used, to avoid, as far as possible, the need for simulation in assessing performance. Both for regular and irregular data, good performance is obtained by noise-proportional thresholding, with thresholds somewhat smaller than the classical universal threshold. The general approach allows outliers in the data to be removed or downweighted, and aspects of such robust techniques are developed and demonstrated in an example. Another natural application is to data that are themselves correlated, where the covariance of the wavelet coefficients is not due to an initial grid transform but is an intrinsic feature of the data. The use of the method in these circumstances is demonstrated by an application to data synthesized in the study of ion channel gating. The basic approach of the paper has many other potential applications, and some of these are discussed briefly.

Extending the Scope of Wavelet Regression Methods by Coefficient-Dependent Thresholding

Various aspects of the wavelet approach to nonparametric regression are considered, with the overall aim of extending the scope of wavelet techniques to irregularly spaced data, to regularly spaced datasets of arbitrary size, to heteroscedastic and correlated data, and to data that contain outliers. The core of the methodology is an algorithm for finding ail of the variances and within-level covariances in the wavelet table of a sequence with given covariance structure. If the original covariance matrix is band-limited, then the algorithm is linear in the length of the sequence. The variance calculation algorithm allows data on any set of independent variable values to be treated, by first interpolating to a fine regular grid of suitable length, and then constructing a wavelet expansion of the gridded data. Various thresholding methods are discussed and investigated. Exact risk formulas for the mean square error of the methodology for given design are derived. Good performance is obtained by noise-proportional thresholding, with thresholds somewhat smaller than the classical universal threshold. Outliers in the data can be removed or downweighted, and aspects of such robust techniques are developed and demonstrated in an example. Another natural application is to correlated data, where the covariance of the wavelet coefficients is not due to an initial grid transform but rather is an intrinsic feature. The use of the method in these circumstances is demonstrated by an application to data synthesized in the study of ion channel gating. Our basic approach has many other potential applications, some of which are discussed briefly.

Optimization of thin-film thermoelectric radiation sensor with comb thermoelectric transducer

An analytical optimization of the structure of the thin-film thermoelectric radiation sensor with the comb thermoelectric transducer is presented. Expressions for the specific total volt–watt sensitivity and the thermal time constant of the thin-film thermoelectric radiation sensor have been obtained. A problem of the optimization of this sensor is solved by the method of Lagrange multipliers. The specific total volt–watt sensitivity has been chosen as a goal function and expression of the thermal time constant has been used as a constraint. The length of the absorbing layer of the radiation sensor and the distance between the boundary of this layer and the line of the disposition of cold thermojunctions of the thermoelectric transducer have been chosen as independent variables. The obtained system of equations for components of the gradient of Lagrange function in extremum point is solved by numerical method. Dependencies of optimum values of the specific total volt–watt sensitivity and corresponding values of independent variables on the thermal time constant, the thickness of the substrate layer, the thermal conductivity of the material of the substrate layer and the convection coefficient of the structure have been determined. The present analytical model of the optimization of the thermoelectric radiation sensor can be used in order to obtain the maximum value of the specific total volt–watt sensitivity under the given value of the thermal time constant.

Estimating maize production in Kenya using NDVI: Some statistical considerations

A regression model approach using a normalized difference vegetation index (NDVI) has the potential for estimating crop production in East Africa. However, before production estimation can become a reality, the underlying model assumptions and statistical nature of the sample data (NDVI and crop production) must be examined rigorously. Annual maize production statistics from 1982-90 for 36 agricultural districts within Kenya were used as the dependent variable; median area NDVI (independent variable) values from each agricultural district and year were extracted from the annual maximum NDVI data set. The input data and the statistical association of NDVI with maize production for Kenya were tested systematically for the following items: (1) homogeneity of the data when pooling the sample, (2) gross data errors and influence points, (3) serial (time) correlation, (4) spatial autocorrelation and (5) stability of the regression coefficients. The results of using a simple regression model with NDVI as the only independent variable are encouraging (r 0.75, p 0.05) and illustrate that NDVI can be a responsive indicator of maize production, especially in areas of high NDVI spatial variability, which coincide with areas of production variability in Kenya.

Biases associated with genotype and sex in prediction of fat-free lean mass and carcass value in hogs.

Carcass and live measurements of 165 market hogs that represented seven genotypes were used to investigate genotype and sex biases associated with the prediction of fat-free lean mass (FFLM) and carcass value. Carcass value was determined as the sum of the product of weight of individual cuts and their average unit prices adjusted for slaughter and processing costs. Independent variables used in the prediction equations included carcass measurements, such as optical probe, midline ruler, ribbed carcass measurements, and electromagnetic scanning (EMSCAN), and live animal ultrasonic scanning. The effect of including subpopulation mean values of independent variables in the prediction equations for FFLM and carcass value was also investigated. Genotype and sex biases were found in equations in which midline backfat, ribbed carcass, EMSCAN, and live ultrasonic scanning were used as single technology sets of measurements. The prediction equations generally undervalued genotypes with above-average carcass value. Biases were reduced when measurements of combined technologies and mean adjusted variables were used. The FFLM and carcass value of gilts were underestimated, and they were overestimated of barrows. Equations that combined OP and EMSCAN technologies were the most accurate and least biased for both FFLM and carcass value. Equations that included carcass weight and midline last-rib backfat thickness measurements were the least accurate and most biased. Genotype and sex biases must be considered when predicting FFLM and carcass value.

Application of factorial design to the modelling of organosolv delignification of Miscanthus sinensis (elephant grass) with phenol and dilute acid solutions

The Battelle-Geneva method of fractionation of lignocellulosic materials was applied to the biomass of an annual cane-like plant, Miscanthus sinensis (elephant grass). A factorial second-order composite design was used to quantify the influences of three variables of the process (independent variables), (1) time, in the interval: 0.37–2.35 h; (2) phenol concentration, in the interval: 41.6–58.4% by weight; (3) hydrochloric acid charge, in the interval: 0.0098–0.0602 g HCl/g dry Miscanthus, on five dependent variables: (1) pulp yield, (2) residual lignin in pulps, (3) dissolved reducing sugars, (4) total polysaccharides in pulp, and (5) selectivity of the process, measured as the ratio pulp yield/residual lignin in pulp. Experimental results were fitted to second-order linear models by means of a multiple regression method. Expressions obtained showed R 2 values varying between 0.80 and 0.99, obtaining fittings from acceptable to good depending on each case. The model predicted a maximum in the selectivity for the following values of independent variables: time, 1 h 48 min: phenol concentration, 53.2%; acid charge, 0.0394 g HCl/g dry Miscanthus. With regard to the other responses variations shown were, in general, logical according to the increase or decrease of the independent variables.

Nondeterministic decision tables in process control

In this paper we define nondeterministic decision tables to describe process control rules specified imprecisely. An example of such a control rule is ‘if temperature ishigh and pressure islow then open valveslightly”. The definition of nondeterministic decision tables is based on fuzzy sets and associated logic. We show how nondeterministic decision tables are interpreted and specified actions executed based on measured values of independent control variables. When nondeterministic decision tables are formulated based on rules given by experts it is necessary to determine whether they have any redundant rules, missing rules or contradictory rules. We define these terms for nondeterministic decision tables and show how such logical errors can be detected in certain cases.

Weak convergence of the extreme values of independent random variables in banach spaces with unconditional bases

We generalize well-known results concerning the weak convergence of maxima of real independent random variables to the case of random variables taking values in the Banach spaces with unconditional bases.

An improved technique for agricultural implement draught analysis

Agricultural implement draft requirements show considerable spatial variability due to variations in soil properties and fracturing of soil. A large sample size is necessary to obtain a representative mean draft value for a given soil type and condition because of this variability. Moreover, empirical polynomial/multi-linear regression models for implement draft are often subjected to multi-collinearity problems. Proper design of experiments can assist in the complete elimination of these multicollinearity problems. An implement test procedure has been developed which addresses the problems of soil variability and multi-collinearity. Proper choice of values for independent variables in the experimental design phase can assist in transforming these variables to an orthogonal domain which completely overcomes multi-collinearity problems. The orthogonal regression technique using transformed variables and the conventional polynomial/multi-linear regression techniques using real variables were used to analyze draft data for a moldboard plow in a Capay clay soil to illustrate advantages of the orthogonal technique.

On the convergence in law of almost all sums of independent random variables

The paper deals with sums of independent and identically distributed random variables defined on some probability space which are multiplied by random coefficients. These coefficients are the values of independent random variables defined on another probability space. We obtain conditions for the weak convergence of weighted sums, for almost all coefficients, to some infinitely divisible distribution. The limit distribution for these sums is found.

Beta2-microglobulin and other early predictors of human immunodeficiency virus type 1-related wasting

The objective of this study was to determine whether beta 2-microglobulin, neopterin, nutritional status, clinical status, immunosuppression, and hematologic status are predictors of human immunodeficiency virus (HIV)-related wasting and wasting syndrome. In addition, we aimed to determine which factors are early predictors and which are late predictors of wasting. For this cohort study of HIV-1-seropositive men seen semiannually from 1984 to 1991, a nested case-control design was used to analyze the predictive value of independent variables collected at baseline (first study visit for the seropositive cohort, first seropositive visit for seroconverters), 12 to 18 months prior, 6 to 12 months prior, and less than 6 months prior to the time at which case patients and control subjects were identified. Data on beta 2-microglobulin, neopterin, educational status, and diet were only available at baseline. A total of 41 case patients and 161 control subjects (n = 202) were identified. These were homosexual/bisexual men who were either HIV-seropositive on entering the study (n = 177) or who seroconverted during the study period (n = 25). Case patients were defined as men who had lost more than 10% of their baseline weight or who had a clinical diagnosis of wasting syndrome using the 1987 Centers for Disease Control definition. Control subjects had less than 5% weight loss from baseline or no weight loss at all. Four control subjects were matched to each case patient (where possible) by age and duration of follow-up.(ABSTRACT TRUNCATED AT 250 WORDS)

Odds versus Probabilities in Logit Equations: A Reply to Roncek

Odds versus Probabilities in Logit Equations: A Reply to Roncek

Pulmonary mechanics measurements in normal calves

The mechanics of ventilation were assessed in 25 normal conscious crossbred calves and immature cattle, aged 24–406 days and weighing 60–360 kg. An oesophageal balloon was used to measure transpulmonary pressure and a pneumotachograph attached to a face mask measured respiratory flows. A regression analysis with body weight as the independent variable and pulmonary function values as the dependent variables demonstrated growth related changes in pulmonary function, confirming those previously described. Mean pulmonary function values differed in a number of respects from previously reported values for cattle of similar size. The response of individual cattle to the pulmonary function testing procedure probably accounted for a major part of these differences.