Minimum Number Of Variables Research Articles

Relationships of bryophytes and lichens to environmental gradients in Maine peatlands

The most important environmental gradients of Maine peatlands are geologic substrate and alkalinity. Other gradients are coastal-inland climate, moisture content of the peat, P and K concentrations, and shade. Abundance weighted means of pH, Ca, and moisture content of peat are given for the 48 most frequently occurring bryophyte and lichen species. A TWINSPAN differentiated twenty associations. Environments of the first four TWINSPAN dichotomies differed largely by pH and related variables, though Fe, %H2O, shade, microtopography, and degree of humification were also significant. A CCA with forward selection entered pH, P, Fe, Na, %H2O, shade, and a climate factor as the minimum number of variables which best account for the species variation. Bryophyte and lichen distributions are determined primarily by edaphic and hydrologic factors, which determine the kinds and amounts of mineral solutes in peat interstitial water. Two independent chemical gradients were identified: (1) the acidity-alkalinity gradient related to base cation concentrations, and (2) a gradient of Fe, Al, Mn, and Si related to shallowness of peat and inputs from granitic lithologies.

Chaos in Jerky Flow: Theory and Experiment

Recently, the prediction of chaos in jerky flow based on a nonlinear dynamical model has been verified by demonstrating the existence of correlation dimension for the stress signals obtained on samples of AlCu alloys. However, an unambiguous support of chaos requires the existence of a positive Lyapunov exponent. Here we consider a recent method which uses state space reconstruction by embedding the signals in higher dimension and obtaining the signature of chaos using the property of divergence of near by orbits. The method provides a reasonable estimate of the delay time and the embedding dimension. We first illustrate the method by using the time series obtained from a dynamical model and then apply it to the experimental signals. The analysis shows that the experimental signals are truly chaotic. The minimum number of variables required for the dynamical description of jerky flow appears to be five, consistent with the estimate of the correlation dimension

The BOYS algorithm for determining optimum matching rules

An algorithm is presented which searches, in a step-wise fashion, the optimum rules for linking records from two sources. The rules are optimum in the sense that they use a minimum number of variables which yield gross and net matching errors (bias) within the pre-specified maximum levels, i.e., the algorithm gives a Bias of the Order You Specify (BOYS).

Integrated circuit design for manufacturing through statistical simulation of process steps

The methodology, implementation, and results of a design for manufacturing (DFM) technique as applied to an integrated circuit boron base formation for an n-p-n transistor are presented. The primary purpose of the DFM technique is to achieve acceptable statistical prediction of the results by using the minimum number of variables and reducing the time required to perform physically based simulations. Excellent statistical results are achieved while the number of simulations is reduced by at least a factor of five if judicious statistical techniques are applied. >

Optimal Midterm Scheduling of a Large Scale Hydroelectric System by a Nonlinear Piece-wise Differentiable Network Algorithm

This paper is concerned with optimal midterm scheduling of large scale hydroelectric power systems. A suitable model for this problem with a minimum number of variables is developed, what leads to a problem of minimizing a particular nonlinear piecewise differentiable function of flows in a network. An algorithm tailored to deal efficiently with this problem is described. Special care is taken in order to guarantee convergence to a local optimal solution. The approach (model and algorithm) was aimed to solve the midterm scheduling problems for a huge coupled hydroelectric power system in Southeastern Brazil - this case study is discussed.

Temporal properties of some biological systems and their fractal attractors

In this paper we analyse time series data as the growth of organisms using markers such as treerings and otolith deposits (fish). The series studied belong to two tree species (Pinus uncinata, Fagus sylvatica) and one fish species (Dicentrarchus labrax). Spectral analyses of the time series growth show that the main frequencies of fluctuation may be due to variations of the energy input. However, any causal explanation must consider the internal continuous readjustment in the system as reported by the corresponding chaotic properties of the asymptotic decay of the spectra time structure. Since the output of noisy and chaotic systems tend to show similar spectral densities, an attempt to differentiate them has been carried out. The chaotic behaviour has been characterized by the study of the attractors. The dimmensions of these multiple topologies were 3.2 and 3.4 for the tree species and 2.3 for the fish species. Therefore, we are dealing with fractal attractors and the minimum number of variables that can be used to describe the systems are 4 and 3 respectively. It is suggested that some of the variables that most influence growth are those obtained by the response functions in the case of trees.

Classification of binary mass spectra of toxic compounds with an inductive expert system and comparison with SIMCA class modeling

The performance of an inexpensive, inductive rule-building expert shell system, based on the ID3 algorithm, was compared to that of SIMCA class modeling in classifying the binary mass spectra of 78 toxic and related compounds. The compressed mass spectra consisted of 17 masses chosen by using information theory. The expert rules verified the six main classes and two subclasses found with SIMCA class modeling. These classes were: all benzenes and all alkanes/ alkenes (alka(e)nes); nonhalobenzenes, chlorobenzenes, bromoalka(e)nes, and chloroalka(e)nes; and mono-, dichloroalka(e)nes and polychloroalka(e)nes. Training set classification accuracies obtained with the expert system were 93–100% as opposed to 62–98% for SIMCA. For 73 compounds, the expert rules gave a classification accuracy of 97–100% vs. 79–96% for SIMCA. Predictive accuracy for the four main classes was 78%. In general, fewer masses were involved with the rules than with the SIMCA models, and the rules are normally optimized with regard to minimum number of steps in the rule, not minimum number of variables. The expert rules work best with closed sets of objects where all possibilities can be included in the training sets. The expert rules represent planes partitioning the multidimensional measurement space (hypercube) into a subvolume nearest the SIMCA cylinders for an appropriate class. Overall, the performance of the expert system was very good.

Data consistency, yield and maintenance coefficient for the growth of Candida lypoytica and Pseudomonas aeruginosa on n-hexadecane

When more than the minimum number of variables are measured, and measurement error is taken into account, the results of parameter estimation depend on which of the measured variables are selected for this purpose. The reparameterization of Pirt's models for growth produces multiresponse models with common parameters. By using the covariate adjustment technique, a unit variate linear model with covariates is obtained. This allows a combined point and interval estimates of biomass energetic yield and maintenance coefficient to be obtained using standard multiple regression programmes. When this method was applied using form I and form II of the Pirt's models, good combined estimates were obtained and compared. Using data from the literature for Candida lipolytica produced reliable results. However, for Pseudomonas aeruginosa, which has been known to produce intermediate products, a modified Pirt's model is required for a good estimate of the biomass energetic yield.

On redundant variables in Lagrangian mechanics, with applications to perturbation theory and KS regularization

It is shown that it is possible to make a change of variables in a Lagrangian in such a way that the number of variables is increased. The Euler-Lagrange equations in the redundant variables are obtained in the standard way (without the use of Lagrange Multipliers!). These equations are not independent but they are all valid and consistent. In some cases they are simpler than if the minimum number of variables are used. The redundant variables are supposed to be related to each other by several constraints (not necessarily holonomic), but these constraints are not used in the derivation of the equations of motion. The method is illustrated with the well known Kustaanheimo-Stiefel Regularization. Some interesting applications to perturbation theory are also described.

An Iterative Technique for Determining the Minimal Number of Variables for a Totally Symmetric Function with Repeated Variables

Several analytic procedures exist for transforming a partially symmetric switching function to a totally symmetric switching function by judiciously repeating certain variables. Presumably the best totally symmetric representation for a given function would be the one having the fewest variables. This note presents an iterative technique for finding the totally symmetric realization for a given function that has the absolute minimum number of variables.

Integration of a semi‐implicit model with time‐dependent boundary conditions

Abstract A semi‐implicit barotropic primitive equations model is integrated over a limited area with time dependent boundary conditions using the standard mesh and a finer mesh. Following a theorem by Charney, a minimum number of variables are specified as boundary conditions for the limited area integrations in order to avoid mathematical over‐specification. The comparison of coarse mesh limited area forecasts with the corresponding forecasts made over a much larger domain demonstrates that the essential features, namely the Rossby type perturbations, are handled almost perfectly. The fine mesh forecasts over the same limited area are also very good. Finally, the effect of specifying inaccurate boundary conditions, in the form of twelve‐hour forecasts, is briefly illustrated.

15) Semantic Differential(意味微分)法による建物の色彩効果の測定

The purpose of this study is to measure the color effects of various rooms of buildings by the Semantic Differential Method. This measurement is the psychological "measurement" of the consolidated color effect of a room and is something like the physical measurement of "a color" to be composed of various colors of all the parts of a room. This requires some variables of pairs of adjectives which properly selected to represent the color effect, as the above physical measurement requires three variables, such as dominant wavelength, purity and luminous reflectance. In order to describe the color effect, we may be allow to use as many adjectives available as required. However it should be most desirable to minimize the number of adjectives to be used for the purpose of putting in order the adequate description of the color effect. Thus we intend to establish principles governing relation ships among those adjectives. And then we may be able to evaluate the color effect with combination of some pairs of rated adjectives. This should be a method to describe the characteristics which a room in question has in its consolidated color effect. And in near future we will know also the relation of the psychological color effect to the physical color of a room. At the first stage of the study, this paper is concerned with that with how many and what kind of adjectives the color effects are described and what is the minimum number of variables or dimensios describing them. The process of the experiments are as follows: 1) collecting many adjectives that can describe the color of the room. 2) selecting 30 pairs of adjectives, for instance warm-cold, old-new. 3) selecting 25 color photographs of various room, such as hospital's sick room, movie theatre lobbies. 4) making observers (students of university, both boys and girls) evaluate the 25 photographs by the 30 pairs of adjectives. 5) from the data obtained from the above experiment, calculating correlation matrix among those 30 pairs of adjectives, substituting correlation matrix with factor matrix, then deciding factors of meanings and their loadings. The fact is that the consolidated color effect of the room is described with five factors, that is dynamism, sensory pleasure, freshness, warmth and strength. The significance of this study is to point out the importance of factorsss of dynamism, freshness and warmth. So far the color effect has usually been appreciated only with a factor of sensory pleasure. The development of the method shall be treated separately at a later date.

Studies on the formation of composite complexes by means of an extractive technique

AbstractFor the interpretation of the data obtained on the extraction of metal complexes to organic solvents from aqueous solutions of low and constant ionic strength, the following minimum number of variables has to be considered: the concentrations of the metal atom (M), main ligand (the base A‐), HA, OH−, H2O, organic solvent molecules (Org) and the temperature. This has been done in an attempt to determine the compostion of the composite complexes of type MAn(OH)p(HA)r(Org)•(H2O)t formed in a given system.In this complex s and t can be determined only in special cases, and it is not possible to distinguish by equilibrium methods between isomers with the same values for x = n + r and y = n + p. These isomers can be represented by the formula M(HA)x(H)−y.It can be shown that in principal a distinction can be made between complexes of the type MAn, MAn(OH)p or MAn(OH)p(HA)r.A general method to calculate formation constants for the complex M(HA)x(H)−y from extraction data has been developed. It is also shown that from a comparison of the distribution ratios of the metal between water and several different organic solvents it is possible to determine if the metal forms a complex with the organic solvent molecules.The equations have been applied on the distribution of U(VI) and Th between several different organic solvents and water in the presence of acetylacetone.