Optimal Fixing of the Bandwidth-Parameter for the Empirical Regression1,2

The estimator ?₀(x) of the regression r(x) = E (Y | × = x) from measured points (x_i, y_i), i = 1(1) n, of a continuous two-dimensional random variable (X, Y) with unknown continuous density function f(x, y) and with moments up to the second order can be made with the help of a density estimation f?₀(x, y) (see e.g. SCHMERLING and PEIL, 1980). Here f?₀(x, y) still contains free parameters (so-called band-width-parameters), the values of which have to be optimally fixed in the concrete case. This fixing can be done by using a modification of the maximum-likelihood principle including jackknife techniques. The parameter values can be also found from the estimators for r(x). Here the cross-validation principle can be applied. Some numerical aspects of these possibilities for optimally fixing the bandwidth-parameter are discussed by means of examples. If ?₀(x) is used as a smoothing operator for time series the optimal choice of the parameter values is dependent on the purpose of application of the smoothed time series. The fixing will then be done by considering the so-called filter-characteristic of ?C₀(x).     

Diminished Confidence Levels in the Interval Estimation of an Unknown Regressor in Model I of Linear Regression

For the model y=β₀ + β₁ x + e (model I of linear regression) in the literature confidence estimators of an unknown position x₀ are given at which either the expectation of y is given (see FIELLER, 1944; FINNEY, 1952), or realizations of y are given (see GRAYBILL, 1961). These confidence regions with level 1—α need not be intervals. The occurrence of interval shape is a random event. Its probability is equal to the power of the t test for the examination of the hypothesis H: β₁ = 0. The papers mentioned above claim to provide confidence intervals with level 1 ? α. But because of the restriction of (1 —α)—confidence regions to intervals the true confidence probability is the conditional probability W_c: W_c = P (the confidence region covers x₀| the region has interval shape). Here this conditional probability is shown to be less than 1 —α. Evidence on the possible deviations from 1 —α has been obtained by simulations.     

Radioligand assays — Methods and applications. IV. Uniform regression of hyperbolic and linear radioimmunoassay calibration curves

In order to handle all types of radioimmunoassay (RIA) calibration curves obtained in our laboratory in the same way, we tried to find a non-linear expression for their regression which allows calibration curves with different degrees of curvature to be fitted. Considering the two boundary cases of the incubation protocol we derived a hyperbolic inverse regression function: x = a₁ya₀ + a_?1y^?1, where x is the total concentration of antigen, a_i constants, and y is the specifically bound radioactivity. An RIA evaluation procedure based on this function is described providing a fitted inverse RIA calibration curve and some statistical quality parameters. The latter are on an order which is normal for RIA systems. There is an excellent agreement between fitted and experimentally obtained calibration curves having a different degree of curvature.     

Remarks upon Empirical Regression Belt

In the presented paper the method of the empirical regression belt is demonstrated. An empirical regression curve r(x), which is determined by the realizations (measured points) (x₁, y₁), i = 1,…., n of a continuous two-dimensional random variable (X, Y), is enclosed by a belt, the local width of which varies dependent on local frequency and variance of the measured points. This empirical regression belt yields certain information for evaluating the empirical regression curve, providing a useful basis for the biomathematical forming of a model. By giving three examples derived from morphometrics the authors discuss important qualities of the empirical regression belt.     

A confidence interval for the unknown value of the regressor with given expectation of the regressand in model I of linear regression

In the case of model I of linear regression there is derived a confidence interval for that x_o where the “true line” will reach a given value y_o. The interval can be given by the intersections between the line y = y_o and the hyperbolas providing pointwise confidence intervals of the expectations of y.     

A Further Problem of Interval Estimation of an Unknown Regressor in Model I of Linear Regression

For the model y = α + βx + ? (model I) of linear regression we dealt with in KUHNERT and HORN (1980) the determination of a confidence interval for that x₀ where the expectation Ey reaches a given value y₀. Here we start with realizations of random variables y (i = 1,…, m) being independent of x which are given in addition to the realizations of-y. Now y₀ denotes the unknown value of \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \sum \limits_{i = 1}^m $\end{document} ciEy and x₀ the x-value where the expectation Ey reaches that value y₀. For this x₀ we give a confidence interval. Applications stem from dose response assays.     

Empirical regression as a conditional expected value of a special distribution-mixture for a modelfree quantitative recording of stochastical relations

An “empirical” distribution function F?(x, y) is estimated from measured points (xi, yi), i =1(1)n, of a continuous two-dimensional random variable (X, Y) with unknown continuous density function f(x, y). The density function F?(x, y) of F?(x, y) is a mixture of n two-dimensional normal densities. The first order moments of F?(x, y) are the sample means x and y, whilst the second order moments are only proportional to the sample variances and the sample covariance. This “empirical” distribution F?(x, y) is used for evaluation of an empirical regression curve where a free parameter has to be fixed by an optimality criterion. The procedure is demonstrated by an example from morphometrical research.     

Heme complexes of rabbit hemopexin,human hemopexin and human serum albumin: Electron spin resonance and Mőssbauer spectroscopic studies

The electron spin resonance (ESR) spectra of human and rabbit ferriheme-hemopexin complexes at 30^oK show an ESR absorption characterized by g_x = 1.60, g_y = 2.25 and g_z = 2.86, characteristic of low-spin ferriheme-proteins. The low-spin nature of the heme-iron in heme-hemopexin is corroborated by the observation of nuclear hyperfine splitting in M?ssbauer spectra at 4.2^oK. The similarity of the ESR spectra of ferriheme-hemopexin with those of low-spin cytochromes which coordinate heme via two histidine residues points to a similar coordination mechanism in hemopexin. In contrast, the ESR spectra of the 1:1 and 2:1 complexes of heme with human serum albumin display signals at g = 6.0 and g = 2.0, characteristic of high-spin ferrihemeproteins.     

一种模型模拟结果的统计检验方法

模拟结果的准确性是衡量生态学模型是否成功的关键,但采用统计学方法判别模型模拟结果与观察值相符程度的报道较少。根据两个直线回归方程能否合并为一个方程的统计学检验方法,提出了通过检验观察值与模拟值直线回归方程和1∶1直线方程截距与斜率是否相同,进而在统计显著水平上判断生态学模型模拟值与观察值一致性的统计学检验方法。数据检验表明,此方法可以较好解决判断生态学模型模拟结果准确性的问题。     

Microbial biomass on particulate organic matter in seawater of the euphotic zone

Microbial biomass on suspended organic matter in seawater of the euphotic zone of Saanich Inlet was investigated. The viable microorganisms were measured by the glucose-uptake method. Microbial carbon on particulate organic matter in seawater was determined to be, on the average, 9.9 μg of C/liter, and there was a regression relationship as y = 0.0062 x − 1.79 with an unbiased variance V_yx^1/2 = 0.38, where x = particulate organic carbon in seawater (micrograms of C/liter) and y = logarithm of microbial carbon (micrograms of C/liter).     

On a Class of Almost Unbiased Ratio Estimators

A class of almost unbiased ratio estimators for population mean σ is derived by weighting sample σ = (1/n) σ y_i, ratio estimators σ and an estimator, σ (y_i/x_i). It is shown that NIETO DE PASCUAL (1961) estimator is a particular member of the class and an optimum estimator in the class (in the minimum variance sense) is identified. The results are illustrated through two numerical examples.     

Activation of phosphates to substitution(II). A comparison of catalyses initiated directly by VO2+ and by oxidation of VO2+ by MnO4−

Vanadium(V)-induced hydrolyses of triphosphates in aqueous solutions were initiated in two ways: (1) oxidizing vanadium(IV)-polyphosphate complexes to produce metastable vanadium(V) complexes; (2) forming VO₂⁺-polyphosphate complexes by acidification of solutions of VO₄^3? and polyphosphate to yield equilibrium mixtures of V(V), polyphosphate, and their complexes. Hydrolysis rates for the complexes formed at 40°C ? T ? 25°C follow the order V₂PPP_i = 2(VPPP_i) ≌ (VO₂) ATP ? V(PPP_i)₂ ≌ PPP_i. The hydrolysis of (V(V))₂(PPP_i) was not very temperature sensitive; the activation enthalpy appears small and the activation entropy large and negative. Mechanistic studies reveal that requirements for the activated state in metal-ion-catalyzed hydrolysis of polyphosphates include monodentate polyphosphate ligated cis to H₂O or OH^? in the coordination sphere of the metal ion:

     

Improved method for measuring the apparent CO2 photocompensation point resolves the impact of multiple internal conductances to CO2 to net gas exchange

There is a growing interest in accurate and comparable measurements of the CO₂ photocompensation point (Γ*), a vital parameter to model leaf photosynthesis. The Γ* is measured as the common intersection of several CO₂ response curves, but this method may incorrectly estimate Γ* by using linear fits to extrapolate curvilinear responses and single conductances to convert intercellular photocompensation points (C_i*) to chloroplastic Γ*. To determine the magnitude and minimize the impact of these artefacts on Γ* determinations, we used a combination of meta‐analysis, modelling and original measurements to develop a framework to accurately determine C_i*. Our modelling indicated that the impact of using linear fits could be minimized based on the measurement CO₂ range. We also propose a novel method of analysing common intersection measurements using slope–intercept regression. Our modelling indicated that slope–intercept regression is a robust analytical tool that can help determine if a measurement is biased because of multiple internal conductances to CO₂. Application of slope–intercept regression to Nicotiana tabacum and Glycine max revealed that multiple conductances likely have little impact to C_i* measurements in these species. These findings present a robust and easy to apply protocol to help resolve key questions concerning CO₂ conductance through leaves.     

Fluorescence properties of the light-harvesting bacteriochlorophyll protein from Rhodopseudomonas sphaeroides R-26

The light-harvesting bacteriochlorophyll-protein (BChl-protein) from Rhodopseudomonas sphaeroides, R-26 mutant, exhibits a strong optical absorption peak near 850 nm (Q_y band) and a weaker peak at 590 nm (Q_x band). This pigment-protein appears to contain two BChl molecules per subunit, and previous circular dichroism studies indicated the presence of excitonic interactions between the BChl molecules. The complex exhibits a fluorescence maximum near 870 nm at room temperature. Excitation in the Q_y region results in polarization p values that vary only from +0.12 at 820 nm to +0.14 near 900 nm. These values are appreciably smaller than that for monomeric BChl in viscous solvents (p > 0.4). By contrast, using Q_x excitation the p value is ?0.25 for the BChl-protein complex, which is close to that observed for the BChl monomer. For the BChl-protein these polarization values do not change greatly at a temperature of 90 K; however, the Stokes' shift of the fluorescence emission increases significantly over that at room temperature.     

Evolution of dissipative system: a theoretical basis of Margalef's principle on ecosystem

The concepts of fitness and survival in logistic models are shown to be independent if we follow certain intuitive definitions for these concepts. This conclusion follows from a simple topological analysis of the function f_b (x) = bx (1?x), which is just the standard form of the logistic growth equations.     

Kinetic analysis of the growth of Spirulina sp. in batch culture

Batch cultivation of Spirulina sp. was carried out under limited light at 30°C in the pH range of 9.2 to 9.7. The specific growth rate D was calculated from the tangent of the growth curve and the cell concentration at that time, and the amount of light energy absorbed per unit time per unit cell weight (E_x), namely, the specific absorption rate of light energy, was also calculated from the total amount of radiant flux of transmitted light at the surface of the culture vessel and cell concentration of the culture solution. A plot against E_x of D in the linear growth phase in batch culture and at various phases in continuous culture gave, for E_x of less than 1.0 kcal/g·h, points scattered near a straight line with slope m 0.037 g/kcal and an intercept on the ordinate, −b, of −0.0046 h⁻¹, and, for higher E_x values, points scattered near a curve of gradually decreasing slope which tended to approach a constant value.A Lineweaver-Burk plot of the reciprocal of D plus b against that of E_x yielded an equation for the growth rate which represented well the growth curve in batch culture. This equation also expressed the linear increase of D with increase of E_x at high cell concentration in the culture solution. The relation between cell growth rate and cell fluidity is discussed by use of a vector equation obtained by applying this relation to a culture solution contained in a given closed surface.     

Some Early Developments in Ratio Estimation

John Graunt (1662) was the first to estimate the ratio y/x where y represents the total population and x the known total number of registered births in the same areas during the preceding year. About 1765 Messance (Stephan, 1948) and Moheau (1778) published very carefully prepared estimates for France based on enumeration of population in certain districts and on the count of births, deaths and marriages as reported for the whole country. The districts from which the ratio of inhabitants to birth was determined only constituted a sample. Laplace (1786) prepared similar estimates in 1802 based on a two-stage sampling plan. Recently Hansen and Hurwitz (1943) showed that the ratio estimate (y_i/n_i)X of Y is unbiased where all x_i's are known and the n^th cluster is selected with p.p.s. More recently Hájek (1949), Lahiri (1951), Midzuno (1952) and Sen (1952) developed independently the sampling of n clusters with p.p.s to the totals of the sizes of the sample clusters S(x_i). Des Raj (1954) and Sen (1952, 1953) gave unbiased estimate of the variance of the estimator which was generally non-negative for samples with smaller probabilities. Rao and Vijayan (1977) gave an unbiased estimator which is non-negative for samples with larger probabilities. Hájek (1949) provided an almost unbiased estimator of the variance of the estimator. The paper discusses situations where Hájek's estimator of variance should be preferred to the Rao-Vijayan estimator and vice versa.     

The qualitative analysis of a difference equation of population growth

The difference equation f _b :[0,1]–[0,1] defined by f _b (x)=b x(1–x) is studied. In particular complete qualitative information is obtained for the parameter value b=3.83. For example the number of fixed points of (f _b )ⁱ is given by

Novel naphthyloxy derivatives – Potent histamine H3 receptor ligands. Synthesis and pharmacological evaluation

A series of 1- and 2-naphthyloxy derivatives were synthesized and evaluated for histamine H₃ receptor affinity. Most compounds showed high affinities with K_i values below 100?nM. The most potent ligand, 1-(5-(naphthalen-1-yloxy)pentyl)azepane (11) displayed high affinity for the histamine H₃ receptor with a K_i value of 21.9?nM. The antagonist behaviour of 11 was confirmed both in vitro in the cAMP assay (IC₅₀?=?312?nM) and in vivo in the rat dipsogenia model (ED₅₀?=?3.68?nM). Moreover, compound 11 showed positive effects on scopolamine induced-memory deficits in mice (at doses of 10 and 15?mg/kg) and an analgesic effect in the formalin test in mice with ED₅₀?=?30.6?mg/kg (early phase) and ED₅₀?=?20.8?mg/kg (late phase). Another interesting compound, 1-(5-(Naphthalen-1-yloxy)pentyl)piperidine (13; H₃R K_i?=?53.9?nM), was accepted for Anticonvulsant Screening Program at the National Institute of Neurological Disorders and Stroke/National Institute of Health (Rockville, USA). The screening was performed in the maximal electroshock seizure (MES), the subcutaneous pentylenetetrazole (scPTZ) and the 6-Hz psychomotor animal models of epilepsy. Neurologic deficit was evaluated by the rotarod test. Compound 13 inhibited convulsions induced by the MES with ED₅₀ of 19.2?mg/kg (mice, i.p.), 17.8 (rats, i.p.), and 78.1 (rats, p.o.). Moreover, 13 displayed protection against the 6-Hz psychomotor seizures (32?mA) in mice (i.p.) with ED₅₀ of 33.1?mg/kg and (44?mA) ED₅₀ of 57.2?mg/kg.Furthermore, compounds 11 and 13 showed in vitro weak influence on viability of tested cell lines (normal HEK293, neuroblastoma IMR-32, hepatoma HEPG2), weak inhibition of CYP3A4 activity, and no mutagenicity. Thus, these compounds may be used as leads in a further search for histamine H₃ receptor ligands with promising in vitro and in vivo activity.