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.     

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).     

Optimization of 1-Deoxynojirimycin Extraction from Mulberry Leaves by Using Response Surface Methodology

Mulberry 1-deoxynojirimycin (DNJ, a potent α-glycosidase inhibitor) has therapeutic potency against diabetes mellitus. However, the amount of DNJ in mulberry leaves is low (about 0.1%), and a more effective extraction method is needed. Ultrasound-assisted extraction (UAE) was applied in this study for mulberry DNJ extraction, and five factors, the percentage of ethanol in the extraction solvent (x ₁), ratio of the extraction solvent to mulberry sample (x ₂), ultrasonic power (x ₃), extraction temperature (x ₄) and extraction time (x ₅), were investigated by fractional factorial 2^(5-1) design (FFD) to obtain the optimum extraction efficiency (DNJ yield, Y ₁) and extraction productivity (total yield, Y ₂). The results showed that x ₂, x ₃ and x ₅ had significant impact on Y ₁ and Y ₂, and were further optimized by response surface methodology (RSM). Under the optimized conditions (x ₂, x ₃ and x ₅ of 7 ml/g, 180 W and 260 s, respectively), DNJ-enriched powder (0.8%) was produced with high extraction efficiency (98%) and productivity (20%), enabling this product to be used for nutraceutical purposes.     

Relationship between surplus energy and body weight in fish populations

This paper theoretically analyses the relationship between surplus energy, which is available for either somatic growth or reproduction, and body weight. From the data of metabolism and growth of the biwamasu, Oncorhynchus rhodurus, obtained by Miura et al., a Bernoulli's differential equation is induced to represent the relationship between body weight and the sum of surplus energy and active metabolic rate. Solving this equation gives the amount of surplus energy, f(W_x), as follows:f(W_x) = (αW_x^1−γ+β^1−γ)^1/(1−γ)−W_x, in which α, β and γ are constants and W_x is body weight at age x. The function is applied to ten fish populations and consequently it is found to be useful for a wider age range and a wider variety of fishes than the conventional function.     

No-escape regions and oscillations in second order predator-prey recurrences

We are concerned with the second order recurrence x _n+1 = x _n f(x _n, y _n), y _n+1 = y _n g(x _n, y _n), where n N ₀, x ₀ > 0, y ₀ > 0, and the reproduction rates f and g simulate predator-prey interaction. Under conditions on the sign of f – 1 and g–1 we show the existence of a nontrivial no-escape region D, i.e. a compact set D {(x, y): x > 0, y > 0} which is invariant under the recurrence and has the property that every sequence enters D after finitely many steps. Under further conditions on the shape of the isoclines {f = 1} and {g = 1} and on the stationary points {f = 1} {g = 1} we are able to show the existence of sustained oscillations.This work has been supported by the Deutsche Forschungsgemeinschaft     

Self‐recruitment in a Caribbean reef fish: a method for approximating dispersal kernels accounting for seascape

Characterizing patterns of larval dispersal is essential to understanding the ecological and evolutionary dynamics of marine metapopulations. Recent research has measured local dispersal within populations, but the development of marine dispersal kernels from empirical data remains a challenge. We propose a framework to move beyond point estimates of dispersal towards the approximation of a simple dispersal kernel, based on the hypothesis that the structure of the seascape is a primary predictor of realized dispersal patterns. Using the coral reef fish Elacatinus lori as a study organism, we use genetic parentage analysis to estimate self‐recruitment at a small spatial scale (<1 km). Next, we determine which simple kernel explains the observed self‐recruitment, given the influx of larvae from reef habitat patches in the seascape at a large spatial scale (up to 35 km). Finally, we complete parentage analyses at six additional sites to test for export from the focal site and compare these observed dispersal data within the metapopulation to the predicted dispersal kernel. We find 4.6% self‐recruitment (CI_95%: ±3.0%) in the focal population, which is explained by the exponential kernel y = 0.915^x (CI_95%: y = 0.865^x, y = 0.965^x), given the seascape. Additional parentage analyses showed low levels of export to nearby sites, and the best‐fit line through the observed dispersal proportions also revealed a declining function y = 0.77^x. This study lends direct support to the hypothesis that the probability of larval dispersal declines rapidly with distance in Atlantic gobies in continuously distributed habitat, just as it does in the Indo‐Pacific damselfishes in patchily distributed habitat.     

On the analysis of straight line data in pharmacology and biochemistry

The determination of drug potency, efficacy and receptor affinity constants, common calculations in pharmacology and biochemistry, require estimates of the slope and intercept of a linear regression line obtained from measured points (x_i, y_i). Three questions not explicitly covered in the basic statistical literature and, consequently, answered differently by scientists, arise often. (1) When there exist several y's corresponding to each value of the controlled parameter x, should all of these be used as points or only their average value at that x in constructing the line? (2) What are precise confidence limits of an abscissa corresponding to a specified ordinale? (3) What are confidence limits for the intercepts of a regression line whose slope is constrained to +1 or -1? In this paper we show that all the data should be used (question 1) and provide derivations for the formulas used to get the confidence limits mentioned in questions (2) and (3).     

Sequential Classification Based on Regression

Let us consider m general populations π₁, …,π_m. Each object belonging to these populations is represented by (p ± 1) characteristics x₁, x₂,…,x_p,y. A certain object, which is an element of one of the m general populations π₁,…,π_m has to be classified into the correct population. It will be assumed that knowledge of the value of the characteristic y would permit its correct classification, but that the observation of this characteristic is expensive, difficult or dangerous, as e.g. in medical applications. y is correlated with a set of p characteristics x₁,x₂,…,x_p, which are observed sequentially. The classification procedure is based on the division of the space of the observed value of characteristics x₁,x₂,…,x_p into nonintersecting areas determined so as to minimize the value of BAYES' risk given by equation (3).     

Production of S-adenosyl- L-methionine by a mutant strain of Kluyveromyces lactis

S-Adenosyl-l-methionine (AdoMet) was produced by a mutant strain Kluyveromyces lactis AM-65 grown on whey. A full factorial design method of three factors – (NH₄)₂SO₄ (factor x ₁), corn steep liquor (factor x ₂) and l-methionine (factor x ₃) on three levels – was used to determine the optimal medium conditions for the production of AdoMet. A time course shake-flask experiment in optimal whey medium (x ₁=3.1 g l^–1, x ₂=12.7 g l^–1, x ₃=4.6 g l^–1) was also carried out and the results confirmed the results of the factorial design and subsequent quadratic modelling and optimization of AdoMet production which reached 90 mg g^–1 cell dry wt.     

Robust One-Way ANOVA under Possibly Non-Regular Conditions

Consider the one-way ANOVA problem of comparing the means m₁, m₂, …, m_c of c distributions F₁(x) = F(x — m₁), …, F_c(x) = F(x — m_c). Solutions are available based on (i) normal-theory procedures, (ii) linear rank statistics and (iii) M-estimators. The above model presupposes that F₁, F₂, …, F_c have equal variances (= homoscedasticity). However practising statisticans content that homoscedasticity is often violated in practice. Hence a more realistic problem to consider is F₁(x) = F((x — m₁)/σ₁), …, F_c(x) = F((x — m_c)/σ_c), where F is symmetric about the origin and σ₁, …, σ_c are unknown and possibly unequal (= heteroscedasticity). Now we have to compare m₁, m₂, …, m_c. At present, nonparametric tests of the equality of m₁, m₂, …, m_c are available. However, simultaneous tests for paired comparisons and contrasts and do not seem to be available. This paper begins by proposing a solution applicable to both the homoscedastic and the heteroscedastic situations, assuming F to be symmetric. Then the assumptions of symmetry and the identical shapes of F₁, …, F_c are progressively relaxed and solutions are proposed for these cases as well. The procedures are all based on either the 15% trimmed means or the sample medians, whose quantiles are estimated by means of the bootstrap. Monte Carlo studies show that these procedures tend to be superior to the Wilcoxon procedure and Dunnett's normal theory procedure. A rigorous justification of the bootstrap is also presented. The methodology is illustrated by a comparison of mean effects of cocaine administration in pregnant female Sprague-Dawley rats, where skewness and heteroscedascity are known to be present.     

Water potential and gas exchange did not reflect performance of Pinus radiata D. Don in an agroforestry system under conditions of soil-water deficit in a temperate environment

In order to understand how radiata pines respond to declining supply of soil-water in agroforestry systems, we monitored water potential in xylem (ψ _x ), osmotic potential (ψ) and relative water content (q) for fascicles at pre-dawn and at mid-day for 3-year-old trees that were raised from either seedlings (Seedling) or from tissue culture (TC3 and TC4), and grown either alone (Control) or over lucerne (Medicago sativa) pasture (Lucerne). Water relations at dawn were mostly similar for all the pines, except late in the season when ψ was lower, bulk turgor pressure (P), deduced as the difference between ψ _x and ψ, was higher, for TC3 than for the other two pines. At mid-day, Seedling often had higher ψ _x and ψ, but because of its poor osmotic adjustment (OA) had lower P, than either TC3 or TC4. The cell walls were more elastic in Seedling with modulus of elasticity (e) of 6.5 MPa compared with 8.1 MPa for both TC3 and TC4, while loss of turgor was estimated to occur at ψ _x of −1.45 MPa for Seedling, −1.38 MPa for TC3 and −1.35 MPa for TC4. All trees irrespective of their origin had higher ψ _x , P, CO₂ assimilation (A), and stomatal conductance (g _s ), but lower ψ, in Control than in Lucerne in which the soil profile was consistently drier. The trends in ψ _x , ψ, q and A did not reflect the known differences in dry weight of trees, P was in the order TC3 > TC4 > Seedling, consistent with previously reported tree weights. Both TC3 and TC4 had higher P, due to their larger OA, than Seedling, although the latter had higher A. Thus ψ _x and A that are routinely measured may not always adequately explain differences in growth amongst pines; it is advisable that ψ be determined to allow deductions of P be made when using water relations to analyse plant growth.     

Evaluation of the maximum specific growth rate of a yeast indicating non-linear growth trends in batch culture

The maximum specific growth rate (μ_max) of an ethanolic D-xylose-fermenting yeast, Pichia stipitis, showing non-linear growth trends in batch culture, was calculated using the rate equation μ₂ = (1/Δt) ln(x ₂/x ₁). The absolute error Δμ, affecting μ₂, was derived using an equation given by Borzani (1994). Based on the assumption of linearity of growth curves between two closest time points, the relation between the two rate formulae, μ₁ = (1/xˉ)dx _t /dt and μ₂ = (1/Δt) ln(x ₂/x ₁) was established. In a particular condition, when μ₁ = μ₂, an equation has been developed, the roots of which are the specific growth rates at different time points. This revised version was published online in July 2006 with corrections to the Cover Date.     

Perturbation analysis of a two-locus model with directional selection and recombination

A population genetic two-locus model with additive, directional selection and recombination is considered. It is assumed that recombination is weaker than selection; i.e., the recombination parameter r is smaller than the selection coefficients. This assumption is appropriate for describing the effects of two-locus selection at the molecular level. The model is formulated in terms of ordinary differential equations (ODES) for the gamete frequencies x = (x ₁, x ₂, x ₃, x ₄), defined on the simplex S ₄. The ODEs are analyzed using first a regular pertubation technique. However, this approach yields satisfactory results only if r is very small relative to the selection coefficients and if the initial values x(0) are in the interior part of S ₄. To cope with this problem, a novel two-scale perturbation method is proposed which rests on the theory of averaging of vectorfields. It is demonstrated that the zeroth-order solution of this two-scale approach approximates the numerical solution of the model well, even if recombination rate is on the order of the selection coefficients.     

Genetic analysis of frost hardiness traits in tuber-bearingSolanum species

The inheritance of frost hardiness and cold acclimation potential traits was studied in three segregating populations derived from a cross betweenSolanum commersonii Dun. PI 243503 (cmm) andSolanum cardiophyllum Lindl., PI 184762 (cph), two parental genotypes with contrasting frost hardiness and cold acclimation potential. The levels of frost hardiness and cold acclimation potential were expressed as the LT₅₀, the temperature at which 50% of the cells in leaf discs were killed, as measured by the ion leakage method, following a controlled freeze test There was considerable variation in both frost hardiness and cold acclimation potential in all three segregating populations (F₁ F₁ xcmm, and F₁ xcph). Frost hardiness and cold acclimation potential were not correlated, suggesting that these two traits are under independent genetic control. The analysis of generation means indicated that the variation for both traits could be best explained by an additive-dominance model, with additive gene effects the most important Broad-sense heritability was 0.73 and 0.74 in the F₁ population, for frost hardiness and cold acclimation potential, respectively, and was 0.85 for either trait in the F₁ xcmm population, indicating that these two traits are highly inheritable. Our results suggest that it should be possible to incorporate the frost hardiness and cold acclimation traits from S.commersonii into cultivated potato species.     

A Strategy for Synthesis of Carbon Nitride Induced Chemically Doped 2D MXene for High‐Performance Supercapacitor Electrodes

A step‐by‐step strategy is reported for improving capacitance of supercapacitor electrodes by synthesizing nitrogen‐doped 2D Ti₂CT_x induced by polymeric carbon nitride (p‐C₃N₄), which simultaneously acts as a nitrogen source and intercalant. The NH₂CN (cyanamide) can form p‐C₃N₄ on the surface of Ti₂CT_x nanosheets by a condensation reaction at 500–700 °C. The p‐C₃N₄ and Ti₂CT_x complexes are then heat‐treated to obtain nitrogen‐doped Ti₂CT_x nanosheets. The triazine‐based p‐C₃N₄ decomposes above 700 °C; thus, the nitrogen species can be surely doped into the internal carbon layer and/or defect site of Ti₂CT_x nanosheets at 900 °C. The extended interlayer distance and c‐lattice parameters (c‐LPs of 28.66 Å) of Ti₂CT_x prove that the p‐C₃N₄ grown between layers delaminate the nanosheets of Ti₂CT_x during the doping process. Moreover, 15.48% nitrogen doping in Ti₂CT_x improves the electrochemical performance and energy storage ability. Due to the synergetic effect of delaminated structures and heteroatom compositions, N‐doped Ti₂CT_x shows excellent characteristics as an electrochemical capacitor electrode, such as perfectly rectangular cyclic voltammetry results (CVs, R² = 0.9999), high capacitance (327 F g^?1 at 1 A g^?1, increased by ≈140% over pristine‐Ti₂CT_x), and stable long cyclic performance (96.2% capacitance retention after 5000 cycles) at high current density (5 A g^?1).     

前期水淹对牛鞭草后期干旱胁迫光合生理响应的影响

水淹和干旱是限制植物生长的两种主要环境因子。三峡库区消落带由于其特殊的地形条件和人工水文节律,呈现以年度为周期的“水淹-落干”交替变化的水文变动特征,在消落带生长的植物因此受到水淹和干旱交替胁迫的双重影响。为了探究库区蓄水对消落带植被干旱耐受性的影响,以当年生牛鞭草扦插苗为试验对象,设置对照组(CK)、表土水淹组(SF)、全淹组(TF)、对照-干旱组(CD)、表土水淹-干旱组(SFD)、全淹-干旱组(TFD)6个处理组,研究不同水分处理对牛鞭草光合特性的影响。结果表明:(1)水淹和干旱胁迫均对牛鞭草光合特性造成显著影响;(2)水淹胁迫阶段,与CK组相比,牛鞭草SF和TF组净光合速率、气孔限制值和水分利用效率显著下降,胞间CO_2浓度显著上升;(3)干旱胁迫阶段,牛鞭草CD和SFD组净光合速率、气孔导度、胞间CO_2浓度和蒸腾速率等光合参数显著低于CK组,TFD组净光合速率、气孔导度、胞间CO_2浓度和蒸腾速率等指标与CK组无显著差异;(4)复水阶段,各处理组净光合速率、气孔导度、胞间CO_2浓度和蒸腾速率等指标均与CK组无显著差异。研究表明,前期水淹并未增加牛鞭草对后期干旱胁迫的敏感性,牛鞭草对水淹和干旱胁迫均具有较好的耐受性,有助于牛鞭草对库区消落带生境变化的适应性。     

真菌性鼻鼻窦炎发病相关因素及临床特征分析

目的:探究影响真菌性鼻鼻窦炎发病的有关因素,并分析其临床特征。方法:选取在我院就诊的150例真菌性鼻鼻窦炎患者及150例慢性鼻鼻窦炎患者,回顾性分析2组患者的临床资料,将两者进行对照研究,通过多因素Logistic回归分析和检验的方法,对患者的术前资料进行分析,进而探讨影响真菌性鼻鼻窦炎发病的因素及其临床特征。通过真菌特异性六胺银染色的方法,对150例真菌性鼻鼻窦炎患者进行分型。结果:以年龄(x_1)、病程(x_2)、涕血(x_3)、头痛(x_4)、单侧或双侧病变(x_5)和钙化斑(x_6)为变量,获得了真菌性鼻鼻窦炎发病的Logistic回归预测方程:y=-8.714+1.201 x_1+0.497 x_2+4.576 x_3+1.188 x_4+2.697x_5+4.118 x_6,P=exp(y)/[1+exp(y)]。与慢性鼻鼻窦炎的发病情况对比,发现真菌性鼻鼻窦炎的发生多位女性患者,年龄在40岁以上,病程在3年以内,主要症状为头痛和涕血,影像学检查有单侧病变,且有钙化斑出现(P0.05)。在150例真菌性鼻鼻窦炎患者中,慢性侵袭性46例,非侵袭性104例。结论:真菌性鼻鼻窦炎的发病可以通过其相关因素的Logistic回归预测方程进行预测,其临床表现有明显的特征性。     

Effect of a denture cleanser on the concentration of volatile sulphur compounds and denture biofilm in institutionalised elderly

doi:10.1111/j.1741‐2358.2009.00341.x
Effect of a denture cleanser on the concentration of volatile sulphur compounds and denture biofilm in institutionalised elderly Objective: To determine the effectiveness of a denture cleanser in reducing the concentration of volatile sulphur compounds (VSC) and its antimicrobial action. Background: Micro‐organisms from the denture biofilm can cause local and systemic disease and halitosis. Denture cleansers are important adjuncts in oral care, but there is limited investigation on their effect in malodour compounds. Material and methods: Nineteen institutionalised elderly who wore at least an upper denture were selected; their VSC concentrations were measured and the denture biofilm was collected. In phase 1, the subjects wore their old denture and data were collected before (B₀) and after 7(A₁), 14(A₂), 28(A₃) days of continuous daily use of the denture cleanser. In phase 2, new dentures were inserted and measurements were made at 30(A_1.1), 60(A_2.2), 90(A_3.3) days of treatment. Results: The VSC concentration increased from B₀ to A₁ (p < 0.05)_, but no differences were found for the others intervals of times. Total micro‐organism data did not show a statistical difference between times in Phase I, but in Phase II, there was a statistical difference (p < 0.05) and a progressive re‐colonisation was observed. Conclusion: Within the limits of this study, it was concluded that the denture cleanser had no antimicrobial effect and VSC levels were not reduced.     

A Semiparametric Estimator of the Crossing Point in the Two‐Sample Linear Shift Function: Application to Crossing Lifetime Distributions

Let X and Y be two random variables with continuous distribution functions F and G. Consider two independent observations X₁, … , X_m from F and Y₁, … , Y_n from G. Moreover, suppose there exists a unique x* such that F(x) > G(x) for x < x* and F(x) < G(x) for x > x* or vice versa. A semiparametric model with a linear shift function (Doksum, 1974) that is equivalent to a location‐scale model (Hsieh, 1995) will be assumed and an empirical process approach (Hsieh, 1995) is used to estimate the parameters of the shift function. Then, the estimated shift function is set to zero, and the solution is defined to be an estimate of the crossing‐point x*. An approximate confidence band of the linear shift function at the crossing‐point x* is also presented, which is inverted to yield an approximate confidence interval for the crossing‐point. Finally, the lifetime of guinea pigs in days observed in a treatment‐control experiment in Bjerkedal (1960) is used to demonstrate our procedure for estimating the crossing‐point. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)