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)     

A New Functional Equation Analogous to CAUCHT-PEXIDER Functional Equation and its Application

The CAUCHY-PEXIDER functional equation H (x±y)=F(x) G(y) is generalized to the form H ((x^c±y^c)^1/c) = F(x) G(y), c≠0, assuming the function H(x) possesses a measurable majorant on a set of positive measure. The result is used to obtain a characterization of WEIBULL distribution. This functional equation is generalized to functions of vector variables.     

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).     

Photosynthesis performance in sweet almond [<Emphasis Type="Italic">Prunus dulcis</Emphasis> (Mill) D. Webb] exposed to supplemental UV-B radiation

Due to anthropogenic influences, solar UV-B irradiance at the earth’s surface is increasing. To determine the effects of enhanced UV-B radiation on photosynthetic characteristics of Prunus dulcis, two-year-old seedlings of the species were submitted to four levels of UV-B stress, namely 0 (UV-B_c), 4.42 (UV-B₁), 7.32 (UV-B₂) and 9.36 (UV-B₃) kJ m⁻² d⁻¹. Effects of UV-B stress on a range of chlorophyll (Chl) fluorescence parameters (FPs), Chl contents and photosynthetic gas-exchange parameters were investigated. UV-B stress promoted an increase in minimal fluorescence of dark-adapted state (F₀) and F₀/F_m, and a decrease in variable fluorescence (F_v, F_v/F_m, F_v/F₀ and F₀/F_m) due to its adverse effects on photosystem II (PSII) activity. No significant change was observed for maximal fluorescence of dark-adapted state (F_m). Enhanced UV-B radiation caused a significant inhibition of net photosynthetic rate (P _N) at UV-B₂ and UV-B₃ levels and this was accompanied by a reduction in stomatal conductance (g _s) and transpiration rate (E). The contents of Chl a, b, and total Chl content (a+b) were also significantly reduced at increased UV-B stress. In general, adverse UV-B effects became significant at the highest tested radiation dose 9.36 kJ m⁻² d⁻¹. The most sensitive indicators for UV-B stress were F_v/F₀, Chl a content and P _N. Significant P<0.05 alteration in these parameters was found indicating the drastic effect of UV-B radiation on P. dulcis.     

Purification and Subsite Affinities of exo-lnulinase from Penicillium trzebinskii

An exo-inulinase was highly purified from the culture broth of Penicillium trzebinskii by anion exchange, hydrophobic, and gel filtration chromatographies. The enzyme was homogeneous by disc electrophoresis. The molecular weight was 8.7 × 10⁴, and the isoelectric point was pH 4.3. The enzyme hydrolyzed not only inulin and sucrose but also inulooligosaccharides [1^F(1-β-D-fructofuranosyl)_n-1fructose, F_n (n= 2—5)] and fructooligosaccharides [1^F(1-β-D-fructofuranosyl)_n-1 sucrose, GF_n, (n = 2—8)] liberating the nonreducing terminal fructose of the substrates. The substrate specificity was investigated. The K_m (mM) and k_o (sec^?1were: inulin, 0.042 and 159; sucrose, 6.5 and 169; F₂, 2.1 and 62.8; F₃, 0.40 and 126; F₄, 0.47 and 171; and F₅, 0.47 and 131, respectively. Dependence of K_m and k_o values on the degree of polymerization of substrates was observed. The subsite affinities in the active site were 1.05, 4.57, 1.45, 0.09, and — 0.16kcal/mol for subsite 1, 2, 3, 4, and 5, respectively.     

Solution properties of synthetic polypeptides. XII. Enthalpy changes accompanying helix-coil transition of polypeptide

For helix-coil transitions of polypeptide in binary mixtures consisting of helix-forming solvent and coil solvent, the transition enthalpy ΔH(T,x) has been found to depend significantly on temperature (T) and solvent composition (x). For such systems, calorimetric measurements may yield some averages of ΔH(T,x) which are no longer amenable to direct comparison with ΔH itself. Theoretical equations relating calorimetric data to ΔH(T,x) are derived and tested favorably with experimental data. It is demonstrated that the transition enthaply from heat capacity measurements is approximately equal to ΔH_cfm, while those from heat of dilution and heat of solution measurements are equal to ΔH_c. Here ΔH_c denotes the value of ΔH at the transition point and f_m represents the maximum helical content attained in a thermally induced transition. The discrepancies among calorimetric data are also discussed.     

Characterization of the WEIBULL Distribution by Properties of Order Statistics

Let X_1:n, X_2:n, X_3:n…, X_n:n be the order statistics of n independent random variables with the common (absolutely continuous strictly increasing) distribution function F. The main results given in this article are:

• 1 For any fixed r and two distinct numbers s₁ and s₂ (1<r<s₁<s₂≦n) the distributions of V_i and W_i (defined in (1.11) and (1.12) are identical for i = 1,2 iff F(x) is WEIBULL (1.2).
• 2 The statistics D₁ and D₂ (as in (1.8) and (1.9)) are independent iff F(x) is WEIBULL (1.2).
• 3 The statistics U_i (1≦j≦n?1) and X_i:n (i ≦ j) are independent iff F(x) is WEIBULL (1.2).
• 4 Let X, X₁, X₂, …, X_k be random variables such that

These conditions are necessary and sufficient for F(x) to be WEIBULL .     

An Unbalanced Nested Model with Random Effects Having Unequal Variances

Consider the model Y_ijk=μ + a_i + b_ij + e_ijk (i=1, 2,…, t; j=1,2,…, B_i; k=1,2…,n_ij), where μ is a constant and a¹,b_ij and e_ijk are distributed independently and normally with zero means and variances σ²_ad_ij and σ², respectively, where it is assumed that the d_i's and d_ij's are known. In this paper procedures for estimating the variance components (σ², σ²_a and σ²_b) and for testing the hypothesis σ²_b = 0 and σ²_a = 0 are presented. In the last section the mixed model y_ijk, where x_ijkkm are known constants and β_m's are unknown fixed effects (m = 1, 2,…,p), is transformed to a fixed effect model with equal variances so that least squares theory can be used to draw inferences about the β_m's.     

Some Theorems Concerning Characterization of the WEIBULL Distribution

This paper presents a number of characterizations of the WEIBULL distribution. Some of these results are generalizations of the corresponding results for the exponential distribution. Some characterizing properties lead to a functional equation f(x) · f(y) = f((x^c+y^c)^i/c) which is analogous to the CAUCHY functional equation. While the first two characterizations assume somewhat less accessible information concerning the probability distribution, the third and fourth require more readily available information regarding the expected values.     

Circularly polarized luminescence of Eu(III) complexes with chiral 1,1′-bi-2-naphtol-derived bisphosphate ligands

The interest for lanthanide circularly polarized luminescence (CPL) has been quickly growing for 10 years. However, very few of these studies have involved correlation between the dissymmetry factor (g_lum) and the chemical modifications in a series of chiral ligands. Four polymeric compounds of Eu(III) were prepared by using a series of binaphtyl derivatives for which the size of the π system as well as the number of stereogenic elements (i.e., the binaphtyl moiety) are modulated. The resulting {[Eu(hfac)₃((S)/(R)-L^x)]}_n (x = 1 and 3) and {[Eu(hfac)₃((S,S,S)/(R,R,R)-L^x)]}_n (x = 2 and 4) have been characterized by powder X-ray diffraction by comparison with the X-ray structures on single crystal of the Dy(III) analogs. In solution, the structure of the complexes is deeply modified and becomes monomeric. The nature of the ligand induces change in the shape of the CPL spectra in CH₂Cl₂ solution. Furthermore, a large |g_lum| = 0.12 of the magnetic-dipole transition for the [Eu(hfac)₃((S,S,S)/(R,R,R)-L²)] complex involving the ligand with three stereogenic elements and an extended ?? system has been measured. This report also shows CPL measurements in solid state for the series of {[Eu(hfac)₃((S)/(R)-L^x)]}_n (x = 1 and 3) and {[Eu(hfac)₃((S,S,S)/(R,R,R)-L^x)]}_n (x = 2 and 4) polymers.     

Photoinhibition and xanthophyll cycle activity in bayberry (Myrica rubra) leaves induced by high irradiance

The effect of high irradiance (HI, photosynthetically active photon flux density of 1 300 μmol m⁻² s⁻¹) on net photosynthetic rate (P _N), chlorophyll fluorescence parameters, and xanthophyll cycle components were studied in fruit tree bayberry leaves. HI induced the photoinhibition and inactivation of photosystem 2 (PS2) reaction centres (RCs), which was characterized by decreased P _N, maximum yield of fluorescence after dark adaptation (F_m), photochemical efficiency of PS2 (F_v/F_m) and quantum yield of PS2 (Φ_PS2), and increased reduction state of Q_A (1-q_P) and non-photochemical quenching (NPQ). Initial fluorescence (F₀) showed a decrease after the first 2 h, and subsequently increased from the third hour exposure to HI. Furthermore, a greater increase in the ratio (F_i-F₀)/(F_p-F₀) which is an expression of the proportion of the Q_B non-reducing PS2 centres, whereas a remarked decrease in the slope of F_i to F_p which represents the rate of Q_A reduction was observed in leaves after HI exposure. Additionally, HI caused an increase in the pool size of the xanthophyll cycle pigments and sustained elevated contents of zeaxanthin (Z), antheraxanthin (A), and de-epoxidation state (DES) at the end of the irradiation period. During HI, decreased F_m, F_v/F_m, Φ_PS2, NPQ, slope of F_i to F_p, V+A+Z, and DES, and increased F₀, 1-q_P, ratio (F_i-F₀)/(F_p-F₀), and V were observed in dithiothreitol (DTT)-fed leaves compared to control ones under the same conditions. Hence photoinhibition caused by HI in bayberry was probably attributed to inactivation of PS2 RCs, and photoprotection from photodamage were mainly related to the xanthophyll cycle-dependent heat dissipation in excess photons.     

DYNAMICS OF ARBUSCULE DEVELOPMENT AND DEGENERATION IN A ZEA MAYS MYCORRHIZA

A quantitative light and electron microscope study of developing and degenerating mycorrhizal arbuscules of Glomus fasciculatum in Zea mays was carried out in order to estimate three parameters during the colonization cycle. These were: 1) V_v(f,c), the fraction of the host cell volume occupied by a volume of fungus; 2) V_v(cy,c), the fraction of the host cell volume occupied by host cytoplasm; 3) S_v(pr,c), the surface-area-to-volume ratio of the host protoplast to the whole host cell. Uninfected cortical cells had an S_v(pr,c) of 0.13 μm²/μm³. As the fungus penetrates the cell wall, the protoplast invaginates, causing a decrease in protoplast volume and an increase in protoplast S_v. The S_v(pr,c) of a cell containing a mature arbuscule is 1.275 μm²/μm³. Because of the shrinkage of the protoplast, the S_v of the protoplast to its own volume rather than the original cell volume is 2.55 μm²/μm³, or almost a 20-fold increase. Total cell size is unaffected. When the arbuscule is mature, the fungus occupies 42% of the cell, with 24% as 1-μm-diam branches, and 18% as trunk. Arbuscular branch formation progresses at a linear rate and is the most important factor in causing the increased host S_v. The correlation coefficient for V_v(br,c) the volume fraction for arbuscular branches, vs. Sv(pr,c) is r = 0.932 (P < 0.001). Degeneration of the arbuscule is marked by a rapid decrease in branches, host S_v, and host cytoplasm. The trunk develops and degenerates at a slower rate than the branches.     

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.     

Chlorophyll fluorescence performance of sweet almond [Prunus dulcis (Miller) D. Webb] in response to salinity stress induced by NaCl

One-year old sweet almond (Prunus dulcis) seedlings were submitted to four levels of salt stress induced by NaCl, namely 0.3, 0.5, 0.7, and 1.0 S m⁻¹. Effects of salt stress on a range of chlorophyll (Chl) fluorescence parameters (Chl FPs) and Chl contents were investigated in order to establish an eco-physiological characterization of P. dulcis to salinity. Salt stress promoted an increase in F₀, F_s, and F₀/F_m and a decrease in F_m, F′_m, F_v/F_m, q_P, ΔF/F′_m, F_v/F₀, and UQF_(rel), in almost all Chl fluorescence yields (FY) and FPs due to its adverse effect on activity of photosystem 2. No significant changes were observed for quenchings q_N, NPQ, and q_N(rel). The contents of Chl a and b and their ratio were also significantly reduced at increased salt stress. In general, adverse salinity effects became significant when the electric conductivity of the nutrient solution (EC_n) exceeded 0.3 S m⁻¹. The most sensitive salt stress indicators were F_v/F₀ and Chl a content, and they are thus best used for early salt detection in P. dulcis. Monitoring of a simple Chl FY, such as F₀, also gave a good indication of induced salt stress due to the significant correlations observed between the different Chl FYs and FPs. Even essential Chl FYs, like F₀, F_m, F′_m, and F_s, and mutually independent Chl FPs, like F_v/F₀ and q_P, were strongly correlated with each other.     

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).     

Interactions of Elevated CO2 Concentration and Drought Stress on Photosynthesis in Eucalyptus Cladocalyx F. Muell

Response of net photosynthetic rate (P _N), stomatal conductance (g _s), intercellular CO₂ concentration (c _i), and photosynthetic efficiency (F_v/F_m) of photosystem 2 (PS2) was assessed in Eucalyptus cladocalyx grown for long duration at 800 (C₈₀₀) or 380 (C₃₈₀) μmol mol^-1 CO₂ concentration under sufficient water supply or under water stress. The well-watered plants at C₈₀₀ showed a 2.2 fold enhancement of P _N without any change in g _s. Under both C₈₀₀ and C₃₈₀, water stress decreased P _N and g _s significantly without any substantial reduction of c _i, suggesting that both stomatal and non-stomatal factors regulated P _N. However, the photosynthetic efficiency of PS2 was not altered. This revised version was published online in June 2006 with corrections to the Cover Date.     

The Estimation of a Multivariate Fitness Function from Several Samples Taken from a Population

The situation is considered where the multivariate distribution of certain variables X₁, X₂, …, X_p is changing with time in a population because natural selection related to the X's is taking place. It is assumed that random samples taken from the population at times t₁, t₂, …, t_s are available and it is desirable to estimate the fitness function w_t(x₁, x₂,…,x_p) which shows how the number of individuals with X_i = x_i, i = 1, 2, …, p at time t is related to the number of individuals with the same X values at time zero. Tests for population changes are discussed and indices of the selection on the population dispersion and the population mean are proposed. The situation with a multivariate normal distribution is considered as a special case. A maximum likelihood method that can be applied with any form of population distribution is proposed for estimating w_t. The methods discussed in the paper are illustrated with data on four dimensions of male Egyptian skulls covering a time span from about 4500 B.C. to about 300 A.D. In this case there seems to have been very little selection on the population dispersion but considerable selection on means.     

Genetic analysis of anther culture response in wheat carrying alien translocations

A bread wheat cultivar, Saratovskaya 29, (S29), its nearly isogenic lines carrying alien translocations [Lr9 from Aegilops umbellulata (Eg29) and (Lr19) from Agropyron elongatum (Ps29)] and two F₁ hybrids between three nearly isogenic lines of S29 that differed by the Lr19+Rht1,Pro1+Pro2 and Ppd1+Ppd2 gene complexes, namely the S29 (Lr19+Rht1)/S29 (Ppd1+Ppd2) F₁ and the S29 (Pro1+Pro2)/S29 (Lr19+Rht1) F₁ were studied for their culture response with the following results. (1) Translocations with Lr9 and Lr19 decreased embryo frequency and green plant regeneration. (2) Both F₁ hybrids showed a decrease in embryo frequency. One of the F₁ hybrids, S29 (Lr19+Rht1)/S29 (Ppd1+Ppd2) showed a decrease, with respect to S29 for green plant regeneration; the other F₁ S29 (Pro1+Pro2)/S29 (Lr19+Rht1), equalled S29 for green plant regeneration. (3) The gene complex of the F₁ hybrid S29 (Pro1+Pro2)/S29 (Lr19+Rht1) was better than that of the F₁ hybrid S29 (Lr19+Rht1)/S29 (Ppd1+Ppd2) for embryo induction and green plant regeneration. This effect was possibly induced by interactions between the Pro1+Pro2 and Lr19+Rht1 genes or was the result of direct actions of the Pro1+Pro2 genes.     

Cardiac responses to maximal anisotonic isometric contractions during handgrip and leg extension

A group of 14-healthy men performed anisotonic isometric contractions (AIC), for 60 s, at an intensity of 100% maximal voluntary contraction force (MVC) during handgrip (HG) and leg extension (LE). Heart rate (f _c), stroke volume index (SVI) and cardiac output index (Q_cI) were measured during the last 10 s of both AIC by an impedance reography method. Force (F) exerted by the subjects was recorded continuously and reported as a relative force (F _r) (% MVC). The F generated during MVC was greater for LE than for HG (502.I N compared to 374.6 N, P < 0.001). The rate of decrease in F _r was significantly slower for LE than HG for the first 25 s of the exercise (phase 1 of AIC). The F _r developed by the subjects at the end of AIC was 40% MVC for both LE and HG. The increase in f _c was greater for LE (63 beats · min^–1) than for HG (52 beats · min^–1), P < 0.01. The SVI decreased significantly from the resting level by 17.0 ml · m^–2 and by 18.2 ml · m^–2 for LE and HG, respectively. The Q_cI increased insignificantly for HG by 0.091 · min^–1 · m^–2 andsignificantly forLE by 0.561 · min^–1 · m^–2 (P < 0.001). It was concluded that although both AIC caused a significant decrease in SVI, greater increases in f _c and Q_c were observed for LE than for HG. The greater f _c and Q_c reported during LE was probably related to the greater relative force exerted by LE during phase 1 of AIC. It seems, therefore that central command might have dominated for phase 1 of AIC but that the muscle reflex also contributed significantly to the control of the cardiac response to the high intensity AIC.