Extinction probabilities in branching processes: A note on holgate and Lakhani's paper

Within the class of offspring distributions with given meanm>1 and probability of no offspringp _o, the probabilityq of ultimate extinction in a Galton-Watson branching process starting from one individual satisfiesp ₀<q(m,p₀)≤q<1. A short table illustrates the lower boundq(m,p ₀). Work done at the Mathematics Department, University of Washington, Seattle, U.S.A.     

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.     

Limitations in substrate utilization efficiency by Zymomonas mobilis

Summary Optimal growth conditions for Zymomonas mobilis have been established using continuous cultivation methods. Optimal substrate utilization efficiency occurs with 2.5 g l^–1 yeast extract, 2.0 g l^–1 ammonium sulfate and 6.0 g l^–1 magnesium sulfate in the media. Catabolic activity is at its maximum with glucose uptake rates of 16–18 g l^–1 h^–1 and ethanol production rates of 8–9 g l^–1 h^–1, Q_g values of 22–26 and Q_p values between 11 and 13, which results in 40 g l^–1 h^–1 ethanol yields using a 100 g l^–1 substrate feed. Any increase in these parameters goes on cost of substrate utilization efficiency. Calcium pantothenate can not substitute yeast extract.Abbreviations G Glucose (%) - Pant Calcium pantothenate (mg l^–1) - D Dilution rate (h^–1) - NH₄ Ammonium sulfate (%) - M_g Magnesium sulfate (%) - S₁ Residual glucose in the fermenter (g l^–1) - S₀ Glucose feed (g l^–1) - Eth Ethanol concentration (g l^–1) - GUR Glucose uptake rate (g l^–1 h^–1) - Q_g Specific glucose uptake rate (g g^–1 h^–1) - Q_p Specific ethanol production rate (g g^–1 h^–1) - EPR Ethanol production rate (g l^–1 h^–1) - Y_g Yield coefficient for glucose (g g^–1) - Y_p Conversion efficiency (%) - C Biomass concentration (g l^–1) Present address: (Until June 1982) Institut für Mikrobiologie, TH Darmstadt, 6100 Darmstdt, Federal Republic of Germany     

Relationships between root permeability to water,leaf conductance and transpiration rate in sunflower (Helianthus annuus L.) cultivars

Summary The relations between leaf conductance (g_l) transpiration rate and root permeability to water (R_p) of three sunflower (Helianthus annuus L.) cultivars grown in a controlled environment cabinet are described.No differences in transpiration rates were found but it was shown that plants with low values of R_p have active stomatal closure with favourable consequences for water use efficiency under water limiting conditions.R_p was estimated by applying hydrostatic pressure on the root system. Values of R_p per unit root volume ranged from 0.34×10^–5 to 16.75×10^–5 (s MPa^–1). There were significant inter-cultivar differences (P<0.05) in R_p and g_l and an inverse correlation between R_p and the maximum values cf g_l within cultivars.Pressure applied on the root system is proposed as a useful tool for the determination of differences in the root permeability to water amongst sunflower cultivars.     

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.     

Ethanol production from sweet sorghum juice in batch and fed-batch fermentations by <Emphasis Type="Italic">Saccharomyces cerevisiae</Emphasis>

Sweet sorghum juice supplemented with 0.5% ammonium sulphate was used as a substrate for ethanol production by Saccharomyces cerevisiae TISTR 5048. In batch fermentation, kinetic parameters for ethanol production depended on initial cell and sugar concentrations. The optimum initial cell and sugar concentrations in the batch fermentation were 1 × 10⁸ cells ml⁻¹ and 24 °Bx respectively. At these conditions, ethanol concentration produced (P), yield (Y _ps) and productivity (Q _p ) were 100 g l⁻¹, 0.42 g g⁻¹ and 1.67 g l⁻¹ h⁻¹ respectively. In fed-batch fermentation, the optimum substrate feeding strategy for ethanol production at the initial sugar concentration of 24 °Bx was one-time substrate feeding, where P, Y _ps and Q _p were 120 g l⁻¹, 0.48 g g⁻¹ and 1.11 g l⁻¹ h⁻¹ respectively. These findings suggest that fed-batch fermentation improves the efficiency of ethanol production in terms of ethanol concentration and product yield.     

Effects of branch position on water relations and gas exchange of European larch trees in an alpine community

Water relations and gas exchange were studied in the crowns of small European larch (Larix decidua Mill.) trees with respect to branch position. The upper-crown branches showed significantly higher branch sap flux rate (F _la) and branch conductance (g _b) compared to the lower crown (P<0.001). Values of leaf conductance (g _l), transpiration rate (E) and net photosynthesis (A), averaged for different ranges of atmospheric vapour pressure deficit (VPD), were also higher in the upper crown position. We suppose that the up to 2.6-fold smaller soil-to-leaf hydraulic conductance observed in the lower branches (P<0.001, compared to upper branches) could contribute to the decreased values of F _la, g _b, g _l, and E in the lower crown position. Variation in tracheid lumen diameter with respect to crown position (P<0.001) supported the hypothesis that branches growing at the crown base are hydraulically more constrained than branches located at the top of the tree. Leaf area to sapwood area ratio (A _la/A _sa) exhibited 1.4 times smaller values in lower crown (P<0.01), however, this could not compensate the effect of decreased hydraulic conductivity of the lower-crown branches.     

Photosynthetic Response to Soil Water Contents of an Annual Pioneer C4 Grass (Agriophyllum squarrosum) in Hunshandak Sandland,China

Net photosynthetic rate (P _N), transpiration rate (E), stomatal conductance (g _s), and leaf water potential (Ψ_l) of an annual pioneer C₄ grass (Agriophyllum squarrosum) were compared under different simulated precipitation events in a field of Hunshandak Sandland, China. The increase of soil water content (SWC) had significant effect on these physiological traits (p<0.001). In the vegetative stage, the values of P _N, E, and g _s went up sharply when SWC increased at the beginning, while they went down with continuous increase of SWC. P _N, E, and g _s increased 1.4, 1.7, and 1.7 fold, respectively, with SWC range from 6.7 to 11.6 %. In the reproductive stage, similar trends were found, except for the climate with a higher SWC. This indicated that A. squarrosum was very sensitive to the small increment of SWC which might have a large photosynthetic potential. Ψ_l increased by about 8 % as the SWC changed from 6.7 to 8.8 %, and then maintained a steady level when the SWC was higher than 8.8 %, while the values of P _N, E, and g _s kept increasing even after this SWC. This might indicate that the adjustment of Ψ_l response to the changes of SWC lagged that of the photosynthetic parameters. This revised version was published online in August 2006 with corrections to the Cover Date.     

Estimation and Verification of Hypotheses in Some Zyskind-Martin Models with Missing Values

Several theorems on estimation and verification of linear hypotheses in some Zyskind-Martin (ZM) models are given. The assumptions are as follows. Let y = Xβ + e or (y, Xβ, σ²V) be a fixed model where y is a vector of n observations, X is a known matrix nXp with rank r(X) = r ≦ p < n, where p is a number of coordinates of the unknown parameter vector β, e is a random vector of errors with covariance matrix σ²V, where σ² is unknown scalar parameter, V is a known non-negative definite matrix such that R(X) ? R(V). Symbol R(A) denotes a vector space generated by columns of matrix A. The expected value of y is Xβ. In this paper four following Zyskind-Martin (ZM) models are considered: ZMd, ZMa, ZMc and ZMqd (definitions in sec. 1) when vector y y₁ y₂ involves a vector y₁ of m missing values and a vector y₂ with (n — m) observed values. A special transformation of ZM model gives again ZM model (cf. theorem 2.1). Ten properties of actual (ZMa) and complete (ZMc) Zyskind-Martin models with missing values (cf. theorem 2.2) test functions F are given in (2.11)) are presented. The third propriety constitutes a generalization of R. A. Fisher's rule from standard model (y, Xβ, σ²I) to ZM model. Estimation of vector y₁ (cf. 3.3) of vector β (cf. th. 3.2) and of scalar σ² (cf. th. 3.4) in actual ZMa model and in diagonal quasi-ZM model (ZMqd) are presented. Relation between y? ₁ and β is given in theorem 3.1. The results of section 2 are illustrated by numerical example in section 4.     

Confidence Intervals on Ratios of Variance Components for the Unbalanced Two Factor Nested Model

The model considered in this article is the two-factor nested unbalanced variance component model: for p = 1, 2, …, P; q = 1, 2, …, Q_p; and r = 1, 2, …, R_pq. The random variables Y_pqr are observable. The constant μ is an unknown parameter, and A_p, B_pq and C_pqr are (unobservable) normal and independently distributed random variables with zero means and finite variances σ²_A, σ²_B, and σ²_C, respectively. Approximate confidence intervals on ?_A and ?_B using unweighted means are derived, where The performance of these approximate confidence intervals are evaluated using computer simulation. The simulated results indicate that these proposed confidence intervals perform satisfactorily and can be used in applied problems.     

Influence of the concentrations of d-xylose and yeast extract on ethanol production by Pachysolen tannophilus

To determine the most favorable conditions for the production of ethanol by Pachysolen tannophilus, this yeast was grown in batch cultures with various initial concentrations of two of the constituents of the culture medium: d-xylose (s_o), ranging from 1 g·l⁻¹ to 200 g·l⁻¹, and yeast extract (l_o), ranging from 0 g·l⁻¹ to 8 g·l⁻¹. The most favorable conditions proved to be initial concentrations of S_o=25 g·l⁻¹ and l_o=4 g·l⁻¹, which gave a maximum specific growth rate of 0.26 h⁻¹, biomass productivity of 0.023 g·l⁻¹·h⁻¹, overall biomass yield of 0.094 g·g⁻¹, specific xylose-uptake rate (q_s) of 0.3 g·g⁻¹·h⁻¹ (for t=50 h), specific ethanol-production rate (q_E) of 0.065 g·g⁻¹·h⁻¹ and overall ethanol yield of 0.34 g·g⁻¹; q_s values decreased after the exponential growth phase while q_E remained practically constant.     

Growth-associated production of poly-3-hydroxybutyrate byBacillus mycoides

Bacillus mycoides strain RIJ B-017, a growth-associated poly-3-hydroxybutyrate (PHB) producer was grown on sucrose-containing media. PHB accumulated in cells up to 72% of dry cell mass. The overall maximum value of PHB yield (Y _p/s) and productivities (Q _p andq _p) 250 mg_p/g_s, 120 mg_p L⁻¹ h⁻¹ and 30 mg_p g_x ⁻¹ h⁻¹, respectively, were obtained at 15 g/L sucrose. Differential scanning calorimeter heating curve showed two peaks, one at 95.9 °C and another at 165.4°C with a shoulder around 154.6 °C. The viscosity-average molar mass in chloroform at 27°C was 505 kDa. The carbon content of PHB was 55.4% of the mass.     

Synthesis and receptor binding studies of some new arylcarboxamide derivatives as sigma-1 ligands

We describe here the synthesis and the binding interaction with σ₁ and σ₂ receptors of a series of new arylcarboxamide derivatives variously substituted on the aromatic portions. Maintaining a partial scaffold of a series of compounds previously synthesized by us, we evaluate the effect of the substitution on σ binding. The synthesized compounds have been tested to estimate their affinity and selectivity toward σ₁ and σ₂ receptors. Two out of 16 derivatives showed an interesting σ₁ affinity (21.2 and 13.6 nM—compounds 2m and 2p) and a good selectivity (K_i(σ₂)/K_i(σ₁) >140 and >40, respectively).     

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).     

Glucose repression of xylitol production in Candida tropicalis mixed-sugar fermentations

Glucose repressed xylose utilization inCandida tropicalis pre-grown on xylose until glucose reached approximately 0–5 g l^–1. In fermentations consisting of xylose (93 g l^–1) and glucose (47 g l^–1), xylitol was produced with a yield of 0.65 g g^–1 and a specific rate of 0.09 g g^–1 h^–1, and high concentrations of ethanol were also produced (25 g l^–1). If the initial glucose was decreased to 8 g l^–1, the xylitol yield (0.79 g g^–1) and specific rate (0.24 g g^–1 h^–1) increased with little ethanol formation (<5 g l^–1). To minimize glucose repression, batch fermentations were performed using an aerobic, glucose growth phase followed by xylitol production. Xylitol was produced under O₂ limited and anaerobic conditions, but the specific production rate was higher under O₂ limited conditions (0.1–0.4 vs. 0.03 g g^–1 h^–1). On-line analysis of the respiratory quotient defined the time of xylose reductase induction.     

Inhibitory effect of dihydroxyacetone onGluconobacter oxydans: Kinetic aspects and expression by mathematical equations

Summary Microbial conversion of glycerol into dihydroxyacetone (DHA) byGluconobacter oxydans was subjected to inhibition by excess substrate. Comparison of cultures containing increasing initial DHA contents (0 to 100 g l^–1) demonstrated that DHA also inhibited this fermentation process. The first effect was on bacterial growth (cellular development stopped when DHA concentration reached 67 gl^–1), and then on oxidation of glycerol (DHA synthesis only occurred when the DHA concentration in the culture medium was lower than 85 g l^–1). Productivity, specific rates and, to a lesser extent, conversion yields decreased as initial concentrations of DHA increased. The changes in the specific parameters according to increasing initial DHA contents were described by general equations. These formulae satisfactorily express the concave aspect of the curves and the reduction in biological activity when the cells were in contact with DHA concentrations of up to 96 g l^–1.Abbreviations X, S, P biomass, substrate, product concentrations - r _x,r _s,r _p rates of growth, consumption and production - ,q _s,q _p specific rates of growth, glycerol consumption and DHA production - Y _x/s, Y_p/s conversion yields of substrate into biomass and product - K _s constant of affinity of cells to the substrate - K _ip product inhibition constant - P _m threshold concentration of DHA in substrate     

An adaptive on-line control feed rate system in a laboratory scale bakers yeast process

Summary A new control policy for the on-line optimization of the nutrient supply in bakers yeast process is proposed. A feed rate corresponding to minimal substrate uptake time was shown to be optimal for cell yield and specific growth rate. Cultivation results of baker's yeast are presented.Nomenclature c glucose concentration in wort (mol.l^–1) - C total glucose used (mol) - c_e ethanol concentration in wort (mg.l^–1) - c_p glucose concentration in fresh medium (mol.l^–1) - dt/dc glucose consumption time (sec.mol^–1) - F substrate feed rate (litre.hr^–1) - q_c glucose uptake rate (mol.hr^–1) - Q_c specific glucose uptake rate (moll.g^–1.hr^–1) - qO₂ oxygen uptake rate (mol.hr^–1) - QO₂ specific oxygen uptake rate (mol.g^–1.hr^–1) - r_x productivity (g.l^–1.hr^–1) - t time (hr) - x biomass concentration (g.l^–1) - X total biomass (g) - Y_x/c cell yield (g.g^–1): (g.mol^–1) - Y_o/c consumed oxygen to glucose ratio (mol.mol^–1)     

Evaluation of distant carbon sources in biosurfactant production by a gamma ray-induced Pseudomonas putida mutant

Pseudomonas putida 33 wild strain, subjected to gamma ray mutagenesis and designated as P. putida 300-B mutant was used as microbial rhamnolipid-producer by using distant carbon sources (viz. hydrocarbons, waste frying oils ‘WFOs’, vegetable oil refinery wastes and molasses) in the minimal media under shake flask conditions. The behavior of glucose as co-substrate and growth initiator was examined. The 300-B mutant strain showed its ability to grow on all the substrates tested and produced rhamnolipid surfactants to different extents however; soybean and corn WFOs were observed to be preferred carbon sources followed by kerosene and paraffin oils, respectively. The best cell biomass (3.5 g l⁻¹) and rhamnolipids yield (4.1 g l⁻¹) were obtained with soybean WFO as carbon source and glucose as growth initiator under fed-batch cultivation showing an optimum specific growth rate (μ) of 0.272 h⁻¹, specific product yield (q_p) of 0.318 g g⁻¹ h and volumetric productivity (P_V) of 0.024 g l⁻¹ h. The critical micelle concentration of its culture supernatant was observed to be 91 mg rhamnolipids l⁻¹ and surface tension as 31.2 mN m⁻¹.     

Approximate Confidence Intervals for Contrasts in the Balanced Three Factor Mixed Model

When conducting a statistical analysis of data from a designed experiment, an investigator is often interested in confidence intervals for contrasts of the fixed effects. If the analysis involves a mixed linear model, exact confidence intervals for contrasts of the fixed effects are not always available. In such cases, confidence intervals with approximate coverage probabilities must be used. As will be shown, this problem may be generalized to that of constructing a confidence interval for the parameter μ, where X is a normal random variable with mean μ and variance ∑ a_qθ_q, where a₁…,a_Q are known constants, U_q = n_qS/θ_q is a chi-squared random variable with n_q degrees of freedom, for each q = 1,…, Q, and X,U₁,…, U_Q are mutually independent. In this paper, we consider the case where Q = 3 and a₃ ≤0.     

Kinetic studies of recombinant human interferon-gamma expression in continuous cultures of <Emphasis Type="Italic">E. coli</Emphasis>

A series of continuous cultures was performed to understand the product formation kinetics of recombinant human interferon gamma (rhIFN-γ) in Escherichia coli at different dilution rates ranging from 0.1 to 0.3 h⁻¹ in different media. A T7 promoter-based vector was used for expression of IFN-γ in E. coli BL21 (DE3) cells. The recombinant protein was produced as inclusion bodies, thus allowing a rapid buildup of rhIFN-γ inside the cell, with the specific product yield (Y _p/X ) reaching a maximum value of 182 mg g⁻¹ dry cell weight (DCW). In all the media tested, the specific product formation rate (q _p ) was found to be strongly correlated with the specific growth rate (μ), demonstrating the growth-associated nature of product formation. The q _p values show no significant decline with time postinduction, even though the recombinant protein has been over produced inside the cell. The maximum q _p level of 75.5 mg g⁻¹ h⁻¹ was achieved at the first hour of induction at the dilution rate of 0.3 h⁻¹. Also, this correlation between q _p and μ was not critically dependent on media composition, which would made it possible to grow cells in defined media in the growth phase and then push up the specific growth rate just before induction by pulse addition of glucose and yeast extract. This would ensure the twin objectives of high biomass and high specific productivities, leading to high volumetric product concentration.