Construction of Prediction Intervals in Location-Scale Families

Let x₁ ≤x₂ ≤x₃ … ≤x_r be the r smallest observations out of n observations from a location-scale family with density $ \frac{1}{\sigma}f\left({\frac{{x - \mu}}{\sigma}} \right) $ where μ and σ are the location and the scale parameters respectively. The goal is to construct a prediction interval of the form $ \left({\hat \mu + k_1 \hat \sigma,\,\hat \mu + k_2 \hat \sigma} \right) $ for a location-scale invariant function, T(Y) = T(Y₁, …, Y_m), of m future observations from the same distribution. Given any invariant estimators $ \hat \mu $ and $ \hat \sigma $, we have developed a general procedure for how to compute the values of k₁ and k₂. The two attractive features of the procedure are that it does not require any distributional knowledge of the joint distribution of the estimators beyond their first two raw moments and $ \hat \mu $ and $ \hat \sigma $ can be any invariant estimators of μ and σ. Examples with real data have been given and extensive simulation study showing the performance of the procedure is also offered.     

Growth characteristics of a thermotolerant strain of lodderomyces elongisporus grown on sucrose

A thermotolerant yeast species of Lodderomyces elongisporus EH 60 was isolated and physiologically characterized. This yeast possesses a high specific growth rate with μ_max = 0.61 h^?1. The dependence of the specific growth rate and cell yield on temperature, dilution rate, sucrose concentration and pH-value is investigated. Sucrose concentrations greater than 10 g/l inhibit the growth velocity. The specific growth rate μ can be calculated by a simple combination equation in the form: . The total optimum values for a sucrose-based continuous growth process with regard to the optimum cell yeild are: Y_S = 0.50 g DM/g S. T_opt. = 38,6 °C and D_opt. = 0,35 h^?1. The function Y_S = f(D, T) is represented by a total model.     

Oxygen mass transfer and gas holdup in a bubble column bioreactor with biosynthesis liquids

The influence of the rheology of some antibiotic biosynthesis liquids produced by Streptomyces aureofaciens, Nocardia mediterranei and Penicillium chrysogenum on the volumetric liquid phase oxygen transfer coefficient, k_La, and gas holdup, ε_G, together with the influence of superficial gas velocity, were studied in a bubble column bioreactor, using samples of fermentation liquids taken from industrial stirred tank fermenters, at 30-hour intervals during fermentation batch. The results were compared to those of previous studies from literature on non-Newtonian homogeneous fluids, such as CMC-Na, xanthan and starch solutions, respectively. In the heterogeneous broths, ε_G and k_La decreased with increasing apparent viscosity of the broth and increased with increasing superficial velocity. The experimental data were correlated using non-linear regression with correlation coefficients above 0.85.     

Kinetics of the liquid-phase oxidation of acid ferrous sulfate by the bacterium Thiobacillus ferrooxidens

The kinetics of the batch-wise liquid-phase oxidation of ferrous sulfate by the organism Thiobacillus ferrooxidans has been studied over a range of temperatures from 20°C to 31°C and in the presence of an abundant supply of oxygen, carbon dioxide, and other nutrients. The rate of oxidation was found to be accurately described by the equation where t = time hr, S = concentration of ferrous ions g Fe⁺⁺/1., μ_m = maximum specific growth rate of bacteria, hr^?1. Y = mass of bacteria produced per gram of iron oxidized g/g, K = saturation constant, g Fe⁺⁺/l., and X = concentration of bacteria g/1. The value for the maximum specific growth rate, μ_m, was found to vary from 0.12 hr^?1 at 20°C to 0.20 hr^?1 at 31°C, while the value for the saturation constant K varied randomly between 1 and 2 g/1. A method has also been described which permitted evaluation of the relevant rate constants μ_m and K without direct knowledge of the bacterial population. This method was found to yield values of μ_m and K which agreed with values determined accurately by a statistical regression analysis of the experimental data.     

Viscosity of heparin as a function of dielectric constant and of desulfation

The effect of dielectric constant (D) of the solvent on the viscosity of heparin was examined using the relation \documentclass{article}\pagestyle{empty}\begin{document}$ \eta _{{\rm sp}} /c = [\eta ]_\infty (1 + k/\sqrt c) $\end{document}, where [η]_∞ is the shielded intrinsic viscosity obtained by extrapolating \documentclass{article}\pagestyle{empty}\begin{document}$ \eta _{{\rm sp}} /c\,{\rm vs}{\rm . }\,1/\sqrt c ) $\end{document} to infinite concentration, and k is an interaction parameter independent of the dielectric constant of the solvent. This equation was previously reported by the authors⁹ for describing the reduced viscosities of strong polyelectrolytes in salt-free polar solvents. It was found that the [η]_∞ of heparin increases linearly with increasing dielectric constant of the solvent whereas the k values were, within experimental error, independent of D in the range 54.7 < D < 93.2 examined. Graded hydrolysis of heparin from its acid form (heparinic acid) at 57°C resulted in samples of varying degree of desulfation with corresponding decrease in biological activity. It was found that both [η]_∞ and k decrease with increasing desulfation.     

The role of salinity and sodicity in the dieback of Acacia xanthophloea in Ngorongoro Caldera, Tanzania

Dieback of Acacia xanthophloea (Benth.) has opened up the once densely forested Lerai area in Ngorongoro Caldera, Tanzania. Soil samples were taken from profiles in the Ngorongoro Conservation Area and Lake Manyara National Park at sites of dieback and at sites with healthy A. xanthophloea trees. Dieback sites had significantly greater electrical conductivity (EC), water‐soluble Na⁺, K⁺, Cl^?, SO and sodium adsorption ratios (SAR) than healthy sites. The following mean values were recorded: EC (179 versus 70 mS m^?1; P < 0.001, Student's t‐test, n = 8 and 10, respectively; 40–60 cm); Na⁺ (99 versus 30 mmol_c kg^?1, P < 0.001, n = 7 and 8 respectively); K⁺ (11 versus 3 mmol_c kg^?1, P < 0.05); Cl^? (36 versus 7 mmol_c kg^?1, P < 0.01); SO (31 versus 5 mmol_c kg^?1, P < 0.01); and SAR (28 versus 8 mmol l^?1/2, P < 0.01). Water‐soluble Na⁺, Cl^? and SO concentrations in the Lerai profiles have probably resulted in toxicity and osmotic stress which contributed to dieback. Accumulation of salts may have occurred because of reduced flow of freshwater through Lerai and/or flow of water from Lake Magadi into Lerai. Forest recovery may be possible if salinity is reduced. Management strategies for reducing salinity have been implemented and included re‐establishing streams that flow through Lerai. Exclusion of elephants (Loxodonta africana) from Lerai is another management strategy presently under consideration.     

The Unstirrable Water Layer Is Unstirrable because It Does Not Exist

A number of membrane‐permeation models require the incorporation of an unstirred or unstirrable water layer (UWL). An example occurs in PAMPA models when the effective permeation rate of lipophilic acids and bases, P_e, falls behind the expected permeation rate, P_m, at pH values providing a high concentration of unionized species in the donor phase. In such cases, the compound has an apparent pK_a of a weaker acid or base. The explanation is that an UWL adjacent to the membrane provides a rate‐limiting diffusion barrier for such compounds. The thickness of the UWL is correlated with the difference between the aqueous pK_a and the apparent pK_a (pK ). Here, we provide an explanation for the pK term that requires no UWL. It comes from the fact that, in the process of passing into a membrane, an ionizable compound undergoes a change in pK_a. At some point along its path into the membrane, the compound attains a maximum free energy, at which point it is as likely to continue into the membrane, as it is to return to the donor phase. This is the transition state for absorption. The pK is the pK_a of the compound at the transition state. This is a testable hypothesis (see text). The relevance of absorption to permeation depends on the rate‐limiting step of permeation.     

Kinetics of ethidium's intercalation in packaged bacteriophage T7 DNA: effects of DNA packing density

The kinetics of ethidium's intercalative binding to DNA packaged in bacteriophage T7 and two T7 deletion mutants have been determined, using enhancement of fluorescence to quantitate binding. At a constant ethidium concentration, the results can be described as first-order binding with two different rate constants, k (= k₁ + k_?1) and k (= k₂ + k_?2). The larger rate constant (k) was at least four orders of magnitude smaller than the comparable first-order forward rate constant for binding to DNA released from its capsid. At 25°C values of k decreased as the amount of DNA packaged per internal volume increased. This latter observation indicates that the rate of ethidium's binding to packaged T7 DNA is limited by an event that occurs inside of the DNA-containing region of T7, not by the crossing of T7 capsid's outer shell. Arrhenius plots of kM are biphasic, indicating a transition for packaged DNA at a temperature of 20°C. The data indicate that k s are limited by either sieving of ethidium during its passage through the packaged DNA or subsequent hindered intercalation.     

Effects of temperature on microbial ethanol production. III. The influence of the temperature on the relation existing between the specific ethanol formation rate of the yeast Saccharomyces cerevisiae Sc 5 and the ethanol concentration in the culture medium

The ethanol-inhibitory behaviour of the yeast Saccharomyces cerevisiae Sc 5 was found to be characterized by a continual-linear relation between the specific ethanol formation rate and the ethanol concentration. Therefore the simple equation could be applied for it. It is shown that this model is correct only then, if all of the process parameters are in their optimum. Out of the optimum temperature range the characteristics of the function ν = f(P) change in such a way that in regard to the ethanol concentration P twc linear relations exist for each suboptimum temperature: and a non-linear equation is current for each superoptimum temperature: where b_T is also a function of the temperature and always less than 1. Taking as a basis these equations the specific ethanol formation rate of the used strain can be calculated for the whole biokinetic P/T-sphere of ethanol production.     

Multiple intermediates in the reaction of bovine beta-trypsin with bovine pancreatic trypsin inhibitor (Kunitz)

The kinetics of the formation of the complex between bovine β-trypsin and the bovine basic pancreatic trypsin inhibitor (BPTI) was investigated using three different signals: the displacement of proflavine, the optical density changes in the UV region, and the loss of the enzymatic activity. For the three different signals, with inhibitor in excess over bovine β-trypsin ([BPTI] ≥ 5 × [bovine β-trypsin]), the time course of the reaction corresponds to a pseudo-first-order process. The concentration dependence of the rate is second order at low BPTI concentrations and tends to first order at high inhibitor concentrations. This behavior may be explained by relatively rapid preequilibria followed by limiting first-order processes according to The values of K_i, k_+i, and k_(on)i ( = k_+i/K_i) have been determined for the different reactions at three pH values: 6.80, 4.80, and 3.50. The kinetic parameters differ widely for the processes reflected by the various signals; the difference increases upon lowering pH. The results indicate that the formation of the bovine β-trypsin–BPTI complex is not an all-or-nothing process, but involves several intermediates corresponding to discrete reaction steps, which are differently affected by ionization processes.     

The effect of ethanol on continuous culture stability

The stability characteristics of a continuous culture system were studied following the addition of the natural product inhibitor, ethanol. For a steady state culture of Klebsiella (Aerobacter) aerogenes there was a linear dependence of growth rate on ethanol concentration. Following impulse and step addition of the inhibitor, response patterns of the growth rate (μ) and overall metabolism (Q_o2, Q_Co2, Q_AC) were observed. A mathematical model of the transient behavior of a product-limited system is proposed, and analog computer solutions fitted to the experimental data. The transient response of the growth rate could best be described by second or higher order equations, e.g., with values of the second order time constant (T₂) = 5 min, and damping coefficient (ξ) = 0.4.     

Kinetics of product inhibition in alcohol fermentation-temperature effect in the “sake” brewing

One of the kinteic equations derived previously from a series of sophisticated batch and continuous alcohol fermentations by using a respiration-deficient mutant of baker's yeast is as follows: where dp/dt = ethanol production rate, v0 = specific rate of ethanol production at p = 0, k₂ = empirical constant, K′_s = saturation constant, S = glucose concentration, and X = cell mass concentration. The above equation was confirmed in the previous paper to fit, the brewing of “sake.” The temperature of the specific brewing is not always constant (10 to 18°C). The effect of temperature on v0 was assessed from the Arrhenius plot, assuming that k₂ was independent of temperature. Values of dp/dt taken from the “sake” brewing data were rearranged, taking the temperature change into account. These datu, corrected for the temperature, were found to follow quite favorably the kinetic equation mentioned above. So far, a prediction of the ethanol production rate in practice was rectified to the extent of p = 19%.     

Performance,kinetics, and substrate utilization in a continuous yeast fermentation with cell recycle by ultrafiltration membranes

Summary A continuous single stage yeast fermentation with cell recycle by ultrafiltration membranes was operated at various recycle ratios. Cell concentration was increased 10.6 times, and ethanol concentration and fermentor productivity both 5.3 times with 97% recycle as compared to no recycle. Both specific growth rate and specific ethanol productivity followed the exponential ethanol inhibition form (specific productivity was constant up to 37.5 g/l of ethanol before decreasing), similar to that obtained without recycle, but with greater inhibition constants most likely due to toxins retained in the system at hight recycle ratios.By analyzing steady state data, the fractions of substrate used for cell growth, ethanol formation, and what which were wasted were accounted for. Yeast metabolism varied from mostly aerobic at low recycle ratios to mostly anaerobic at high recycle ratios at a constant dissolved oxygen concentration of 0.8 mg/kg. By increasing the cell recycle ratio, wasted substrate was reduced. When applied to ethanol fermentation, the familiar terminology of substrate used for Maintenance must be used with caution: it is not the same as the wasted substrate reported here.A general method for determining the best recycle ratio is presented; a balance among fermentor productivity, specific productivity, and wasted substrate needs to be made in recycle systems to approach an optimal design.Nomenclature B Bleed flow rate, l/h - C _T Concentration of toxins, arbitrary units - D Dilution rate, h^-1 - F Filtrate or permeate flow rate, removed from system, l/h - F _o Total feed flow rate to system, l/h - K _s Monod form constant, g/l - P Product (ethanol) concentration, g/l - P _o Ethanol concentration in feed, g/l - PP} Adjusted product concentration, g/l - PD Fermentor productivity, g/l-h - R Recycle ratio, F/F _o - S Substrate concentration in fermentor, g/l - S _o Substrate concentration in feed, g/l - V Working volume of fermentor, l - V _MB Viability based on methylene blue test - X Cell concentration, g dry cell/l - X _o Cell concentration in feed, g/l - Y _ATP Cellular yield from ATP, g cells/mol ATP - Y _ATPS Yield of ATP from substrate, mole ATP/mole glucose - Y _G True growth yield or maximum yield of cells from substrate, g cell/g glucose - Y _P Maximum theoretical yield of ethanol from glucose, 0.511 g ethanol/g glucose - Y _P/S Experimental yield of product from substrate, g ethanol/g glucose - Y _x/s Experimental yield of cells from substrate, g cell/g glucose - S _NP/X Non-product associated substrate utilization, g glucose/g cell - k ₁, k₂, k₃, k₄ Constants - k ₁ ^APP , k ₂ ^APP Apparent k ₁, k₃ - k ₁ ^TRUE True k ₁ - m Maintenance coefficient, g glucose/g cell-h - m ^* Coefficient of substrate not used for growth nor for ethanol formation, g glucose/g cell-h - Specific growth rate, g cells/g cells-h, reported as h^-1 - _m Maximum specific growth rate, h^-1 - v Specific productivity, g ethanol/g cell-h, reported as h^-1 - v _m Maximum specific productivity, h^-1     

Energetics of chemolithoautotrophy in the hydrothermal system of Vulcano Island, southern Italy

The hydrothermal system at Vulcano, Aeolian Islands (Italy), is home to a wide variety of thermophilic, chemolithoautotrophic archaea and bacteria. As observed in laboratory growth studies, these organisms may use an array of terminal electron acceptors (TEAs), including O₂, , Fe(III), , elemental sulphur and CO₂; electron donors include H₂, , Fe²⁺, H₂S and CH₄. Concentrations of inorganic aqueous species and gases were measured in 10 hydrothermal fluids from seeps, wells and vents on Vulcano. These data were combined with standard Gibbs free energies () to calculate overall Gibbs free energies (ΔG_r) of 90 redox reactions that involve 16 inorganic N‐, S‐, C‐, Fe‐, H‐ and O‐bearing compounds. It is shown that oxidation reactions with O₂ as the TEA release significantly more energy (normalized per electron transferred) than most anaerobic oxidation reactions, but the energy yield is comparable or even higher for several reactions in which , or Fe(III) serves as the TEA. For example, the oxidation of CH₄ to CO₂ coupled to the reduction of Fe(III) in magnetite to Fe²⁺ releases between 94 and 123 kJ/mol e^?, depending on the site. By comparison, the aerobic oxidation of H₂ or reduced inorganic N‐, S‐, C‐ and Fe‐bearing compounds generally yields between 70 and 100 kJ/mol e^?. It is further shown that the energy yield from the reduction of elemental sulphur to H₂S is relatively low (8–19 kJ/mol e^?) despite being a very common metabolism among thermophiles. In addition, for many of the 90 reactions evaluated at each of the 10 sites, values of ΔG_r tend to cluster with differences < 20 kJ/mol e^?. However, large differences in ΔG_r (up to ～ 60 kJ/mol e^?) are observed in Fe redox reactions, due largely to considerable variations in Fe²⁺, H⁺ and H₂ concentrations. In fact, at the sites investigated, most variations in ΔG_r arise from differences in composition and not in temperature.     

A kinetic study of the alcoholic fermentation of grape juice

The alcoholic fermentation of grape juice by a wine yeast was studied batchwise at pH 3.6 and 4.05 to develop kinetic equations relating cell concentration, N, to product concentration, P. In the exponential growth phase where A, B, and C are constants, and μ is the specific growth rate. In the stationary phase, where the cell population is constant, was found to apply. This equation, which incorporates a stoichiometric constant, P_m, predicted correctly the operation of a continuous fermentor at pH 3.6 and at 4.05. To study more fully the effect of alcohol concentration on yeast growth, a continuous fermentor was used in which the grape juice feed was supplemented with pure alcohol. At pH 3.6 the specific growth rate varied as, There was no growth inhibition below an alcohol concentration of 2.6 g./100 cc., but inhibition was complete above 6.85 g./100 cc. This is a modified form of the relation suggested by Hinshelwood.¹ The data suggest that growth in batch culture was limited not only by alcohol but also by some other factor, probably a nutritional deficiency.     

The parabolic pattern of animal growth: determination of equation parameters and their temperature dependencies

1. Parabolic (power) growth is characteristic of many aquatic poikilothermic animals for certain stages of their development. The parabolic pattern describing growth in weight (or length) under constant ambient conditions can be expressed in the following general form: where Y is growth rate (or specific growth rate), X is animal size, and Ω and τ are coefficients. The constancy of ambient conditions is of cardinal importance in determining τ. The problem of maintaining a constant level of nutrition can be reliably solved only by the presence of food in excess of demand. Data satisfying these requirements have demonstrated that τ does not depend on factors such as temperature, and can be assumed to be independent of ambient conditions. In the growth rate-weight equation, τ ranges between 0.5 and 0.85 for animals representing a variety of taxonomic groups. 2. The coefficient Ω. is affected by ambient conditions (e. g. temperature, amount of food). Its value reflects the ‘level’ of the growth rate-size relationship under given conditions. For a specific time period, Ω can be computed from the following formula: where X₁ and X₂ are the animal sizes (weights, lengths) at time t₁ and t₂, the beginning and end of the time period. The calculated value of Ω corresponds to the average intensity of the ambient factor (F) affecting the growth during the period between the two observations. If the values of the Ω are calculated for wide range of the factor, the relationship between the Ω. and F, Ω=f(F), can be determined. The function can be then incorporated into the parabolic equation of growth, as 3. Dependence of the development rate (1/D, where D is time interval needed to complete a given stage) on temperature (T), and dependence of Ω on T, are both described by sigmoid-shape curves. The broad intermediate part of these curves, a range to which animals are adapted in nature, can be approximated by straight line functions. For two groups, pan-size sockeye salmon (Oncorhynchus nerka) and different species of chironomid larvae, it was shown that an equation combining parabolic growth and linear temperature patterns describes accurately the variability observed in growth rates under experimental and natural conditions.     

Definition and validation of operating equations for poly(vinyl alcohol)‐poly(lactide‐co‐glycolide) microfiltration membrane‐scaffold bioreactors

The aim of this work is to provide operating data for biodegradable hollow fiber membrane bioreactors. The physicochemical cell culture environment can be controlled with the permeate flowrate, so this aim necessitates the provision of operating equations that enable end‐users to set the pressures and feed flowrates to obtain their desired culture environment. In this paper, theoretical expressions for the pure water retentate and permeate flowrates, derived using lubrication theory, are compared against experimental data for a single fiber poly(vinyl alcohol)–poly(lactide‐co‐glycolide) crossflow module to give values for the membrane permeability and slip. Analysis of the width of the boundary layer region where slip effects are important, together with the sensitivity of the retentate and permeate equations to the slip parameter, show that slip is insignificant for these membranes, which have a mean pore diameter of 1.1 µm. The experimental data is used to determine a membrane permeability, of k = 1.86 × 10^?16 m², and to validate the model. It was concluded that the operating equation that relates the permeate to feed ratio, c, lumen inlet flowrate, Q _l,in, lumen outlet pressure, P ₁, and ECS outlet pressure, P ₀, is (1) where A and B are constants that depend on the membrane permeability and geometry (and are given explicitly). Finally, two worked examples are presented to demonstrate how a tissue engineer can use Equation (1) to specify operating conditions for their bioreactor. Biotechnol. Bioeng. 2010;107: 382–392. © 2010 Wiley Periodicals, Inc.     

Buoyant densities of natural and synthetic DNA's in CsCl and Cs2SO4 considered as sequence-dependent properties

The buoyant densities of natural and synthetic DNA's can be accurately interrelated if second-neighbor influences are taken into account. We derive the following expressions, based partly on the buoyant densities of six synthetic DNA's, for the buoyant densities ρ (g/cm³) of DNA's having random sequences. In CsCl, and in Cs₂SO₄, . In these equations, H_G is the mole fraction of G : C base pairs in the DNA and the buoyant densities are calculated relative to densities for E. coli DNA of 1.703 and 1.426 (g/cm³) in CsCl and Cs₂SO₄, respectively.