Convergence to Normality of the Asymptotic Quasi‐Score Function on a Linear Model

The asymptotic quasi‐likelihood method is considered for the model y_t = f_t(θ) + M_t, t = 0,1, …,T where f_tθ) is a linear predictable process of the parameter of interest θ, M_t is a martingale difference, and the nature of E(M_t² | ℱ_t–1) is unknown. This paper is concerned with the limiting distribution of the asymptotic quasi‐score function of such a model. Confidence intervals and hypothesis testing of θ is derived from the limiting distribution. Comparison is made between the estimates obtained through this method and those obtained through the least squares method.     

Bounds on the total population for species governed by reaction-diffusion equations in arbitrary two-dimensional regions

Analysis based on the integration of differential inequalities is employed to derive upper and lower bounds on the total populationN(t) = ∫ _R θ(x ₁,x ₂,t) dx ₁ dx ₂ of a biological species with an area-density distribution function θ=θ(x ₁,x ₂,t) (≥0) governed by a reaction-diffusion equation of the form ∂θ/∂t =D∇²θ +fθ −gθ ⁿ⁺¹ whereD (>0),n (>0),f andg are constant parameters, θ=0 at all points on the boundary ∂R of an (arbitrary) two-dimensional regionR, and the initial distribution (θ(_{x 1},x ₂, 0) is such thatN(0) is finite. Forg≥0 withR the entire two-dimensional Euclidean space, a lower bound onN(t) is obtained, showing in particular thatN(∞) is bounded below by a finite positive quantity forf≥0 andn>1. An upper bound onN(t) is obtained for arbitrary bounded or unbounded)R withn=1,f andg negative, and ∫ _R θ(x ₁,x ₂, 0)² dx ₁ dx ₂ sufficiently small in magnitude, implying that the population goes to extinction with increasing values of the time,N(∞)=0. Forg≥0 andR of finite area, the analysis yields upper bounds onN(t), predicting eventual extinction of the population if eitherf≤0 or if the area ofR is less than a certain grouping of the parameters in cases for whichf is positive. These results are directly applicable to biological species with distributions satisfying the Fisher equation in two spatial dimensions and to species governed by certain specialized population models.     

Unconditional Non-Asymptotic One-Sided Tests for Independent Binomial Proportions When the Interest Lies in Showing Non-Inferiority and/or Superiority

For two independent binomial proportions Barnard (1947) has introduced a method to construct a non-asymptotic unconditional test by maximisation of the probabilities over the ‘classical’ null hypothesis H₀= {(θ₁, θ₂) ∈ [0, 1]²: θ₁ = θ₂}. It is shown that this method is also useful when studying test problems for different null hypotheses such as, for example, shifted null hypotheses of the form H₀ = {(θ₁, θ₂) ∈ [0, 1]²: θ₂ ≤ θ₁ ± Δ } for non-inferiority and 1-sided superiority problems (including the classical null hypothesis with a 1-sided alternative hypothesis). We will derive some results for the more general ‘shifted’ null hypotheses of the form H₀ = {(θ₁, θ₂) ∈ [0, 1]²: θ₂ ≤ g(θ₁ )} where g is a non decreasing curvilinear function of θ₁. Two examples for such null hypotheses in the regulatory setting are given. It is shown that the usual asymptotic approximations by the normal distribution may be quite unreliable. Non-asymptotic unconditional tests (and the corresponding p-values) may, therefore, be an alternative, particularly because the effort to compute non-asymptotic unconditional p-values for such more complex situations does not increase as compared to the classical situation. For ‘classical’ null hypotheses it is known that the number of possible p-values derived by the unconditional method is very large, albeit finite, and the same is true for the null hypotheses studied in this paper. In most of the situations investigated it becomes obvious that Barnard's CSM test (1947) when adapted to the respective null space is again a very powerful test. A theorem is provided which in addition to allowing fast algorithms to compute unconditional non-asymptotical p-values fills a methodological gap in the calculation of exact unconditional p-values as it is implemented, for example, in Stat Xact 3 for Windows (1995).     

The ontogeny of the locomotor wave in sevruga fish (Acipenser stellatus Pall.)

Continuous filming of the swimming movements of sevruga prelarvae (Acipenser stellatus Pall.) was performed over the first to the fifteenth post-hatching days. These data were used to determine three locomotor characteristics: {f(v, θ), A(v, θ), w(v, θ)} where f is the frequency of the transverse oscillations; A is the amplitude of the tail fin movements; w is the speed of the locomotor wave; v is the speed of the locomotion; and θ is the number of days during which the filming was carried out. In addition, the comparison of two characteristics was performed. These are the step length L(v, θ) and the wavelength λ(v, θ), where L ≡ vT is the distance that a fish covers in time T ≡ 1/f and λ is λ ≡ wT. The results led to the conclusion that the prelarva swimming movements achieve the carangiform mode by the end of the second week. This is characteristic of adults and coincides with the beginning of external feeding. The mode is represented by an equation that follows from the generalized Bainbridge’s law: f = f ₀ + f ₁ v/H. The equation includes one anatomical parameter H of total length and two kinematic parameters f ₀ and f ₁, which can be calculated by the linear approximation method. These are the kinematic parameters that are changed in the early ontogenesis when 1 ≤ θ ≤ 15. However, the parameters become stable when θ ≥ 15. This means that the parameter values are constant and similar to those of adult fish. The similar properties of stabilization and variability have the kinematic parameters of other locomotor characteristics.

     

Immobilization of oxyreductases on inorganic supports based on alumina. Immobilization of lactate dehydrogenase on alumina by adsorption

Lactate dehydrogenase (LDH) was adsorbed on low-(γ, η) and high -(θ, α) temperature forms of alumina. θ-Al₂O₃ exhibited the greatest adsorption ability. The maximum adsorption value was 30 mg LDH/g of a carrier. The conditions for irreversible adsorption have been determined. An adsorption isotherm on θ-Al₂O₃ for pH 6.0 has been obtained; the LDH_ads surface area and the carrier surface portion accessible to the enzyme molecules have been calculated. The reaction kinetic parameter were determined by taking into account the reaction proceeding in the intradiffusional region. The specific catalytic activity (A_spec) of LDH_ads at small surface coverage of θ-Al₂O₃ is five times less than A_spec of the native enzyme and K_M^imm with respect to NADH exceeds K_M^nat by two orders or magnitude. The is evidence for a strong LDH–Al₂O₃ interaction and a considerable deformation of the enzyme globule. A_spec and K_M decrease as the amount of the enzyme attached to the carrier increases. Due to adsorption. LDH becomes thermostable and durable. The LDH_ads samples conserve 20–40% of their activity at room temperature during a year.     

Parameter Estimation for the Bateman Function via Moments of the Empirical Curve

The parameters of the function f(t)=c(e^?at-e^?bt) are related in a simple way to the moments ^∞ tⁿf(t)^dt(n=0, 1, 2). Using empirical values of f, the moments can be estimated by numerical integration. Therefrom estimates of the parameters are obtained by elementary algebra.     

Determination of DNA base compositions from melting profiles in dilute buffers

Equations were determined for the dependency of the melting temperature (T_m) of DNA upon the logarithm of the sodium ion concentration, for four DNA samples of widely different base compositions (θ_GC). The slopes of these T_m versus log M equations wore found to decrease with increasing θ_{G C}of the samples. An empirical equation relating T_m, log M (Na⁺) and θ_{G C} was derived, which also accounts for differences in T_m versus log M slopes. Data from the literature for some synthetic polynucleotides and for the crab(Cancer pagarus) satellite poly AT are discussed in relation to the above finding. The changes in T_m versus log M slopes with θ_{G C} are interpreted in terms of changes in the thermodynamic parameters ΔS and ΔH with base composition.     

Kinetics and mechanism of the decomposition of μ-amido-μ-hydroxo(tetraamminecobalt(III))(tetraaquacobalt(III)) ion in acidic aqueous solution

The title complex undergoes decomposition in acidic aqueous solution resulting in equimolar concentration of aquapentaamminecobalt(III) and hexa- aquacobalt(II). The kinetic studies over the ranges of 0.048 M ⩽ [H⁺] ⩽ 0.385 M, 25 ⩽ θ_c ⩽ 41.5°C and at I = 0.5 M reveals that the intricate mechanism involves protonation equilibrium of the title complex, followed by a rate determining bridge cleavage. The further follow-up reaction is a fast electron transfer process to form products. The rate expression derived from the mechanism is k_obs = k₁K₁[H⁺]/(1 + K₁[H⁺]) where the values of k, and K, are found to be 8.9 × 10⁻⁴ s⁻¹ and 3.5 M⁻¹ respectively at 25 °C. The results are compared with that obtained for the decomposition reactions of mononuclear aquaammine complexes of cobalt(III).     

Fitting Mixed Poisson Regression Models Using Quasi-Likelihood Methods

This paper is to investigate the use of the quasi-likelihood, extended quasi-likelihood, and pseudo-likelihood approach to estimating and testing the mean parameters with respect to two variance models, M1: φ μ^θ(1+μphis;) and M2: φ μ^θ(1+τ). Simulation was conducted to compare the bias and standard deviation, and type I error of the Wald tests, based on the model-based and robust variance estimates, using the three semi-parametric approaches under four mixed Poisson models, two variance structures, and two sample sizes. All methods perform reasonably well in terms of bias. Type I error of the Wald test, based on either the model-based or robust estimate, tends to be larger than the nominal level when over-dispersion is moderate. The extended quasi-likelihood method with the variance model M1 performs more consistently in terms of the efficiency and controlling the type I error than with the model M2, and better than the pseudo-likelihood approach with either the M1 or M2 model. The model-based estimate seems to perform better than the robust estimate when the sample size is small.     

Bounds on the total particle number for species governed by reaction-diffusion equations in the infinite spatial domain

Differential inequality methods are developed for establishing upper and lower bounds on the total particle numberN(t)=∫θ(x,t) d³ x associated with solutions to nonlinear reaction-diffusion equations of the form ∂θ/∂t=D∇²θ+fθ-gθ ⁿ⁺¹ , whereD(>0),n(>0),f andg are constant parameters. If finite in a neighborhood oft=0,N(t) is bounded below for allt≥0 by a certain derived function oft for equations withg≥0. An upper bound onN(t) is obtained for equations withn=1,f<0 andg<0. These results provide general preservation and extinction criteria for the total particle number.     

Generalized stable population theory

In generalizing stable population theory we give sufficient, then necessary conditions under which a population subject to time dependent vital rates reaches an asymptotic stable exponential equilibrium (as if mortality and fertility were constant). If x ₀(t) is the positive solution of the characteristic equation associated with the linear birth process at time t, then rapid convergence of x ₀(t) to x ₀ and convergence of mortality rates produce a stable exponential equilibrium with asymptotic growth rate x ₀–1. Convergence of x ₀(t) to x ₀ and convergence of mortality rates are necessary. Therefore the two sets of conditions are very close. Various implications of these results are discussed and a conjecture is made in the continuous case.     

On-line parameter and state estimation of continuous cultivation by extended Kalman filter

Summary The on-line estimation of biomass concentration and of three variable parameters of the non-linear model of continuous cultivation by an extended Kalman filter is demonstrated. Yeast growth in aerobic conditions on an ethanol substrate is represented by an unstructured non-linear stochastic t-variant dynamic model. The filter algorithm uses easily accessible data concerning the input substrate concentration, its concentration in the fermentor and dilution rate, and estimates the biomass concentration, maximum specific growth rate, saturation constant and substrate yield coefficient. The microorganismCandida utilis, strain Vratimov, was cultivated on the ethanol substrate. The filter results obtained with the real data from one cultivation experiment are presented. The practical possibility of using this method for on-line estimation of biomass concentration, which is difficult to measure, is discussed.Nomenclature D dilution rate (h^-1) - DO₂ dissolved oxygen concentration (%) - E identity matrix - F Jacobi matrix of the deterministic part of the system equations g - g continuousn-vector non-linear real function - h m-vector non-linear real function - K Kalman filter gain matrix - K _S saturation constant (kgm^-3) - K_S expectation of the saturation constant estimate - M Jacobi matrix of the deterministic part of the measurement equations h - P(t₀) co-variance matrix of the initial values of the state - P(t_k/t_k) c-variance matrix of the error in (t _k|t _k) - P(t_k+1/t_k) co-variance matrix of the error in (t _k+1|t _k - Q co-variance matrix of the state noise - R co-variance matrix of the output noise - S substrate concentration (kgm^-3) - S _i input substrate concentration - t time - t _k discrete time instant with indexk=0, 1, 2,... - u(t) input vector - v(t_k) measurement (output) noise sequence - w(t) n-vector white Gaussian random process - x(t₀) initial state of the system - (t₀) expectation of the initial state values - x(t) n-dimensional state vector - x(t_k) state vector at the time instantt _k - (t_k|t_k) expectation of the state estimate at timet _k when measurements are known to the timet _k - (t_k+1|t_k) expectation of the state prediction - X biomass concentration (kgm^-3) - expectation of the biomass concentration estimate - y(t_k) m-dimensional output vector at the time instantt _k - Y _XIS substrate yield coefficient - _X|S expectation of the substrate yield coefficient estimate - specific growth rate (h^-1) - _M maximum specific growth rate (h^-1) - expectation of the maximum specific growth rate estimate - state transition matrix     

Dynamic light-scattering studies of internal motions in DNA. I. Applicability of the rouse-zimm model

The intermediate scattering function G(K,t) for any polymer model obeying a linear separable Langevin equation can be expressed in terms of the eigenvalues and eigenvectors of its normal coordinate transformation. An algorithm for the extract numerical evaluation of G(K,t) for linear Rouse-Zimm chains in the presence of hydrodynamic interaction has been developed. The computed G(K,t)² were fit to C(t) = A exp(?t/τA) + B, and apparent diffusion coefficients calculated according to D_app ≡ 1/(2τ_AK²). G(K,t)² was surprisingly well-fit by single-exponential decays, especially at both small and large values of Kb, where K is the scattering vector and b the root-mean-squared subunit extension. Plots of D_app vs K² in-variably showed a sigmoidal rise from D₀ at K² = O up to a constant plateau value at large K²b². Analytical expression for G(K,t), exact in the limit of short times, were obtained for circular Rouse-Zimm chains with and without hydrodynamic interaction, and also for free-draining linear chains, and in addition for the independent-segment-mean-force (ISMF) model. The predicted behaviors for G(K,t) at large Kb (or KR_G) was found in all cases to be single-exponential with 1/τ ∝ K² at large Kb, in agreement with the computational results. A simple procedure for estamating all parameter of the Rouse-Zimm model from a plot of D_app vs K² is proposed. Experimental data for both native and pH-denatured calf-thymus DNA in 1.0M Nacl with and without EDTA clearly plateau behavior of D_app at large values of K, in harmony with the present Rouse-Zimm and ISMF theories, and in sharp contrast to previous predictions based on the Rouse-Zimm model.     

Higher-Order Structure of Mammalian Chromatin Deduced from Viscoelastometry Data

Abstract

The results of viscoelastometry (VE) for mammalian DNA have been puzzling because they have two orders of magnitude smaller measured viscoelastic relaxation times for mammalian chromosomes than that expected for DNA linear coils of chromosomal size. In an attempt to resolve this discrepancy, we have applied a recent model of Gl chromosome structure (J.Y. Ostashevsky, Mol Biol. Cell 9, 3031–3040, 1998) in which the 30 nm chromatin fiber of each chromosome forms a string of loop clusters (micelles). This model has two parameters: the number of loops per micelle (f) and the average loop size (M_f), which can be estimated independently from VE data. Using our VE data for plateau phase V79 Chinese hamster cells (unirradiated and X-irradiated with doses up to 40 Gy) we show that f-13, which is close to other estimates made using the model (f ranges from 10–20), and M_f～ 2 Mbp, which is similar to estimates made from our nucleoid data (1.3 Mbp) and to estimates made in the literature using a variety of techniques (1–3 Mbp).     

Diffusion models for firing of a neuron with varying threshold

A stochastic model for the firing of a neuron with refractory properties is treated analytically. Refractory behavior is modeled by a threshold function θ(t) which is infinite immediately after the neuron fires, as well as during the absolute refractory period, and then decreases monotonically to the quiescent threshold level, θ_∞, during the relative refractory period. Using Wald's identity, input-output relations are derived analytically for the exponential threshold which has a time constant equal to the membrane time constant. A method for computing these relations for a general threshold is presented and is explicitly used for the general exponential threshold and the Hagiwara threshold, θ(t) = θ_∞e^α/t, where a is a constant.     

An enzyme rate equation for the overall rate of reaction of gel-immobilized glucose oxidase particles under buffered conditions. II. Two limiting substrates

The overall rate of reaction of gel-immobilized glucose oxidase particles in buffered media has been investigated theoretically under two substrate diffusion limited conditions by the numerical solution of the diffusion equations. It has been found that the Enzyme Rate Equation (Atkinson and Lester), Biotechnol. Bioeng., 16 , 1299 (1974), together with an analytical solution which describes the asymptotic conditions associated with a large particle size, provides an adequate estimation of the values resulting from the numerical solution outside the region of the parameter space defined by 0.4 < M_g′, M₀′ < 10. When the dimensionless parameter (B₀′/B_g′)(M_g′²/M₀′²) is greater than unity the overall rate of reaction is limited principally by the external concentration and when the parameter has a value less than unity, by the external oxygen concentration. The results are generally applicable to enzymes whose kinetics are similar to those of glucose oxidase or for which the equation describing glucose oxidase kinetics provides an adequate curve-fit of experimental data.     

Estimation of coefficient of coancestry using molecular markers in maize

Summary The coefficient of coancestry (f_AB) between individuals A and B is the classical measure of genetic relationship. f_AB is determined from pedigree records and is the probability that random alleles at the same locus in A and B are copies of the same ancestral allele or identical by descent (ibd). Recently, the proportion of molecular marker variants shared between A and B (S_AB) has been used to measure genetic relationship. But S_AB is an upwardly-biased estimator of f_AB, especially between distantly-related lines. f_AB, S_AB, and adjusted (to remove bias) estimates of molecular marker similarity (f _AB ^M ) were compared. RFLP banding patterns at 46 probe-restriction enzyme combinations were obtained for 23 maize inbred lines derived from the Iowa Stiff Stalk Synthetic (BSSS) maize (Zea mays L.) population, and for 4 non-BSSS lines. f _AB ^M was estimated as , where _A (or _B) was the average proportion of RFLP variants shared between inbred A (or inbred B) and the non-BSSS lines. The average f_AB among 253 pairwise combinations of BSSS lines was 0.212, whereas the average S_AB was 0.397. The average f _AB ^M was 0.162, indicating that the upward bias in S_AB was effectively removed. S_AB and f_AB were significantly different ( = 0.05) in 76.3% of the comparisons, whereas 24.9% of the f _AB ^M values differed significantly from f_AB. The latter result suggests that selection and/or drift were present during inbred line development and that f_AB may not be an accurate measure of the true proportion of ibd alleles between two lines. Cluster analyses based on S _AB ^M and f _AB ^M grouped lines according to pedigree, although several exceptions were noted. The presence of shared molecular marker variants between unrelated lines must be considered when setting S_AB-based minimum distances for varietal protection. Under simplified conditions, more than 250 molecular marker loci are necessary to obtain sufficiently precise estimates of coefficient of coancestry using molecular markers.A contribution from Limagrain Genetics, a Group Limagrain company     

Genetical assessment of induced quantitative variation following hierarchical selfing

The method of Virk, Jinks and Pooni⁽⁷⁾ has been further elaborated and illustrated with a simple example from the plant height data of Borojević and Borojević⁽³⁾ experiment on 15 kR gamma-ray-irradiated Bankut-1205 wheat variety in the M₅, M₆ and M₇ generations. A substantial amount of the induced variation for plant height has been found to be of additive and fixable nature. The practical utility of the method for testing the adequacy of a simple model and estimating the genetical components of variation has been amply demonstrated.The simplicity and distinctiveness of the new approach arises from the omission of rank 0 statistics corresponding to the M₁ plants and arriving at the genetical equivalance of rank 1 statistics in the hierarchical analysis of variance performed on the simple pedigreed data generated in a selfing series initiated in the M₁ generation following mutagenic treatment of a pure-breeding line. The new analysis avoids any assumptions about the independence or kind of dependence of mutational events and provides estimates of the additive and dominance genetical components of variation, from a single generation from M₃ onwards.     

A quantitative analysis of excluded-site effects for highly cooperative binding systems

Binding isotherms can provide quantitive information regarding the stability of a molecular complex. Theorectical studies in recent years have been directed to systems in which a single ligand can exclude more than one polymer site (excluded-site effect). This system has minium of thre parameters to describe the binding data: the intrinsic binding constant, B; the remote-neighbor cooperative paramaters, σ_q and the number of excluded sites, q. It is suggested in the present communication that precise values for these three parameters can be obtained by utilizing the characteristics of two forms of data representation: θ vs ln m and θ/m vs θ, where θ is the degree of saturation (0?θ?1) and m is the molality of free ligand. The matrix generation method is used to obtain empirical equations relating the midpoint location and slope at the midpoint of the θ vs ln m plot to the three molecular parameters. A modified Scatchard theory is also presented for highly cooperative systems, which results in an expression relaing the maximum in the θ/m vs θ plot to the molecular parameters σ_q and q, thus providing the third equation for the three unknown parameters. The novel method f analysis is illustrated with the AMP-poly(L -arginine) and oligocytidylate–T7 DNA sstems.     

Characteristic features of temperature evolution in ultracold plasmas

The theoretical interpretation of recent experiments on the time evolution of the temperature in freely expanding, ultracold plasma clouds released from a magneto-optical trap is discussed. The most interesting result of those experiments was the asymptotic behavior T _e ∝ t ^{−(1,2±0.1)}, instead of the behavior proportional to t ⁻², which was expected for a rarefied monatomic gas in the inertial expansion stage. It is shown that such a substantially slower temperature fall can be well explained by the specific properties of the equation of state of ultracold plasma with a large Coulomb coupling parameter; whereas the heat release in inelastic processes (in particular, three-body recombination) turns out to be relatively unimportant in the first approximation. This conclusion is confirmed by approximate analytic estimates from the model of virializing the energies of charged particles and also by the results of ab initio computer simulations; moreover, the computations demonstrate that the law of decrease in the electron temperature is established very rapidly, when the virialization criterion begins to be satisfied only to within a factor of order unity.