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.     

Helix-coiled transition in heteropolymers. I. Ground-state energy

A new technique is presented for treating the ground state of an heteropolymer with a random sequence of components. An exact system of equations is found for determining the ground state energy E which is equal to the polymer free energy f in the lowest-order approximation in T/V (V/2 is the large “surface” energy arising at the boundaries between coiled and “helical” sections: V ? T, U_k; U₁ and –U₂ are the free energies of the components counted from the corresponding coiled state energies). These equations are essentially simplified at certain fixed values of the ratio U₁/U₂. For integer values of U₂/U₁ and U₁/U₂ a solution is obtained with an accuracy exp(–V/U_k). The ground-state energy as a function of U₁ and U₂ is shown to be highly irregular: its derivatives have jumps at an infinite number of points. These jumps provide a fine structure of the melting curves. A smoothed over the jumps function E′ is found by way of analytic continuation from the integer values of U₁/U₂ and U₂/U₁. The accuracy of the approximation f ≈ E is estimated and the correctional term of order T/V is determined.     

Molecular phylogeny of Macrolycus (Coleoptera: Lycidae) with description of new species from China

Macrolycus is a genus of net‐winged beetles with 69 species distributed in the eastern Palearctic and northernmost part of the Oriental region. The first molecular phylogeny of Macrolycus was produced using an rrnL + tRNA‐Leu + nad1 mtDNA fragment. The major lineages and species limits were identified with morphology and molecular data. We propose that Cerceros is a subgenus of Macrolycus to enable identification of all adult specimens in the genus without DNA sequencing. Two species groups are proposed in Macrolycus s. str. and six in Cerceros. Additionally, twelve Macrolycus species are newly described from China: M. aquilinus, M. baihualingensis, M. bicolor, M. guangxiensis, M. jianfenglingensis, M. kuatunensis, M. lizipingensis, M. parvus, M. phoeniceus, M. rhodoneurus, M. rosaceus and M. sichuanensis. Macrolycus holzschuhi is proposed to be a junior subjective synonym of M. jeanvoinei. The highest diversity of Macrolycus is found in southern China. The species from the main islands of Japan are placed in two species groups: M. excellens is a sister to remaining species of the M. murzini group and the M. flabellatus group is a monophylum of closely related species in a sister position to the M. bicolor group.     

Consistency of the Asymptotic Quasi-Likelihood Estimate on Linear Models

Consider a model y_t = f_t(θ) + M_t, 0 ⩽ t ⩽ T where θ∈ Θ in an unknown parameter, f_t(θ) is a linear predictable process, M_t is a martingale difference, and the nature of E(M²_t/ℱ_t—1) is unknown. This paper presents an estimating procedure for θ based on the asymptotic quasi-likelihood methodology. Conditions under which the asymptotic quasi-likelihood estimate converges to the true parameter θ₀ are discussed. This method is applied to several simulated examples, and estimates of the unknown parameter are obtained by means of a two-stage technique. Comparison is made between the estimates obtained via this method and those obtained via the ordinary least squares method. Discussion is provided on the application of the model.     

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.     

Automobile driving as psychophysical discrimination

The driver tries to keep the car in the center of the lane. If the car is too near the left edge, this causes the driver to make a “corrective” right turn. If the car is near the right edge, a “corrective” left turn is made. Therefore, a quantity which decreases with increasing distance Δ _L from the left edge may be considered as a stimulusS _R producing the reactionR _R of turning to the right. A similar situation holds for the distance Δ _R from the right edge. When the car is in the center of the lane, Δ _L = Δ _R andS _R =S _L , the stimuli are equal. We thus have here a situation analogous to the one studied by H. D. Landahl in his theory of psychophysical discrimination. In general a reactionR _R (resp.R _L ) will occur only ifR _R −R _L ≥h ^* (resp.R _L −R _R ≥h ^*) whereh ^* is a threshold. Applying Landahl’s theory to this situation, we find thath ^* determines the distance from the edge, at which a corrective turn is made. This distance is not constant, but a function of the speedv of the car. The requirement that a corrective turn should be madebeforre the car runs off the road leads to an expression for the maximum safe speed. Because of the transcendency of the equations involved, closed solutions cannot be obtained. It is, however, shown that the expression for maximum safe speed, given in a previous paper (Bull. Math. Biophysics,21, 299–308, 1959), is a rough first approximation to the expressions found now.     

Tests of Independence and Zero Correlations Among P Random Variables

Suppose it is desired to determine whether there is an association between any pair of p random variables. A common approach is to test H₀ : R = I, where R is the usual population correlation matrix. A closely related approach is to test H₀ : R_pb = I, where R_pb is the matrix of percentage bend correlations. In so far as type I errors are a concern, at a minimum any test of H₀ should have a type I error probability close to the nominal level when all pairs of random variables are independent. Currently, the Gupta-Rathie method is relatively successful at controlling the probability of a type I error when testing H₀: R = I, but as illustrated in this paper, it can fail when sampling from nonnormal distributions. The main goal in this paper is to describe a new test of H₀: R_pb = I that continues to give reasonable control over the probability of a type I error in the situations where the Gupta-Rathie method fails. Even under normality, the new method has advantages when the sample size is small relative to p. Moreover, when there is dependence, but all correlations are equal to zero, the new method continues to give good control over the probability of a type I error while the Gupta-Rathie method does not. The paper also reports simulation results on a bootstrap confidence interval for the percentage bend correlation.     

Approximate Michaelis-Menten kinetics displayed in a stochastic model of cell-mediated cytotoxicity

A nonlinear continuous-time Markov chain describing a two-step process of cytolytic cells binding to target and the subsequent lysis and release of label is shown to have kinetics which resemble standard enzyme-substrate kinetics. The Michaelis-Menten saturation function is found as a special case resulting when the target population is in excess. A comparison theorem for the pseudo-steady-state distribution Π is constructed to enable examination of that distribution whose expected value E and variance V satisfy - K_mE + (C_T − E)(T_T − E) + V = 0, where K_m is the Michaelis half-saturation constant and C_T and T_T are the initial populations of the two cell types. Using Π as an initial condition, the release of label process is examined. The main result is that the fraction of specific release, ƒ, has the approximate form when T_t is large, so that a nonlinear regression procedure is appropriate for the determination of the parameters.     

Autonomy of the wingless mutation in Drosophila melanogaster

Summary T(Y;2) translocations were used to cytologically localise the wingless locus of Drosophila melanogaster. We found that an existing T(Y;2), which is an insertion of a segment of 2L into the Y chromosome, has wg ⁺ within this insert. This Y chromosome was used to generate an attached XY chromosome containing wg ⁺. The mutation claret-nondisjunctional (ca ^nd) was used to induce the loss of this XY chromosome and thus generate gynandromorphs with wg ¹/wg ¹ male tissue and wg ⁺/wg ¹/wg ¹ female tissue. Analysis of these gynanders demonstrated that a genotypically wingless mutant hemithorax is usually also phenotypically mutant in these half body mosaics; thus wg ¹ is discautonomous. This observation is of interest as it is known that wg is not cell autonomous.     

Quasielastic light scattering from solutions of lollipop-shaped particles

An expression is derived for the field correlation function of the light scattered from a solution of lollipop-shaped particles. Such particles are a tractable model of certain bacteriophages. They are assumed to consist of an ellipsoidal head containing optically anisotropic scattering material and a tail which does not scatter. Because of the tail, Brownian rotational movement occurs around a center of rotational friction which is at a distance r₀ from the center of the head. The dependence of the field correlation function C(τ) on the rotational diffusion coefficient D_R is given by the factor Σ_lB_l exp[?l(l + 1)D_Rτ]. It is shown that the tail causes the coefficients B_l to be different from zero for all values of l. Therefore, C(τ) contains a term proportional to exp(?2D_Rτ), which is not present when r₀ = 0. We give plots of B_l for various combinations of parameters. It turns out that dynamic light scattering may be used to measure r₀.     

The mathematical theory of group selection. I. Full solution of a nonlinear Levins E = E(x) model

The first complete overtime solution is obtained for a group selection model of Levins E = E(x) type with recolonization but no other gene flow between islands. Assuming a subdivided population at carrying capacity, the model describes selection at a biallelic locus (A, a) where a is opposed by Mendelian selection but is favored by a lower rate of extinction of demes having high a frequency. By contrast to the linear diffusion equations encountered in classical mathematical genetics, the PDE governing the dynamics is now nonlinear in the metapopulation gene frequency distribution φ(x, t); furthermore, the initial conditions now heavily influence the equilibrium distribution φ_∞(x). A fully explicit formula (20) expressing this dependence is derived. The results indicate that a fixation is never reached, but (A, a) polymorphism in the metapopulation will result if , where s 1 parametrizes the strength of Mendelian selection, E(x) is the Levins extinction operator, h (typically in the open interval (0, 1)) is the dominance of a, and B is a parameter measuring the flatness of the initial distribution f(x) in the x → 1 limit.     

Notes on some rare Dicranaceae

Abstract

Dicranella riparia is shown to be more appropriately treated as Kiaeria riparia comb. nov.; Kiaeria glacialis is shown to be a misfit in Dicranum; Oncophorus sardous is placed in synonymy of O. wahlenbergii; Arctoa anderssonii is shown to be a distinct species.     

Beschreibung einer neuen Carabus (Lamprostus)-Art aus Persien (Coleoptera: Carabidae)

Abstract

A new species of Carabus (Lamprostus) from the province of Gilan, Iran, is described and illustrated: Carabus (Lamprostus) staveni sp. nov., Carabus (Pachystus) rechingerae Mandl, 1972, is considered a junior synonym of Carabus (Lamprostus) calleyi nigrinus Motschulsky, 1865. The specific status of Carabus (Sphodristocarabus) korgei Heinz, 1970, is restored (stat. rev.) and Carabus separatus delirensis Deuve, 2000, is considered to be a junior synonym of it. Carabus (Megodontus) stroganowi javahardensis Deuve, 2000, is considered to be a synonym of Carabus (Megodontus) heinrichi Mandl, 1966; both taxa are from the same type locality.     

A statistical model of the reproduction of aphids

1. The logistic function has been generally used to describe the reproductive process of a “population” of animal. However, this model can not give us any information about the reproductive process of “individuals” in the population. In this study a statistical model on the basis of the reproduction of individuals of barley aphid is presented to find the proportion of the mature individuals, the heterogeneity in reproductive ability of the aphids, etc.
2. The model is constructed as follows:
3. The probability that j insects are found on a plant at time t₀ is represented as Q(j).
4. The probability that h individuals of j have reproductive ability, say, mature individuals, in the period t₀ to t₁ is represented as B(h/j)=_jC_hw^h(1−w)^j−h, where w is the proportion of mature individuals.
5. In a population with a homogeneous reproductive ability, the probability that each parent lays i offspring in the period t₀ to t₁ is represented as P(i/m)=e^−mmⁱ/i!, where m is mean. And, in a population, m changes according to the gamma distribution. Hence the probability that a parent lays i offspring between t₀ and t₁ is represented as , where p and k are parameters of negative binomial distribution. The probability that h parents on a plant lays s offspring is represented as .
6. From the assumptions mentioned above, the probability that s offspring are to be found at time t₁ on a plant with the original j individuals at time t₀ is represented by
7. The experimental populations were demonstrated to fit well to the model.

     

Genetic interactions suggest that Danforth's short tail (Sd) is a gain-of-function mutation

Danforth's short tail (Sd) is a semidominant mutation on mouse chromosome 2 that acts cell autonomously in the notochord and leads to its disintegration, and thus causes severe defects in somite patterning and vertebral column development. The molecular nature of the Sd gene and mutation is unknown, and it is unclear whether Sd is a loss-of-function mutation and the semidominant inheritance of the Sd phenotype is due to haploinsufficiency, or whether Sd represents a gain-of-function mutation in a gene essential for notochord development and maintenance. Here, we report on the genetic interaction between Sd and an insertional mutation called Etl4^lacZ, which provides genetic evidence that Sd is a gain-of-function mutation. Etl4^lacZ is an enhancer trap insertion, which gives rise to lacZ expression in distinct cell types, including the notochord. In homozygosity, the lacZ insertion leads to abnormal vertebrae in the caudal part of the vertebral column. Etl4^lacZ maps approximately 0.75 cM distal to Sd, and in double heterozygotes modifies the Sdphenotype contrarily, depending on the chromosomal configuration of the Sd and Etl4^lacZ mutations: when Etl4^lacZ is present on the chromosome wild type for Sd (Sd +/+ Etl4^lacZ; trans configuration), the Sd phenotype is enhanced, i.e., vertebral malformations extend to more anterior positions and the vertebral body of the axis is further reduced. Conversely, when Etl4^lacZ is present on the same chromosome as Sd (Sd Etl4^lacZ /+ +; cis configuration), the Sd phenotype is attenuated, i.e., vertebral malformations are confined to more posterior levels, and the dens axis, which is severely reduced or absent in Sd heterozygotes, is restored. The different effect of the Etl4^lacZ insertion on Sd, depending on its presence in trans or cis, suggests a direct interaction of the transgene insertion with the Sd gene. Additionally, the attenuation of the Sd phenotype by Etl4^lacZ in cis suggests that Sd is a gain-of-function mutation and lends support to the idea that Etl4^lacZ is a new allele of Sd. Dev. Genet. 23:86–96, 1998. © 1998 Wiley-Liss, Inc.     

TFS1: A suppressor of cdc25 mutations in Saccharomyces cerevisiae

Summary The TFS1 gene of Saccharomyces cerevisiae is a dosage-dependent suppressor of cdc25 mutations. Overexpression of TFS1 does not alleviate defects of temperature-sensitive adenylyl cyclase (cdc35) or ras2 disruption mutations. The ability of TFS1 to suppress cdc25 is allele specific: the temperature-sensitive cdc25-1 mutation is suppressed efficiently but the cdc25-5 mutation and two disruption mutations are only partially suppressed. TFS1 maps to a previously undefined locus on chromosome XII between RDN1 and CDC42. The DNA sequence of TFS1 contains a single long open reading frame encoding a 219 amino acid polypeptide that is similar in sequence to two mammalian brain proteins. Insertion and deletion mutations in TFS1 are haploviable, indicating that TFS1 is not essential for growth.