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).     

On a Characterization of the Exponential Distribution by Weak Homoscedasticity of Record Values

A sequence {X_n, n≤1} of independent and identically distributed random values with continuous cumulative distribution function F(x) is considered. X_j is a record value of this sequence if X_j ≤ max (X₁, X₂, …, X_j?1). We define L(n)=min.(j!j>L(n?1.), X_j<X_L(n?1)), with L(0) = 1. Let Z_n=X_L(n)? X_L(n?1), n ≤ 1. We will show that the conditional variance of Z_n given X_L(n?1)=x does not depend on × if and only if F(x) is exponential.     

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.     

Evaluation of lipoprotein size-density distributions from sedimentation coefficient distributions obtained at several solvent densities. I. Theory

A method is presented for the treatment of distribution functions obtained by ultra-centrifugal sedimentation velocity experiments on the plasma lipoproteins, so that adequate corrections can he made for the effects of diffusion and concentration dependence of the sedimentation coefficient. The method involves the use of modified equations derived from those presented in 1952 by Gosting for the transform from g* (S) to g(S) distributions. The evaluation of the molecular parameters of lipoprotein density and size, from a set of g(S_i°) distribution functions obtained in solvents of varying density, is also outlined. Preparations of the β-lipoprotein of human plasma are found to follow a bivariate normal distribution that requires evaluation of five parameters, x?₁, σ₁, x?₂, σ₂and p. The first two represent the mean and standard deviation of the lipoprotein density, the third and fourth the same quantities for the size, expressed as ft “logarithmic diameter parameter”, and the final value is a measure of the correlation between these two variables.     

Estimating the abundance of subterranean propagules of submersed aquatic plants

1. Data on sample means (x|) and variances (s²) of propagule abundance for five typos of aquatic plants growing in a variety of habitats were collected. The data set consisted of 379 values for x| and s², based on 4942 individual sample units (sediment samples), drawn from the literature or from data collected as part of this study. 2. Regression analysis relating log s² to log x| yielded an equation which was solved for the number of sample units (n) required to achieve a given degree of precision. For precise estimates [standard error (SE) = 20% of x|], values of n between twenty-seven and 234 are required when propagule density is low (<200m^?2), whereas eight to twenty-six sample units are required when propaguie density is high (200–1000 m^?2). For larger SE (i.e. 30% of x|), n decreased by about 50%. Sampler area (20 to 1600cm²) did not affect estimates of n. 3. Time required to collect and process sediment cores (collected with either a 5, 10, or 15cm corer) was approximately 7, 10, or 13min, respectively. Combining this information with the required number of samples is useful in planning studies designed to measure changes in the abundance of underground propagules of submersed aquatic plants.     

Calibration of FST-hemispheres against bottom shear stress in a laboratory flume*

SUMMARY.

• 1 Fliesswasserstammtisch (FST)-hemispheres of identical size but different densities were exposed on a horizontal plane on the pebble-covered bottom of a laboratory flume at streaming to shooting, turbulent and fully developed flow. The heaviest hemisphere moved was used as an indicator of shear stress, a flow force acting on the flume bottom.
• 2 The relationship between shear stress and hemisphere density was practically the same for three different sets of hemispheres, namely one prototype set newly prepared for the calibrations, one prototype set intensively used in the field prior to calibrations, and one randomly selected new set bought commercially.
• 3 Shear stress (y, dyn cm^?2) was related to hemisphere density (x, g cm^?3) by y= x^2.85 (n= 69; r²= 0.993). For lighter hemispheres this relationship was better explained by the linear model y= 7.32x– 6.60 (n= 35; r²=0.983).

     

Perception of the electromagnetic field emitted by a mobile phone

Electromagnetic sensibility refers to the ability to perceive the electromagnetic field (EMF) without necessarily developing health symptoms attributed to EMF exposure. A large sample of young healthy adults (n = 84) performed two forced‐choice tasks on the perception of the GSM mobile phone EMF (902 MHz pulsed at 217 Hz), “Was the field on?” and “Did the field change?” (3 conditions × 100 trials for each task, n = 600 trials in total). A monetary prize was announced for good performance (correct response rate ≥75%, n = 600 trials). The performance was no better than expected by chance, and thus none of the participants won the prize. Two participants showed extraordinary performance in one of the task conditions (“Was the field on?”, n = 100 trials), with correct response rates of 97% (P = 1.28 × 10^?25) and 94% (P = 9.40 × 10^?22), but they failed to replicate the result in the retest of six blocks of the same condition 1 month later. Six participants had reported being able to perceive the mobile phone EMF in the preliminary inquiry, but they performed no better than the others. This study provides empirical evidence against the existence of electromagnetic sensibility to the mobile phone EMF, demonstrating the necessity for replication in EMF studies. Bioelectromagnetics 29:154–159, 2008. © 2007 Wiley‐Liss, Inc.     

On a Class of Almost Unbiased Ratio Estimators

A class of almost unbiased ratio estimators for population mean σ is derived by weighting sample σ = (1/n) σ y_i, ratio estimators σ and an estimator, σ (y_i/x_i). It is shown that NIETO DE PASCUAL (1961) estimator is a particular member of the class and an optimum estimator in the class (in the minimum variance sense) is identified. The results are illustrated through two numerical examples.     

The estimation of a bivariate fitness function from two samples taken from a population

Summary The fitness of animals subjected to natural selection can be defined as the probability of surviving selection for a given interval of time, or some convenient multiple of this. If the fitness is related to some measurable variablesX, Y, Z,… then the relationship is expressed mathematically in the fitness functionw(x, y, z,…) and this function can be estimated by comparing the joint distribution ofX, Y, Z,… in samples taken before and after selection. In an earlier paper (Manly, 1975) the problems involved in estimating a fitness function of one variable were discussed. In the present paper various methods for estimating a bivariate fitness function are proposed and compared on some semiartificial sample data. It is concluded that either a generalized version ofO’Donald’s (1968) method of moments or a weighted multiple regression method will be most satisfactory. Alternative methods involving assumptions of normality will need to be used with great care.     

Sample Size Calculations for the Mean in a Two Component Nonstandard Mixture Distribution

We are concerned with calculating the sample size required for estimating the mean of the continuous distribution in the context of a two component nonstandard mixture distribution (i.e., a mixture of an identifiable point degenerate function F at a constant with probability P and a continuous distribution G with probability 1 – P). A common ad hoc procedure of escalating the naïve sample size n (calculated under the assumption of no point degenerate function F) by a factor of 1/(1 – P), has about 0.5 probability of achieving the pre‐specified statistical power. Such an ad hoc approach may seriously underestimate the necessary sample size and jeopardize inferences in scientific investigations. We argue that sample size calculations in this context should have a pre‐specified probability of power ≥1 – β set by the researcher at a level greater than 0.5. To that end, we propose an exact method and an approximate method to calculate sample size in this context so that the pre‐specified probability of achieving a desired statistical power is determined by the researcher. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

Differences in beech (Fagus crenata) regeneration between two types of Japanese beech forest and along a snow gradient

Differences in beech (Fagus crenata) regeneration were quantitatively investigated using power function analysis for the size–class (diameter at breast height, DBH) distribution and juvenile-to-canopy tree (J/C) ratio along a snow gradient throughout Japan. In snowy areas, all species combined, as well as F. crenata alone, showed constant regeneration, with parameter b≈−1.6 for the power function y=ax ^b (x=DBH, y=density), which is related to the DBH–class distribution. The good fit of the data to the function suggests that beech regenerates constantly with self-thinning patch dynamics. Parameter a, which indicates the abundance of small trunks, was high. Furthermore, the mean J/C ratio was ≈8, i.e., each parent beech tree produced eight juveniles. These results suggest that beech regenerates constantly with gap dynamics in snowy beech forests on the Japan Sea side of Japan (snowy). However, the fit of F. crenata was lower and nonsignificant in some forests in less snowy areas, despite the high fit of all species combined. In these areas, the mean of a was low, and b was often near zero for F. crenata regressions. These results suggest that the abundance of beech was low, and self-thinning was not evident because of the initial low abundance. Moreover, the mean J/C ratio was <1.0, suggesting that juvenile density was lower than that of canopy trees. Thus, the regeneration of F. crenata on the Pacific Ocean side of Japan (less snowy) is rather sporadic. Less snowy conditions may promote seed desiccation, predation of beechnuts and seedlings, and water stress. Lower F. crenata density may also reduce predator satiation and wind pollination.     

Torsional and Bending Rigidity of the Double Helix from Data on Small DNA Rings

Abstract

We have calculated the variance of equilibrium distribution of a circular wormlike polymer chain over the writhing number, ?(Wr)²?, as a function of the number of Kuhn statistical segments, n, For large n these data splice well with our earlier results obtained for a circular freely jointed polymer chain. Assuming that ?(ΔLk)²? = ?(ΔTw)²? + ?(Wr)²? we have compared our results with experimental data on the chain length dependence of the ?(ΔLk) ²? value recently obtained by Horowitz and Wang for small DNA rings. This comparison has shown an excellent agreement between theory and experiment and yielded a reliable estimate of the torsional and bending rigidity parameters. Namely, the torsional rigidity constant is C = 3.0·10^?19 erg cm, and the bending rigidity as expressed in terms of the DNA persistence length is a = 500 A. The obtained value of C agrees well with earlier estimates by Shore and Baldwin as well as by Horowitz and Wang whereas the a value is in accord with the data of Hagerman. We have found the data of Shore and Baldwin on the chain length dependence of the ?(ΔLk) ²? value to be entirely inconsistent with our theoretical results.     

Spatial Distribution of the Potential on a Cylindrical Surface Simulating the Somatic Membrane: Model Studies

In our study, we represent the theoretical and numerical analysis of a stochastic version of the Hodgkin–Huxley model applied to a two-dimensional spatial cylindrical area simulating the neuronal somatic membrane. We characterized the spatiotemporal dynamics of the membrane potential by its local value V _m (x, y, t) and the integral of this value with respect to time F(x, y, T) within an interval [0, T]. Analysis of the model showed that (i) there are nonzero gradients of F(x, y, T) at any distribution of ion channels; (ii) the maximum gradient F(x, y, T) decreases down to zero with the time T, if the channels are distributed homogeneously, and acquire some positive constant value, if the channels are distributed inhomogeneously; the gradient F(x, y, T) depends on the gradient of spatial distribution of the channels; and (iii) under conditions of spatial redistribution of the channels with preservation of their number, the dynamics of V _m (x, y, t) does not change.     

Chemical Studies on Components of Dried Bonito, “Katsuobushi”

Volatile components obtained by the extraction of “Katsuobushi” with 80% ethanol and by the subsequent steam distillation of the extract were fractionated by the usual methods, and the resulting hydrocarbon fraction was investigated. Gas chromatographic study on this fraction originated from “Katsuobushi” of bonito (Katsuwonus pelamis) revealed 9 hydrocarbons, including n-tetradecane, n-pentadecane, n-hexadecane, n-heptadecane, n-octadecane, n-nonadecane, n-eicosane, n-heneicosane and n-docosane, which were tentatively identified by the retention times with the aid of authentic hydrocarbons. n-Pentadecane and n-heptadecane that were main components among these hydrocarbons were identified further by NMR and IR spectrometry. “Katsuobushi” of frigate mackerel (Auxis thazard), mackerel (Scomber Japonicus Houttuyn) or muroaji (Decapterus muroadsi) also contained n-penta-decane and n-heptadecane in large amounts, but did other hydrocarbons in negligible amounts.

Possible mechanisms of the hydrocarbon formation during the processing of “Katsuobushi” were discussed.     

Phylogenetic relationships in the Sceloporus variabilis (Squamata: Phrynosomatidae) complex based on three molecular markers,continuous characters and geometric morphometric data

The monophyly of the Sceloporus variabilis group is well established with five species and two species complexes, but phylogenetic relationships within species complexes are still uncertain. We studied 278 specimens in 20 terminals to sample all taxa in the “variabilis group,” including three subspecies in the “variabilis complex,” and two outgroups (Sceloporus grammicus and Sceloporus megalepidurus). We assembled an extensive morphological data set with discrete and continuous characters (distances and scale counts), including geometric morphometric data (landmark coordinates of three shapes), and a three‐marker molecular data set as well (ND4, 12S and RAG1). We conducted parsimony and Bayesian phylogenetic inferences on these data, including several partitioning and weighting schemes. We suggest elevating three subspecies to full species status. Therefore, we recommend recognition of nine species in the “variabilis group.” First, S. variabilis is sister to Sceloporus teapensis. In turn, Sceloporus cozumelae is sister to Sceloporus olloporus. These four species are a monophyletic group, which is sister to Sceloporus smithi. Finally, Sceloporus marmoratus is sister of the clade of five species. The other species in the “variabilis group” (Sceloporus chrysostictus, Sceloporus couchii and Sceloporus parvus) are a paraphyletic grade at the base of the tree. Our analyses reject the existence of the “variabilis complex.” We conducted a parsimony‐based ancestral reconstruction on body size (snout–vent length), femoral pores and dorsal scales and related morphological changes to geographic distribution of the species. Our phylogenetic hypothesis will allow best designs of comparative studies with species in the “variabilis group,” one of the earliest divergent lineages in the genus.     

Calculations of the circular dichroism of double-helical nucleic acids. II. Effects involving n leads to pi transitions

The circular dichroism of double-helical nucleic acids was calculated as a function of geometry, including terms involving n → π* transitions. The “nonbonding” n or σ orbitals were of the azine type, delocalized, but concentrated at the nitrogen atoms of the purines and pyrimidines. Dynamic coupling of the magnetic moments of the n → π* transitions with the electric moments of π → π* transitions generated important terms. Mixing of electric dipole character into n → π* transitions by the static electric field perturbation of the molecule is of lesser importance. The largest contributions of n → π* transitions to the circular dichroism of double-helical nucleic acids are comparable in magnitude to the sum of π → π* terms only for geometries where the circular dichroism is weak. Using both n → π* and π → π* contributions one is able to match experimental and calculated circular dichroism spectra for DNA's over a much wider range of conditions than was possible previously.     

Bayesian Estimation in a Generalized Negative Binomial Distribution

A generalized negative binomial (GNB) distribution was introduced by JAIN and CONSUL (1971) and was modified by NELSON (1975). The probability function of the distribution is defined by the function p(x; m, β, θ)= θ^x (1 - θ)^m+βx—x for x=0, 1, …, and zero otherwise, where m>0, 0<θ<1 and β=0 or 1≦β<θ^?1. The Bayes estimators for a number of parametric functions of θ when m and β are known are derived. The prior information on θ may be given by a beta distribution, B(a, b), to which no subjective significance is attached. It has been illustrated that the parameters in the prior distribution can be assigned by a computer. Comparisons are made of the Bayes estimate of P(X=k) to the corresponding ML estimate and the MVU estimate for any given sample to the order n^?1 for different values of k..     

Optimized Temperature Effect of Li‐Ion Diffusion with Layer Distance in Li(NixMnyCoz)O2 Cathode Materials for High Performance Li‐Ion Battery

Understanding and optimizing the temperature effects of Li‐ion diffusion by analyzing crystal structures of layered Li(Ni_xMn_yCo_z)O₂ (NMC) (x + y + z = 1) materials is important to develop advanced rechargeable Li‐ion batteries (LIBs) for multi‐temperature applications with high power density. Combined with experiments and ab initio calculations, the layer distances and kinetics of Li‐ion diffusion of LiNi_xMn_yCo_zO₂ (NMC) materials in different states of Li‐ion de‐intercalation and temperatures are investigated systematically. An improved model is also developed to reduce the system error of the “Galvanostatic Intermittent Titration Technique” with a correction of NMC particle size distribution. The Li‐ion diffusion coefficients of all the NMC materials are measured from ?25 to 50 °C. It is found that the Li‐ion diffusion coefficient of LiNi_0.6Mn_0.2Co_0.2O₂ is the largest with the minimum temperature effect. Ab initio calculations and XRD measurements indicate that the larger Li slab space benefits to Li‐ion diffusion with minimum temperature effect in layered NMC materials.     

Bivariate Modified Power Series Distribution Some Properties,Estimation and Applications

The class of bivariate modified power series probability distribution (BMPSD) has been defined by P(X = x, Y=y) =a(x, y) (g(?₁ ?₂))^x (h(?₁, ?₂))^xwhere a(x,y) is a sub-set of the Cartesian product of the set of non-negative integers and g(?₁, ?₂), h(?₁ ?₂) and f(?₁, (?₁, ?₂) are positive finite and successively differentiable functions of ?₁and ?₂. It includes a very large number of well known probability distributions. The recurrence relations for central moments and factorial moments have been determined. Also, the M.L. estimators for ?₁ and ?₂ and their asymptotic biases and variances are obtained. Some important properties are discussed. The results of an BMPSD have been applied to derive the corresponding results for the bivariate generalized negative bino-mial distribution and the bivariate Lagrangian Poisson distribution.