On testing hypotheses concerning standardized mortality ratios

This paper describes tests of hypotheses concerning the equality of any k standardized mortality ratios (or, equivalently, of any k indirect adjusted rates) from p(≥k) populations. The distinction is made between the situation where the standard population is chosen independently of the p populations and one where the standard is formed by pooling all p populations. Different test procedures are required for these two situations. When the pooled standard is used, the appropriate test procedure is applicable only when k = p. Experimental evidence is given showing that when the pooled standard is used both test procedures lead to the same conclusion concerning the hypothesis for the case k = p. The recommendation is made, therefore, to use the “incorrect” test procedure when the standard is a pooled one even when k < p.     

Accurate Computation of Survival Statistics in Genome-Wide Studies

A key challenge in genomics is to identify genetic variants that distinguish patients with different survival time following diagnosis or treatment. While the log-rank test is widely used for this purpose, nearly all implementations of the log-rank test rely on an asymptotic approximation that is not appropriate in many genomics applications. This is because: the two populations determined by a genetic variant may have very different sizes; and the evaluation of many possible variants demands highly accurate computation of very small p-values. We demonstrate this problem for cancer genomics data where the standard log-rank test leads to many false positive associations between somatic mutations and survival time. We develop and analyze a novel algorithm, Exact Log-rank Test (ExaLT), that accurately computes the p-value of the log-rank statistic under an exact distribution that is appropriate for any size populations. We demonstrate the advantages of ExaLT on data from published cancer genomics studies, finding significant differences from the reported p-values. We analyze somatic mutations in six cancer types from The Cancer Genome Atlas (TCGA), finding mutations with known association to survival as well as several novel associations. In contrast, standard implementations of the log-rank test report dozens-hundreds of likely false positive associations as more significant than these known associations.     

ON THE MEASURE OF EXCITABILITY

Recent time-intensity data by Rushton (1932) on the sciatic nerve of the frog are shown to provide additional support to the writer''s suggestion (1932, a) that integrals of the equation See PDF for Equation where V is the applied voltage, p is the local excitatory process and K and k are constants adequately represent the just effective direct current stimuli when the threshold value of p is made a linear function of the voltage of the form h ± α V where h and α are constants. The measurement of excitability is discussed and it is shown that the criteria for "true" measurements are not likely to be found by the agreement of the data with canonical time-intensity functions as suggested by Lapicque (1931) but rather in the establishing of standard experimental conditions. These conditions may permit the use of chronaxie as a measure of excitability, but it seems more likely that the constant k of the above equation will have to be adopted. There is sufficient evidence to cast considerable doubt on the validity of any conclusions drawn from the existing measurements of chronaxie although those derived through a particular technique may be valid. The problem requires a thorough experimental investigation in terms of integrals of the above equation.     

Simulation of Interstitial Fluid Flow in Ligaments: Comparison among Stokes,Brinkman and Darcy Models

In this paper, we use Stokes, Brinkman and Darcy equations to approximate the porous continuum media of ligament tissues respectively, simulate the flow field with FLUENT software, and study the shear stress on the cell surface due to the interstitial fluid flow. Since the Brinkman equation approaches Stokes equation well in high hydraulic permeability (k_p) condition (k_p ≥1.0×10^-8 m² in our numerical simulation), and it is an approximation to Darcy model in low k_p condition (k_p ≤5.0×10^-12 m² in our numerical simulation), we used the Brinkman model to simulate the interstitial fluid flow in the ligament where k_p is approximately 1.0×10^-16 m². It shows k_p and anisotropic property have a little effect on the flow field, but have a great effect on the shear stress on the membrane of interstitial cells (τ_cell). There is a linear relationship between τ_cell and , when k_p =1.0×10^-16 m² and the maximum τ_cell (τ_cell,max) is approximately 10 Pa. The anisotropic property will affect τ_cell''s distribution on the cell surface. When k_x/k_y>1, low τ_cell dominates the cell, while when k_x/k_y<1, high τ_cell dominants the cell.     

Use of known Coefficients of Variation in the Estimation of the Common mean of two Normal Populations

The problem of estimating the common mean of two normal populations N(?, a1?2) and N(?, a2?2) where the coefficients of variation of two populations respectively, are known constants, on the basis of two independent random samples, one from each population, is considered. The minimum mean square estimator is proposed. It is also shown that the proposed estimator is Best Asymptotic Normal (BAN) estimator. It is pointed out that the result can be generalized to k population problem. It is remarked that the same method works, also for the problem of estimating the common standard deviation of k normal populations when coefficients of variation are known.     

ON THE RELATION OF DIRECT CURRENTS TO CONDENSER DISCHARGES AS STIMULI

Data on the electrical stimulation of sciatic-gastrocnemius preparations of the frog by both direct currents and condenser discharges at the same time are discussed in relation to the validity of the differential equation See PDF for Equation where p is the local excitatory process, V the stimulating current or voltage, and K and k are constants. It is concluded that the constant k is the same whether it is derived from the data of the one stimulus or the other when the same fibres are being stimulated.     

Robust Umbrella Tests for a Generalized Behrens-Fisher Problem

This paper is concerned with testing for umbrella alternatives in a k-sample location problem when the underlying populations have possibly different shapes. Following CHEN and WOLFE (1990b), rank-based modifications of the HETTMANSPERGER-NORTON (1987) tests are considered for both the settings where the peak of the umbrella is known and where it is unknown. The proposed procedures are exactly distribution-free when the continuous populations are identical with any shape. Moreover, the modified test for peak-known umbrella alternatives remains asymptotically distribution-free when the continuous populations are assumed to be symmetric, even if they differ in shapes. Comparative results of a Monte Carlo study are presented.     

Gametic Frequency of Second Chromosomes of the T-007 Type in a Natural Population of DROSOPHILA MELANOGASTER in Texas

The T-007 second chromosome, which was isolated from a natural population of Drosophila melanogaster in south Texas in 1970, is known to show, when made heterozygous in males with a standard cn bw second chromosome, a transmission frequency (k) of 0.35—much lower than the theoretically expected 0.5. Natural populations of this species in Texas contain second chromosomes that, against the standard cn bw genetic background, are associated with distorted transmission frequencies comparable to that of the T-007 chromosome. In order to explain how such chromosomes can persist in natural populations in nontrivial frequencies, it has been postulated that, although such chromosomes show reduced k values when tested under the genetic background of a laboratory stock such as cn bw, they may show, on the average, k values larger than 0.5 under natural genetic backgrounds. If this were true, the frequency of chromosomes of the T-007 type (T chromosomes) should be higher in male than in female gametes under natural genetic backgrounds. The present study was conducted to examine this possibility. The results clearly showed that the frequency of such chromosomes was much higher among male than among female gametes, and that the transmission frequency of this type of chromosome was higher than 0.5 under natural genetic backgrounds. These results suggest that T chromosomes behave like Segregation Distorter (SD) chromosomes in natural populations of this species in Texas. A possible relationship between T-007 and SD chromosomes is suggested.     

Estimating Litter Decomposition Rate in Single-Pool Models Using Nonlinear Beta Regression

Litter decomposition rate (k) is typically estimated from proportional litter mass loss data using models that assume constant, normally distributed errors. However, such data often show non-normal errors with reduced variance near bounds (0 or 1), potentially leading to biased k estimates. We compared the performance of nonlinear regression using the beta distribution, which is well-suited to bounded data and this type of heteroscedasticity, to standard nonlinear regression (normal errors) on simulated and real litter decomposition data. Although the beta model often provided better fits to the simulated data (based on the corrected Akaike Information Criterion, AIC_c), standard nonlinear regression was robust to violation of homoscedasticity and gave equally or more accurate k estimates as nonlinear beta regression. Our simulation results also suggest that k estimates will be most accurate when study length captures mid to late stage decomposition (50–80% mass loss) and the number of measurements through time is ≥5. Regression method and data transformation choices had the smallest impact on k estimates during mid and late stage decomposition. Estimates of k were more variable among methods and generally less accurate during early and end stage decomposition. With real data, neither model was predominately best; in most cases the models were indistinguishable based on AIC_c, and gave similar k estimates. However, when decomposition rates were high, normal and beta model k estimates often diverged substantially. Therefore, we recommend a pragmatic approach where both models are compared and the best is selected for a given data set. Alternatively, both models may be used via model averaging to develop weighted parameter estimates. We provide code to perform nonlinear beta regression with freely available software.     

Multiple liquid-liquid partition: II. Theory of Martin-Synge distribution (MSD)

The theory of Martin-Synge distribution (MSD) was refined, with special attention being focused upon the derivation of the separation functions. The separation function for the fundamental distribution of MSD was obtained in the form v = t²(αk₁ + 1)(αk₁ + β)[(αk₁ + 1)^1/2 + (αk₁ + β)^1/2]²/αk₁(β ? 1)², where ν is the number of aliquots v_m driven through the apparatus, t the abscissa of the standard normal distribution, α = v_m/v₈ the phase ratio, β = k₁/k₂≥ 1 the separation factor, and k₁ the partition coefficient of the more rapidly moving component; ν was shown to have minima at given αk₁ values. The separation function of the single withdrawal of MSD was presented in the form N = u + 1 = t²(2αk₁ + β + 1)²/(β ? 1)²+ 1, where N is the number of partition units; N is minimal when αk₁ = 0. The elution volumes and standard deviations of the two compounds to be separated were mathematically analyzed in a manner similar to that previously presented when dealing with the theory of counter-current distribution (CCD). As in CCD, the elution volumes in MSD were found to have minima at given αk₁ values. However, the standard deviations of the elution curves also have minima in respect to αk₁ in MSD, which is a different situation as compared to CCD. The selection of optimal operating conditions was found to be more critical in MSD than in CCD.     

Effect of coat color mutations on behavioral polymorphism in farm populations of American minks (<Emphasis Type="Italic">Mustela vison</Emphasis> Schreber, 1777) and sables (<Emphasis Type="Italic">Martes zibellina</Emphasis> Linnaeus, 1758)

Behavioral polymorphism estimated by the expression of the defensive reaction towards humans has been studied in farm-bred American minks and sables with different color types. Most animals (both minks and sables) from farm populations displayed passive defensive behavior towards humans in the standard hand catch test. Coat color genes have been found to have pleiotropic effects; they influence both the penetrance and expressivity of domestication behavior: in animals with aberrant color types (both sapphire minks and white-and-black sables), the proportion of animals with domestication behavior and the expressivity of this behavior are significantly higher (p < 0.01 and p < 0.001, respectively).     

A rapid assay for the binding of actinomycin to DNA.

The theory of countercurrent distribution (CCD) was reviewed and extended. The separation function for the fundamental distribution of CCD was presented in the form n = t²(αk₁+β)²/αk₁(β?1)² where n is the number of transfers, t the abscissa of the standard normal distribution, α = v_m/v₈ the phase ratio, β = k₁/k₂≥ 1 the separation factor, and k₁ the partition coefficient of the more radidly moving component; n was found to be minimal on the condition αk₁ = β. The separation function for the single withdrawal of CCD was obtained in the form N = u + 1 = t²{(αk₁ + 1)^1/2 + [β(αk₁ + β)]^1/2}²/(β ? 1)²+ 1, where N is the number of partition units. From this equation it appears that N is minimal when αk₁ = 0. Compared with the former separation functions presented in the literature, these separation functions have the advantage of giving directly the relationships among the phase ratio, the absolute partition coefficient, the separation factor, the resolution degree, and the number of transfers or partition units required. In addition, the dependencies of the elution volumes and the widths of the elution curves on α, β, and the partition coefficients were considered mathematically by means of differential calculus. The elution volumes were found to have minima at certain αk₁ values. The standard deviations, on the contrary, did not have minima in respect to αk₁. The theory presented can be used for selecting proper operating conditions while separating chemical compounds.     

Local homology recognition and distance measures in linear time using compressed amino acid alphabets

Methods for discovery of local similarities and estimation of evolutionary distance by identifying k-mers (contiguous subsequences of length k) common to two sequences are described. Given unaligned sequences of length L, these methods have O(L) time complexity. The ability of compressed amino acid alphabets to extend these techniques to distantly related proteins was investigated. The performance of these algorithms was evaluated for different alphabets and choices of k using a test set of 1848 pairs of structurally alignable sequences selected from the FSSP database. Distance measures derived from k-mer counting were found to correlate well with percentage identity derived from sequence alignments. Compressed alphabets were seen to improve performance in local similarity discovery, but no evidence was found of improvements when applied to distance estimates. The performance of our local similarity discovery method was compared with the fast Fourier transform (FFT) used in MAFFT, which has O(L log L) time complexity. The method for achieving comparable coverage to FFT is revealed here, and is more than an order of magnitude faster. We suggest using k-mer distance for fast, approximate phylogenetic tree construction, and show that a speed improvement of more than three orders of magnitude can be achieved relative to standard distance methods, which require alignments.     

Capillary operators

The goal of this work is an examination of capillary exchange models as mathematical operators. The concentration function relations for the Krogh cylinder of a single capillary, basic to many organ models, are studied via the theory of operators on the Lebesgue normed spacesL _p[0,∞], (1<-p<-∞). A discussion is included of theL _p -normsvis-à-vis the coefficient of variation currently used in finding capillary parameters and evaluating parameter searches. The capillary model determines two operators on the space of locally integrable functions: O _K (relating extravascular concentration to intravascular) and K _{a, k} (relating intravascular concentration to input), wherek is the ratio of permeabilitysurface area (PS) to extravascular volume, and α is the ratio of PS to flow. These operators are shown to induce contractive (‖O _K ‖ _p <-1, ‖K _{a, k} ‖ _p <-1), isotone, linear operators onL _p . The uniform convergence relation $$K_{a,k} = \mathop {\lim _{(p)} }\limits_{N \to \infty } \left( {\sum\limits_{n = 0}^N {P_n (a)O_k^n } } \right)$$ (as operators onL _p) is derived, whereP _n (a) is the Poisson probabilitye ^?a a ⁿ /n!. For the important special cases ofp=∞, 1, 2 the norms are found (‖O_k‖=‖K_a,k‖_p=1). Consideration is also given to the norms and operators when the functions involved are limited to a finite interval of time.     

Reactions of iron-sulfur proteins with the aquated electron

The reaction of parsley 2Fe-2S ferredoxin in the normal oxidized state with e_aq^? generated by pulse radiolysis techniques has been studied at ～25°C, pH 7–8, I = 0.10 M (NaClO₄). Rate constants k_e (e_aq^? decay) and k_p (protein absorbance change) are the same, second-order rate constant 9.7 × 10⁹ M^?1 sec^?1. The reaction exhibits close to 100% efficiency. With 8Fe-8S ferredoxin from Clostridium pasteurianum under identical conditions it now appears that k_p (although sometimes significantly smaller) is equal to k_e. Varying efficiencies are also observed with this protein depending on the batch used. The reasons for such variable behavior are not fully understood. With oxidized and reduced forms of Chromatium v. high-potential iron-sulfur protein (HIPIP), k_e and k_p are essentially the same, but the highest efficiency observed is only ～50%. The prevailing pattern is therefore that rate constants k_e and k_p are generally in step for proteins having a single (or identical) active site(s). When the active site is buried as with HIPIP the efficiency of the reaction appears to decrease.     

Crowding Effects on Association Reactions at Membranes

The effect of macromolecular crowding on the binding of ligands to a receptor near membranes is studied using Brownian dynamics simulations. The receptor is modeled as a reactive patch on a hard surface and the ligands and crowding agents are modeled as spheres that interact via a steep repulsive interaction potential. When a ligand collides with the patch, it reacts with probability p_rxn. The association rate constant (k_∞) can be decomposed into contributions from diffusion-limited (k_D) and reaction-limited (k_R) rates, i.e., 1/k_∞ = 1/k_D + 1/k_R. The simulations show that k_D is a nonmonotonic function of the volume fraction of crowding agents for receptors of small sizes. k_R is always an increasing function of the volume fraction of crowding agents, and the association rate constant k_∞ determined from both contributions has a qualitatively different dependence on the macromolecular crowding for high and low values of the reaction probability p_rxn. The simulation results are used to predict the velocity of the membrane protrusion driven by actin filament elongation. Based on the simple model where the protrusive force on the membrane is generated by the intercalation of actin monomers between the membrane and actin filament ends, we predict that crowding increases the local concentration of actin monomers near the filament ends and hence accelerates the membrane protrusion.     

Effect of coat color genes on the hair pigmentation morphology in the american mink (<Emphasis Type="Italic">Mustela vison</Emphasis> Schr. L.)

The morphological patterns of hair pigmentation (the size and shape of pigment granules and their distribution among layers) have been studied in four compound coat color forms of the American mink: moil-sapphire also known as violet (genotype m/m a/a p/p); moil-silver or sage (genotype m/m p/p); the color form determined by genotype m/+ a/a; and platinum leopard (S ^k /+ a/+ p/p). The hair pigmentation pattern specific for each coat color form and its difference from the standard coat color of the American mink (genotype +/+) has been determined. The possible mechanisms of the phenotypic expression of the nonallelic genes contributing to the described compound color forms are discussed.     

ON THE EXCITATION OF TISSUE BY MEANS OF CONDENSER DISCHARGES

Equations are derived for the capacity-voltage relations for stimulation of tissue by condenser discharges, using the hypothesis that the local excitatory process p grows under the influence of an applied potential V according to the equation, See PDF for Equation where K and k are constants. It is further assumed that the local excitatory process becomes adequate when it attains a value h ± α V where h and α are constants and V is the applied potential at the particular instant that the adequate value is attained. The equations so obtained are applied to the data of several authors on several types of tissue and the agreements obtained are sufficiently good. It is shown in one case that the direct current equation and the condenser discharge equation each derived from the above bases are consistent when applied to data from the same preparation.     

Deviations from Hardy-Weinberg Proportions: Sampling Variances and Use in Estimation of Inbreeding Coefficients

An analysis is made of the distribution of deviations from Hardy-Weinberg proportions with k alleles and of estimates of inbreeding coefficients (f) obtained from these deviations.—If f is small, the best estimate of f in large samples is shown to be 2Σ _i(T_ii/N_i)/(k - 1), where T_ii is an unbiased measure of the excess of the ith homozygote and N_i the number of the ith allele in the sample [frequency = N_i/(2N)]. No extra information is obtained from the T_ij, where these are departures of numbers of heterozygotes from expectation. Alternatively, the best estimator can be computed from the T_ij, ignoring the T_ii. Also (1) the variance of the estimate of f equals 1/(N(k - 1)) when all individuals in the sample are unrelated, and the test for f = 0 with 1 d.f. is given by the ratio of the estimate to its standard error; (2) the variance is reduced if some alleles are rare; and (3) if the sample consists of full-sib families of size n, the variance is increased by a proportion (n - 1)/4 but is not increased by a half-sib relationship.—If f is not small, the structure of the population is of critical importance. (1) If the inbreeding is due to a proportion of inbred matings in an otherwise random-breeding population, f as determined from homozygote excess is the same for all genes and expressions are given for its sampling variance. (2) If the homozygote excess is due to population admixture, f is not the same for all genes. The above estimator is probably close to the best for all f values.