Speed Constancy or Only Slowness: What Drives the Kappa Effect

In the Kappa effect, two visual stimuli are given, and their spatial distance affects their perceived temporal interval. The classical model assumes constant speed while a competing Bayesian model assumes a slow speed prior. The two models are based on different assumptions about the statistical structure of the environment. Here we introduce a new visual experiment to distinguish between these models. When fit to the data, both the two models replicated human response, but the slowness model makes better behavioral predictions than the speed constancy model, and the estimated constant speed is close to the absolute threshold of speed. Our findings suggest that the Kappa effect appears to be due to slow speeds, and also modulated by spatial variance.     

Visco-hyperelastic law for finite deformations: a frequency analysis

Some biological tissues are repeatedly stimulated under cyclic loading, and this stimulation can be combined with large pressures, thus leading to large deformations. For such applications, visco-hyperelastic models have been proposed in the literature and used in finite-element studies. An extensively used quasi-linear model (QLVH), which assumes linear evolution equations, is compared with a nonlinear model (NLVH), which assumes a multiplicative split of the deformation gradient. The comparison is made here using sets of simulations covering a large frequency range. Lost and stored energies are computed, and the additional parameter of the NLVH model is set to two values found in the literature (NLVH-2 and NLVH-30 models). The predicted behaviour is very similar for all models at small strains, with each time constant (and corresponding viscous modulus) being associated with a damping peak and a stored-energy increase. When the strain amplitude is increased, the ratio of lost to stored energy increases for the QLVH model, but decreases for the NLVH models. The NLVH-30 model also displays a shift of the peak damping towards higher frequencies. Before reaching a steady state, all models display a decay of energy independent of the frequency, and the additional parameter of the NLVH model permits the modelling of complex types of evolution of the damping. In conclusion, this study compares the behaviour of two viscous hyper-elastic laws to allow an informed choice between them.     

Strategies for sperm chemotaxis in the siphonophores and ascidians: a numerical simulation study

Chemotactic swimming behaviors of spermatozoa toward an egg have been reported in various species. The strategies underlying these behaviors, however, are poorly understood. We focused on two types of chemotaxis, one in the siphonophores and the second in the ascidians, and then proposed two models based on experimental data. Both models assumed that the radius of the path curvature of a swimming spermatozoon depends on [Ca(2+)](i), the intracellular calcium concentration. The chemotaxis in the siphonophores could be simulated in a model that assumes that [Ca(2+)](i) depends on the local concentration of the attractant in the vicinity of the spermatozoon and that a substantial time period is required for the clearance of transient high [Ca(2+)](i). In the case of ascidians, trajectories similar to those in experiments could be adequately simulated by a variant of this model that assumes that [Ca(2+)](i) depends on the time derivative of the attractant concentration. The properties of these strategies and future problems are discussed in relation to these models.     

Maximum-likelihood estimation of phylogeny from DNA sequences when substitution rates differ over sites

Felsenstein's maximum-likelihood approach for inferring phylogeny from DNA sequences assumes that the rate of nucleotide substitution is constant over different nucleotide sites. This assumption is sometimes unrealistic, as has been revealed by analysis of real sequence data. In the present paper Felsenstein's method is extended to the case where substitution rates over sites are described by the gamma distribution. A numerical example is presented to show that the method fits the data better than do previous models.      

Estimating the degree of saturation in mutant screens

Large-scale screens for loss-of-function mutants have played a significant role in recent advances in developmental biology and other fields. In such mutant screens, it is desirable to estimate the degree of "saturation" of the screen (i.e., what fraction of the possible target genes has been identified). We applied Bayesian and maximum-likelihood methods for estimating the number of loci remaining undetected in large-scale screens and produced credibility intervals to assess the uncertainty of these estimates. Since different loci may mutate to alleles with detectable phenotypes at different rates, we also incorporated variation in the degree of mutability among genes, using either gamma-distributed mutation rates or multiple discrete mutation rate classes. We examined eight published data sets from large-scale mutant screens and found that credibility intervals are much broader than implied by previous assumptions about the degree of saturation of screens. The likelihood methods presented here are a significantly better fit to data from published experiments than estimates based on the Poisson distribution, which implicitly assumes a single mutation rate for all loci. The results are reasonably robust to different models of variation in the mutability of genes. We tested our methods against mutant allele data from a region of the Drosophila melanogaster genome for which there is an independent genomics-based estimate of the number of undetected loci and found that the number of such loci falls within the predicted credibility interval for our models. The methods we have developed may also be useful for estimating the degree of saturation in other types of genetic screens in addition to classical screens for simple loss-of-function mutants, including genetic modifier screens and screens for protein-protein interactions using the yeast two-hybrid method.     

Multinomial Distribution and Ascertainment by Sex

New ascertainment models taking into account partitioning by sex and without any constraint concerning dominance of alleles are proposed. These originate beginning from two major pathways. The first pathway assumes independence and that the family sizes for both males and females are known. The second pathway assumes dependence and that only the total family size is known. Ascertainment probabilities based on several different types of dependence are found. Results are obtained for incomplete multiple ascertainment.     

Analysis of cell growth in a polymer scaffold using a moving boundary approach

Two mathematical models of chondrocyte generation and nutrient consumption are developed to analyze the behavior of cell growth in a biodegradable polymer matrix. Substrate reaction and diffusion are analyzed in two regions: one consisting of cells and nutrients and the other consisting of only nutrients. A pseudo-steady state approximation for the transport of nutrients in these two regions is utilized. The rate of growth is determined by a moving boundary equation that equates the rate at which the interfacial region between the cells and the void space moves to a substrate dependent growth reaction. The change in the location of this interfacial region with time therefore depicts the rate at which the cells propagate. The two limiting cases discussed in this article represent extremes in how the cells will grow in the polymer matrix; one case assumes that cells grow inward from the external boundary, and the other case assumes that cells grow parallel to the external boundary. The results of both models are compared to experimental data found in the literature. It is found through these comparisons that the model parameters, including the unit cell spacing parameter L, the metabolic rate constant k, the growth rate constant k(G), and external mass transfer coefficient, K, may vary as the thickness of the polymer matrix is changed, however, unrealistic and large changes in the diffusion coefficients were required to account for the full range of experimental data. Furthermore, these results suggest modification of the functional form of the growth kinetics to include substrate or product inhibition, or death terms. Based upon diffusion/reaction concepts, these models for cell growth in a biodegradable polymer give bounds for the upper and lower limits of the cellular growth rate and nutrient consumption in a polymer matrix and will aid in the development of more extensive models. (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 56: 422-432, 1997.     

Production models for nonlinear stochastic age-structured fisheries

The overriding feature of stock-recruitment data for most fisheries is the amount of variability involved. Previous production models have assumed either an underlying linear stock-recruitment relationship [11] or an equilibrium condition [23]. Here a production model is derived for an age-structured fishery exhibiting nonlinear stochastic recruitment under nonequilibrium conditions. In the first section deterministic age-structured production models are reviewed, and in the next section corresponding random variable models are presented. Equations for the first and second order moments for each age class, for the stock, and for the yield are then derived using two approaches. The first approach assumes that third and order higher moments associated with the noise can be neglected (thus extending the “small noise” approach in [23]). The second approach assumes that the distributions associated with the random variables can be characterized by a particular two parameter distribution. This latter approximation can be applied to systems with “large noise,” and precision will not be lost for situations where the exact form of the distribution, associated with the stock-recruitment data, is unknown. Equations are derived for the solution under equilibrium recruitment and constant harvesting conditions. Detailed expressions are also obtained for the case where the random variables are assumed to satisfy a gamma distribution.     

On the kinetics of anaerobic power

ABSTRACT: BACKGROUND: This study investigated two different mathematical models for the kinetics of anaerobic power. Model 1 assumes that the work power is linear with the work rate, while model 2 assumes a linear relationship between the alactic anaerobic power and the rate of change of the aerobic power. In order to test these models, a cross country skier ran with poles on a treadmill at different exercise intensities. The aerobic power, based on the measured oxygen uptake, was used as input to the models, whereas the simulated blood lactate concentration was compared with experimental results. Thereafter, the metabolic rate from phosphocreatine break down was calculated theoretically. Finally, the models were used to compare phosphocreatine break down during continuous and interval exercises. RESULTS: Good similarity was found between experimental and simulated blood lactate concentration during steady state exercise intensities. The measured blood lactate concentrations were lower than simulated for intensities above the lactate threshold, but higher than simulated during recovery after high intensity exercise when the simulated lactate concentration was averaged over the whole lactate space. This fit was improved when the simulated lactate concentration was separated into two compartments; muscles + internal organs and blood. Model 2 gave a better behavior of alactic energy than Model 1 when compared against invasive measurements presented in the literature. During continuous exercise, model 2 showed that the alactic energy storage decreased with time, whereas model 1 showed a minimum value when steady state aerobic conditions were achieved. During interval exercise the two models showed similar patterns of alactic energy. CONCLUSIONS: The current study provides useful insight on the kinetics of anaerobic power. Overall, our data indicates that blood lactate levels can be accurately modeled during steady state, and suggests a linear relationship between the alactic anaerobic power and the rate of change of the aerobic power.     

Reproductive performance in Ohio dairy herds in the 1990s

The objective of this study was to evaluate trends in reproductive performance in Ohio dairy herds during the 1990s. Stringent criteria for herd inclusion were applied to DHI records to ensure high quality and reliability of the data. The final data set contained 44,425 monthly herd summary records from 1772 herds from years 1992, 1994, 1996 and 1998. Outcomes of interest were calving interval length, calving-to-conception interval, days to first breeding, services per conception and first service conception rate. PROC MIXED in SAS (version 8.1) was used and the monthly records were treated as repeated measures nested within years and herds. First-order autoregressive covariance structure was used to model the covariance between the repeated measures within herds. The data were analyzed for the entire herd as well as for the first lactation cows separately. During the 1990s reproductive performance declined in Ohio dairy herds. Herd average calving interval lengthened from 13.6 to 14.1 months and calving-to-conception interval increased from 136 to 150 days between 1992 and 1998, respectively. Days to first service and number of services increased while first service conception rate declined on a herd level. The reproductive performance of first lactation cows, however, remained constant during this same period. Overall herd reproductive performance was associated with herd size and fat-corrected rolling herd average milk production (FCM). As milk yield increased, first service conception rate decreased and services per conception increased. Larger herds had lower first service conception rate and needed more services per conception, but they started breeding their cows earlier resulting in a slightly shorter calving interval and calving-to-conception interval compared to smaller herds.     

Calculations for multi-type age-dependent binary branching processes

This article provides a method for calculating the joint probability density for the topology and the node times of a tree which has been produced by an multi-type age-dependent binary branching process and then sampled at a given time. These processes are a generalization, in two ways, of the constant rate birth–death process. There are a finite number of types of particle instead of a single type: each particle behaves in the same way as all others of the same type, but different types can behave differently. Secondly, the lifetime of a particle (before it either dies, changes to another type, or splits into 2) follows an arbitrary distribution, instead of the exponential lifetime in the constant rate case. Two applications concern models for macroevolution: the particles represent species, and the extant species are randomly sampled. In one application, 1-type and 2-type models for macroevolution are compared. The other is aimed at Bayesian phylogenetic analysis where the models considered here can provide a more realistic and more robust prior distribution over trees than is usually used. A third application is in the study of cell proliferation, where various types of cell can divide and differentiate.     

Simplified models for packed-bed biofilm reactors

For a packed-bed biofilm reactor two reactor models are proposed. One model is for the limiting case of a biofilm with a constant biofilm thickness in which diffusion within the biofilm is shown to be negligible. The second model assumes that the thickness of the biofilm is limited by the concentration of substrate within the biofilm. The analytical solutions for these reactor models are shown to agree very well with the numerical solutions to the exact differential equations.     

Kakusan4 and Aminosan: two programs for comparing nonpartitioned, proportional and separate models for combined molecular phylogenetic analyses of multilocus sequence data

Proportional and separate models able to apply different combination of substitution rate matrix (SRM) and among-site rate variation model (ASRVM) to each locus are frequently used in phylogenetic studies of multilocus data. A proportional model assumes that branch lengths are proportional among partitions and a separate model assumes that each partition has an independent set of branch lengths. However, the selection from among nonpartitioned (i.e., a common combination of models is applied to all-loci concatenated sequences), proportional and separate models is usually based on the researcher's preference rather than on any information criteria. This study describes two programs, 'Kakusan4' (for DNA sequences) and 'Aminosan' (for amino-acid sequences), which allow the selection of evolutionary models based on several types of information criteria. The programs can handle both multilocus and single-locus data, in addition to providing an easy-to-use wizard interface and a noninteractive command line interface. In the case of multilocus data, SRMs and ASRVMs are compared at each locus and at all-loci concatenated sequences, after which nonpartitioned, proportional and separate models are compared based on information criteria. The programs also provide model configuration files for mrbayes, paup*, phyml, raxml and Treefinder to support further phylogenetic analysis using a selected model. When likelihoods are optimized by Treefinder, the best-fit models were found to differ depending on the data set. Furthermore, differences in the information criteria among nonpartitioned, proportional and separate models were much larger than those among the nonpartitioned models. These findings suggest that selecting from nonpartitioned, proportional and separate models results in a better phylogenetic tree. Kakusan4 and Aminosan are available at http://www.fifthdimension.jp/. They are licensed under gnugpl Ver.2, and are able to run on Windows, MacOS X and Linux.     

Defective regression models for cure rate modeling with interval‐censored data

Regression models in survival analysis are most commonly applied for right‐censored survival data. In some situations, the time to the event is not exactly observed, although it is known that the event occurred between two observed times. In practice, the moment of observation is frequently taken as the event occurrence time, and the interval‐censored mechanism is ignored. We present a cure rate defective model for interval‐censored event‐time data. The defective distribution is characterized by a density function whose integration assumes a value less than one when the parameter domain differs from the usual domain. We use the Gompertz and inverse Gaussian defective distributions to model data containing cured elements and estimate parameters using the maximum likelihood estimation procedure. We evaluate the performance of the proposed models using Monte Carlo simulation studies. Practical relevance of the models is illustrated by applying datasets on ovarian cancer recurrence and oral lesions in children after liver transplantation, both of which were derived from studies performed at A.C. Camargo Cancer Center in São Paulo, Brazil.     

DETERMINATION OF STEADY STATE GENERATION TIME DISTRIBUTIONS FROM LABELLED MITOSIS EXPERIMENTAL DATA

The proper application of detailed deterministic cell kinetic models depends on the way in which cells are assigned their generation times. A method is presented for the determination of population generation time distributions from labelled mitoses experiments. the model assumes that the generation time of each new cell is a function of both the steady-state generation time distribution function of the population, and also the generation time frequency-function of the previous generation of cells. This approach is applied to two different cell types to successfully simulate extended labelled mitoses curves using a population balance model with constant maturation rates.     

Analysis of double-substrate limited growth

Mathematical models which relate the growth rate of a microorganism to a single limiting substrate concentration have long been established. In recent years, it has become apparent that, under certain conditions, the growth rate of an organism may be simultaneously limited by two or more substrates. Mathematical models of double-substrate limitation fall into two categories: interactive and noninteractive models. A discussion of both types of models is presented in both conceptual and mathematical terms. An analogous case of an enzyme which requires two different substrates to produce a single product is presented. This enzyme analog indicates that both types of double-substrate limitation models appear to be feasible under certain conditions. Based upon stoichiometry and specific growth rate-substrate concentration contour plots, a method for determining the operational conditions which will lead to double-substrate limitation is presented.     

Copulatory behavior unaccompanied by ovulation in the Japanese monkey (Macaca fuscata)

Copulatory behavior unrelated to conception is sometimes observed in some non-human primates including the Japanese monkey. In the present study, the authors examined whether a mature follicle or a newly formed fresh corpus luteum was observed in the ovaries of female Japanese monkeys which displayed the copulatory behavior unrelated to conception. Post-conception copulatory behaviors were observed in three out of four females usually kept in individual cages in an air-conditioned room, and in two out of three females without infants kept in an outdoor group cage. However, neither a mature Graafian follicle nor a fresh corpus luteum formed newly after conception was observed in any of these females by laparoscopic examinations conducted immediately after termination of the copulatory behavior. In females with infants born in the preceding birth season, copulatory behaviors were observed in three out of four females kept in the outdoor group cage, and in two out of four females in a free-ranging troop. Ovulation was confirmed in one case out of the three kept in the outdoor group cage, but neither a mature follicle nor a newly formed corpus luteum was observed in the remaining four females. These findings suggest that copulatory behavior in the Japanese monkey is not always controlled by the development of a follicle or ovulation in the ovary.     

Accuracy of rate estimation using relaxed-clock models with a critical focus on the early metazoan radiation

In recent years, a number of phylogenetic methods have been developed for estimating molecular rates and divergence dates under models that relax the molecular clock constraint by allowing rate change throughout the tree. These methods are being used with increasing frequency, but there have been few studies into their accuracy. We tested the accuracy of several relaxed-clock methods (penalized likelihood and Bayesian inference using various models of rate change) using nucleotide sequences simulated on a nine-taxon tree. When the sequences evolved with a constant rate, the methods were able to infer rates accurately, but estimates were more precise when a molecular clock was assumed. When the sequences evolved under a model of auto-correlated rate change, rates were accurately estimated using penalized likelihood and by Bayesian inference using lognormal and exponential models of rate change, while other models did not perform as well. When the sequences evolved under a model of uncorrelated rate change, only Bayesian inference using an exponential rate model performed well. Collectively, the results provide a strong recommendation for using the exponential model of rate change if a conservative approach to divergence time estimation is required. A case study is presented in which we use a simulation-based approach to examine the hypothesis of elevated rates in the Cambrian period, and it is found that these high rate estimates might be an artifact of the rate estimation method. If this bias is present, then the ages of metazoan divergences would be systematically underestimated. The results of this study have implications for studies of molecular rates and divergence dates.