Efficient approximate k‐fold and leave‐one‐out cross‐validation for ridge regression

In model building and model evaluation, cross‐validation is a frequently used resampling method. Unfortunately, this method can be quite time consuming. In this article, we discuss an approximation method that is much faster and can be used in generalized linear models and Cox’ proportional hazards model with a ridge penalty term. Our approximation method is based on a Taylor expansion around the estimate of the full model. In this way, all cross‐validated estimates are approximated without refitting the model. The tuning parameter can now be chosen based on these approximations and can be optimized in less time. The method is most accurate when approximating leave‐one‐out cross‐validation results for large data sets which is originally the most computationally demanding situation. In order to demonstrate the method's performance, it will be applied to several microarray data sets. An R package penalized, which implements the method, is available on CRAN.     

Dynamic data replacement and adaptive scheduling policies in spark

Improper data replacement and inappropriate selection of job scheduling policy are important reasons for the degradation of Spark system operation speed, which directly causes the performance degradation of Spark parallel computing. In this paper, we analyze the existing caching mechanism of Spark and find that there is still more room for optimization of the existing caching policy. For the task structure analysis, the key information of Spark tasks is taken out to obtain the data and memory usage during the task runtime, and based on this, an RDD weight calculation method is proposed, which integrates various factors affecting the RDD usage and establishes an RDD weight model. Based on this model, a minimum weight replacement algorithm based on RDD structure analyzing is proposed. The algorithm ensure that the relatively more valuable data in the data replacement process can be cached into memory. In addition, the default job scheduling algorithm of the Spark framework considers a single factor, which cannot form effective scheduling for jobs and causes a waste of cluster resources. In this paper, an adaptive job scheduling policy based on job classification is proposed to solve the above problem. The policy can classify job types and schedule resources more effectively for different types of jobs. The experimental results show that the proposed dynamic data replacement algorithm effectively improves Spark's memory utilization. The proposed job classification-based adaptive job scheduling algorithm effectively improves the system resource utilization and shortens the job completion time.

     

An effective approach for generating a three-Cys<Subscript>2</Subscript>His<Subscript>2</Subscript> zinc-finger-DNA complex model by docking

Background  

Determination of protein-DNA complex structures with both NMR and X-ray crystallography remains challenging in many cases. High Ambiguity-Driven DOCKing (HADDOCK) is an information-driven docking program that has been used to successfully model many protein-DNA complexes. However, a protein-DNA complex model whereby the protein wraps around DNA has not been reported. Defining the ambiguous interaction restraints for the classical three-Cys₂His₂ zinc-finger proteins that wrap around DNA is critical because of the complicated binding geometry. In this study, we generated a Zif268-DNA complex model using three different sets of ambiguous interaction restraints (AIRs) to study the effect of the geometric distribution on the docking and used this approach to generate a newly reported Sp1-DNA complex model.     

Prediction of Rate‐Limiting Reactions for Growth‐Associated Production Using a Constraint‐Based Approach

Identification of a rate‐limiting step in pathways is a key challenge in metabolic engineering. Although the prediction of rate‐limiting steps using a kinetic model is a powerful approach, there are several technical hurdles for developing a kinetic model. In this study, an in silico screening algorithm of key enzyme for metabolic engineering is developed to identify the possible rate‐limiting reactions for the growth‐coupled target production using a stoichiometric model without any experimental data and kinetic parameters. In this method, for each reaction, an upper‐bound flux constraint is imposed and the target production is predicted by linear programming. When the constraint decreases the target production at the optimal growth state, the reaction is thought to be a possible rate‐limiting step. For validation, this method is applied to the production of succinate or 1,4‐butanediol (1,4‐BDO) in Escherichia coli, in which the experimental engineering for eliminating rate‐limiting steps has been previously reported. In succinate production from glycerol, nine reactions including phosphoenolpyruvate carboxylase are predicted as the rate‐limiting steps. In 1,4‐BDO production from glucose, eight reactions including pyruvate dehydrogenase are predicted as the rate‐limiting steps. These predictions include experimentally identified rate‐limiting steps, which would contribute to metabolic engineering as a practical tool for screening candidates of rate‐limiting reactions.     

Prozeßberechnung der enzymatischen Saccharosehydrolyse in Abhängigkeit von der Temperatur

The calculation determining enzymatic metabolism under variable reaction conditions is possible on the basis of its reaction kinetics. In this connection a scientific and mathematical well established model is given, which allows to calculate metabolism that is catalized enzymatically. Experimental evidence for the validity of this model is given for cases both soluble and immobilized Invertase preparation are used. It is substantiated by the fact that the experimental values are in good agreement with the calculated data.     

Comparaison de deux modèles hybrides simulant la propagation de la lumière dans les tissus biologiques

In this paper, two numerical hybrid methods to model photon transport phenomena in biological tissues are compared. The coupled radiative transfer–diffusion model is based on the finite element solution of the radiative transfer equation and its approximation. The hybrid Monte-Carlo–diffusion consists in modeling the propagation of laser light in turbid media with the pure statistical Monte-Carlo method in the vicinity of the source and the boundaries and the diffusion approximation elsewhere in the domain. We apply these codes to calculate the spatially resolved reflectance amplitude and phase resulting from an intensity modulated laser beam. The results show that the hybrid methods can be used to simulate light propagation with good accuracy and speed.     

On Estimating the Relationship between Longitudinal Measurements and Time‐to‐Event Data Using a Simple Two‐Stage Procedure

Summary Ye, Lin, and Taylor (2008, Biometrics 64 , 1238–1246) proposed a joint model for longitudinal measurements and time‐to‐event data in which the longitudinal measurements are modeled with a semiparametric mixed model to allow for the complex patterns in longitudinal biomarker data. They proposed a two‐stage regression calibration approach that is simpler to implement than a joint modeling approach. In the first stage of their approach, the mixed model is fit without regard to the time‐to‐event data. In the second stage, the posterior expectation of an individual's random effects from the mixed‐model are included as covariates in a Cox model. Although Ye et al. (2008) acknowledged that their regression calibration approach may cause a bias due to the problem of informative dropout and measurement error, they argued that the bias is small relative to alternative methods. In this article, we show that this bias may be substantial. We show how to alleviate much of this bias with an alternative regression calibration approach that can be applied for both discrete and continuous time‐to‐event data. Through simulations, the proposed approach is shown to have substantially less bias than the regression calibration approach proposed by Ye et al. (2008) . In agreement with the methodology proposed by Ye et al. (2008) , an advantage of our proposed approach over joint modeling is that it can be implemented with standard statistical software and does not require complex estimation techniques.     

<Emphasis Type="Italic">RAD18</Emphasis> gene product of yeast <Emphasis Type="Italic">Saccharomyces cerevisiae</Emphasis> controls mutagenesis induced by hydrogen peroxide

Within eukaryotes, tolerance to DNA damage is determined primarily by the repair pathway controlled by the members of the RAD6 epistasis group. Genetic studies on a yeast Saccharomyces cerevisiae model showed that the initial stage of postreplication repair (PRR), i.e., initiation of replication through DNA damage, is controlled by Rad6–Rad18 ubiquitin-conjugating enzyme complex. Mutants of these genes are highly sensitive to various genotoxic agents and reduce the level of induced mutagenesis. In this case, the efficiency of mutagenesis suppression depends on the type of damage. In this study we showed that DNA damage induced by hydrogen peroxide at the same mutagen doses causes significantly more mutations and lethal events in the rad18 mutant cells compared to control wild-type cells.     

EQUALITY AND THE TREATMENT‐ENHANCEMENT DISTINCTION

In From Chance to Choice, Allen Buchanan, Dan Brock, Norman Daniels and Daniel Wikler propose a new way of defending the moral significance of the distinction between genetic treatments and enhancements. They develop what they call a ‘normal function model’ of equality of opportunity and argue that it offers a ‘limited’ defence of this distinction. In this article, I critically assess their model and the support it (allegedly) provides for the treatment‐enhancement distinction. First, I argue that there is a troubling tension in the normal function model. Secondly, I argue that neither of the rationales invoked by Buchanan et al. really serves to justify this model or the results they seek to derive from it with respect to the significance of the distinction between treatments and enhancements.     

Mathematical Modelling of the <Emphasis Type="Italic">Aux/IAA</Emphasis> Negative Feedback Loop

The hormone auxin is implicated in regulating a diverse range of developmental processes in plants. Auxin acts in part by inducing the Aux/IAA genes. The associated pathway comprises multiple negative feedback loops (whereby Aux/IAA proteins can repress Aux/IAA genes) that are disrupted by auxin mediating the turnover of Aux/IAA protein. In this paper, we develop a mathematical model of a single Aux/IAA negative feedback loop in a population of identical cells. The model has a single steady-state. We explore parameter space to uncover a number of dynamical regimes. In particular, we identify the ratio between the Aux/IAA protein and mRNA turnover rates as a key parameter in the model. When this ratio is sufficiently small, the system can evolve to a stable limit cycle, corresponding to an oscillation in Aux/IAA expression levels. Otherwise, the steady-state is either a stable-node or a stable-spiral. These observations may shed light on recent experimental results.     

Macrophage response to <Emphasis Type="Italic">Mycobacteriumtuberculosis</Emphasis> infection

The immune response to Mycobacterium tuberculosis (Mtb) infection is the formation of multicellular lesions, or granolomas, in the lung of the individual. However, the structure of the granulomas and the spatial distribution of the immune cells within is not well understood. In this paper we develop a mathematical model investigating the early and initial immune response to Mtb. The model consists of coupled reaction-diffusion-advection partial differential equations governing the dynamics of the relevant macrophage and bacteria populations and a bacteria-produced chemokine. Our novel application of mathematical concepts of internal states and internal velocity allows us to begin to study this unique immunological structure. Volume changes resulting from proliferation and death terms generate a velocity field by which all cells are transported within the forming granuloma. We present numerical results for two distinct infection outcomes: controlled and uncontrolled granuloma growth. Using a simplified model we are able to analytically determine conditions under which the bacteria population decreases, representing early clearance of infection, or grows, representing the initial stages of granuloma formation.     

Gating Models of the Anomalous Mole-Fraction Effect of Single-Channel Current in <Emphasis Type="Italic">Chara</Emphasis>

The dependence of single-channel current on the Tl+/K+ mole fraction exhibiting a minimum at [Tl+]/[K+] of about 1:15 is proportional to open probability in bursts. Five models are suggested to explain modulation of gating by the Tl+/K+ ratio. Three models start from a channel with 4 identical subunits, each with an allosteric binding site for K+ or Tl+. In the first model, ion binding is directly observable as a transition from one Markov state to another. This model can explain the dependence of the apparent single-channel current on Tl+ concentrations. However, the predicted linear dependence on ion concentrations of the apparent rate constants was not observed in measurements in 25 or 250 mM KNO3 and 250 mM Tl NO3. The second model can overcome this problem by introducing saturation kinetics for ion binding. In the third model, gating is caused by inherent vibrations of the protein, and the rate constants of the related transitions depend on the occupation of the allosteric sites. The fourth model is based on the foot-in-the-door approach with the essential feature that two K+ ions in the selectivity filter are necessary to keep the pore radius suitable for K+ ions. The fifth model is also a foot-in-the-door model, but non-Markovian because, similar to model 3, it is assumed that the conformation of the protein (and thus the rate constants of the Markov model of the time series) depends on the force exerted by the temporal average over the states of a Markov model of ion occupation. These ions may reside in the pore itself or outside.     

The dynamic transfer of <Superscript>3</Superscript>H and <Superscript>14</Superscript>C in mammals: a proposed generic model

Associated with the present debate regarding the potential revival of nuclear energy there is an increased interest in assessing the radiological risk to the public and also the environment. Tritium and ¹⁴C are key radionuclides of interest in many circumstances (e.g. heavy water reactors, waste storage and fusion reactors). Because the stable analogues of these two radionuclides are integral to most biological compounds, their modelling should follow general principles from life sciences. In this paper, a model of the dynamics of ¹⁴C and ³H in mammals is proposed on the basis of metabolic understanding and of, as far as possible, readily available data (e.g. for organ composition and metabolism). The model is described together with validation tests (without calibration) for a range of farm animals. Despite simplifications, the model tests are encouraging for a range of animal types and products (tissues and milk), and further improvements are suggested.     

The Use of Two‐Way Linear Mixed Models in Multitreatment Meta‐Analysis

Summary Meta‐analysis summarizes the results of a series of trials. When more than two treatments are included in the trials and when the set of treatments tested differs between trials, the combination of results across trials requires some care. Several methods have been proposed for this purpose, which feature under different labels, such as network meta‐analysis or mixed treatment comparisons. Two types of linear mixed model can be used for meta‐analysis. The one expresses the expected outcome of treatments as a contrast to a baseline treatment. The other uses a classical two‐way linear predictor with main effects for treatment and trial. In this article, we compare both types of model and explore under which conditions they give equivalent results. We illustrate practical advantages of the two‐way model using two published datasets. In particular, it is shown that between‐trial heterogeneity as well as inconsistency between different types of trial is straightforward to account for.     

3D models for vascular lumen segmentation in MRA images and for artery-stenting simulation

Arterial stenoses and aneurysms are increasingly treated using stents. The goal of this work is to facilitate the pre-operative choice of the stent's length and diameter. Two models are used to accomplish this task: a deformable cylindrical simplex (DCS) model of the arterial intra-luminal wall and a right generalized cylinder (RGC) model representing the stent's geometrical properties. An angiographic 3D image is first segmented using the DCS model to create a patient-specific vascular model. The RGC model of a folded stent is then slid along the vessel centerline until an interactively chosen delivery location, and the model's geometry is modified to simulate the unfolding of the stent. Lastly, the DCS model is re-meshed to fit the shape of the unfolded-stent model and thus to simulate the shape of the arterial lumen boundaries after stenting. Accuracy of the segmentation was quantitatively evaluated in images of arterial phantoms with stenoses ranging from 50 to 95%. Mean error of the resulting diameter estimation was 4.24%. The simulation of the stent insertion is qualitatively illustrated using data of a patient with an aneurysm in the aorta arch.     

A functional compartmental model of the <Emphasis Type="Italic">Synechocystis</Emphasis> PCC 6803 phycobilisome

In the light-harvesting antenna of the Synechocystis PCC 6803 phycobilisome (PB), the core consists of three cylinders, each composed of four disks, whereas each of the six rods consists of up to three hexamers (Arteni et al., Biochim Biophys Acta 1787(4):272–279, 2009). The rods and core contain phycocyanin and allophycocyanin pigments, respectively. Together these pigments absorb light between 400 and 650 nm. Time-resolved difference absorption spectra from wild-type PB and rod mutants have been measured in different quenching and annihilation conditions. Based upon a global analysis of these data and of published time-resolved emission spectra, a functional compartmental model of the phycobilisome is proposed. The model describes all experiments with a common set of parameters. Three annihilation time constants are estimated, 3, 25, and 147 ps, which represent, respectively, intradisk, interdisk/intracylinder, and intercylinder annihilation. The species-associated difference absorption and emission spectra of two phycocyanin and two allophycocyanin pigments are consistently estimated, as well as all the excitation energy transfer rates. Thus, the wild-type PB containing 396 pigments can be described by a functional compartmental model of 22 compartments. When the interhexamer equilibration within a rod is not taken into account, this can be further simplified to ten compartments, which is the minimal model. In this model, the slowest excitation energy transfer rates are between the core cylinders (time constants 115–145 ps), and between the rods and the core (time constants 68–115 ps).     

Ice‐storm disturbance and long‐term forest dynamics in the Adirondack Mountains

Ice storms cause periodic disturbance to temperate forests of eastern North America. They are the primary agents of disturbance in some eastern forests. In this paper, a forest gap model is employed to explore consequences of ice storms for the long‐term dynamics of Tsuga canadensis‐northem hardwoods forests. The gap model LINKAGES was modified to simulate periodic ice storm disturbance in the Adirondack Mountains of New York. To adapt the gap model for this purpose, field data on ice storm disturbance are used to develop a polytomous logistic regression model of tree damage. The logistic regression model was then incorporated into the modified forest gap model, LINK ADIR, to determine the type of damage sustained by each simulated tree. The logistic regression model predicts high probabilities of bent boles or severe bole damage (leaning, snapping, or uprooting) in small‐diameter trees, and increasing probability of canopy damage as tree size increases. Canopy damage is most likely on gentle slopes; the probability of severe bole damage increases with increasing slope angle. In the LINKADIR simulations, tree damage type determines the probability of mortality; trees with severe bole damage are assigned the highest mortality rate. LINKADIR predicts Tsuga canadensis dominance in mesophytic old‐growth forests not disturbed by ice storms. When ice storms are simulated, the model predicts Acer saccharum‐dominated forests with higher species richness. These results suggest that ice storms may function as intermediate disturbances that enhance species richness in forested Adirondack landscapes.