Applying Methods from Differential Geometry to Devise Stable and Persistent Air Layers Attached to Objects Immersed in Water

We describe a few mathematical tools which allow to investigate whether air-water interfaces exist(under prescribedconditions)and are mechanically stable and temporally persistent.In terms of physics,air-water interfaces are governed by theYoung-Laplace equation.Mathematically they are surfaces of constant mean curvature which represent solutions of a nonlinearelliptic partial differential equation.Although explicit solutions of this equation can be obtained only in very special cases,it is-under moderately special circumstances-possible to establish the existence of a solution without actually solving thedifferential equation.We also derive criteria for mechanical stability and temporal persistence of an air layer.Furthermorewe calculate the lifetime of a non-persistent air layer.Finally,we apply these tools to two examples which exhibit the symmetriesof 2D lattices.These examples can be viewed as abstractions of the biological model represented by the aquatic fernSalvinia.     

Impacts of small hydropower plants on macroinvertebrate communities

Several nitrogen (N) field experiments were carried out in Nanjing and Anyang, China, to study the dynamic characteristics of biomass accumulation and N uptake, and to define the dilution curve for critical N concentration in cotton reproductive organ over the growth period. The results show that the total biomass and N accumulation were affected significantly by the rate of N application, exhibiting a sigmoid curve over time. The beginning time of fast N accumulation was 1–5 d earlier than that of biomass accumulation. The cotton lint yield was correlated with N concentration in the reproductive organ and fluctuated with varying N concentration, indicating the existence of luxurious N consumption in the cotton reproductive organ. The N concentration increased with increasing N application rates, and decreased gradually during the growth period. The relationship between biomass and N concentration can be described with a power equation. The patterns of the N concentration dilution model were consistent at both experimental sites, but the model parameter values of a differed. The results presented in this paper indicate that a critical N concentration dilution curve for cotton reproductive organ is independent of ecological region and can be described with a power equation.     

Accumulation characteristics of biomass and nitrogen and critical nitrogen concentration dilution model of cotton reproductive organ

Several nitrogen (N) field experiments were carried out in Nanjing and Anyang, China, to study the dynamic characteristics of biomass accumulation and N uptake, and to define the dilution curve for critical N concentration in cotton reproductive organ over the growth period. The results show that the total biomass and N accumulation were affected significantly by the rate of N application, exhibiting a sigmoid curve over time. The beginning time of fast N accumulation was 1–5 d earlier than that of biomass accumulation. The cotton lint yield was correlated with N concentration in the reproductive organ and fluctuated with varying N concentration, indicating the existence of luxurious N consumption in the cotton reproductive organ. The N concentration increased with increasing N application rates, and decreased gradually during the growth period. The relationship between biomass and N concentration can be described with a power equation. The patterns of the N concentration dilution model were consistent at both experimental sites, but the model parameter values of a differed. The results presented in this paper indicate that a critical N concentration dilution curve for cotton reproductive organ is independent of ecological region and can be described with a power equation.     

Accumulation characteristics of biomass and nitrogen and critical nitrogen concentration dilution model of cotton reproductive organ

Several nitrogen (N) field experiments were carried out in Nanjing and Anyang, China, to study the dynamic characteristics of biomass accumulation and N uptake, and to define the dilution curve for critical N concentration in cotton reproductive organ over the growth period. The results show that the total biomass and N accumulation were affected significantly by the rate of N application, exhibiting a sigmoid curve over time. The beginning time of fast N accumulation was 1–5 d earlier than that of biomass accumulation. The cotton lint yield was correlated with N concentration in the reproductive organ and fluctuated with varying N concentration, indicating the existence of luxurious N consumption in the cotton reproductive organ. The N concentration increased with increasing N application rates, and decreased gradually during the growth period. The relationship between biomass and N concentration can be described with a power equation. The patterns of the N concentration dilution model were consistent at both experimental sites, but the model parameter values of a differed. The results presented in this paper indicate that a critical N concentration dilution curve for cotton reproductive organ is independent of ecological region and can be described with a power equation.     

Acceleration Workspace of Cooperating Multi-Finger Robot Systems

We present a mathematical method for acceleration workspace analysis of cooperating multi-finger robot systems using a model of point-contact with friction. A new unified formulation from dynamic equations of cooperating multi-finger robots is derived considering the force and acceleration relationships between the fingers and the object to be handled. From the dynamic equation, maximum translational and rotational acceleration bounds of an object are calculated under given constraints of contact conditions, configurations of fingers, and bounds on the torques of joint actuators for each finger. Here, the rotational acceleration bounds can be applied as an important manipulability index when the multi-finger robot grasps an object. To verify the proposed method, we used a set of case studies with a simple multi-finger mechanism system. The achievable acceleration boundary in task space can be obtained successfully with the proposed method and the acceleration boundary depends on the configurations of fingers.     

Time delay and cross-correlated Gaussian noises-induced stochastic stability and regime shift between steady states for an insect outbreak system

In this paper, we focus on investigating the stochastic stability and the regime transition between the endangered state and the boom state for a time-delayed insect growth system driven by correlated external and internal noises. By use of the Fokker Planck equation, the method of small time delay approximation and the fast descent method, we explore in detail the joint action of noise terms and time delay on the mean reproduction and depression time for the insect population. Our investigations indicate that the pseudo-resonance phenomenon of the mean first-passage time (MFPT) occurs because of the impact of different noises and time delay. Through the numerical calculation, it is discovered that multiplicative noise can speed up the shift of the insect population from the boom state to the endangered one, while the noise correlation and time delay can propel the insect system to evolve from the endangered state to the boom state and improve the biological stability. In addition, the impact of the additive noise on the stability of the biological system depends on the positive and negative situation of the noise correlation. On the other hand, during the process of suppressing the insect explosion, it is beneficial to the pest control to amplify the association noise strength and weaken the intensities of the multiplicative, additive noises and time delay. However, during the process of eliminating the pests, it can produce nice effect on the disinsection to increase time delay, the intensities of multiplicative and additive noises and weaken the strength of noise correlation.     

The Genetic Architecture of Flowering Time and Photoperiod Sensitivity in Maize as Revealed by QTL Review and Meta Analysis

The control of flowering is not only important for reproduction,but also plays a key role in the processes of domestication and adaptation.To reveal the genetic architecture for flowering time and photoperiod sensitivity,a comprehensive evaluation of the relevant literature was performed and followed by meta analysis.A total of 25 synthetic consensus quantitative trait loci(QTL)and four hot-spot genomic regions were identified for photoperiod sensitivity including 11 genes related to photoperiod response or flower morphogenesis and development.Besides,a comparative analysis of the QTL for flowering time and photoperiod sensitivity highlighted the regions containing shared and unique QTL for the two traits.Candidate genes associated with maize flowering were identified through integrated analysis of the homologous genes for flowering time in plants and the consensus QTL regions for photoperiod sensitivity in maize(Zea mays L.).Our results suggest that the combination of literature review,meta-analysis and homologous blast is an efficient approach to identify new candidate genes and create a global view of the genetic architecture for maize photoperiodic flowering.Sequences of candidate genes can be used to develop molecular markers for various models of marker-assisted selection,such as marker-assisted recurrent selection and genomic selection that can contribute significantly to crop environmental adaptation.     

A Procedure for the Design of Novel Assisting Devices for the Sit-to-Stand

The Sit-to-Stand （STS） is an activity most people perform numerous times daily. Standing up deals with the transition from two stabilized postures, namely seated to standing, with movement of all body segments except the feet. During the STS the body＇s Center of Gravity （COG） is moved upward from a sitting position to a standing position without losing balance and requiring a good coordination of many muscles. Three main phases of the STS movement can be recognized. One begins to stand up by inclining the upper body forward, which moves body mass toward the feet in order to maintain balance after lift-off. Prior to leaving the chair, hip and knee extensor muscles are activated to provide antigravity support for these joints, this action is commonly referred to as ＂weight shift＂. Finally; after leaving the chair, the leg and trunk joints are straightened to achieve upright stance. The STS task can be considered of major importance for impaired and elderly people to achieve minimal mo- bility and independence. In this paper we detail a procedure for the design of assisting devices to be used for the STS. In par- ticular, an experimental procedure is described firstly to track and record point trajectories and the orientation of the trunk during the STS. This analysis is then used to get information for the design of assisting devices. A proposal and simulation results are presented for a novel mechatronic system. In particular, for the case under study experimental tests are used to drive the actua- tion system for the reported simulation. A functional mechatronic scheme is then proposed to control the device during its operation.     

CDS: a fold-change based statistical test for concomitant identification of distinctness and similarity in gene expression analysis

The problem of identifying differential activity such as in gene expression is a major defeat in biostatistics and bioinformatics.Equally important,however much less frequently studied,is the question of similar activity from one biological condition to another.The foldchange,or ratio,is usually considered a relevant criterion for stating difference and similarity between measurements.Importantly,no statistical method for concomitant evaluation of similarity and distinctness currently exists for biological applications.Modem microarray,digital PCR(dPCR),and Next-Generation Sequencing(NGS) technologies frequently provide a means of coefficient of variation estimation for individual measurements.Using fold-change,and by making the assumption that measurements are normally distributed with known variances,we designed a novel statistical test that allows us to detect concomitantly,thus using the same formalism,differentially and similarly expressed genes(http://cds.ihes.fr).Given two sets of gene measurements in different biological conditions,the probabilities of making type I and type II errors in stating that a gene is differentially or similarly expressed from one condition to the other can be calculated.Furthermore,a confidence interval for the fold-change can be delineated.Finally,we demonstrate that the assumption of normality can be relaxed to consider arbitrary distributions numerically.The Concomitant evaluation of Distinctness and Similarity(CDS) statistical test correctly estimates similarities and differences between measurements of gene expression.The implementation,being time and memory efficient,allows the use of the CDS test in high-throughput data analysis such as microarray,dPCR,and NGS experiments.Importantly,the CDS test can be applied to the comparison of single measurements(N:1) provided the variance(or coefficient of variation) of the signals is known,making CDS a valuable tool also in biomedical analysis where typically a single measurement per subject is available.     

A Generalized Simplest Equation Method and Its Application to the Boussinesq-Burgers Equation

In this paper, a generalized simplest equation method is proposed to seek exact solutions of nonlinear evolution equations (NLEEs). In the method, we chose a solution expression with a variable coefficient and a variable coefficient ordinary differential auxiliary equation. This method can yield a Bäcklund transformation between NLEEs and a related constraint equation. By dealing with the constraint equation, we can derive infinite number of exact solutions for NLEEs. These solutions include the traveling wave solutions, non-traveling wave solutions, multi-soliton solutions, rational solutions, and other types of solutions. As applications, we obtained wide classes of exact solutions for the Boussinesq-Burgers equation by using the generalized simplest equation method.     

A quantitative method for the analysis of mammalian cell proliferation in culture in terms of dividing and non-dividing cells

The application of the exponential growth equation is the standard method employed in the quantitative analyses of mammalian cell proliferation in culture. This method is based on the implicit assumption that, within a cell population under study, all division events give rise to daughter cells that always divide. When a cell population does not adhere to this assumption, use of the exponential growth equation leads to errors in the determination of both population doubling time and cell generation time. We have derived a more general growth equation that defines cell growth in terms of the dividing fraction of daughter cells. This equation can account for population growth kinetics that derive from the generation of both dividing and non-dividing cells. As such, it provides a sensitive method for detecting non-exponential division dynamics. In addition, this equation can be used to determine when it is appropriate to use the standard exponential growth equation for the estimation of doubling time and generation time.     

A master equation for a spatial population model with pair interactions

We derive a closed master equation for an individual-based population model in continuous space and time. The model and master equation include Brownian motion, reproduction via binary fission, and an interaction-dependent death rate moderated by a competition kernel. Using simulations we compare this individual-based model with the simplest approximation, the spatial logistic equation. In the limit of strong diffusion the spatial logistic equation is a good approximation to the model. However, in the limit of weak diffusion the spatial logistic equation is inaccurate because of spontaneous clustering driven by reproduction. The weak-diffusion limit can be partially analyzed using an exact solution of the master equation applicable to a competition kernel with infinite range. This analysis shows that in the case of a top-hat kernel, reducing the diffusion can increase the total population. For a Gaussian kernel, reduced diffusion invariably reduces the total population. These theoretical results are confirmed by simulation.     

SeinFit,a Computer Program for the Estimation of the Seinhorst Equation

A computer program, "SeinFit," was created to determine the Seinhorst equation that best fits experimental data on the relationship between preplant nematode densities and plant growth. Data, which can be entered manually or imported from a text file, are displayed in a data window while the corresponding graph is shown in a graph window. Various options are available to manipulate the data and the graph settings. The best-fitting Seinhorst equation can be calculated by two methods that are both based on the evaluation of the residual sum of squares. Depending on the method, a range of values for different parameters of the Seinhorst equation can be chosen, as well as the number of steps in each range. Data, graphs, and values of the parameters of the Seinhorst equation can be printed. The program allows for quick calculation of the danaage threshold density - one of the parameters of the Seinhorst model. Versions written for Macintosh or DOS-compatible machines are currently available through the Society of Nematologists'' World Wide Web site (http://ianrwww.unl.edu/ianr/plntpath/ nematode/SOFTWARE/nemasoft.htm).     

A general secular equation for cooperative binding of n-mer ligands to a one-dimensional lattice

The binding of n-mer ligands to a one-dimensional lattice involving many ligand species and complex multiple-binding mechanisms is studied. We show that, when derived using the sequence-generating function method of Lifson, the secular equation of any binding system with a finite number of "elementary units" can be expressed in a matrix determinant form that is very symmetric and easy to construct. In other words, for any binding system whose elementary units are known, the secular equation of the system can be obtained readily without going through the formal derivation of the equation. We also show that the "determinant" secular equation obtained using the present procedure can be employed directly to the calculation of binding isotherms.     

The hypercycle,traveling waves,and Wright's equation

A formal relation between the hypercycle equation and the delay differential equation of E. M. Wright is exhibited using a traveling waves approach. Several unsolved questions in either problem can be related and interpreted, in particular new motivation for the study of Wright's equation is obtained.     

On the use of apparent kinetic parameters for immobilized enzyme with noncompetitive substrate inhibition

The use of a simple rate equation with apparent parameters to describe the kinetic behavior of an immobilized enzyme with noncompetitive substrate inhibition was assessed. To do so, the reaction rate was calculated as a function of the interfacial substrate concentration, and the results were used to identify the apparent kinetic parameters by nonlinear regression. This procedure was repeated for different values of the diffusional constraints and of the inhibition constant. The equation using apparent parameters can describe the global kinetic behavior, provided that the diffusional and inhibitory constraints are not too high. When the constraints are high, a Michaelis-Menten equation can be used to model the kinetics for interfacial concentrations lower than the concentration leading to the maximum reaction rate.     

Oscillation frequencies of tapered plant stems

Free oscillations of upright plant stems, or in technical terms, slender tapered rods with one end free, can be described by considering the equilibrium between bending moments in the form of a differential equation with appropriate boundary conditions. For stems with apical loads, where the mass of the stem is negligible, Mathematica 4.0 returns solutions for tapering modes α = 0, 0.5, and 1. For other values of α, including cases where the modulus of elasticity varies over the length of the stem, approximations leading to an upper and a lower estimate of the frequency of oscillation can be derived. For the limiting case of ω = 0, the differential equation is identical with Greenhill's equation for the stability against Euler buckling of a top-loaded slender pole. For stems without top loads, Mathematica 4.0 returns solutions only for two limiting cases, zero gravity (realized approximately for oscillations in a horizontal orientation of the stem) and for ω = 0 (Greenhill's equation). Approximations can be derived for all other cases. As an example, the oscillation of an Arundo donax plant stem is described.     

Binding of positive charged ligands to DNA. The effect of ionic strength, charge and size of the ligand

The electrostatic interaction of extended cationic ligands with DNA has been considered on the basis of the analytical solution of a simplified Poisson--Boltzmann equation for the charged polyion cylinder. The control numerical solution of rigorous Poisson--Boltzmann equation shows that the assumption about the absence of coions in the vicinity of the highly charged polyion cylinder does not significantly influence the accuracy of solution and DNA electrostatic free energy evaluation. It was found that the basic contribution to the free energy of electrostatic ligand-DNA interaction is the mixing entropy change due to release of counterions from the vicinity of DNA. The equation for the dependence of the ligand to DNA binding constant K upon ionic strength c has been derived without introduction of any empirical parameters. This equation is consistent with the experimental data and can be used for the determination of a number of ligand--DNA ionic contacts in a wide range of salt concentrations. The main consequences of Manning and Record et al. theories can be considered as limiting cases of the theory presented. In particular the equation d(lnK)/d(lnc) = -0.88 N by Record et al. has a restricted range of application and it can be used only for a relative approximate estimation of the number of electrostatic bonds in ligand-DNA complexes. The analysis of electrostatic interaction of DNA with ligands which neutralize only part of phosphate groups in the binding site of DNA was also performed.(ABSTRACT TRUNCATED AT 250 WORDS)