Testing the hypothesis on the relationship between aerodynamic roughness length and albedo using vegetation structure parameters

Surface albedo (α) and aerodynamic roughness length (z ₀), which partition surface net radiation into energy fluxes, are critical land surface properties for biosphere–atmosphere interactions and climate variability. Previous studies suggested that canopy structure parameters influence both α and z ₀; however, no field data have been reported to quantify their relationships. Here, we hypothesize that a functional relationship between α and z ₀ exists for a vegetated surface, since both land surface parameters can be conceptually related to the characteristics of canopy structure. We test this hypothesis by using the observed data collected from 50 site-years of field measurements from sites worldwide covering various vegetated surfaces. On the basis of these data, a negative linear relationship between α and log(z ₀) was found, which is related to the canopy structural parameter. We believe that our finding is a big step toward the estimation of z ₀ with high accuracy. This can be used, for example, in the parameterization of land properties and the observation of z ₀ using satellite remote sensing.     

A model study of instability of the inverse problem in electrocardiography.

The inverse problem in electrocardiography is studied analytically using a concentric spheres model with no symmetry assumptions on the potential distribution. The mathematical formulation is presented, and existence and uniqueness of the solution are briefly discussed. Solution to the inverse problem is inherently very unstable. The magnitude of this instability is demonstrated using the derived analytical inverse solution for the spherical model. Regularization methods used to date are based on a regularization parameter that does not relate to any measurable physiological parameters. This paper presents a regularization method that is based on a parameter in the form of an a priori bound on the L2 norm of the inverse solution. Such a bound can be obtained from the theoretical estimates based on the measured values of the body surface potentials together with experimental knowledge about the magnitudes of the epicardial potentials. Based on the presented regularization, an exact form of the regularized solution and estimates of its accuracy are derived.     

Optimizing selection for function-valued traits

We consider a function-valued trait z(t) whose pre-selection distribution is Gaussian, and a fitness function W that models optimizing selection, subject to certain natural assumptions. We show that the post-selection distribution of z(t) is also Gaussian, compute the selection differential, and derive an equation that expresses the selection gradient in terms of the parameters of W and of the pre-selection distribution. We make no assumptions on the nature of the “time” parameter t.      

Computation of cell survival in heavy ion beams for therapy

A simplified method for the calculation of mammalian cell survival after charged particle irradiation is presented that is based on the track structure model of Scholz and Kraft [1, 2]. Utilizing a modified linear-quadratic relation for the x-ray survival curve, one finds that the model yields linear-quadratic relations also for heavy ion irradiation. If survival is calculated as a function of specific energy, z, in the cell nucleus – thus reducing the stochastic fluctuations of energy deposition – the increase in slope of the survival curve and therefore the coefficient β _z can be estimated with sufficient accuracy from the initial slope, α _z . This permits the tabulation of the coefficients α _z for the particle types and energies of interest, and subsequent fast calculations of survival levels at any point in a mixed particle beam. The complexity of the calculations can thereby be reduced in a wide range of applications, which permits the rapid calculations that are required for treatment planning in heavy ion therapy. The validity of the modified computations is assessed by the comparison with explicit calculations in terms of the original model and with experimental results for track-segment conditions. The model is then used to analyze the influence of beam fragmentation on the biological effect of charged particle beams penetrating to different depths in tissue. In addition, cell-survival rates after neutron irradiation are computed from the slowing-down spectra of secondary charged particles and are compared to experimental observations. Received: 10 August 1996 / Accepted in revised form: 16 December 1996     

A simulation program based on a structured population model for biotechnological yeast processes

Summary A segregated population model for budding yeasts and a simulation program based on it are presented. They enable the study of bioprocesses utilizing yeasts in steady and perturbed conditions and in particular the comparison between the model predictions and the experimental results obtained by flow cytometry, which allows the measurement of segregated parameters of cell populations.Nomenclature a genealogical age - A parameter of the budding law - CV coefficient of variation - F _in(t) volumetric input flow - F _out(t) volumetric output flow - h parameter of the division law - K _s parameter of the Monod's law - m cell mass - M _i discretized cell mass - m _b (a,s) critical mass level for budding - m _p cell mass at the time of budding - n(t) cell number per unit volume - n _p number of sub-populations - n _c number of channels - p (a, i, j, k) discrete density function - Q parameter of the budding law - s(t) substrate concentration - S _in(t) substrate concentration in the input flow - t time - T _m minimal length of the budded phase - V(t) culture volume - x(t) biomass concentration - Y yield coefficient - channel width - (s) specific growth rate - _max parameter of the Monod's law     

Forecasting of the flowering time for wild species observed at Guidonia, central Italy

It is well known that forecasting the flowering time of wild vegetation is useful for various sectors of human activity, particularly for all agricultural practices. Therefore, continuing previous work by Cenci et al., we will present here three new phenoclimatic models of the flowering time for a set of wild species, based on an original data sample of flowering dates for more than 500 species, observed at Guidonia (42° N in central Italy) by Montelucci in the period 1960–1982. However, on applying the bootstrap technique to each species sample to check its basic statistical parameters, we found only about 200 to have data samples with an approximately Gaussian distribution. Eventually only 57 species (subdivided into eight monthly subsets from February to September) were used to formulate the models satisfactorily. The flowering date (represented by the z variable), is expressed in terms of two variables x and y by a nonlinear equation of the form z=αx ^β +γy. The x variable represents either the degree-day sum (in model 1), or the daily-maximum-temperature sum (in model 2), or the daily-global-insolation sum (in model 3), while y for all three models corresponds to the rainy-day sum. Note that all summations involved in the computation of the variables x and y take place over a certain period of time (preceding the flowering phase), which is a parameter to be determined by the fitting procedure. This parameter, together with the threshold temperature (needed to compute the degree-days in model 1), represents the two implicit parameters of the process, thus the total number of parameters (including these last two) becomes respectively, five for model 1, and four for the other two models. The preliminary results of this work were reported at the XVI International Botanical Congress (1–7 August 1999, St. Louis, Missouri USA). Received: 4 November 1999 / Revised: 10 May 2000 / Accepted: 10 May 2000     

Method for calculating 3-D coordinates from molecular stereograms

The three-dimensional coordinates for the -carbon atoms of crambin and basic pancreatic trypsin inhibitor (BPTI) were determined from the respective -carbon trace stereograms using an improved Simplex algorithm. This algorithm was used in a two-step process to estimate thez-coordinate values. In one approach, an average interatomic distance value, an approximate viewing angle, and a table of digitized values forx _left,y _left andx _right,y _right are provided in the first step. In the second step, thez-coordinate values are derived by varyingz to minimize the bond distance error (Rossmann and Argos, 1980). In another approach, only a reference bond distance table is provided along with the table ofx _left,y _left andx _right,y _right digitized values. In the first step, the viewing angle (), a combined scale and viewing distance parameter (q), a rotational angular distortion from digitizing and/or photocopying (z), and translational distortion factors (x _err andy _err) are calculated. In the second step, thez-coordinate values are varied to minimize the bond distance error. RMS difference values of less than 1.5 Å were obtained for both crambin and BPTI -carbon atoms.     

Computational analysis of CFSE proliferation assay

CFSE based tracking of the lymphocyte proliferation using flow cytometry is a powerful experimental technique in immunology allowing for the tracing of labelled cell populations over time in terms of the number of divisions cells undergone. Interpretation and understanding of such population data can be greatly improved through the use of mathematical modelling. We apply a heterogenous linear compartmental model, described by a system of ordinary differential equations similar to those proposed by Kendall. This model allows division number-dependent rates of cell proliferation and death and describes the rate of changes in the numbers of cells having undergone j divisions. The experimental data set that we specifically analyze specifies the following characteristics of the kinetics of PHA-induced human T lymphocyte proliferation assay in vitroL (1) the total number of live cells, (2) the total number of dead but not disintegrated cells and (3) the number of cells divided j times. Following the maximum likelihood approach for data fitting, we estimate the model parameters which, in particular, present the CTL birth- and death rate “functions”. It is the first study of CFSE labelling data which convincingly shows that the lymphocyte proliferation and death both in vitro and in vivo are division number dependent. For the first time, the confidence in the estimated parameter values is analyzed by comparing three major methods: the technique based on the variance–covariance matrix, the profile-likelihood-based approach and the bootstrap technique. We compare results and performance of these methods with respect to their robustness and computational cost. We show that for evaluating mathematical models of differing complexity the information-theoretic approach, based upon indicators measuring the information loss for a particular model (Kullback–Leibler information), provides a consistent basis. We specifically discuss methodological and computational difficulties in parameter identification with CFSE data, e.g. the loss of confidence in the parameter estimates starting around the sixth division. Overall, our study suggests that the heterogeneity inherent in cell kinetics should be explicitly incorporated into the structure of mathematical models.      

Species-area and species-distance relationships of terrestrial mammals in the Thousand Island Region

Summary The species-area and species-distance relationships of terrestrial mammals in the Thousand Island Region of the St. Lawrence River are totally consistent with the basic predictions of the equilibrium theory of island biogeography. The power model provides the best fit for the species-area relationship, and the z-value of 0.305 does not differ significantly from Preston's canonical value (0.26). Distance (D) is a normal determinant (Se -D ²) of mammalian richness, and 93% of the variability in richness is accounted for by island area and isolation. The high z-values and poor species-distance correlations reported in previous studies of mammalian island biogeography, rather than evidencing non-equilibrium, are predictions consistent with the equilibrium theory for distant archipelagoes or, equivalently, poor immigrators such as mammals.     

An unstructured kinetic model to study NaCl effect on volatile ester fermentation by <Emphasis Type="Italic">Candida etchellsii</Emphasis> for soy sauce production

Salt-tolerant aromatic yeast is an important microorganism arising from the solid state fermentation of soy sauce. The fermentation kinetics of volatile esters by Candida etchellsii was studied in a batch system. The data obtained from the fermentation were used for determining the kinetic parameters of the model. Batch experimental results at four NaCl levels (180, 200, 220, and 240 g/L) were used to formulate the parameter estimation model. The kinetic parameters of the model were optimized by specifically designed Runge-Kutta Genetic Algorithms (GA). The resulting mathematical model for volatile ester production, cell growth and glucose consumption simulates the experimental data well. The resulting new model was capable of explaining the behavior of volatile ester fermentation. The optimized parameters (μ_o, X _max, K _i, α, β, Y _X/S, m, and Y _P/S) were characterized by a correlation of functions assuming salinity dependence. The kinetic models optimized by GA describe the batch fermentation process adequately, as demonstrated by our experimental results.     

Speciation-rate dependence in species–area relationships

The general tendency for species number (S) to increase with sampled area (A) constitutes one of the most robust empirical laws of ecology, quantified by species–area relationships (SAR). In many ecosystems, SAR curves display a power-law dependence, S∝A^z. The exponent z is always less than one but shows significant variation in different ecosystems. We study the multitype voter model as one of the simplest models able to reproduce SAR similar to those observed in real ecosystems in terms of basic ecological processes such as birth, dispersal and speciation. Within the model, the species–area exponent z depends on the dimensionless speciation rate ν, even though the detailed dependence is still matter of controversy. We present extensive numerical simulations in a broad range of speciation rates from ν=10^-3 down to ν=10^-11, where the model reproduces values of the exponent observed in nature. In particular, we show that the inverse of the species–area exponent linearly depends on the logarithm of ν. Further, we compare the model outcomes with field data collected from previous studies, for which we separate the effect of the speciation rate from that of the different species lifespans. We find a good linear relationship between inverse exponents and logarithm of species lifespans. However, the slope sets bounds on the speciation rates that can hardly be justified on evolutionary basis, suggesting that additional effects should be taken into account to consistently interpret the observed exponents.     

Sensitivity analysis of a model of mammalian neural membrane

The sensitivity of the strength-duration (S-D) relationship to changes in the parameters describing the sodium channel of mammalian neuronal membrane was determined by computer simulation. A space-clamped patch of neuronal membrane was modeled by a parallel nonlinear sodium conductance, linear leakage conductance, and membrane capacitance. Each parameter that governs the activation (m) and inactivation (h) variables of the sodium channel was varied from −50% to +50% of its default value, and for each variation a S-D relationship was generated. Individual changes in six of the eleven parameters (α _m A, α _m D, α _h A, β _m A, β _m B, and β _h B) generated substantial changes in the rheobase current and chronaxie time (Tch) of the model. Changing the parameter values individually did not correct for the model's failure to generate excitation after the release from a long duration hyperpolarization (anode break excitation). Scaling a combination of five parameters (α _m A, α _m B, α _h A, β _m A, and β _h B) by an equal amount produced a model that generated anode break excitation and increased Tch, but also decreased the amplitude of the action potential. To reproduce the amplitude of the action potential, the maximum sodium conductance and sodium Nernst potential were increased. These modifications generated a model that had S-D properties closer to experimental results, could produce anode break excitation, and reproduced the action potential amplitude. Received: 6 October 1997 / Accepted in revised form: 3 April 1998     

A generic constitutive model for the passive porcine coronary artery

Constitutive models describing the arterial mechanical behavior are important in the development of catheterization products, to be used in arteries with a specific radius. To prove the possible existence of a constitutive model that, provided with a generic set of material and geometric parameters, is able to predict the radius-specific mechanical behavior of a coronary artery, the passive pressure–inner radius (P–r _i ) and pressure–axial force change (P–ΔF _z ) relations of seven porcine left anterior descending coronary arteries were measured in an in-vitro set-up and fitted with the model of Driessen et al. in J Biomech Eng 127(3):494–503 (2005), Biomech Model Mechanobiol 7(2):93–103 (2008). Additionally, the collagen volume fraction, physiological axial pre-stretch, and wall thickness to inner radius ratio at physiological loading were determined for each artery. From this, two generic parameter sets, each comprising four material and three geometric parameters, were obtained. These generic sets were used to compute the deformation of each tested artery using a single radius measurement at physiological loading as an artery-specific input. Artery-specific P–r _i and P–ΔF _z relations were predicted with an accuracy of 32 μm (2.3%) and 6 mN (29% relative to ΔF _z -range) on average compared to the relations measured in-vitro. It was concluded that the constitutive model provided with the generic parameters found in this study can well predict artery-specific mechanical behavior.     

Tissue-specific expression of hormonal carcinogenesis target genes in rats treated with polycyclic aromatic hydrocarbons

We have investigated the effect of polycyclic aromatic hydrocarbons (PAHs) on expression of the estrogen-metabolizing genes CYP1A1, CYP1B1, CYP19 and also ERα, and cyclinD1 genes, regulating cell division in estrogen-depended tissues. Treatment of rats with benzo(a)pyrene (BP) or 3-methylcholantrene (MCA) significantly up-regulated CYP1A1, CYP1B1 gene expression in liver, uterus and ovary, whereas α-naphthoflavone (α-NF) did not have any effect. The high level of aromatase gene (CYP19) expression was detected in ovary only. Treatment of rats with BP or MCA significantly down-regulated expression of this gene (15- and 5,5-fold, respectively), whereas α-NF was ineffective. Administration of BP but not MCA or α-NF increased ERα and cyclinD1 gene expression in rat liver. The levels of ERα and cyclinD1 mRNA levels remained unchanged in uterus of after treatment of rats with these PAHs. BP administration increased ERα and cyclinD1 mRNA levels (3,5- and 2,5-fold, respectively) in ovary, while MCA and α-NF were ineffective. Thus, our results give evidence for tissue-specific effects of PAHs on expression of genes, which participate in hormonal carcinogenesis. On the other hand, the fact that BP and MCA treatments influenced the expression of estrogen-metabolizing genes and genes, which control cell division, supports the viewpoint that PAHs may be one of the causes of endocrine disorders and subsequent hormonal carcinogenesis.     

Quantitative studies on the mating system of opium poppy (Papaver somniferum L.)

Summary Nearly 400 individuals at two locations and over a number of years were crossed and subsequently scored for selfing versus outcrossing in eight monohybrid populations of opium poppy (Papaver somniferum). Two different marker loci, petal colour (R/r) and capsule size (B/b) were used to determine the male gametes that had effected fertilizations in F₂ recessives (rr and bb). The estimates of the outcrossing parameter were found to vary with year, location and for the marker locus used ( range: 0.0988–0.3704). Study of two dihybrid crosses involving the two loci simultaneously, further confirmed that outcrossing at the R/r locus was significantly greater than that at the B/b locus. The nature of the outcrossing was, in general, nonrandom. Selfmg predominated in this species; however, there was a high frequency of natural outcrossing for generating variations in P. somniferum.CIMAP publication No. 1086     

Nitrogen and carbon fixation byAnabaena sp. isolated from a rice paddy and grown under P and light limitations

Anabaena sp., isolated from a rice paddy, was investigated for its nitrogen fixation as measured by acetylene reduction activity (ARA) in P-limited continuous and light-limited semi-continuous cultures. Growth rate (μ) under P limitation was a function of cell P content (q _p). Both the photosynthetic capacity (P_max) and photosynthetic efficiency (α) increased with μ when expressed per cell, but not per unit chla. The ARA of steady-state cells under P limitation increased with μ and was linearly related to C-fixation rate. This was apparently a consequence of the control of C-fixation by P limitation. In light-limited cells, steady state ARA, both at the culture light intensity and in the dark, increased asymptotically with μ, but the activity in the dark was only about 51% of that in the light. When the light level of steady-state cells grown at a high in intensity was switched to a low level, ARA decreased exponentially with time. Dark ARA activity also showed a similar decline, but at much lower levels. Thus, ARA depended not only on light history, but also immediate photosynthesis. Steady-state ARA at the ambient intensity or in the dark showed a strong correlation with¹⁴C-fixation rate. ARA of light-limited cells showed the same light-saturation characteristics as their¹⁴C-fixation, with the same initial saturation intensity,I _k. The ratios of P_max to the maximum ARA (ARA_max), and α to the slope of ARA (α_ara) were identical. A comparison of gross to net photosynthesis and N₂ fixation suggested that there was little leakage or excretion of fixed C or N.     

In situ and experimental evidence of the influence of turbulence on cell division processes of Peridinium cinctum forma westii (Lemm.) Lefèvre

Comparison of the diel variations of the wind intensity and the division rate (DR) of Peridinium cinctum forma westii (Lemm.) Lefèvre in situ reveals that the intensity of the wind blowing throughout the whole day does not affect the DR. On the other hand, a strong inhibitory effect is noticed when the wind episodes occur during the time period 18.00–02.00 h. Systematic hourly sampling and staining of Peridinium cells showed that nuclear division takes place between 23.00 and 02.00 h and is completed before cytokinesis begins. Thus the time period 18.00–02.00 h corresponds to the premitotic and mitotic phases of cell division, and the turbulence generated by the wind affects the process of nuclear division.

The relationship between water turbulence and the DR of Peridinium which was observed in Lake Kinneret (Israel) has been checked under experimental conditions. Peridinium was grown without shaking, with continuous rotary shaking and with intermittent shaking at 100 r min^-1. The specific growth rate (k), generation time (G) and mortality rate were followed and compared. The results obtained confirm the facts observed in situ and clarify some aspects. Intermittent shaking of 2 h day^-1 during the dark phase reveals the inhibitory effect of agitation on nuclear division. Continuous shaking causes a high rate of cell mortality. Shaking during the light period does not affect the division process.

The effect of turbulence on the DR of Peridinium explains why the timing of the bloom in Lake Kinneret is a function of the duration and intensity of the mixing period in the lake.     

On the general dynamic model of oceanic island biogeography

Aim To investigate the biological meaning of equations used to apply the general dynamic model (GDM) of oceanic island biogeography proposed by R. J. Whittaker, K. A. Triantis and R. J. Ladle. Location Analyses are presented for 17 animal groups living on the Aeolian Islands, a volcanic archipelago in the central Mediterranean, near Sicily. Methods In addition to the mathematical implementation of the GDM proposed by Whittaker, Triantis and Ladle, and termed here logATT² (, where S is species number or any other diversity metric, t is island age, A is island area, and a, b, c and d are fitted parameters), a new implementation based on the Arrhenius equation of the species–area relationship (SAR) is investigated. The new model (termed powerATT²) is: . For logATT² and powerATT² models, equations were developed to calculate (1) the expected number of species at equilibrium (i.e. when the island has reached maturity) per unit area (S_eq), and (2) the time required to obtain this value (t_eq). Whereas the intercept in the Gleason model (S = C + z log A) or the coefficient of the Arrhenius power model (S = CA^z) of the SAR can be considered measures of the expected number of species per unit area, this is not the case for the parameter a of the ATT² models. However, values of S_eq can be used for this purpose. The index of ‘colonization ability’ (CAB), calculated as the ratio , may provide a measure of the mean number of species added per unit area per unit time. Results Both ATT² models fitted most of the data well, but the powerATT² model was in most cases superior. Equilibrial values of species richness (S_eq) varied from c. 3 species km^?2 (reptiles) to 100 species km^?2 (mites). The fitted curves for the powerATT² model showed large variations in d, from 0.03 to 3. However, most groups had values of d around 0.2–0.4, as commonly observed for the z‐values of SARs modelled by a power function. Equilibration times ranged from about 170,000 years to 400,000 years. Mites and springtails had very high values of CAB, thus adding many more species per unit area per unit time than others. Reptiles and phytophagous scarabs showed very low values, being the groups that added fewest species per unit area per unit time. Main conclusions Values of equilibrial species richness per unit area are influenced by species biology (e.g. body size and ecological specialization). Theoretical and empirical evidence suggests that higher immigration rates should increase the z‐values of the Arrhenius model. Thus, in the same archipelago, groups with larger z‐values should be characterized by higher dispersal ability. Results obtained here for the parameter d conform to this prediction.     

Contribution of the allelicMtz 3 andMtz 4 allotype genes to the formation of individual rabbit serum α2-macroglobulin molecules

The contribution of the allelicMtz ³ andMtz ⁴ genes to the formation of individual rabbit serum α₂-macroglobulin (α₂M) molecules was examined by precipitation of α₂M from rabbits of known genotype with antiallotype antisera. The α₂M was isolated fromz ³z³ andz ⁴z⁴ homozygous andz ³z⁴ heterozygous rabbits, iodinated with I¹²⁵ and precipitated by sequential reactions with antiallotype antiserum and goat anti-rabbit IgG. Purified unlabeled α₂M or α₂M in serum was used to inhibit competitively the reaction of antiallotype antiserum and labeled α₂M. Nearly all α₂M molecules have z3 or z4 antigenic determinants; approximately 50% of α₂M molecules in heterozygotes have both. Altogether, the z3, z3,4, and z4 molecules in heterozygotes have approximately 60% of the number of z3 and 40% of the number of z4 determinants as compared to the respective homozygotes. Unlike all other known allelic blood protein systems of rabbits, allelic exclusion does not occur in α₂M molecules of heterozygotes; rather, hybrid molecules are formed. Presented in part at the Fifty-fourth and Fifty-fifth Annual Meetings of the Federation of American Societies for Experimental Biology, Atlantic City, New Jersey, April 12–17, 1970, and Chicago, Illinois, April 12–17, 1971. This investigation was supported in part by U.S. Public Health Service Grants AI-09241 and AI-07043. B.H.B. performed this investigation in partial fulfillment of the requirements for the Doctor of Philosophy Degree in the Graduate College; he is supported by a postdoctoral fellowship from the Schweppe Foundation. K.L.K. is the recipient of U.S. Public Health Service Research Career Development Award AI-28687.