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1.
The time evolution of slowly evolving discrete dynamical systems x
i + 1
= T(r
i
,x
i
), defined on an interval [0, L], where a parameter r
ichanges slowly with respect to i is considered. For certain transformations T, once r
i reaches a critical value the system faces a non-zero probability of extinction because some x
j [0, L]. Recent ergodic theory results of Ruelle, Pianigiani, and Lasota and Yorke are used to derive a simple expression for the probability of survival of these systems. The extinction process is illustrated with two examples. One is the quadratic map, T(r, x) = rx(1 – x), and the second is a simple model for the growth of a cellular population. The survival statistics for chronic myelogenous leukemia patients are discussed in light of these extinction processes. Two other dynamical processes of biological importance, to which our results are applicable, are mentioned. 相似文献
2.
The estimator ?0(x) of the regression r(x) = E (Y | × = x) from measured points (xi, yi), i = 1(1) n, of a continuous two-dimensional random variable (X, Y) with unknown continuous density function f(x, y) and with moments up to the second order can be made with the help of a density estimation f?0(x, y) (see e.g. SCHMERLING and PEIL, 1980). Here f?0(x, y) still contains free parameters (so-called band-width-parameters), the values of which have to be optimally fixed in the concrete case. This fixing can be done by using a modification of the maximum-likelihood principle including jackknife techniques. The parameter values can be also found from the estimators for r(x). Here the cross-validation principle can be applied. Some numerical aspects of these possibilities for optimally fixing the bandwidth-parameter are discussed by means of examples. If ?0(x) is used as a smoothing operator for time series the optimal choice of the parameter values is dependent on the purpose of application of the smoothed time series. The fixing will then be done by considering the so-called filter-characteristic of ?C0(x). 相似文献
3.
Five new methods for determining the relations between kinetic data of fermentations are described and applied to an industrial antibotic fermentation process. The input data for these method are the elements of the distance matrix dij, which quantify the sum of the deviation squares between the time dependent kinetics x (t) of the fermentation runs i and j. For each measurable or calculable kinetic state variable, one n x n distance matrix must be calculated where n is the number of fermentation runs. All methods compare these distance matrices by statistical or graph-theoretical approaches. The algorithms obtained are universally applicable if enough kinetic data are available, especially from more than 10 comparable fermentation runs. The algorithms were developed for the use in knowledge acquisition modules of expert systems. 相似文献
4.
5.
L. Qu J. F. Hancock 《TAG. Theoretical and applied genetics. Theoretische und angewandte Genetik》2001,103(1):136-143
It has been suggested that ratios of coupling- to repulsion-phase linked markers can be used to distinguish between allopolyploids
and autopolyploids, because repulsion-phase linkages are much more difficult to detect in autopolyploids with polysomic inheritance
than allopolyploids with disomic inheritance. In this report, we analyze the segregation pattern of repulsion-phase linked
markers in polyploids without complete preferential pairing. The observed repulsion-phase recombination fraction (R) in such
polyploids is composed of a fraction due to crossing-over (Rc) and another fraction due to independent assortment (Ri). Ri is the minimum distance that can be detected between repulsion-phase linked markers. Because Ri is high in autopolyploids (0.3373, 0.4000, 0.4286 and 0.4444) for autopolyploids of 2n=4x, 6x, 8x and 10x), large population sizes are required to reliably detect repulsion linkages. In addition, the default linkage used in mapping-programs
must be greater than the corresponding Ri to determine whether a polyploid is a true autopolyploid. Unfortunately, much lower default linkages than the Ris have been used in recent polyploid studies to determine polyploid type, and markers have been incorporated into polyploid
maps based on the R values. Herein, we describe how mapping repulsion linkages can result in spurious results, and present
methods to accurately detect the degree of preferential pairing in polyploids using repulsion linkage analysis.
Received: 29 February 2000 / Accepted: 17 July 2000 相似文献
6.
Fluctuations and Noise in Kinetic Systems: Application to K+ Channels in the Squid Axon 总被引:2,自引:0,他引:2
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We consider the equilibrium or steady-state noise power density spectrum in the quantity N = Σxi=0 aiNi for an ensemble of independent and equivalent systems each of which can exist in the discrete set of states i = 0, 1, ···, x. Ni is the number of systems of the ensemble in state i and the ai's are constants. There is a transition rate constant αij for an arbitrary transition i → j; the kinetic equations are linear. There are possible applications to enzyme and biochemical kinetics generally, to membrane transport, muscle contraction, binding on macromolecules, etc. In each case, noise measurements would provide information about the kinetic scheme. The particular application considered here is to K+ channels or gates (one channel = one system) in the squid axon membrane: aiK is the K+ conductance of a channel in state i and the kinetic scheme is of the Hodgkin-Huxley type (HH). Here we allow an arbitrary set of ai's. This is a generalization of our treatment of K+ channel noise in an earlier paper. The theory is discussed and some calculations made using Fishman's recent experimental results on K+ channel noise as a guide. Preliminary indications are that the HH choice of ai's may be oversimplified and that a0 0, a1 ≠ a0, ax ≠ ax-1. Quite possibly the ai's increase from a0 to ax, though the early ai's must be relatively small to give the observed induction behavior in gK(t). An increase in equal steps is unsatisfactory because this is essentially HH with x = 1 (no induction). More refined experiments may modify these tentative conclusions. In any case, it appears from Fishman's work that noise measurements will probably be very useful in distinguishing between rival models of K+ channels. 相似文献
7.
B. F. J. Manly 《Biometrical journal. Biometrische Zeitschrift》1981,23(3):267-281
The situation is considered where the multivariate distribution of certain variables X1, X2, …, Xp is changing with time in a population because natural selection related to the X's is taking place. It is assumed that random samples taken from the population at times t1, t2, …, ts are available and it is desirable to estimate the fitness function wt(x1, x2,…,xp) which shows how the number of individuals with Xi = xi, i = 1, 2, …, p at time t is related to the number of individuals with the same X values at time zero. Tests for population changes are discussed and indices of the selection on the population dispersion and the population mean are proposed. The situation with a multivariate normal distribution is considered as a special case. A maximum likelihood method that can be applied with any form of population distribution is proposed for estimating wt. The methods discussed in the paper are illustrated with data on four dimensions of male Egyptian skulls covering a time span from about 4500 B.C. to about 300 A.D. In this case there seems to have been very little selection on the population dispersion but considerable selection on means. 相似文献
8.
Summary The authors studied the dependence between the ability of systems regulating the level of peripheral leucocytes to damp the fluctuations of this level, occurring under conditions of repeated stressing of the organism by non-specific stress factors (isolation, starvation, handling for blood withdrawal) and the tolerance of the organism to the action of ionizing radiation (summary exposure to X-rays leading to death at repeated irradiation). This regulatory ability was expressed with the aid of the slope (coefficientb) of regression between the leucocytary valuesx
i, fluctuating in time, and the subsequent differences
i
(
i
=x
i+1–x
i
). The highest tolerance to lethal action of radiation is correlated to such a regulatory behaviour of the organism at which the time necessary for adaptation of the system is shortest. The authors point out the suitability of the employed regulatory characteristic for the quantitative study of adaptability and resistance of the organism and its relatedness to the damping ratio, used in the automatic control theory. 相似文献
9.
Marc Artzrouni 《Journal of mathematical biology》1986,24(4):405-422
In an age-structured population that grows exponentially, each age groupP
i(t) at periodt is asymptotically equivalent tox
0
t
for some positive number x0. In this paper we show that the speed at which the ith age group reaches its exponential state of equilibrium can be measured by the rate at which the ratio vi(t)=Pi(t)/pi(t–1) converges tox
0. The age specific rate of convergence is determined by considering a quantityr satisfyingv
i(t)-x
0
¦ r
t
whent is large;R
i=Infr (over all initial populations,r satisfying the above inequality) is the R-factor used in numerical analysis to measure the rate at which the sequencev
i
(t) converges tox
0;S
i
=- In Ri is then defined as the rate of convergence to stability of the ith age group. The case of constant net maternity rates is studied in detail; in this contextS
0 is compared to the population entropyH, which was proposed by Tuljapurkar (1982) as a measure of the rate of convergence to stability. 相似文献
10.
Vig A Ohmacht R Jámbor E Bugyi B Nyitrai M Hild G 《European biophysics journal : EBJ》2011,40(5):619-626
During the polymerization of actin, hydrolysis of bound ATP occurs in two consecutive steps: chemical cleavage of the high-energy
nucleotide and slow release of the γ-phosphate. In this study the effect of phalloidin and jasplakinolide on the kinetics
of P
i
release was monitored during the formation of actin filaments. An enzyme-linked assay based spectrophotometric technique
was used to follow the liberation of inorganic phosphate. It was verified that jasplakinolide reduced the P
i
release in the same way as phalloidin. It was not possible to demonstrate long-range allosteric effects of the toxins by
release of P
i
from F-actin. The products of ATP hydrolysis were released by denaturation of the actin filaments. HPLC analysis of the samples
revealed that the ATP in the toxin-bound region was completely hydrolysed into ADP and P
i
. The effect of both toxins can be sufficiently explained by local and mechanical blockade of P
i
dissociation. 相似文献
11.
Let X1:n, X2:n, X3:n…, Xn:n be the order statistics of n independent random variables with the common (absolutely continuous strictly increasing) distribution function F. The main results given in this article are:
- 1 For any fixed r and two distinct numbers s1 and s2 (1<r<s1<s2≦n) the distributions of Vi and Wi (defined in (1.11) and (1.12) are identical for i = 1,2 iff F(x) is WEIBULL (1.2).
- 2 The statistics D1 and D2 (as in (1.8) and (1.9)) are independent iff F(x) is WEIBULL (1.2).
- 3 The statistics Ui (1≦j≦n?1) and Xi:n (i ≦ j) are independent iff F(x) is WEIBULL (1.2).
- 4 Let X, X1, X2, …, Xk be random variables such that
12.
Modrak-Wójcik A Kirilenko A Shugar D Kierdaszuk B 《European biophysics journal : EBJ》2008,37(2):153-164
Kinetics of the reactions of purine nucleoside phosphorylases (PNP) from E. coli (PNP-I, the product of the deoD gene) and human erythrocytes with their natural substrates guanosine (Guo), inosine (Ino), a substrate analogue N(7)-methylguanosine
(m7Guo), and orthophosphate (Pi, natural cosubstrate) and its thiophosphate analogue (SPi), found to be a weak cosubstrate, have been studied in the pH range 5–8. In this pH range Guo and Ino exist predominantly
in the neutral forms (pKa 9.2 and 8.8); m7Guo consists of an equilibrium mixture of the cationic and zwitterionic forms (pKa 7.0); and Pi and SPi exhibit equilibria between monoanionic and dianionic forms (pKa 6.7 and 5.4, respectively). The phosphorolysis of m7Guo (at saturated concentration) with both enzymes exhibits Michaelis kinetics with SPi, independently of pH. With Pi, the human enzyme shows Michaelis kinetics only at pH ∼5. However, in the pH range 5–8 for the bacterial enzyme, and 6–8
for the human enzyme, enzyme kinetics with Pi are best described by a model with high- and low-affinity states of the enzymes, denoted as enzyme-substrate complexes with
one or two active sites occupied by Pi, characterized by two sets of enzyme-substrate dissociation constants (apparent Michaelis constants, K
m1 and K
m2) and apparent maximal velocities (V
max1 and V
max2). Their values, obtained from non-linear least-squares fittings of the Adair equation, were typical for negative cooperativity
of both substrate binding (K
m1 < K
m2) and enzyme kinetics (V
max1/K
m1 > V
max2/K
m2). Comparison of the pH-dependence of the substrate properties of Pi versus SPi points to both monoanionic and dianionic forms of Pi as substrates, with a marked preference for the dianionic species in the pH range 5–8, where the population of the Pi dianion varies from 2 to 95%, reflected by enzyme efficiency three orders of magnitude higher at pH 8 than that at pH 5.
This is accompanied by an increase in negative cooperativity, characterized by a decrease in the Hill coefficient from n
H ∼1 to n
H ∼0.7 for Guo with the human enzyme, and to n
H ∼0.7 and 0.5 for m7Guo with the E. coli and human enzymes, respectively. Possible mechanisms of cooperativity are proposed. Attention is drawn to the substrate properties
of SPi in relation to its structure. 相似文献
13.
Predictive models in aerobiology: data transformation 总被引:1,自引:1,他引:0
Francisco Javier Toro Marta Recio María del Mar Trigo Baltasar Cabezudo 《Aerobiologia》1998,14(2-3):179-184
This paper attempts to evaluate the effect of mathematical transformations of pollen and meteorogical data used in aerobiological
forecasting models. Stepwise multiple regression equations were developed in order to facilitate short term forecasts during
the pre-peak period. The daily mean pollen data (x
i) expressed as number of pollen grains per cubic metre of air were used directly and transformed into different scales: log(x
i + 1), ln((x
11000/Σp) + 1) and √x
i, where Σp is the sum of the daily mean values throughout the season. Thirteen meteorological parameters and the variable time were
used as forecasting variables. The most reliable forecasts were obtained with data transformed by ‘square root’ and with untransformed
data. Based on the results obtained, we recommend that the data be transformed by means of the square root if they do not
show a normal distribution and that non-linear statistics be used in this kind of study. 相似文献
14.
B. M. Bennett 《Biometrical journal. Biometrische Zeitschrift》1984,26(7):735-739
If {Ui} i = 1, …, k is a sequence of binary responses of ni subjects at each of k successive dose levels xi, there is the problem of the statistical treatment of the observed proportions Pi = Ui/ni when neither the probit nor the logit transformation may be assumed. This paper considers the use of the midranks of the responses for point and interval estimation of relative potency in the case of parallel line assay in particular. More generally the problem of combining the results of several independent estimates using ranks is discussed. Several examples illustrate the method. 相似文献
15.
ATP-dependent potassium channels of muscle cells: Their properties,regulation, and possible functions 总被引:8,自引:0,他引:8
N. W. Davies N. B. Standen P. R. Stanfield 《Journal of bioenergetics and biomembranes》1991,23(4):509-535
ATP-dependent potassium channels are present at high density in the membranes of heart, skeletal, and smooth muscle and have a lowP
open at physiological [ATP]i. The unitary conductance is 15–20 pS at physiological [K+]
o
, and the channels are highly selective for K+. Certain sulfonylureas are specific blockers, and some K channel openers may also act through these channels. KATP channels are probably regulated through the binding of ATP, which may in turn be regulated through changes in the ADP/ATP ratio or in pHi. There is some evidence for control through G-proteins. The channels have complex kinetics, with multiple open and closed states. The main effect of ATP is to increase occupancy of long-lived closed states. The channels may have a role in the control of excitability and probably act as a route for K+ loss from muscle during activity. In arterial smooth muscle they may act as targets for vasodilators. 相似文献
16.
Chen C. R. Condron L. M. Sinaj S. Davis M. R. Sherlock R. R. Frossard E. 《Plant and Soil》2003,256(1):115-130
Vegetative conversion from grass to forest may influence soil nutrient dynamics and availability. A short-term (40 weeks) glasshouse experiment was carried out to investigate the impacts of ryegrass (Lolium perenne) and radiata pine (Pinus radiata) on soil phosphorus (P) availability in 15 grassland soils collected across New Zealand using 33P isotopic exchange kinetics (IEK) and chemical extraction methods. Results from this study showed that radiata pine took up more P (4.5–33.5 mg P pot–1) than ryegrass (1.1–15.6 mg pot–1) from the soil except in the Temuka soil in which the level of available P (e.g., E
1min Pi, bicarbonate extractable Pi) was very high. Radiata pine tended to be better able to access different forms of soil P, compared with ryegrass. There were no significant differences in the level of water soluble P (Cp, intensity factor) between soils under ryegrass and radiata pine, but the levels of Cp were generally lower compared with original soils due to plant uptake. The growth of both ryegrass and radiata pine resulted in the redistribution of soil P from the slowly exchangeable Pi pool (E
> 10m Pi, reduced by 31.8% on the average) to the rapidly exchangeable Pi (E
1min-1d Pi, E
1d-10m Pi) pools in most soils. The values of R/r
1 (the capacity factor) were also generally greater in most soils under radiata pine compared with ryegrass. Specific P mineralisation rates were significantly greater for soils under radiata pine (8.4–21.9%) compared with ryegrass (0.5–10.8%), indicating that the growth of radiata pine enhanced mineralisation of soil organic P. This may partly be ascribed to greater root phosphatase activity for radiata pine than for ryegrass. Plant species × soil type interactions for most soil variables measured indicate that the impacts of plant species on soil P dynamics was strongly influenced by soil properties. 相似文献
17.
Sun Ping 《Biometrical journal. Biometrische Zeitschrift》1995,37(2):199-203
In the study of spatial patterns, the statistic I' = (n — 1)s2/x was commonly used. In this paper, we found that x — s2 has an approximated normal distribution with zero mean if the xi's (i = 1 to n) are independent identically distributed Poisson variables. Based on this conclusion, the hypothesis that a point pattern is completely random can be tested directly. And a method for the test of spatial patterns was proposed which can be sued as an alternative to the Chi-square based dispersion index test. 相似文献
18.
Oligomers of (?)-epicatechin with 4β → 8 interflavan bonds, and as many as five monomer units, have been studied by conformational analysis and time-resolved fluorescence. The conformational analysis yields 2x?1 conformations for each oligomer with x monomer units. There are two conformations accessible at each interflavan bond. These conformations are denoted by + and ?. The dominant conformations for the trimer and higher oligomers have an interaction between the phenolic hydroxyl groups on monomers i and i+2. This interaction involves the hydroxyl group at C(5) on monomer i, and either C(13) or C(8) of monomer i+2, depending on whether the conformation of the two intervening interflavan bonds is + + or + ?, respectively. Minor contributions to the ensemble for the tetramer and pentamer are made by conformations that contain the sequence of successive interflavan bonds denoted by ?+ or ??. In ?+ the interaction between monomer units i and i + 2 involves an aliphatic hydroxyl with a phenolic hydroxyl, and there are no hydroxyl-hydroxyl interactions between units iand i + 2 in ??. The onset of a different decay law for the fluorescence when x increases from 3 to 4 may be associated with the appearance of the ?+ and ?? conformations as minor constituents in the ensemble. 相似文献
19.
A. R. Sen 《Biometrical journal. Biometrische Zeitschrift》1993,35(1):1-13
John Graunt (1662) was the first to estimate the ratio y/x where y represents the total population and x the known total number of registered births in the same areas during the preceding year. About 1765 Messance (Stephan, 1948) and Moheau (1778) published very carefully prepared estimates for France based on enumeration of population in certain districts and on the count of births, deaths and marriages as reported for the whole country. The districts from which the ratio of inhabitants to birth was determined only constituted a sample. Laplace (1786) prepared similar estimates in 1802 based on a two-stage sampling plan. Recently Hansen and Hurwitz (1943) showed that the ratio estimate (yi/ni)X of Y is unbiased where all xi's are known and the nth cluster is selected with p.p.s. More recently Hájek (1949), Lahiri (1951), Midzuno (1952) and Sen (1952) developed independently the sampling of n clusters with p.p.s to the totals of the sizes of the sample clusters S(xi). Des Raj (1954) and Sen (1952, 1953) gave unbiased estimate of the variance of the estimator which was generally non-negative for samples with smaller probabilities. Rao and Vijayan (1977) gave an unbiased estimator which is non-negative for samples with larger probabilities. Hájek (1949) provided an almost unbiased estimator of the variance of the estimator. The paper discusses situations where Hájek's estimator of variance should be preferred to the Rao-Vijayan estimator and vice versa. 相似文献
20.
Both Pi-repressible acid phosphatases, IIb (mycelial) and IIc (extracellular), synthesized by Neurospora crassa and purified to apparent homogeneity by 7.5% PAGE, are monomers, are inhibited by 2 mm ZnCl2 and are non-specifically stimulated by salts. However, the IIc form is activated by p-nitrophenylphosphate (in a negative co-operativity effect with a K
0.5 of 2.5 mm) whereas form IIb shows Michaelis kinetics, with a K
m of 0.5 mm. Thus, since both enzymatic forms may be expressed by the same gene (pho-3), it is possible that post-translational modifications lead to the excretion of an enzymatic form with altered Michaelis kinetics compared with the enzymatic form retained by the mycelium. 相似文献