Quantifying the strength of the linear causal coupling in closed loop interacting cardiovascular variability signals

 The coherence function measures the amount of correlation between two signals x and y as a function of the frequency, independently of their causal relationships. Therefore, the coherence function is not useful in deciding whether an open-loop relationship between x and y is set (x acts on y, but the reverse relationship is prevented) or x and y interact in a closed loop (x affects y, and vice versa). This study proposes a method based on a bivariate autoregressive model to derive the strength of the causal coupling on both arms of a closed loop. The method exploits the definition of causal coherence. After the closed-loop identification of the model coefficients, the causal coherence is calculated by switching off separately the feedback or the feedforward path, thus opening the closed loop and fixing causality. The method was tested in simulations and applied to evaluate the degree of the causal coupling between two variables known to interact in a closed loop mainly at a low frequency (LF, around 0.1 Hz) and at a high frequency (HF, at the respiratory rate): the heart period (RR interval) and systolic arterial pressure (SAP). In dogs at control, the RR interval and the SAP are highly correlated at HF. This coupling occurs in the causal direction from the RR interval to the SAP (the mechanical path), while the coupling on the reverse causal direction (the baroreflex path) is not significant, thus pointing out the importance of the direct effects of respiration on the RR interval. Total baroreceptive denervation, by opening the closed loop at the level of the influences of SAP on RR interval, does not change these results. In elderly healthy men at rest, the RR interval and SAP are highly correlated at the LF and the HF. At the HF, a significant coupling in both causal directions is found, even though closed-loop interactions are detected in few cases. At the LF, the link on the baroreflex pathway is negligible with respect to that on the reverse mechanical one. In heart transplant recipients, in which SAP variations do not cause RR interval changes as a result of the cardiac denervation, the method correctly detects a significant coupling only on the pathway from the RR interval to the SAP. Received: 28 June 2001 / Accepted in revised form: 23 October 2001     

Exploring directionality in spontaneous heart period and systolic pressure variability interactions in humans: implications in the evaluation of baroreflex gain

Although in physiological conditions RR interval and systolic arterial pressure (SAP) are likely to interact in a closed loop, the traditional cross-spectral analysis cannot distinguish feedback (FB) from feedforward (FF) influences. In this study, a causal approach was applied for calculating the coherence from SAP to RR (K(s-r)) and from RR to SAP (K(r-s)) and the gain and phase of the baroreflex transfer function. The method was applied, compared with the noncausal one, to RR and SAP series taken from 15 healthy young subjects in the supine position and after passive head-up tilt. For the low frequency (0.04-0.15 Hz) spectral component, the enhanced FF coupling (K(r-s) = 0.59 +/- 0.21, significant in 14 subjects) and the blunted FB coupling (K(s-r) = 0.17 +/- 0.17, significant in 4 subjects) found at rest indicated the prevalence of nonbaroreflex mechanisms. The tilt maneuver recovered FB influences (K(s-r) = 0.47 +/- 0.16, significant in 14 subjects), which were stronger than FF interactions (K(s-r) = 0.34 +/- 0.19, significant in 9 subjects). At the respiratory frequency, the RR-SAP regulation was balanced at rest (K(s-r) = 0.30 +/- 0.18 and K(r-s) = 0.29 +/- 0.20, significant in 11 and 8 subjects) and shifted toward FB mechanisms after tilt (K(s-r) = 0.35 +/- 0.19 and K(r-s) = 0.19 +/- 0.11, significant in 14 and 8 subjects). The causal baroreflex gain estimates were always lower than the corresponding noncausal values and decreased significantly from rest to tilt in both frequency bands. The tilt-induced increase of the phase lag from SAP to RR suggested a shift from vagal to sympathetic modulation. Thus the importance of nonbaroreflex interactions pointed out the necessity of accounting for causality in the cross-spectral analysis of the interactions between cardiovascular variables in healthy humans.     

The global asymptotic stability of prey-predator systems with second-order dissipation

Models of biological development, evolution and control should take into account that very small numbers of cells or chemicals or individuals eventually grow into stable, large populations. The simplified two-component model used in these studies includes the following: (1) first-order decay; (2) first-order autocatalysis; (3) negative feedback; (4) positive feedback; (5) second-order decay; (6) second-order autocatalysis. A positive definite Lyapunov function is constructed and shown to have a negative definite total derivative. The stationary statex>0,y>0, therefore possesses global asymptotic stability. This means that sustained oscillations cannot occur. Another stationary state,x=y=0, is shown to be unstable. This means that infinitesimally small perturbations ofx=y=0 will result in evolution of the variables to the stable stationary state. This result contrasts with that obtained with the Lotka-Volterra model in that small perturbations ofx=y=0 for that model result in sustained, oscillating excursions; the smaller the initial perturbations, the larger these excursions will be. A simulation illustrates that stable populations of 10²⁰ x's andy's can arise from a singlex andy.x grows more or less continuously, buty remains extremely small for 80 per cent of the time interval required for the variables to approach their stable populations. Proceedings article from the Dissipative Structures section of the Tenth Symposium on Biomathematics and Computer Science in the Life Sciences, University of Texas, Houston. March 29–31, 1973. Symposium Chairman: Stuart O. Zimmerman. Session Chairman and Proceedings Editors: Charles Walter and Hugo M. Martinez.     

A confidence interval for the unknown value of the regressor with given expectation of the regressand in model I of linear regression

In the case of model I of linear regression there is derived a confidence interval for that x_o where the “true line” will reach a given value y_o. The interval can be given by the intersections between the line y = y_o and the hyperbolas providing pointwise confidence intervals of the expectations of y.     

A Further Problem of Interval Estimation of an Unknown Regressor in Model I of Linear Regression

For the model y = α + βx + ? (model I) of linear regression we dealt with in KUHNERT and HORN (1980) the determination of a confidence interval for that x₀ where the expectation Ey reaches a given value y₀. Here we start with realizations of random variables y (i = 1,…, m) being independent of x which are given in addition to the realizations of-y. Now y₀ denotes the unknown value of \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \sum \limits_{i = 1}^m $\end{document} ciEy and x₀ the x-value where the expectation Ey reaches that value y₀. For this x₀ we give a confidence interval. Applications stem from dose response assays.     

Methodological evaluation of a new chemiluminescence immunoassay for thyrotropin using acridinium ester-labelled antibody

A recently available immunochemiluminometric assay (ICMA) for TSH developed by Ciba Corning Corp. has been evaluated. This system (Magic Lite) uses an acridinium-ester-labelled antibody and magnetizable particle for bound-free separation. In each assay only two calibrators are carried out and used to re-scale a manufacturer-generated curve stored in the memory of the luminometer. The precision of the response (RLU) estimated by all duplicates of 14 runs was about 4% for responses >12,000 RLU (corresponding to a concentration interval 0.7–113 μlU/ml) and worsened in the lower range (up to 10% CV); the sensitivity, computed from the mean within-assay precision profile, was 0.028 μlU/ml; the between-assay precision ranged from 4.6 to 13.1 CV%. Regression analysis of ICMA results (y) against consensus values of Behring IRMA (x) on 15 QC sera assayed in an inter-laboratory survey (concentration range 1–30 μlU/ml) gave y = ?0.003 + 0.98x indicating a good agreement of the two techniques. Similar conclusions have been derived from the comparison of the ICMA results (y) in the low TSH concentration range (< 1 μlU/ml) against the IRMA Boots Celltech (x) on 80 patient samples (y = 0.04 + 1.04x).     

A New Functional Equation Analogous to CAUCHT-PEXIDER Functional Equation and its Application

The CAUCHY-PEXIDER functional equation H (x±y)=F(x) G(y) is generalized to the form H ((x^c±y^c)^1/c) = F(x) G(y), c≠0, assuming the function H(x) possesses a measurable majorant on a set of positive measure. The result is used to obtain a characterization of WEIBULL distribution. This functional equation is generalized to functions of vector variables.     

Causal relationships between heart period and systolic arterial pressure during graded head-up tilt

In physiological conditions, heart period (HP) affects systolic arterial pressure (SAP) through diastolic runoff and Starling's law, but, the reverse relation also holds as a result of the continuous action of baroreflex control. The prevailing mechanism sets the dominant temporal direction in the HP-SAP interactions (i.e., causality). We exploited cross-conditional entropy to assess HP-SAP causality. A traditional approach based on phases was applied for comparison. The ability of the approach to detect the lack of causal link from SAP to HP was assessed on 8 short-term (STHT) and 11 long-term heart transplant (LTHT) recipients (i.e., less than and more than 2 yr after transplantation, respectively). In addition, spontaneous HP and SAP variabilities were extracted from 17 healthy humans (ages 21-36 yr, median age 29 yr; 9 females) at rest and during graded head-up tilt. The tilt table inclinations ranged from 15 to 75° and were changed in steps of 15°. All subjects underwent recordings at every step in random order. The approach detected the lack of causal relation from SAP to HP in STHT recipients and the gradual restoration of the causal link from SAP to HP with time after transplantation in the LTHT recipients. The head-up tilt protocol induced the progressive shift from the prevalent causal direction from HP to SAP to the reverse causality (i.e., from SAP to HP) with tilt table inclination in healthy subjects. Transformation of phases into time shifts and comparison with baroreflex latency supported this conclusion. The proposed approach is highly efficient because it does not require the knowledge of baroreflex latency. The dependence of causality on tilt table inclination suggests that "spontaneous" baroreflex sensitivity estimated using noncausal methods (e.g., spectral and cross-spectral approaches) is more reliable at the highest tilt table inclinations.     

Coevolutionary dynamics of adaptive radiation for food-web development

To investigate how complex food-webs can develop through repeated evolutionary diversification, a predator–prey model was analyzed. In the model, each individual has two traits: trait x as a predator and trait y as a prey. These traits constitute a two-dimensional phenotype space, in which the whole group of individuals are represented as a phenotype distribution. Predator–prey interactions among the phenotypes are determined by their relative positions in the phenotype space. Each phenotypic cluster was treated as a species. Each species evolves in y to escape from predation, while it evolves in x to chase their prey. Analytical investigation provided two predictions. First, coupled evolutionary diversifications of y and x may occur when the x of predators have caught up with their prey’s y, which may be repeated. Second, complex food-webs may develop when species’ competitive strengths are kept similar within the communities. If the functional response is close to the ratio-dependent response, the competitive strengths of all species are similar when the relationship between predators and prey corresponds to the ideal free distribution (IFD). These predictions were confirmed by numerical simulations. Electronic supplementary material  The online version of this article doi:() contains supplementary material, which is available to authorized users.     

Empirical regression as a conditional expected value of a special distribution-mixture for a modelfree quantitative recording of stochastical relations

An “empirical” distribution function F?(x, y) is estimated 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). The density function F?(x, y) of F?(x, y) is a mixture of n two-dimensional normal densities. The first order moments of F?(x, y) are the sample means x and y, whilst the second order moments are only proportional to the sample variances and the sample covariance. This “empirical” distribution F?(x, y) is used for evaluation of an empirical regression curve where a free parameter has to be fixed by an optimality criterion. The procedure is demonstrated by an example from morphometrical research.     

Optimal Fixing of the Bandwidth-Parameter for the Empirical Regression1,2

The estimator ?₀(x) of the regression r(x) = E (Y | × = x) from measured points (x_i, y_i), 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).     

A methodological basis for description and analysis of systems with complex switch-like interactions

 A wide range of complex systems appear to have switch-like interactions, i.e. below (or above) a certain threshold x has no or little influence on y, while above (or below) this threshold the effect of x on y saturates rapidly to a constant level. Switching functions are frequently described by sigmoid functions or combinations of these. Within the context of ordinary differential equations we present a very general methodological basis for designing and analysing models involving complicated switching functions together with any other non-linearities. A procedure to determine position and stability properties of all stationary points lying close to a threshold for one or several variables, so-called singular stationary points, is developed. Such points may represent homeostatic states in models, and are therefore of considerable interest. The analysis provides a profound insight into the generic effects of steep sigmoid interactions on the dynamics around homeostatic points. It leads to qualitative as well as quantitative predictions without using advanced mathematical methods. Thus, it may have an important heuristic function in connection with numerical simulations aimed at unfolding the predictive potential of realistic models. Received 25 January 1996; received in revised form 29 June 1997     

Tunable white light emission from single‐phased Li2SrSiO4:Dy3+ phosphors by co‐doping with Eu3+

A series of single‐phase full‐color emitting Li₂Sr_1−x−ySiO₄:xDy³⁺,yEu³⁺ phosphors were synthesized by solid‐state reaction and characterized by X‐ray diffraction and photoluminescence analyses. The samples showed emission peaks at 488 nm (blue), 572 nm (yellow), 592 nm (orange) and 617 nm (red) under 393 nm excitation. The photoluminescence excitation spectra, comprising the Eu–O charge transfer band and 4f–4f transition bands of Dy³⁺ and Eu³⁺, range from 200 to 500 nm. The Commission Internationale de I'Eclairage chromaticity coordinates for Li₂Sr_0.98−xSiO₄:0.02Dy³⁺,xEu³⁺ phosphors were simulated. By manipulating Eu³⁺ and Dy³⁺ concentrations, the color points of Li₂Sr_1−x−ySiO₄:xDy³⁺,yEu³⁺ were tuned from the greenish‐white region to white light and eventually to reddish‐white region, demonstrating that a tunable white light can be obtained by Li₂Sr_1−x−ySiO₄:xDy³⁺,yEu³⁺ phosphors. Li₂Sr_0.98−xSiO₄:0.02Dy³⁺, xEu³⁺ can serve as a white‐light‐emitting phosphor for phosphor‐converted light‐emitting diode. Copyright © 2014 John Wiley & Sons, Ltd.     

Diminished Confidence Levels in the Interval Estimation of an Unknown Regressor in Model I of Linear Regression

For the model y=β₀ + β₁ x + e (model I of linear regression) in the literature confidence estimators of an unknown position x₀ are given at which either the expectation of y is given (see FIELLER, 1944; FINNEY, 1952), or realizations of y are given (see GRAYBILL, 1961). These confidence regions with level 1—α need not be intervals. The occurrence of interval shape is a random event. Its probability is equal to the power of the t test for the examination of the hypothesis H: β₁ = 0. The papers mentioned above claim to provide confidence intervals with level 1 ? α. But because of the restriction of (1 —α)—confidence regions to intervals the true confidence probability is the conditional probability W_c: W_c = P (the confidence region covers x₀| the region has interval shape). Here this conditional probability is shown to be less than 1 —α. Evidence on the possible deviations from 1 —α has been obtained by simulations.     

Use of Transformed Auxiliary Variable in Estimating the Finite Population Mean

For estimating the finite population mean Y- of the study character y, an estimator using a transformed auxiliary variable has been defined. The bias and mean-squared error (MSE) of the proposed estimator have been obtained. The regions of preference have been obtained under which it is better than usual unbiased estimator y-, the ratio estimator y-_R = y-X-/x-, Sisodia and Dwivedi (1981) estimator y-_s = y-(X- + C_x)/(x- + C_x) and Singh and Kakran (1993) estimator y-_k = y[X- + β₂(x)]/[x- + β₂(x)]. An empirical study has been carried out to demonstrate the superiority of the suggested estimator over the others.     

Exact Bayesian bin classification: a fast alternative to Bayesian classification and its application to neural response analysis

We investigate the general problem of signal classification and, in particular, that of assigning stimulus labels to neural spike trains recorded from single cortical neurons. Finding efficient ways of classifying neural responses is especially important in experiments involving rapid presentation of stimuli. We introduce a fast, exact alternative to Bayesian classification. Instead of estimating the class-conditional densities p(x|y) (where x is a scalar function of the feature[s], y the class label) and converting them to P(y|x) via Bayes’ theorem, this probability is evaluated directly and without the need for approximations. This is achieved by integrating over all possible binnings of x with an upper limit on the number of bins. Computational time is quadratic in both the number of observed data points and the number of bins. The algorithm also allows for the computation of feedback signals, which can be used as input to subsequent stages of inference, e.g. neural network training. Responses of single neurons from high-level visual cortex (area STSa) to rapid sequences of complex visual stimuli are analysed. Information latency and response duration increase nonlinearly with presentation duration, suggesting that neural processing speeds adapt to presentation speeds. Action Editor: Alexander Borst     

A neural network approach for the prediction of in vitro culture parameters for maximum biomass yields in hairy root cultures

The present study deals with ANN based prediction of culture parameters in terms of inoculum density, pH and volume of growth medium per culture vessel and sucrose content of the growth medium for Glycyrrhiza hairy root cultures. This kind of study could be a model system in exploitation of hairy root cultures for commercial production of pharmaceutical compounds using large bioreactors. The study is aimed to evaluate the efficiency of regression neural network and back propagation neural network for the prediction of optimal culture conditions for maximum hairy root biomass yield. The training data for regression and back propagation networks were primed on the basis of function approximation, where final biomass fresh weight (f_wt) was considered as a function of culture parameters. On this basis the variables in culture conditions were described in the form of equations which are for inoculum density: y=0.02x+0.04, for pH of growth medium: y=x+2.8, for sucrose content in medium: y=9.9464x+(−9.7143) and for culture medium per culture vessel: y=10x. The fresh weight values obtained from training data were considered as target values and further compared with predicted fresh weight values. The empirical data were used as testing data and further compared with values predicted from trained networks. Standard MATLAB inbuilt generalized regression network with radial basis function radbas as transfer function in layer one and purelin in layer two and back propagation having purelin as transfer function in output layer and logsig in hidden layer were used. Although in comparative assessment both the networks were found efficient for prediction of optimal culture conditions for high biomass production, more accuracy in results was seen with regression network.     

Properties of the nonlethal recombinational repair deficient mutants of bacteriophage T4

Summary The rate at which ³H thymidine is incorporated into DNA is increased in T4w-infected cells compared to wild-type when measured late in infection under conditions of low thymidine concentration. This increased DNA synthesis is sensitive to hydroxyurea but not to mitomycin C, and can be prevented by the addition of chloramphenicol early in infection. Also, DNA replicative intermediates isolated from T4w-infected cells late in infection sediment significantly faster than those isolated from wild-type-infected cells. In contrast, DNA replicative intermediates isolated from T4x-or T4y-infected cells sediment more slowly than those produced by wild-type T4. Cells coinfected with wild-type T4⁺ and T4x, y or w; or T4w and T4x or y, produce wild-type DNA replicative intermediates. Cells coinfected with T4x and T4y produce more slowly sedimenting DNA replicative intermediates. Cells coinfected with T4w and wild-type T4 show wild-type rates of DNA synthesis while cells coinfected with T4w and T4x or T4y show increased rates of DNA synthesis over that observed with wild-type alone.     

Assessing baroreflex gain from spontaneous variability in conscious dogs: role of causality and respiration

A double exogenous autoregressive (XXAR) causal parametric model was used to estimate the baroreflex gain (alpha(XXAR)) from spontaneous R-R interval and systolic arterial pressure (SAP) variabilities in conscious dogs. This model takes into account 1) effects of current and past SAP variations on the R-R interval (i.e., baroreflex-mediated influences), 2) specific perturbations affecting R-R interval independently of baroreflex circuit (e.g., rhythmic neural inputs modulating R-R interval independently of SAP at frequencies slower than respiration), and 3) influences of respiration-related sources acting independently of baroreflex pathway (e.g., rhythmic neural inputs modulating R-R interval independently of SAP at respiratory rate, including the effect of stimulation of low-pressure receptors). Under control conditions, alpha(XXAR) = 14.7 +/- 7.2 ms/mmHg. It decreases after nitroglycerine infusion and coronary artery occlusion, even though the decrease is significant only after nitroglycerine, and it is completely abolished by total arterial baroreceptor denervation. Moreover, alpha(XXAR) is comparable to or significantly smaller than (depending on the experimental condition) the baroreflex gains derived from sequence, power spectrum [at low frequency (LF) and high frequency (HF)], and cross-spectrum (at LF and HF) analyses and from less complex causal parametric models, thus demonstrating that simpler estimates may be biased by the contemporaneous presence of regulatory mechanisms other than baroreflex mechanisms.