Comment on "correlated noise in a logistic growth model"

We argue the results published by Bao-Quan Ai et al [Phys. Rev E 67, 022903 (2003)] on "correlated noise in a logistic growth model " are not correct. Their conclusion that for larger values of the correlation parameter, lambda, the cell population is peaked at x=0, which denotes the high extinction rate is also incorrect. We find the reverse behaviour corresponding to their results, that increasing lambda, promotes the stable growth of tumour cells. In particular, their results for steady-state probability, as a function of cell number, at different correlation strengths, presented in figures 1 and 2 show different behaviour than one would expect from the simple mathematical expression for the steady-state probability. Additionally, their interpretation at small values of cell number that the steady state probability increases as they increase the correlation parameter is also questionable. Another striking feature in their figures (1 and 3) is that for the same values of the parameter lambda and alpha, their simulation produces two different curves both qualitatively and quantitatively.

The Y-procedure: How to extract the chemical transformation rate from reaction-diffusion data with no assumption on the kinetic model

The paper presents a new method to extract the chemical transformation rate from reaction–diffusion data with no assumption on the kinetic model (“kinetic model-free procedure”). It is a new non-steady-state kinetic characterization procedure for heterogeneous catalysts. The mathematical foundation of the Y-procedure is a Laplace-domain analysis of the two inert zones in a TZTR followed by transposition to the Fourier domain. When combined with time discretization and filtering the Y-procedure leads to an efficient practical method for reconstructing the concentration and reaction rate in the active zone. Using the Y-procedure the concentration and reaction rate of a non-steady state catalytic process can be determined without any pre-assumption regarding the type of kinetic dependence. The Y-procedure is the basis for advanced software for non-steady state kinetic data interpretation. The Y-procedure can be used to relate changes in the catalytic reaction rate and kinetic parameters to changes in the surface composition (storage) of a catalyst.

Contribution of 30 Biomarkers to 10-year cardiovascular risk estimation in 2 population cohorts: The MONICA, risk, genetics, archiving and monograph (MORGAM) biomarker project

Background— Cardiovascular risk estimation by novel biomarkers needs assessment in disease-free population cohorts, followed up for incident cardiovascular events, assaying the serum and plasma archived at baseline. We report results from 2 cohorts in such a continuing study.
Methods and Results— Thirty novel biomarkers from different pathophysiological pathways were evaluated in 7915 men and women of the FINRISK97 population cohort with 538 incident cardiovascular events at 10 years (fatal or nonfatal coronary or stroke events), from which a biomarker score was developed and then validated in the 2551 men of the Belfast Prospective Epidemiological Study of Myocardial Infarction (PRIME) cohort (260 events). No single biomarker consistently improved risk estimation in FINRISK97 men and FINRISK97 women and the Belfast PRIME Men cohort after allowing for confounding factors; however, the strongest associations (with hazard ratio per SD in FINRISK97 men) were found for N-terminal pro-brain natriuretic peptide (1.23), C-reactive protein (1.23), B-type natriuretic peptide (1.19), and sensitive troponin I (1.18). A biomarker score was developed from the FINRISK97 cohort with the use of regression coefficients and lasso methods, with selection of troponin I, C-reactive protein, and N-terminal pro-brain natriuretic peptide. Adding this score to a conventional risk factor model in the Belfast PRIME Men cohort validated it by improved c-statistics (P=0.004) and integrated discrimination (P<0.0001) and led to significant reclassification of individuals into risk categories (P=0.0008).
Conclusions— The addition of a biomarker score including N-terminal pro-brain natriuretic peptide, C-reactive protein, and sensitive troponin I to a conventional risk model improved 10-year risk estimation for cardiovascular events in 2 middle-aged European populations. Further validation is needed in other populations and age groups.

An improved elastic-viscoplastic soil model

This paper develops an improved and accessible framework for modelling time-dependent behaviour of soils using the concepts of elasticity and viscoplasticity. The mathematical description of viscoplastic straining is formulated based on a purely viscoplastic and measurable phenomenon, namely creep. The resulting expression for the viscoplastic strain rates includes a measure of both effective stress and the corresponding volumetric packing of the soil particles. In this way, the model differs from some earlier viscoplastic models and arguably provides a better conceptual description of time-dependent behaviour. Analytical solutions are developed for the simulation of drained and undrained strain-controlled triaxial compression tests. The model is then used to back-analyze the measured response of normally consolidated to moderately overconsolidated specimens of a soft estuarine soil in undrained triaxial compression. The model captures aspects of soil behaviour that cannot be simulated using time-independent elastic–plastic models. Specifically, it can capture the dependence of stress–strain relationships and undrained shear strength on strain rate, the development of irrecoverable plastic strains at constant stress (creep), and the relaxation of stresses at constant strain

Analysis of Degradation Data of Poly(L-lactide-co-L,D-lactic actide) and Poly(L-lactide) Obtained at Elevated and Physiological Temperatures Using Mathematical Models

The degradation of resorbable polymeric devices often takes months to years. Accelerated testing at elevated temperatures is an attractive but controversial technique. The purposes of this paper include: (a) to provide a summary of the mathematical models required to analyse accelerated degradation data and to indicate the pitfalls of using these models; (b) to improve the model previously developed by Han and Pan; (c) to provide a simple version of the model of Han and Pan with an analytical solution that is convenient to use; (d) to demonstrate the application of the improved model in two different poly(lactic acid) systems. It is shown that the simple analytical relations between molecular weight and degradation time widely used in the literature can lead to inadequate conclusions. In more general situations the rate equations are only part of a complete degradation model. Together with previous works in the literature, our study calls for care in using the accelerated testing technique.

Mathematical modeling of colony formation in algal blooms: phenotypic plasticity in cyanobacteria

In this paper, we analyzed a mathematical model of algal-grazer dynamics, including the effect of colony formation, which is an example of phenotypic plasticity. The model consists of three variables, which correspond to the biomasses of unicellular algae, colonial algae, and herbivorous zooplankton. Among these organisms, colonial algae are the main components of algal blooms. This aquatic system has two stable attractors, which can be identified as a zooplankton-dominated (ZD) state and an algal-dominated (AD) state, respectively. Assuming that the handling time of zooplankton on colonial algae increases with the colonial algae biomass, we discovered that bistability can occur within the model system. The applicability of alternative stable states in algae-grazer dynamics as a framework for explaining the algal blooms in real lake ecosystems, thus, seems to depend on whether the assumption mentioned above is met in natural circumstances.

Some properties of the speciation model for food-web structure - Mechanisms for degree distributions and intervality

We present a mathematical analysis of the speciation model for food-web structure, which had in previous work been shown to yield a good description of empirical data of food-web topology. The degree distributions of the network are derived. Properties of the speciation model are compared to those of other models that successfully describe empirical data. It is argued that the speciation model unities the underlying ideas of previous theories. In particular, it offers a mechanistic explanation for the success of the niche model of Williams and Martinez and the frequent observation of intervality in empirical food webs. (c) 2005 Elsevier Ltd. All rights reserved.

Myocardial infarction in the C57BL/6J mouse - A quantifiable and highly reproducible experimental model

Introduction: The laboratory mouse is a powerful tool in cardiovascular research. In this report, we describe a method for a reproducible mouse myocardial infarction model that would allow subsequent comparative and quantitative studies on molecular and pathophysiological variables. Methods: (A) The distribution of the major coronary arteries including the septal artery in the left ventricle of the C57BL/6J mice (n=20) was mapped by perfusion of latex dye or fluorescent beads through the aorta. (B) The territory of myocardial infarction after the ligation of the most proximal aspect of the left anterior descending (LAD) coronary artery was quantified. (C) The consistency in the histological changes parallel to the infarction at different time points was analyzed. Results: (A) The coronary artery tree of the mouse is different from human and, particularly, in regard to the blood supply of the septum. (B) Contrary to previous belief, the septal coronary artery in the mouse is variable in origin. (C) A constant ligation of the LAD immediately below the left auricular level ensures a statistically significant reproducible infarct size. (D) The ischemic changes can be monitored at a histological level in a way similar to what is described in the human. Conclusion: We illustrate a method for maximal reproducibility of experimental acute myocardial infarction in the mouse model, due to a consistent loss of perfusion in the lower half of the left ventricle. This will allow the study of molecular and physiological variables in a controlled and quantifiable experimental model environment. (C) 2004 Elsevier Inc. All rights reserved.

Nonlinear time series prediction based on a power-law noise model

In this paper we investigate the influence of a power-law noise model, also called noise, on the performance of a feed-forward neural network used to predict time series. We introduce an optimization procedure that optimizes the parameters the neural networks by maximizing the likelihood function based on the power-law model. We show that our optimization procedure minimizes the mean squared leading to an optimal prediction. Further, we present numerical results applying method to time series from the logistic map and the annual number of sunspots demonstrate that a power-law noise model gives better results than a Gaussian model.