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The classic Luria–Delbrück model can be interpreted as a Poisson compound (number of mutations) of exponential mixtures (developing time of mutant clones) of geometric distributions (size of a clone in a given time). This “three-ingredients” approach is generalized in this paper to the case where the split instant distributions of cells are not i.i.d. : the lifetime of each cell is assumed to depend on its birth date. This model takes also into account cell deaths and non-exponentially distributed lifetimes. Previous results on the convergence of the distribution of mutant counts are recovered. The particular case where the instantaneous division rates of normal and mutant cells are proportional is studied. The classic Luria–Delbrück and Haldane models are recovered. Probability computations and simulation algorithms are provided. Robust estimation methods developed for the classic mutation models are adapted to the new model: their properties of consistency and asymptotic normality remain true; their asymptotic variances are computed. Finally, the estimation biases induced by considering classic mutation models instead of an inhomogeneous model are studied with simulation experiments. [ABSTRACT FROM AUTHOR]

This paper introduces a general concept of Eulerian reformulation of Langrangian particle tracking methods in evaluation of platelet damage and activation. It is applied to formulation of a new multistage algorithm describing the delayed activation of platelets due to excessive exposure to supra-critical stress. This new class of multistage Eulerian activation models allows for numerous extensions and generalizations, while preserving its simplicity and flexibility. [ABSTRACT FROM AUTHOR]

Abstract: Network theory has been applied to many aspects of biosciences, including epidemiology. Most epidemiological models in networks, however, have used the standard assumption of either susceptible or infected individuals. In some cases (e.g. the spread of Phytophthora ramorum in plant trade networks), a continuum in the infection status of nodes can better capture the reality of epidemics in networks. In this paper, a Susceptible-Infected-Susceptible model along a continuum in the infection status (SISc) is presented, using as a case study directed networks and two parameters governing the epidemic process (probability of infection persistence (pp ) and of infection transmission (pt )). The previously empirically reported linear epidemic threshold in a plot of pp as a function of pt (Pautasso and Jeger, 2008) is derived analytically. Also the previously observed negative correlation between the epidemic threshold and the correlation between links in and out of nodes (Moslonka-Lefebvre et al., 2009) is justified analytically. A simple algorithm to calculate the threshold conditions is introduced. Additionally, a control strategy based on targeting market hierarchical categories such as producers, wholesalers and retailers is presented and applied to a realistic reconstruction of the UK horticultural trade network. Finally, various applications (e.g., seed exchange networks, food trade, spread of ideas) and potential refinements of the SISc model are discussed. [Copyright &y& Elsevier]

Abstract: This paper deals with the problem of stabilization design and control for a class of genetic regulatory networks (GRNs) with both intrinsic perturbation and extrinsic perturbation. Some delay-dependent mean-square stabilization criteria are put forward for nominal systems and uncertain systems by using an improved free-weighting matrix approach. As a result, the corresponding stabilization controllers and controllers of GRNs are constructed with time delays compensated and suboptimal solutions are obtained via exploiting an iterative procedure together with the linear matrix inequality (LMI) method and the cone complementarity liberalization (CCL) algorithm. Finally, three numerical examples are presented to illustrate the effectiveness of the proposed theoretical results. [Copyright &y& Elsevier]

Abstract: Computational simulation models can provide a way of understanding and predicting insect population dynamics and evolution of resistance, but the usefulness of such models depends on generating or estimating the values of key parameters. In this paper, we describe four numerical algorithms generating or estimating key parameters for simulating four different processes within such models. First, we describe a novel method to generate an offspring genotype table for one- or two-locus genetic models for simulating evolution of resistance, and how this method can be extended to create offspring genotype tables for models with more than two loci. Second, we describe how we use a generalized inverse matrix to find a least-squares solution to an over-determined linear system for estimation of parameters in probit models of kill rates. This algorithm can also be used for the estimation of parameters of Freundlich adsorption isotherms. Third, we describe a simple algorithm to randomly select initial frequencies of genotypes either without any special constraints or with some pre-selected frequencies. Also we give a simple method to calculate the “stable” Hardy–Weinberg equilibrium proportions that would result from these initial frequencies. Fourth we describe how the problem of estimating the intrinsic rate of natural increase of a population can be converted to a root-finding problem and how the bisection algorithm can then be used to find the rate. We implemented all these algorithms using MATLAB and Python code; the key statements in both codes consist of only a few commands and are given in the appendices. The results of numerical experiments are also provided to demonstrate that our algorithms are valid and efficient. [Copyright &y& Elsevier]

Abstract: When examining the structural identifiability properties of dynamic system models, some parameters can take on an infinite number of values and yet yield identical input–output data. These parameters and the model are then said to be unidentifiable. Finding identifiable combinations of parameters with which to reparameterize the model provides a means for quantitatively analyzing the model and computing solutions in terms of the combinations. In this paper, we revisit and explore the properties of an algorithm for finding identifiable parameter combinations using Gröbner Bases and prove useful theoretical properties of these parameter combinations. We prove a set of M algebraically independent identifiable parameter combinations can be found using this algorithm and that there exists a unique rational reparameterization of the input–output equations over these parameter combinations. We also demonstrate application of the procedure to a nonlinear biomodel. [Copyright &y& Elsevier]