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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]

Abstract: It has long been established that when a small-displacement problem involving contact between two or more bodies is solved, conforming algorithm approaches based on BEM are reliable and robust. Nevertheless, the authors have shown in a previous paper that a relative sliding between the bodies in contact, even if small, can originate a fictitious corner in the numerical model, which may alter the stress and the displacement predictions. This problem disappears if a non-conforming algorithm is employed. In this paper a new problem with different features but also presenting artificial alteration of the results is addressed. The compression of a rounded punch on a foundation is analysed for many fillet radii. Conforming and non-conforming algorithms are used. Comparison of results shows that effects of an artificial ‘numerical corner’ may alter even the traction distribution relatively far from it. Consequently, the assumed connection between small displacements and initially conforming discretizations with the use of a conforming approach disappears. An adequate knowledge of the contact problem under consideration is then essential to determine whether the singularity is inherent to the problem or is artificial, a non-conforming algorithm then being recommended in this second case. [Copyright &y& Elsevier]

We consider the problem of choosing the gate sizes or scale factors in a combinational logic circuit in order to minimize the total area, subject to simple RC timing constraints, and a minimum-allowed gate size. This problem is well known to be a geometric program (GP), and can be solved by using standard interior-point methods for small- and medium-size problems with up to several thousand gates. In this paper, we describe a new method for solving this problem that handles far larger circuits, up to a million gates, and is far faster. Numerical experiments show that our method can compute an adequately accurate solution within around 200 iterations; each iteration, in turn, consists of a few passes over the circuit. In particular, the complexity of our method, with a fixed number of iterations, is linear in the number of gates. A simple implementation of our algorithm can size a 10000 gate circuit in 25 s, a 100 000 gate circuit in 4 mm, and a million gate circuit in 40 mm, approximately. For the million gate circuit, the associated GP has three million variables and more than six million monomial terms in its constraints; as far as we know, these are the largest GPs ever solved. [ABSTRACT FROM AUTHOR]

In this paper, generalized versions of two ensemble methods for regression based on variants of the original AdaBoost algorithm are proposed. The generalization of these regression methods consists in restricting the unit simplex for the weights of the instances to a smaller set of weighting probabilities. Various imprecise statistical models can be used to obtain a restricted set of weighting probabilities, whose sizes each depend on a single parameter. For particular choices of this parameter, the proposed algorithms reduce to standard AdaBoost-based regression algorithms or to standard regression. The main advantage of the proposed algorithms compared to the basic AdaBoost-based regression methods is that they have less tendency to over-fitting, because the weights of the hard instances are restricted. Several simulations and applications furthermore indicate a better performance of the proposed regression methods in comparison with the corresponding standard regression methods. [ABSTRACT FROM AUTHOR]

In this paper, the main features and performances of a new numerical scheme, ILILPM (Improved Locally and Instantaneously Linearized Parabolic Model) are described. ILILPM is an improved version of the Parabolic and Backwater (PAB) and Linearized Parabolic Model (LPM) schemes, proposed in literature for the approximate solution of the Parabolic Wave model. The algorithm presented is able to take into account transcritical flow regime and transitions from free-surface to pressurized flow in tree-like channel networks. Due to its unconditional stability, the model allows large computational time steps, leading to very fast simulations during transients for a class of flow conditions larger than those solved by the parent schemes. The model is demonstrated by comparing its results with experimental observations and with the results provided by the numerical solution of the full De Saint-Venant equations. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we propose a multiobjective credibilistic model with fuzzy chance constraints of the portfolio selection problem. The key financial criteria used are short-term return, long-term return, risk and liquidity. The model generates portfolios which are optimal to the extent of achieving the highest credibility values for the objective functions. The problem is solved using a hybrid intelligent algorithm that integrates fuzzy simulation with a real-coded genetic algorithm. The approach adopted here has advantage of handling the multiobjective portfolio selection problem where fuzzy parameters are characterized by general functional forms. Numerical examples are provided to demonstrate effectiveness of the solution approach and efficiency of the model. [Copyright &y& Elsevier]

Abstract: The occurrence of imprecision in the real world is inevitable due to some unexpected situations. The imprecision is often involved in any engineering design process. The imprecision and uncertainty are often interpreted as fuzziness. Fuzzy systems have an essential role in the uncertainty modelling, which can formulate the uncertainty in the actual environment. In this paper, a new approach is proposed to solve a system of fuzzy polynomial equations based on the Gröbner basis. In this approach, first, the h-cut of a system of fuzzy polynomial equations is computed, and a parametric form for the fuzzy system with respect to the parameter of h is obtained. Then, a Gröbner basis is computed for the ideal generated by the h-cuts of the system with respect to the lexicographical order using Faugère’s algorithm, i.e., F 4 algorithm. The Gröbner basis of the system has an upper triangular structure. Therefore, the system can be solved using the forward substitution. Hence, all the solutions of the system of fuzzy polynomial equations can easily be obtained. Finally, the proposed approach is compared with the current numerical methods. Some theorems together with some numerical examples and applications are presented to show the efficiency of our method with respect to the other methods. [Copyright &y& Elsevier]

Abstract: The flow sharing problem is a class of techniques that can be used to find the optimal flow in a capacitated network, which realizes an equitable distribution of flows. This paper extends the integer flow sharing problem by considering fuzzy capacities and fuzzy weights such that the flux received at each sink node and the flow value through each arc are restricted to be multiples of some block unit. Fuzzy capacity describes the flexibility of the upper limit of flow value through each arc. Fuzzy weight represents the degree of satisfaction of the flux to a sink node. Our model has the two following criteria: to maximize the minimal degree of satisfaction among all of the fuzzy capacity constraints and to maximize the minimal degree of satisfaction among the fluxes to all of the sink nodes. Because an optimal flow pattern that simultaneously maximizes the two objectives is usually not feasible, we define non-domination in this setting and propose a pseudo-polynomial algorithm that finds some non-dominated flow patterns. Finally, a numerical example is presented to demonstrate how our algorithm works. [Copyright &y& Elsevier]

Abstract: Fuzzy clustering is an effective clustering approach which associates a data point with multiple clusters. Standard fuzzy clustering models like fuzzy c-means are based on minimizing the total cluster variation, which is defined as the sum of the distances between the data points and their corresponding cluster centers weighted by the membership degrees. In this paper, we propose a fuzzy minimax clustering model by minimizing the maximum value of the set of weighted cluster variations in such a way that they satisfy a prior distribution. We derive a necessary condition for the extremum point of the fuzzy minimax clustering model, and then design an iterative algorithm for solving the extremum point. Several numerical examples on comparing fuzzy c-means and fuzzy minimax clustering models are given, which demonstrate that the prior distribution improves the quality of the clustering results significantly. [Copyright &y& Elsevier]

Abstract: A method of analysis for a class of Petri nets (PNs) called parallel process net with resources (PPNRs) is presented in this paper. The proposed analysis method is based on reduced reachability graph (RRG) of PPNRs to verify the correspondence between required specification of manufacturing system and its PN representation. In order to reduce the reachability graph (RG), a new technique is proposed which incorporates the transition vectors (TVs) to determine all the enabled transitions at a given state of system and to recognize them as dependent or independent. An algorithm, based on the idea of simultaneous execution of concurrently enabled independent transitions, is developed to reduce the RG and its analysis is also performed. Moreover, relationship between the reduction of RG and parallel structure in the PN model is discovered. The proposed technique replaces the RG by a structure which directly depicts concurrent execution and does not show the irrelevant states by presenting the concurrent behavior of system in the reduced state space. The analysis of PPNRs based on RRG generated by proposed method is also presented and demonstrated by a practical example. [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: This paper discusses the Bayesian inference of accelerated life tests (ALT) in the presence of competing failure causes. The time to failure due to a specific cause is described by a Weibull distribution. A two-stage approach is utilized to obtain the estimates of parameters in the model. We use the Bayesian method to estimate the parameters of the distribution of component lifetimes in the first stage, in which two noninformative priors (Jeffreys prior and reference prior) are derived in the case of ALT, and based on these two priors we present the Gibbs sampling procedures to obtain the posterior estimates of the parameters. Besides, to overcome the problem of improper posterior densities under some conditions, we modify the likelihood function to make the posterior densities proper. In the second stage, parameters in the accelerating function are obtained by least squares approach. A numerical example is given to show the effectiveness of the method and a real data from  is analyzed. [Copyright &y& Elsevier]

Abstract: In this paper we show some applications of Advanced and Parallel Computing to the study of mathematical models in Systems Biology and in particular of the network of biochemical reactions occurring inside a cell. Due to their high complexity, the numerical study of these systems must be approached by means of sophisticated Advanced Computing tools. In a deterministic framework, we show two examples of application of Optimal Control techniques to the study of the effects of a drug on enzyme reactions occurring inside a cell, where “ad-hoc” algorithms for the numerical solution of the Hamilton–Jacobi–Bellman equation are used in a parallel environment. [ABSTRACT FROM AUTHOR]

Abstract: The convergence of Chauvin’s PCA learning algorithm with a constant learning rate is studied in this paper by using a DDT method (deterministic discrete-time system method). Different from the DCT method (deterministic continuous-time system method), the DDT method does not require that the learning rate converges to zero. An invariant set of Chauvin’s algorithm with a constant learning rate is obtained so that the non-divergence of this algorithm can be guaranteed. Rigorous mathematic proofs are provided to prove the local convergence of this algorithm. [Copyright &y& Elsevier]

Abstract: This paper presents a novel differential evolution (DE) algorithm to solve the identification problem for Chen and Lü systems. A collection of unknown system parameters of Chen and Lü systems is taken as a manipulated parameter vector, and will be optimally evolved to approximate the actual parameters by using the proposed DE algorithm. Basically, the DE algorithm comprises three main operators of mutation, crossover, and selection to achieve the evolution. In the meanwhile, a cost function defined for solving the identification problem of chaotic systems is also minimized. Two illustrative examples are given to show the validity of the proposed method. [Copyright &y& Elsevier]

Abstract: In this paper, the generalized F-expansion method [Chen J, He HS, Yang KQ. Commun Theor Phys (Beijing, China) 2005;44:307] is improved and a further improved F-expansion method is proposed to seek more types of exact solutions of non-linear evolution equations. With the aid of symbolic computation, we choose the (3+1)-dimensional Kadomstev–Petviashvili equation to illustrate the validity and advantages of the proposed method. As a result, many new and more general solutions are obtained including single and combined non-degenerate Jacobi elliptic function solutions, soliton-like solutions, trigonometric function solutions. This method can also be applied to other non-linear evolution equations in mathematical physics. [Copyright &y& Elsevier]

In this paper, a moving algorithm for on-line identification of continuous-time systems is developed. With the proposed algorithm, the observed input–output data can be directly used to estimate the system parameters without any numerical pre-processing, and by means of a recursive formula the estimates can be updated step by step without repeatedly computing the matrix inversion. In this way, the use of both computer memory and computing time can be reduced. Besides, the computations are simple and straightforward. From the moving identification algorithm, a linear moving model can be obtained to represent the control systems. The on-line optimal control algorithm is also developed via the linear moving model. A slider-crank motion control system is used to illustrate that the proposed on-line identification and optimal control algorithms can give satisfactory results. [Copyright &y& Elsevier]