A diffusion approach to approximating preservation probabilities for gene duplicates

Consider a haploid population and, within its genome, a gene whose presence is vital for the survival of any individual. Each copy of this gene is subject to mutations which destroy its function. Suppose one member of the population somehow acquires a duplicate copy of the gene, where the duplicate is fully linked to the original gene's locus. Preservation is said to occur if eventually the entire population consists of individuals descended from this one which initially carried the duplicate. The system is modelled by a finite state-space Markov process which in turn is approximated by a diffusion process, whence an explicit expression for the probability of preservation is derived. The event of preservation can be compared to the fixation of a selectively neutral gene variant initially present in a single individual, the probability of which is the reciprocal of the population size. For very weak mutation, this and the probability of preservation are equal, while as mutation becomes stronger, the preservation probability tends to double this reciprocal. This is in excellent agreement with simulation studies.

Supermodularity and risk aversion

In this paper, we consider the relationship between supermodularity and risk aversion. We show that supermodularity of the certainty equivalent implies that the certainty equivalent of any random variable is less than its mean. We also derive conditions under which supermodularity of the certainty equivalent is equivalent to aversion to mean-preserving spreads in the sense of Rothschild and Stiglitz. (c) 2006 Elsevier B.V. All rights reserved.

Implicit vector equilibrium problems with applications

Let X and Y be Hausdorff topological vector spaces, K a nonempty, closed, and convex subset of X, C: K--> 2(Y) a point-to-set mapping such that for any x is an element of K, C(x) is a pointed, closed, and convex cone in Y and int C(x) not equal 0. Given a mapping g : K --> K and a vector valued bifunction f : K x K - Y, we consider the implicit vector equilibrium problem (IVEP) of finding x* is an element of K such that f (g(x*), y) is not an element of - int C(x) for all y is an element of K. This problem generalizes the (scalar) implicit equilibrium problem and implicit variational inequality problem. We propose the dual of the implicit vector equilibrium problem (DIVEP) and establish the equivalence between (IVEP) and (DIVEP) under certain assumptions. Also, we give characterizations of the set of solutions for (IVP) in case of nonmonotonicity, weak C-pseudomonotonicity, C-pseudomonotonicity, and strict C-pseudomonotonicity, respectively. Under these assumptions, we conclude that the sets of solutions are nonempty, closed, and convex. Finally, we give some applications of (IVEP) to vector variational inequality problems and vector optimization problems. (C) 2003 Elsevier Science Ltd. All rights reserved.

A numerical study of large sparse matrix exponentials arising in Markov chains

Krylov subspace techniques have been shown to yield robust methods for the numerical computation of large sparse matrix exponentials and especially the transient solutions of Markov Chains. The attractiveness of these methods results from the fact that they allow us to compute the action of a matrix exponential operator on an operand vector without having to compute, explicitly, the matrix exponential in isolation. In this paper we compare a Krylov-based method with some of the current approaches used for computing transient solutions of Markov chains. After a brief synthesis of the features of the methods used, wide-ranging numerical comparisons are performed on a power challenge array supercomputer on three different models. (C) 1999 Elsevier Science B.V. All rights reserved.AMS Classification: 65F99; 65L05; 65U05.

Further results on the relationship between mu-invariant measures and quasi-stationary distributions for absorbing continuous-time Markov chains

This note considers continuous-time Markov chains whose state space consists of an irreducible class, C, and an absorbing state which is accessible from C. The purpose is to provide results on mu-invariant and mu-subinvariant measures where absorption occurs with probability less than one. In particular, the well-known premise that the mu-invariant measure, m, for the transition rates be finite is replaced by the more natural premise that m be finite with respect to the absorption probabilities. The relationship between mu-invariant measures and quasi-stationary distributions is discussed. (C) 2000 Elsevier Science Ltd. All rights reserved.

New methods for determining quasi-stationary distributions for Markov chains

We shall be concerned with the problem of determining quasi-stationary distributions for Markovian models directly from their transition rates Q. We shall present simple conditions for a mu-invariant measure m for Q to be mu-invariant for the transition function, so that if m is finite, it can be normalized to produce a quasi-stationary distribution. (C) 2000 Elsevier Science Ltd. All rights reserved.

Modelling solute transport in structured soils: Performance evaluation of the ADR and TRM models

The movement of chemicals through the soil to the groundwater or discharged to surface waters represents a degradation of these resources. In many cases, serious human and stock health implications are associated with this form of pollution. The chemicals of interest include nutrients, pesticides, salts, and industrial wastes. Recent studies have shown that current models and methods do not adequately describe the leaching of nutrients through soil, often underestimating the risk of groundwater contamination by surface-applied chemicals, and overestimating the concentration of resident solutes. This inaccuracy results primarily from ignoring soil structure and nonequilibrium between soil constituents, water, and solutes. A multiple sample percolation system (MSPS), consisting of 25 individual collection wells, was constructed to study the effects of localized soil heterogeneities on the transport of nutrients (NO3-, Cl-, PO43-) in the vadose zone of an agricultural soil predominantly dominated by clay. Very significant variations in drainage patterns across a small spatial scale were observed tone-way ANOVA, p < 0.001) indicating considerable heterogeneity in water flow patterns and nutrient leaching. Using data collected from the multiple sample percolation experiments, this paper compares the performance of two mathematical models for predicting solute transport, the advective-dispersion model with a reaction term (ADR), and a two-region preferential flow model (TRM) suitable for modelling nonequilibrium transport. These results have implications for modelling solute transport and predicting nutrient loading on a larger scale. (C) 2001 Elsevier Science Ltd. All rights reserved.

Existence results for a damped second order abstract functional differential equation with impulses

In this work we study the existence and regularity of mild solutions for a damped second order abstract functional differential equation with impulses. The results are obtained using the cosine function theory and fixed point criterions. (C) 2009 Elsevier Ltd. All rights reserved.

The existence of solutions for impulsive neutral functional differential equations

This work deals with the existence of mild solutions for a class of impulsive functional differential equations of the neutral type associated with the family of linear closed (not necessarily bounded) operators {A(t) : t is an element of 1}. (C) 2009 Elsevier Ltd. All rights reserved.

Existence results for partial neutral functional differential equations with state-dependent delay

In this paper we study the existence of mild solutions for a class of first order abstract partial neutral differential equations with state-dependent delay. (C) 2008 Elsevier Ltd. All rights reserved.

Global solutions for abstract impulsive neutral differential equations

We study the existence of mild solutions for a class of impulsive neutral functional differential equation defined on the whole real axis. Some concrete applications to ordinary and partial neutral differential equations with impulses are considered. (C) 2010 Elsevier Ltd. All rights reserved.

A Bayesian approach to fuzzy hypotheses testing for the estimation of optimal age for vaccination against measles

Fuzzy Bayesian tests were performed to evaluate whether the mother`s seroprevalence and children`s seroconversion to measles vaccine could be considered as ""high"" or ""low"". The results of the tests were aggregated into a fuzzy rule-based model structure, which would allow an expert to influence the model results. The linguistic model was developed considering four input variables. As the model output, we obtain the recommended age-specific vaccine coverage. The inputs of the fuzzy rules are fuzzy sets and the outputs are constant functions, performing the simplest Takagi-Sugeno-Kang model. This fuzzy approach is compared to a classical one, where the classical Bayes test was performed. Although the fuzzy and classical performances were similar, the fuzzy approach was more detailed and revealed important differences. In addition to taking into account subjective information in the form of fuzzy hypotheses it can be intuitively grasped by the decision maker. Finally, we show that the Bayesian test of fuzzy hypotheses is an interesting approach from the theoretical point of view, in the sense that it combines two complementary areas of investigation, normally seen as competitive. (C) 2007 IMACS. Published by Elsevier B.V. All rights reserved.

Three-point boundary value problems for second-order, ordinary, differential equations

We establish existence results for solutions to three-point boundary value problems for nonlinear, second-order, ordinary differential equations with nonlinear boundary conditions. (C) 2001 Elsevier Science Ltd. All rights reserved.

Topological methods for some boundary value problems

We establish existence of solutions for a finite difference approximation to y = f(x, y, y ') on [0, 1], subject to nonlinear two-point Sturm-Liouville boundary conditions of the form g(i)(y(i),y ' (i)) = 0, i = 0, 1, assuming S satisfies one-sided growth bounds with respect to y '. (C) 2001 Elsevier Science Ltd. All rights reserved.