Analytical study of the effect of recombination on evolution via DNA shuffling

We investigate a multi-locus evolutionary model which is based on the DNA shuffling protocol widely applied in \textit{in vitro} directed evolution. This model incorporates selection, recombination and point mutations. The simplicity of the model allows us to obtain a full analytical treatment of both its dynamical and equilibrium properties, for the case of an infinite population. We also briefly discuss finite population size corrections

Logarithmic perturbation theory for quasinormal modes

Logarithmic perturbation theory (LPT) is developed and applied to quasinormal modes (QNMs) in open systems. QNMs often do not form a complete set, so LPT is especially convenient because summation over a complete set of unperturbed states is not required. Attention is paid to potentials with exponential tails, and the example of a Poschl-Teller potential is briefly discussed. A numerical method is developed that handles the exponentially large wavefunctions which appear in dealing with QNMs.Comment: 24 pages, 4 Postscript figures, uses ioplppt.sty and epsfig.st

On Propagation of Excitation Waves in Moving Media: The FitzHugh-Nagumo Model

BACKGROUND: Existence of flows and convection is an essential and integral feature of many excitable media with wave propagation modes, such as blood coagulation or bioreactors. METHODS/RESULTS: Here, propagation of two-dimensional waves is studied in parabolic channel flow of excitable medium of the FitzHugh-Nagumo type. Even if the stream velocity is hundreds of times higher that the wave velocity in motionless medium (), steady propagation of an excitation wave is eventually established. At high stream velocities, the wave does not span the channel from wall to wall, forming isolated excited regions, which we called "restrictons". They are especially easy to observe when the model parameters are close to critical ones, at which waves disappear in still medium. In the subcritical region of parameters, a sufficiently fast stream can result in the survival of excitation moving, as a rule, in the form of "restrictons". For downstream excitation waves, the axial portion of the channel is the most important one in determining their behavior. For upstream waves, the most important region of the channel is the near-wall boundary layers. The roles of transversal diffusion, and of approximate similarity with respect to stream velocity are discussed. CONCLUSIONS: These findings clarify mechanisms of wave propagation and survival in flow

Generalized eigenfunctions and spectral theory for strongly local Dirichlet forms

We present an introduction to the framework of strongly local Dirichlet forms and discuss connections between the existence of certain generalized eigenfunctions and spectral properties within this framework. The range of applications is illustrated by a list of examples

Functions and graphs

The second in a series of systematic studies by a celebrated mathematician I. M. Gelfand and colleagues, this volume presents students with a well-illustrated sequence of problems and exercises designed to illuminate the properties of functions and graphs. Since readers do not have the benefit of a blackboard on which a teacher constructs a graph, the authors abandoned the customary use of diagrams in which only the final form of the graph appears; instead, the book's margins feature step-by-step diagrams for the complete construction of each graph. The first part of the book employs simple f

Review of three books by Gelfand et al.

This document has since become the rallying point in any discussion of the reform. While it may be early to assess the achievements of this e#ort, there are good reasons to assess the implications of some already recognizable trends. For the purpose of this review, I will limit myself to a brief report, based on the publications available to me, on how the reform movement has a#ected the content of the mathematics curriculum in 9-12 and calculus. It is to be noted that the reform addresses not just content, but also the method of teaching (e.g., the stress on group learning in the classroom, and the integration of calculators and computers into the instruction) and the method of assessment (e.g., in the current educational jargon, the emphasis on "process" over "product" ). These are even more controversia

On the relationship between the load and the variance of relative fitness

Abstract Background Operation of natural selection can be characterized by a variety of quantities. Among them, variance of relative fitness V and load L are the most fundamental. Results Among all modes of selection that produce a particular value V of the variance of relative fitness, the minimal value Lmin of load L is produced by a mode under which fitness takes only two values, 0 and some positive value, and is equal to V/(1+V). Conclusions Although it is impossible to deduce the load from knowledge of the variance of relative fitness alone, it is possible to determine the minimal load consistent with a particular variance of relative fitness. The concept of minimal load consistent with a particular biological phenomenon may be applicable to studying several aspects of natural selection. Reviewers The manuscript was reviewed by Sergei Maslov, Alexander Gordon, and Eugene Koonin.</p