Correlated equilibrium and potential games

Any correlated equilibrium of a strategic game with bounded payoffs and convex strategy sets which has a smooth concave potential, is a mixture of pure strategy profiles which maximize the potential. If moreover, the strategy sets are compact and the potential is strictly concave, then the game has a unique correlated equilibrium.     

Randomly coloring sparse random graphs with fewer colors than the maximum degree

We analyze Markov chains for generating a random k‐coloring of a random graph G_n,d/n. When the average degree d is constant, a random graph has maximum degree Θ(log n/log log n), with high probability. We show that, with high probability, an efficient procedure can generate an almost uniformly random k‐coloring when k = Θ(log log n/log log log n), i.e., with many fewer colors than the maximum degree. Previous results hold for a more general class of graphs, but always require more colors than the maximum degree. © 2006 Wiley Periodicals, Inc. Random Struct. Alg., 2006     

Addendum to “Unstable crack motion is predictable” [2005. JMPS 53, 1071]

Using a scaling relationship discussed in an earlier paper [Abraham, F. F., 2005. Unstable crack motion is predictable. J. Mech. Phys. Solids 53, 1071-1075], we find that the steady-state speed of a unidirectional crack moving in a hyperelastic solid equals the crack speed in a linear solid with our “effective spring constant”.     

Influence of root resistivity on plant water uptake mechanism,part I: numerical solution

The issue of water flow through the root zone of field crops represents a complex problem requiring knowledge of a large spectrum of phenomena from various disciplines. Although many investigations have been devoted to gain better understanding of water dynamics in the root zone, the problem is still insufficiently understood. The main objective of the presented work was to analyze the importance of root water resistivity in the plant water extraction process. The problem was solved numerically for a wide range of the soil–root conductivity ratio (SRCR). Two different types of root water uptake (RWU) mechanisms were obtained. The first one is related to low root resistivity or low SRCR, and, thus, exhibits a so-called “moving uptake front” (MUF) effect observed previously in several experimental studies. The second one is inherent in large values of root resistivity or high values of SRCR (larger than 10⁴), and is strongly dependent on the root density distribution. Deceased.     

Representation of functions of Markov processes as solutions of stochastic equations

Let X_t be a homogeneous Markov process generated by the weak infinitesimal operator A. Let $\text{H}$ be the class of functions f such that f, f²?D_A, the domain of A. The main result of this paper states that for ? ∈ $\text{H}$ can be represented by a stochastic integral and other terms. If the process is generated by a second order differential operator (with ‘poor’ coefficients possibly) on C₀²(R^d) then the process itself can be represented as the solution of an Itô stochastic differential equation.     

Monte Carlo simulation using the Fourier transform of the interatomic potential

When doing Monte Carlo simulations using continuous potentials, the evaluation of the configurational potential energy ink-space by Fourier transformation is shown to be a computationally attractive scheme for systems where the long-range interatomic interaction spans a dimension comparable to the size of the simulated system.     

Fourier analysis,correlation functions and nonadiabatic electron transfer: Wavepackets and exact representations

Summary We investigate the validity of several common approximations in the analysis of nonadiabatic intramolecular electron transfer rate constants. Utilizing the Fourier representation of the golden rule form, we study the evolution of the vibrational correlation function that represents the density-of-states-weighted Franck-Condon factor. In particular, we test the validity of the perturbation theoretic golden rule form and of the Gaussian wavepacket representation for the vibrational wavefunctions against numerically exact quantum mechanical propagations. Although specific cases are found in which both of these break down, for a wide range of conditions (including anharmonic behavior and frequency changes), both the Gaussian wavepacket representation and the golden rule are excellent approximations.     

Isomorphism types of Aronszajn trees

We study the isomorphism types of Aronszajn trees of height ω₁ and give diverse results on this question (mainly consistency results). The second author would like to thank the United States-Israel Binational Science Foundation for partially supporting this research by a grant.     

Linear transformations that preserve certain positivity classes of matrices

For each of several S ? R^n,n, those linear transformations $\text{L}\text{: R}{}^{\mathrm{n,n}}\text{→ R}{}^{\mathrm{n,n}}$ which map S onto S are characterized. Each class is a familiar one which generalizes the notion of positivity to matrices. The classes include: the matrices with nonnegative principal minors, the M-matrices, the totally nonnegative matrices, the D-stable matrices, the matrices with positive diagonal Lyapunov solutions, and the H-matrices, as well as other related classes. The set of transformations is somewhat different from case to case, but the strategy of proof, while differing in detail, is similar.