Persistence of a fig wasp population and evolution of dioecy in figs: a simulation study

The relationship between fig trees and their pollinator wasps is a well-known example of species-specific obligate mutualism. In this article we present a stochastic model of this mutualistic system, referring to data on a dioecious fig (Ficus schwarzii) in Borneo, and examine the conditions for the persistence of a wasp population for a given period. (1) When the average duration of the flowering interval of fig trees is short, even a small fig population can sustain a wasp population successfully. A population whose average period of flowering cycle is half that of another population can sustain a wasp population with a number of trees less than half of the other population. (2) The wasp survival rate (WSR) is higher when (a) the variation of the interval periods of fig flowering is smaller, (b) the fig population size is larger, and (c) figs can prolong their receptivity to wait for a wasp if no wasps are available. (3) WSR is predictable from the average proportion of the fig's receptive phases, in which wasps are available, to their total receptive phases. (4) The persistence period of a wasp population increases exponentially with the number of fig trees. Based on these results we propose a new hypothesis, as a possible scenario, on the evolution of dioecy from monoecy in Ficus. Received: November 13, 1998 / Accepted: July 14, 1999     

UNINSURED COUNTERCYCLICAL RISK: AN AGGREGATION RESULT AND APPLICATION TO OPTIMAL MONETARY POLICY

We consider an incomplete markets economy with capital accumulation and endogenous labor supply. Individuals face countercyclical idiosyncratic labor and asset risk. We derive conditions under which the aggregate allocations and price system can be found by solving a representative agent problem. This result is applied to analyze the properties of an optimal monetary policy in a New Keynesian economy with uninsured countercyclical individual risk. The optimal monetary policy that emerges from our incomplete markets economy is the same as the optimal monetary policy in a representative agent model with preference shocks. When price rigidity is the only friction the optimal monetary policy calls for stabilizing the inflation rate at zero.     

Group-sequential logrank methods for trial designs using bivariate non-competing event-time outcomes

We discuss the multivariate (2L-variate) correlation structure and the asymptotic distribution for the group-sequential weighted logrank statistics formulated when monitoring two correlated event-time outcomes in clinical trials. The asymptotic distribution and the variance–covariance for the 2L-variate weighted logrank statistic are derived as available in various group-sequential trial designs. These methods are used to determine a group-sequential testing procedure based on calendar times or information fractions. We apply the theoretical results to a group-sequential method for monitoring a clinical trial with early stopping for efficacy when the trial is designed to evaluate the joint effect on two correlated event-time outcomes. We illustrate the method with application to a clinical trial and describe how to calculate the required sample sizes and numbers of events.

     

Creating facial animation of characters via MoCap data

We consider the problem of generating 3D facial animation of characters. An efficient procedure is realized by using the motion capture data (MoCap data), which is obtained by tracking the facial markers from an actor/actress. In some cases of artistic animation, the MoCap actor/actress and the 3D character facial animation show different expressions. For example, from the original facial MoCap data of speaking, a user would like to create the character facial animation of speaking with a smirk. In this paper, we propose a new easy-to-use system for making character facial animation via MoCap data. Our system is based on the interpolation: once the character facial expressions of the starting and the ending frames are given, the intermediate frames are automatically generated by information from the MoCap data. The interpolation procedure consists of three stages. First, the time axis of animation is divided into several intervals by the fused lasso signal approximator. In the second stage, we use the kernel k-means clustering to obtain control points. Finally, the interpolation is realized by using the control points. The user can easily create a wide variety of 3D character facial expressions by changing the control points.     

Generalization of Fisher's z-transformation

We deal with the asymptotic expansions of the means and the variances of the correlation coefficients in truncated bivariate normal populations. The Fisher's z-transformation is generalized for stabilizing variance in a truncated normal population. The Hermite moments are introduced, and the relationship among cross moments, central cross moments, and Hermite moments are discussed.