Regularity, partial elimination ideals and the canonical bundle

We present partial elimination ideals, which set-theoretically cut out the multiple point loci of a generic projection of a projective variety, as a way to bound the regularity of a variety in projective space. To do this, we utilize a combination of initial ideal methods and geometric methods. We first define partial elimination ideals and establish through initial ideal methods the way in which, for a given ideal, the regularity of the partial elimination ideals bounds the regularity of the given ideal. Then we explore the partial elimination ideals as a way to compute the canonical bundle of the generic projection of a variety and the canonical bundles of the multiple point loci of the projection, and we use Kodaira Vanishing to bound the regularity of the partial elimination ideals.

     

Synthesis and characterization of poly(methyl methacrylate)‐block‐poly(methylphenylsilane)‐ block‐poly(methyl methacrylate) by atom transfer radical polymerization

ABA block copolymers of methyl methacrylate and methylphenylsilane were synthesized with a methodology based on atom transfer radical polymerization (ATRP). The reaction of samples of α,ω‐dihalopoly(methylphenylsilane) with 2‐hydroxyethyl‐2‐methyl‐2‐bromoproprionate gave suitable macroinitiators for the ATRP of methyl methacrylate. The latter procedure was carried out at 95 °C in a xylene solution with CuBr and 2,2‐bipyridine as the initiating system. The rate of the polymerization was first‐order with respect to monomer conversion. The block copolymers were characterized with ¹H NMR and ¹³C NMR spectroscopy and size exclusion chromatography, and differential scanning calorimetry was used to obtain preliminary evidence of phase separation in the copolymer products. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 30–40, 2003     

Vanishing Fisher Information

There are consistently estimable parameters of interest whose semiparametric Fisher information vanishes at some points of the model in question. Here we investigate how bad this is for estimation.     

A comparison of a theoretical model for quasi-statically and dynamically induced environmental vibration from trains with measurements

This paper presents comparisons between a theoretical ground vibration model and measured data at three sites. The model, which is briefly outlined here, encompasses both the quasi-static and dynamic mechanisms of excitation. The vertical dynamics of a number of vehicles travelling at a constant speed on an infinite track are coupled to a semi-analytical model for a three-dimensional layered ground. This model is also used to demonstrate the roles of the two components of vibration at different frequencies and for train speeds below and above the lowest ground wave speed. It is found that, in most practical cases, the dynamic component gives rise to the higher level of vibration.     

Complex genetic evolution of artificial self‐replicators in cellular automata

It is widely believed that evolutionary dynamics of artificial self‐replicators realized in cellular automata (CA) are limited in diversity and adaptation. Contrary to this view, we show that complex genetic evolution may occur within simple CA. The evolving self‐replicating loops (“evoloops”) we investigate exhibit significant diversity in macro‐scale morphologies and mutational biases, undergoing nontrivial genetic adaptation by maximizing colony density and enhancing sustainability against other species. Nonmutable subsequences enable genetic operations that alter fitness differentials and promote long‐term evolutionary exploration. These results demonstrate a unique example of genetic evolution hierarchically emerging from local interactions between elements much smaller than individual replicators. © 2004 Wiley Periodicals, Inc. Complexity 10: 33–39, 2004