On the limitations of comparing mean square forecast errors

Linear models are invariant under non-singular, scale-preserving linear transformations, whereas mean square forecast errors (MSFEs) are not. Different rankings may result across models or methods from choosing alternative yet isomorphic representations of a process. One approach can dominate others for comparisons in levels, yet lose to another for differences, to a second for cointegrating vectors and to a third for combinations of variables. The potential for switches in ranking is related to criticisms of the inadequacy of MSFE against encompassing criteria, which are invariant under linear transforms and entail MSFE dominance. An invariant evaluation criterion which avoids misleading outcomes is examined in a Monte Carlo study of forecasting methods.     

Activation of a C. elegans Antennapedia homologue in migrating cells controls their direction of migration.

Anterior-posterior patterning in insects, vertebrates and nematodes involves members of conserved Antennapedia-class homeobox gene clusters (HOM-C) that are thought to give specific body regions their identities. The effects of these genes on region-specific body structures have been described extensively, particularly in Drosophila, but little is known about how HOM-C genes affect the behaviours of cells that migrate into their domains of function. In Caenorhabditis elegans, the Antennapedia-like HOM-C gene mab-5 not only specifies postembryonic fates of cells in a posterior body region, but also influences the migration of mesodermal and neural cells that move through this region. Here we show that as one neuroblast migrates into this posterior region, it switches on mab-5 gene expression; mab-5 then acts as a developmental switch to control the migratory behaviour of the neuroblast descendants. HOM-C genes can therefore not only direct region-specific patterns of cell division and differentiation, but can also act within migrating cells to programme region-specific migratory behaviour.     

Trying times for human insulin.

The introduction of human insulin to treat diabetics seemed straightforward. What can account for the problems that have followed?     

The harmonic decomposition reconstruction for the exponential radon transform

The exponential Radon transform, a generalization of the Radon transform, is defined and studied as a mapping of function spaces. It is represented in terms of Fourier transform of its domain and range, and this leads to the harmonic decomposition reconstruction. The results are similar results of Tretiak and Metz. Foundation item: Supported by the National Natural Science Foundation of China (No. 19971064), Key Project of Science and Technology of Hubei Province Education Committee. Biography: Wang Jin-ping (1963-), male, Ph.D. candidate, research direction: numberical solution of singular integral equation and integral transformation etc.     

Resource Search in Unstructured Peer-to-Peer System Based on Multiple-Tree Overlay Structure

We propose a multiple-tree overlay structure for resource discovery in unstructured P2P systems. Peers that have similar interests or hold similar type of resources will be grouped into a tree-like cluster. We exploit the heterogeneity of peers in each cluster by connecting peers with more capacities closer to the root of the tree. The capacity of a peer can be defined in different ways （e.g. higher network bandwidth, larger disk space, more data items of a certain type etc.） according to different needs of users or applications.     

On the verge of <Emphasis Type="Italic">Umdeutung</Emphasis> in Minnesota: Van Vleck and the correspondence principle. Part one

In October 1924, The Physical Review, a relatively minor journal at the time, published a remarkable two-part paper by John H. Van Vleck, working in virtual isolation at the University of Minnesota. Using Bohr’s correspondence principle and Einstein’s quantum theory of radiation along with advanced techniques from classical mechanics, Van Vleck showed that quantum formulae for emission, absorption, and dispersion of radiation merge with their classical counterparts in the limit of high quantum numbers. For modern readers Van Vleck’s paper is much easier to follow than the famous paper by Kramers and Heisenberg on dispersion theory, which covers similar terrain and is widely credited to have led directly to Heisenberg’s Umdeutung paper. This makes Van Vleck’s paper extremely valuable for the reconstruction of the genesis of matrix mechanics. It also makes it tempting to ask why Van Vleck did not take the next step and develop matrix mechanics himself. This paper was written as part of a joint project in the history of quantum physics of the Max Planck Institut für Wissenschaftsgeschichte and the Fritz-Haber-Institut in Berlin.