Anomalies, Local Counter Terms and Bosonization

We re-examine the issue of local counter terms in the analysis of quantum anomalies. We analyze two-dimensional theories and show that the notion of local counter terms need to be carefully defined depending on the physics contents such as whether one is analyzing gauge theory or bosonization. It is shown that a part of the Jacobian, which is apparently spurious and eliminated by a local counter term corresponding to the mass term of the gauge field in gauge theory, cannot be removed by a {\it local} counter term and plays a central role by giving the kinetic term of the bosonized field in the context of path integral bosonization.Comment: 24 pages, A contribution to the Hidenaga Yamagishi commemorative volume of Physics Reports, edited by E. Witten and I. Zahed. Some sentences were made more precise, and a Note Added was adde

Information, Investment, and the Stock Market: A Study of Investment Revision Data of Japanese Manufacturing Industries,

We examined investment behavior in the Japanese manufacturing industry using investment revision data to analyze investment behavior from a fresh angle. We tested the martingale investment hypothesis and then the q-theory of investment by looking at the response of stock return and investment to news arriving at firms. The martingale hypothesis was generally accepted, and we also found evidence for the validity of the q-theory hypothesis. Investment was responsive to profit rate revision and sales revision, but stock return responded only to profit rate revision. Further investigation revealed that investment was also motivated by expansion of market share for sales, especially for industries with rapid technological progress.

Ridge Regression, Hubness, and Zero-Shot Learning

This paper discusses the effect of hubness in zero-shot learning, when ridge regression is used to find a mapping between the example space to the label space. Contrary to the existing approach, which attempts to find a mapping from the example space to the label space, we show that mapping labels into the example space is desirable to suppress the emergence of hubs in the subsequent nearest neighbor search step. Assuming a simple data model, we prove that the proposed approach indeed reduces hubness. This was verified empirically on the tasks of bilingual lexicon extraction and image labeling: hubness was reduced with both of these tasks and the accuracy was improved accordingly.Comment: To be presented at ECML/PKDD 201