Stationary reflection principles and two cardinal tree properties

We study consequences of stationary and semi-stationary set reflection. We show that the semi stationary reflection principle implies the Singular Cardinal Hypothesis, the failure of weak square principle, etc. We also consider two cardinal tree properties introduced recently by Weiss and prove that they follow from stationary and semi stationary set reflection augmented with a weak form of Martin's Axiom. We also show that there are some differences between the two reflection principles which suggest that stationary set reflection is analogous to supercompactness whereas semi-stationary set reflection is analogous to strong compactness.Comment: 19 page

Macroscopic Loop Amplitudes in Two-Dimensional Dilaton Gravity

Macroscopic loop amplitudes are obtained for the dilation gravity in two-dimensions. The dependence on the macroscopic loop length $l$ is completely determined by using the Wheeler-DeWitt equation in the mini-superspace approximation. The dependence on the cosmological constant $\Lambda$ is also determined by using the scaling argument in addition.Comment: 23 pages, LaTeX, TIT/HEP-21

On a Rough Sets based Data Mining Tool in Prolog: An Overview

RoughNon-deterministicInformationAnalysis (RNIA) is a framework for handling rough sets based concepts, which are defined in not only DISs (DeterministicInformationSystems) but also NISs (Non-deterministicInformationSystems), on computers. RNIA is also recognized as a framework of data mining from uncertain tables. This paper focuses on programs in prolog, and briefly surveys a software tool for RNIA.16th International Conference on Applications of Declarative Programming and Knowledge Management (INAP 2005) , October 22-24, 2005, Fukuoka, Japa

Asymptotic Distribution of Multilevel Channel Polarization for a Certain Class of Erasure Channels

This study examines multilevel channel polarization for a certain class of erasure channels that the input alphabet size is an arbitrary composite number. We derive limiting proportions of partially noiseless channels for such a class. The results of this study are proved by an argument of convergent sequences, inspired by Alsan and Telatar's simple proof of polarization, and without martingale convergence theorems for polarization process.Comment: 31 pages; 1 figure; 1 table; a short version of this paper has been submitted to the 2018 IEEE International Symposium on Information Theory (ISIT2018