2,446 research outputs found
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 is completely
determined by using the Wheeler-DeWitt equation in the mini-superspace
approximation. The dependence on the cosmological constant 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
Countably Infinite Multilevel Source Polarization for Non-Stationary Erasure Distributions
Polar transforms are central operations in the study of polar codes. This
paper examines polar transforms for non-stationary memoryless sources on
possibly infinite source alphabets. This is the first attempt of source
polarization analysis over infinite alphabets. The source alphabet is defined
to be a Polish group, and we handle the Ar{\i}kan-style two-by-two polar
transform based on the group. Defining erasure distributions based on the
normal subgroup structure, we give recursive formulas of the polar transform
for our proposed erasure distributions. As a result, the recursive formulas
lead to concrete examples of multilevel source polarization with countably
infinite levels when the group is locally cyclic. We derive this result via
elementary techniques in lattice theory.Comment: 12 pages, 1 figure, a short version has been accepted by the 2019
IEEE International Symposium on Information Theory (ISIT2019
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