On Shattering, Splitting and Reaping Partitions
نویسندگان
چکیده
منابع مشابه
On Shattering, Splitting and Reaping Partitions
In this article we investigate the dual-shattering cardinal H, the dualsplitting cardinal S and the dual-reaping cardinal R, which are dualizations of the well-known cardinals h (the shattering cardinal, also known as the distributivity number of P(ω)/fin), s (the splitting number) and r (the reaping number). Using some properties of the ideal J of nowhere dual-Ramsey sets, which is an ideal ov...
متن کاملAround splitting and reaping
We prove several results on some cardinal invariants of the continuum which are closely related to either the splitting number s or its dual, the reaping number r.
متن کاملPair-splitting, Pair-reaping and Cardinal Invariants of Fσ-ideals
We investigate the pair-splitting number spair which is a variation of splitting number, pair-reaping number rpair which is a variation of reaping number and cardinal invariants of ideals on ω. We also study cardinal invariants of Fσ ideals and their upper bounds and lower bounds. As an application, we answer a question of S. Solecki by showing that the ideal of finitely chromatic graphs is not...
متن کاملOn Convex Optimization, Fat Shattering and Learning
Oracle complexity of the problem under the oracle based optimization model introduced by Nemirovski & Yudin (1978) is considered. We show that the oracle complexity can be lower bounded by fat-shattering dimension introduced by Kearns & Schapire (1990), a key tool in learning theory. Using this result, we proceed to establish upper bounds on learning rates for agnostic PAC learning with linear ...
متن کاملCompressed Shattering
The central idea of compressed sensing is to exploit the fact that most signals of interest are sparse in some domain and use this to reduce the number of measurements to encode. However, if the sparsity of the input signal is not precisely known, but known to lie within a specified range, compressed sensing as such cannot exploit this fact and would need to use the same number of measurements ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematical Logic Quarterly
سال: 1998
ISSN: 0942-5616,1521-3870
DOI: 10.1002/malq.19980440109