Schnorr triviality is equivalent to being a basis for tt-Schnorr randomness

Title
Schnorr triviality is equivalent to being a basis for tt-Schnorr randomness

Type
Talk at
Seventh International Conference on Computability, Complexity and Randomness (CCR 2012)
2-6 July 2012, Cambridge, Great Britain
Isaac Newton Institute

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abstract
slide

INI web seminar

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Weak L^1-computability and Limit L^1-computability

Title
Weak L^1-computability and Limit L^1-computability

Type
Talk at
Ninth International Conference on Computability and Complexity in Analysis
June 24-27, 2012, Cambridge, UK

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abstract
slide
paper

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An integral test for Schnorr randomness and its applications

Title
An integral test for Schnorr randomness and its applications

Type
Talk at
Computability in Europe 2012
18 – 23 June, 2012, University of Cambridge

Abstract
abstract

Slide
slide

Paper
paper

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Schnorr triviality is equivalent to being a basis for tt-Schnorr randomness

Title
Schnorr triviality is equivalent to being a basis for tt-Schnorr randomness

Type
Talk at CS seminar in RIMS, Kyoto University on 7 June 2012.

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Former half slide in Japanese
The latter half is the same as CCR2012.

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Algorithmic interpretation of probability

Title
Algorithmic interpretation of probability

Type
Talk at CAPE lectures, Kyoto University on 29 May 2012.
CAPE lectures

Abstract
Philosophy of probability is one of the big problem in science
discussed so far.
In this talk I first review the history of philosophy of probability.
Then I introduce theory of algorithmic randomness and its
related topic, which is produced by the study of the mathematical
formalization of probability.
Finally I discuss the notion of probability from the algorithmic
point of view by seeing the results that has got recently.

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Slide in Japanese

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The limit of prediction and randomness

Title
The limit of prediction and randomness

Type
Talk at CS seminar in RIMS, Kyoto University on 26 Apr 2012.

Abstract
The former half is about the relation between differentiability and randomness.
I talk about why more computability is needed to characterize Schnorr randomness by differentiability.
The latter half is about the relation between Solomonoff’s induction and the differentiability.
I use a little different setting from Solomonoff’s induction to get a Schnorr randomness version
with long prediction.
I talk more about future work.

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Slide in Japanese

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The convergence rate of SLLN in the case of non-i.i.d.

Title
The convergence rate of SLLN in the case of non-i.i.d.
(with A. Takemura)

Type
Talk at “Annual meeting of Mathematical Society of Japan” on 26-29 Mar 2012.

Abstract
Japanese abstract

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Slides

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At which points are functions differentiable?

Title
At which points are functions differentiable?

Type
Talk at “Annual meeting of Mathematical Society of Japan” on 26-29 Mar 2012.

Abstract
Japanese abstract

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Slides

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Why the event with probability 0 happen

Title
Why the event with probability 0 happen

Type
Young-RICE: Young-Researchers for Improvements of College Education
20 Mar 2012

Abstract
Go to the Japanese page to see the abstract in Japanese.

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Japanese slide (3.1MB)

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Weak L^1-computability and Limit L^1-computability

The result in this paper was included in L1-computability, layerwise computability and Solovay reducibility

News
Mar 12, 2012, Draft

Title
Weak L^1-computability and Limit L^1-computability

Type
Extended abstract

Journal
in preparation

Abstract
The class of the differences between two integral tests for Schnorr ran- domness is an important class related to Schnorr randomness. In this paper we study other randomness versions. We also claim that Solovay reducibility for lower semicomputable functions generalizes layerwise com- putability.

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in preparation

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