I attempt to develop further the statistical interpretation of quantum mechanics proposed by Einstein and developed by Popper, Ballentine, etc. Two ideas are proposed in the present paper. One is to interpret momentum as a property of an ensemble of similarly prepared systems which is not satisfied by any one member of the ensemble of systems. Momentum is regarded as a statistical parameter like temperature in statistical mechanics. The other is the holistic assumption that a probability distribution is determined as (...) a whole as most likely to be realized. This is the same as the chief assumption in statistical mechanics, and maximum likelihood in classical statistics. These ideas enable us to understand statistically (1) the formalism of quantum mechanics, (2) Heisenberg's uncertainty relations, and (3) the origin of quantum equations. They also explain violation of Bell's inequality and the interference of probabilities. (shrink)
This article addresses the problem of automatically extracting legal indices which express the important contents of legal documents. Legal indices are not limited to single-word keywords and compound-word keywords, they are also clause keywords. We approach index extraction using structural information of Japanese sentences, i.e. chunks and clauses. Based on the assumption that legal indices are composed of important tokens from the documents, extracting legal indices is treated as a problem of collecting chunks and clauses that contain as many important (...) tokens as possible. Each token is assigned a weight which is a statistical score, e.g. TF–IDF and Okapi BM25, to indicate its importance. The importance of a chunk or clause is determined based on the average weight of tokens included in that chunk or clause. Then, highly weighted chunks and clauses are recognized as the indices for legal documents. The experimental results on Japanese National Pension Act data show that our proposed method achieves better performance than TextRank, the most popular unsupervised method in extracting single-word and compound-word keywords. In addition, this approach is also applicable to extract clause keywords with high performance. (shrink)
As evidenced by high-throughput sequencers, genomic technologies have recently undergone radical advances. These technologies enable comprehensive sequencing of personal genomes considerably more efficiently and less expensively than heretofore. These developments present a challenge to the conventional framework of biomedical ethics; under these changing circumstances, each research project has to develop a pragmatic research policy. Based on the experience with a new large-scale project—the Genome Science Project—this article presents a novel approach to conducting a specific policy for personal genome research in (...) the Japanese context. In creating an original informed-consent form template for the project, we present a two-tiered process: making the draft of the template following an analysis of national and international policies; refining the draft template in conjunction with genome project researchers for practical application. Through practical use of the template, we have gained valuable experience in addressing challenges in the ethical review process, such as the importance of sharing details of the latest developments in genomics with members of research ethics committees. We discuss certain limitations of the conventional concept of informed consent and its governance system and suggest the potential of an alternative process using information technology. (shrink)
In Zermelo-Fraenkel set theory without the Axiom of Foundation we study the schema version of the principle of dependent choices in connection with Aczel's antifoundation axiom , Boffa's anti-foundation axiom, and axiom of collection.
In this note, we study the complementedness and the distributivity of upper semilattices of Kleene degrees assuming V = L. K denotes the upper semilattice of all Kleene degrees. We prove that if V = L, then some sub upper semilattices of K are non-complemented and some are non-distributive.
Concerning Post's problem for Kleene degrees and its relativization, Hrbacek showed in  and  that if V = L, then Kleene degrees of coanalytic sets are dense, and then for all K ⊆ωω, there are N1 sets which are Kleene semirecursive in K and not Kleene recursive in each other and K. But the density of Kleene semirecursive in K Kleene degrees is not obtained from these theorems. In this note, we extend these theorems by showing that if V (...) = L, then for all K ⊆ ωω, Kleene semirecursive in K Kleene degrees are dense above K. (shrink)
In Aczel , the existence of largest fixed points of set continuous operators is proved assuming the schema version of dependent choices in Zermelo-Fraenkel set theory without the axiom of Foundation. In the present paper, we study whether the existence of largest fixed points of set continuous operators is provable without the schema version of dependent choices, using Boffa's weak antifoundation axioms.