Contextual analysis of mathematical expressions for advanced mathematical search

Abstract-We found a way to use mathematical search to provide better navigation for reading papers on computers. Since the superficial information of mathematical expressions is ambiguous, considering not only mathematical expressions but also the texts around them is necessary. We present how to extract a natural language description, such as variable names or function definitions that refer to mathematical expressions with various experimental results. We first define an extraction task and constructed a reference dataset of 100 Japanese scientific papers by hand. We then propose the use of two methods, pattern matching and machine learning based ones for the extraction task. The effectiveness of the proposed methods is shown through experiments by using the reference set

Semantic distillation: a method for clustering objects by their contextual specificity

Techniques for data-mining, latent semantic analysis, contextual search of databases, etc. have long ago been developed by computer scientists working on information retrieval (IR). Experimental scientists, from all disciplines, having to analyse large collections of raw experimental data (astronomical, physical, biological, etc.) have developed powerful methods for their statistical analysis and for clustering, categorising, and classifying objects. Finally, physicists have developed a theory of quantum measurement, unifying the logical, algebraic, and probabilistic aspects of queries into a single formalism. The purpose of this paper is twofold: first to show that when formulated at an abstract level, problems from IR, from statistical data analysis, and from physical measurement theories are very similar and hence can profitably be cross-fertilised, and, secondly, to propose a novel method of fuzzy hierarchical clustering, termed \textit{semantic distillation} -- strongly inspired from the theory of quantum measurement --, we developed to analyse raw data coming from various types of experiments on DNA arrays. We illustrate the method by analysing DNA arrays experiments and clustering the genes of the array according to their specificity.Comment: Accepted for publication in Studies in Computational Intelligence, Springer-Verla

Quantum decision making by social agents

The influence of additional information on the decision making of agents, who are interacting members of a society, is analyzed within the mathematical framework based on the use of quantum probabilities. The introduction of social interactions, which influence the decisions of individual agents, leads to a generalization of the quantum decision theory developed earlier by the authors for separate individuals. The generalized approach is free of the standard paradoxes of classical decision theory. This approach also explains the error-attenuation effects observed for the paradoxes occurring when decision makers, who are members of a society, consult with each other, increasing in this way the available mutual information. A precise correspondence between quantum decision theory and classical utility theory is formulated via the introduction of an intermediate probabilistic version of utility theory of a novel form, which obeys the requirement that zero-utility prospects should have zero probability weights.Comment: This paper has been withdrawn by the authors because a much extended and improved version has been submitted as arXiv:1510.02686 under the new title "Role of information in decision making of social agents

Erlangen Programme at Large 3.2: Ladder Operators in Hypercomplex Mechanics

We revise the construction of creation/annihilation operators in quantum mechanics based on the representation theory of the Heisenberg and symplectic groups. Besides the standard harmonic oscillator (the elliptic case) we similarly treat the repulsive oscillator (hyperbolic case) and the free particle (the parabolic case). The respective hypercomplex numbers turn to be handy on this occasion, this provides a further illustration to Similarity and Correspondence Principle. Keywords: Heisenberg group, Kirillov's method of orbits, geometric quantisation, quantum mechanics, classical mechanics, Planck constant, dual numbers, double numbers, hypercomplex, jet spaces, hyperbolic mechanics, interference, Fock--Segal--Bargmann representation, Schr\"odinger representation, dynamics equation, harmonic and unharmonic oscillator, contextual probability, symplectic group, metaplectic representation, Shale--Weil representationComment: LaTeX2e, 12 pages, 3 EPS pictures in one figures; v2: the illustration is added, several small improvements; v3: minor corrections, several references are added; v4: minor correction

Pre-primary school teachers’ approaches to mathematics education in Finland

The purpose of this small-scale study is to examine Finnish pre-primary teachers’ approaches to mathematics education. Qualitative analyses from six indepth interviews reveal different strategies and goals. The teachers describe themselves as the facilitating participant, express that mathematics should be framed in playful settings, and assume that it is to be learnt indirectly. The study discerns different pedagogical goals for mathematics education, such as working on counting procedures, preparing for the next school level, building for a better future, and teaching for mathematical literacy. These constitute the teachers’ pedagogical approaches to early mathematics education. Context is experienced as influencing their practice, together with an overall aim to foster a positive attitude towards mathematics. This is discussed in relation to the teachers