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Designing a Semantic Ground Truth for Mathematical Formulae

Sexton, Alan, Sorge, Volker, Suzuki, Masakazu (2010)

Towards a Digital Mathematics Library. Paris, France, July 7-8th, 2010

We report on a new project to design a semantic ground truth set for mathematical document analysis. The ground truth set will be generated by annotating recognised mathematical symbols with respect to both their global meaning in the context of the considered documents and their local function within the particular mathematical formula they occur. The aim of our work is to have a reliable database available for semantic classification during the formula recognition process with the aim of enabling...

Detecting a data set structure through the use of nonlinear projections search and optimization

Victor L. Brailovsky, Michael Har-Even (1998)

Kybernetika

Detecting a cluster structure is considered. This means solving either the problem of discovering a natural decomposition of data points into groups (clusters) or the problem of detecting clouds of data points of a specific form. In this paper both these problems are considered. To discover a cluster structure of a specific arrangement or a cloud of data of a specific form a class of nonlinear projections is introduced. Fitness functions that estimate to what extent a given subset of data points...

Detection of deadlocks and traps in Petri nets by means of Thelen's prime implicant method

Agnieszka Węgrzyn, Andrei Karatkevich, Jacek Bieganowski (2004)

International Journal of Applied Mathematics and Computer Science

A new method of detecting deadlocks and traps in Petri nets is presented. Deadlocks and traps in Petri nets can be represented by the roots of special equations in CNF form. Such equations can be solved by using the search tree algorithm proposed by Thelen. In order to decrease the tree size and to accelerate the computations, some heuristics for Thelen's method are presented.

Deterministic blow-ups of minimal NFA's

Galina Jirásková (2006)

RAIRO - Theoretical Informatics and Applications

The paper treats the question whether there always exists a minimal nondeterministic finite automaton of n states whose equivalent minimal deterministic finite automaton has α states for any integers n and α with n ≤ α ≤ 2n. Partial answers to this question were given by Iwama, Kambayashi, and Takaki (2000) and by Iwama, Matsuura, and Paterson (2003). In the present paper, the question is completely solved by presenting appropriate automata for all values of n and α. However, in order to...

Developing a Metadata Exchange Format for Mathematical Literature

Ruddy, David (2010)

Towards a Digital Mathematics Library. Paris, France, July 7-8th, 2010

This paper describes an effort to develop a metadata element set for the exchange of descriptive metadata about mathematical literature. The approach taken uses the Dublin Core Application Profile (DCAP) framework, based on the DC Abstract Model. A fully developed DCAP for mathematical literature would be valuable, as both a guide and constraint in the creation of metadata records suitable for harvesting via OAI or sharing through other means. Adhering to the DCAP model would also enhance global...

DFIS: A novel data filling approach for an incomplete soft set

Hongwu Qin, Xiuqin Ma, Tutut Herawan, Jasni Mohamad Zain (2012)

International Journal of Applied Mathematics and Computer Science

The research on incomplete soft sets is an integral part of the research on soft sets and has been initiated recently. However, the existing approach for dealing with incomplete soft sets is only applicable to decision making and has low forecasting accuracy. In order to solve these problems, in this paper we propose a novel data filling approach for incomplete soft sets. The missing data are filled in terms of the association degree between the parameters when a stronger association exists between...

Diagonalization in proof complexity

Jan Krajíček (2004)

Fundamenta Mathematicae

We study diagonalization in the context of implicit proofs of [10]. We prove that at least one of the following three conjectures is true: ∙ There is a function f: 0,1* → 0,1 computable in that has circuit complexity 2 Ω ( n ) . ∙ ≠ co . ∙ There is no p-optimal propositional proof system. We note that a variant of the statement (either ≠ co or ∩ co contains a function 2 Ω ( n ) hard on average) seems to have a bearing on the existence of good proof complexity generators. In particular, we prove that if a minor variant...

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