Experimental Support of Argument-based Syntactic Computation

Linguistic theory, cognitive, information, and mathematical modeling are all useful while we attempt to achieve a better understanding of the Language Faculty (LF). This cross-disciplinary approach will eventually lead to the identification of the key principles applicable in the systems of Natural Language Processing. The present work concentrates on the syntax-semantics interface. We start from recursive definitions and application of optimization principles, and gradually develop a formal model of syntactic operations. The result – a Fibonacci- like syntactic tree – is in fact an argument-based variant of the natural language syntax. This representation (argument-centered model, ACM) is derived by a recursive calculus that generates a mode which connects arguments and expresses relations between them. The reiterative operation assigns primary role to entities as the key components of syntactic structure. We provide experimental evidence in support of the argument-based model. We also show that mental computation of syntax is influenced by the inter-conceptual relations between the images of entities in a semantic space.

Processing of Byzantine Neume Notation in Ancient Historical Manuscripts

This article presents the principal results of the doctoral thesis “Recognition of neume notation in historical documents” by Lasko Laskov (Institute of Mathematics and Informatics at Bulgarian Academy of Sciences), successfully defended before the Specialized Academic Council for Informatics and Mathematical Modelling on 07 June 2010.

PREFACE

The Conference on Partial Differential Equations and Applications, Sofia, September 14–16, 2011 (In honor of 65-th Anniversary of Professor Petar Popivanov) took place in the premises of the Institute of Mathematics and Informatics (IMI) of the Bulgarian Academy of Sciences (BAS). The conference was organized by the Section “Differential Equations and Mathematical Physics” of IMI with the participation of research groups on PDE from Universit`a di Cagliari and Universit`a di Torino (Italy), with the organizing committee – N. Kutev (IMI–BAS) – chair, G. Boyadzhiev (IMI–BAS) – secretary, T. Gramchev (Univ. Cagliari) and A. Oliaro (Univ. Torino) – members, and thefollowing program/scientific committee: T. Gramchev (chair), N. Kutev (IMI–BAS), L. Rodino (Universit`a di Torino), M. Ruzhansky (Imperial College London), A. Slavova (IMI–BAS), C. Van Der Mee (Universit`a di Cagliari).

A Simple Example of Localized Parametric Resonance for the Wave Equation

2000 Mathematics Subject Classification: 35L05, 35P25, 47A40.

A Mathematical Apparatus for Domain Ontology Simulation. An Extendable Language of Applied Logic

* This paper was made according to the program of fundamental scientific research of the Presidium of the Russian Academy of Sciences «Mathematical simulation and intellectual systems», the project "Theoretical foundation of the intellectual systems based on ontologies for intellectual support of scientific researches".

A Mathematical Apparatus for Ontology Simulation. Specialized Extensions of the Extendable Language of Applied Logic

* This paper was made according to the program of fundamental scientific research of the Presidium of the Russian Academy of Sciences «Mathematical simulation and intellectual systems», the project "Theoretical foundation of the intellectual systems based on ontologies for intellectual support of scientific researches".

Computer-Assisted Proofs and Symbolic Computations

We discuss some main points of computer-assisted proofs based on reliable numerical computations. Such so-called self-validating numerical methods in combination with exact symbolic manipulations result in very powerful mathematical software tools. These tools allow proving mathematical statements (existence of a fixed point, of a solution of an ODE, of a zero of a continuous function, of a global minimum within a given range, etc.) using a digital computer. To validate the assertions of the underlying theorems fast finite precision arithmetic is used. The results are absolutely rigorous. To demonstrate the power of reliable symbolic-numeric computations we investigate in some details the verification of very long periodic orbits of chaotic dynamical systems. The verification is done directly in Maple, e.g. using the Maple Power Tool intpakX or, more efficiently, using the C++ class library C-XSC.

Weitzenböck Derivations and Classical Invariant Theory II: The Symbolic Method

2000 Mathematics Subject Classification: 13N15, 13A50, 13F20.