Recently, very large-scale decision support systems (DSSs) have been developed, which tackle very complex problems, associated with very extensive and polymorphic information, which probably is geographically highly dispersed. The management, updating, modification and upgrading of the data and program core of such an information system is, as a rule, a very difficult task, which encompasses many hazards and risks. The purpose of the present work was (a) to list the more significant of these hazards and risks and (b) to introduce a new general methodology for designing decision support (DS) systems that are robust and circumvent these risks. The core of this new approach was the introduction of a meta-database, called teleological, on the base of which management, updating, modification, reduction, growth and upgrading of the system may be safely and efficiently achieved. The very same teleological meta-database can be used for the construction of a sound decision support system, incorporating elements of a previous one at a future stage.
The main goal of the present work is to determine the hand that has written two newly discovered documents in Romania. For giving the proper answer, the authors introduced the notion of “Ideal Representative”, namely of an object that very well represents the corresponding ideal alphabet symbol that a writer had in his/her mind when writing a document by hand. Moreover, the authors have introduced a novel method, which leads to the optimal evaluation of the Ideal Representative of any alphabet symbol in association with any handwritten document. Furthermore, the authors have introduced methods for comparing these Ideal Representatives, so as a final decision about the hand that has written a document may be obtained with a highly considerable likelihood. The related analysis manifests that the two documents discovered in Romania in 1998, belong to the great personality of Rigas Feraios. The presented method of automatic handwriting Identification seems to be of general applicability.
In the present paper, a novel approach is introduced for the study, estimation and exact tracking of the finite precision error generated and accumulated during any number of multiplications. It is shown that, as a rule, this operation is very “toxic”, in the sense that it may force the finite precision error accumulation to grow arbitrarily large, under specific conditions that are fully described here. First, an ensemble of definitions of general applicability is given for the rigorous determination of the number of erroneous digits accumulated in any quantity of an arbitrary algorithm. Next, the exact number of erroneous digits produced in a single multiplication is given as a function of the involved operands, together with formulae offering the corresponding probabilities. In case the statistical properties of these operands are known, exact evaluation of the aforementioned probabilities takes place. Subsequently, the statistical properties of the accumulated finite precision error during any number of successive multiplications are explicitly analyzed. A method for exact tracking of this accumulated error is presented, together with associated theorems. Moreover, numerous dedicated experiments are developed and the corresponding results that fully support the theoretical analysis are given. Eventually, a number of important, probable and possible applications is proposed, where all of them are based on the methodology and the results introduced in the present work. The proposed methodology is expandable, so as to tackle the round-off error analysis in all arithmetic operations.
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