Automatic Translation of MSC Diagrams into Petri Nets

Development-engineers use in their work languages intended for software or hardware systems design, and test engineers utilize languages effective in verification, analysis of the systems properties and testing. Automatic interfaces between languages of these kinds are necessary in order to avoid ambiguous understanding of specification of models of the systems and inconsistencies in the initial requirements for the systems development. Algorithm of automatic translation of MSC (Message Sequence Chart) diagrams compliant with MSC’2000 standard into Petri Nets is suggested in this paper. Each input MSC diagram is translated into Petri Net (PN), obtained PNs are sequentially composed in order to synthesize a whole system in one final combined PN. The principle of such composition is defined through the basic element of MSC language — conditions. While translating reference table is developed for maintenance of consistent coordination between the input system’s descriptions in MSC language and in PN format. This table is necessary to present the results of analysis and verification on PN in suitable for the development-engineer format of MSC diagrams. The proof of algorithm correctness is based on the use of process algebra ACP. The most significant feature of the given algorithm is the way of handling of conditions. The direction for future work is the development of integral, partially or completely automated technological process, which will allow designing system, testing and verifying its various properties in the one frame.

Hamilton’s Principle with Variable Order Fractional Derivatives

MSC 2010: 26A33, 70H25, 46F12, 34K37 Dedicated to 80-th birthday of Prof. Rudolf Gorenflo

A Taxonomy of Big Data for Optimal Predictive Machine Learning and Data Mining

Big data comes in various ways, types, shapes, forms and sizes. Indeed, almost all areas of science, technology, medicine, public health, economics, business, linguistics and social science are bombarded by ever increasing flows of data begging to be analyzed efficiently and effectively. In this paper, we propose a rough idea of a possible taxonomy of big data, along with some of the most commonly used tools for handling each particular category of bigness. The dimensionality p of the input space and the sample size n are usually the main ingredients in the characterization of data bigness. The specific statistical machine learning technique used to handle a particular big data set will depend on which category it falls in within the bigness taxonomy. Large p small n data sets for instance require a different set of tools from the large n small p variety. Among other tools, we discuss Preprocessing, Standardization, Imputation, Projection, Regularization, Penalization, Compression, Reduction, Selection, Kernelization, Hybridization, Parallelization, Aggregation, Randomization, Replication, Sequentialization. Indeed, it is important to emphasize right away that the so-called no free lunch theorem applies here, in the sense that there is no universally superior method that outperforms all other methods on all categories of bigness. It is also important to stress the fact that simplicity in the sense of Ockham’s razor non-plurality principle of parsimony tends to reign supreme when it comes to massive data. We conclude with a comparison of the predictive performance of some of the most commonly used methods on a few data sets.

On the Recursive Estimation of the Location and of the Size of the Mode of a Probability Density

2000 Mathematics Subject Classification: 62G07, 62L20.