Background. The range of computer software applications which operate with multimodal data becomes wider and wider. To develop efficient algorithms for data processing, the representation of multimodal data as complex structures is required. Existing approaches are mostly oriented to independent data sets representation and they are not efficient for complex representation of multimodal data. Objective. The development of a mathematical approach which can be used for complex multimodal data representation and processing in computer systems. Methods. The Algebraic System of Aggregates is developed for enabling complex representation of multimodal data. There are logical, ordering and arithmetical operations in the Algebraic System of Aggregates. Logical operations can be used for preparing complex data representations in a form of aggregates which are supposed to be a subject of further data analysis. The precondition for such representation is that data sequences are of different modalities and they are recorded with respect to time.Results. The logical operations on aggregates are proposed and described. They allow to construct different compositions of multimodal data what in its turn enables complex data representation for compound description of objects and processes in different areas including healthcare. The multi-image concept which enables overall description of an object, a subject, or a process of observation carried out in the course of time is also proposed and discussed. Conclusions. The Algebraic System of Aggregates is a tool for complex data representation. It enables multimodal data processing by using a range of operations and relations. The key difference in the fulfilment of logical operations in the Algebraic System of Aggregates and logical operations on sets is that an aggregate is a form of complex representation of data sequences where the order of data in each sequence of each type is important and influences on the order of data in the result of a certain logical operation.
Background. The range of hardware for surveillance, monitoring, and measuring is quite wide now. It gives new opportunities for obtaining large amounts of data which describe behaviour of an object (subject, process, phenomenon) of observation. Since observation is a process fulfilling in a course of time as well as usually it is resulted in obtaining multimodal data sets, it is reasonable to represent this time-based multimodal data as a multi-image of an object of observation by employing the apparatus of the Algebraic System of Aggregates. Objective. The objective of the research is to define ordering operations of the Algebraic System of Aggregates and to present an approach of their application for processing a multi-image of an object of observation. Methods. The research is based on both the Algebraic System of Aggregates and the concept of multi-image which enable complex representation and processing of multimodal data. There are logical, ordering and arithmetical operations in the Algebraic System of Aggregates. Ordering operations can be used for time-based processing of real objects, subjects, processes data represented as multi-images. Results. The ordering operations on aggregates are proposed and described. These operations allow to process data of multi-images with respect to time; in particular, they enable reordering of tuples and tuple elements. Conclusions. The processing of complex data structures of multimodal nature, which are defined, generated, measured, or recorded in terms of time, can be fulfilled based on mathematical apparatus of the Algebraic System of Aggregates, in particular, by using the ordering operations presented in this paper. It can be useful in different areas for data processing of real-world objects (subjects, processes, phenomena), characteristics of which can be measured as multimodal data by multiple sensors and presented as aggregates and multi-images.
Abstract-We analyzed the dynamic behavior of the damping system with a two-mass damper pendulum. The equations of motion of nonlinear systems were built. AFC equation systems have been identified in the linear formulation. Proposed and implemented a new numerical method of determining the optimum parameters of optimal settings two-mass damper.
Abstract-The proposed method of graphical data protection is a combined crypto-steganographic method. It is based on a bit values transformation according to both a certain Boolean function and a specific scheme of correspondence between MSB and LSB. The scheme of correspondence is considered as a secret key. The proposed method should be used for protection of large amounts of secret graphical data.
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