The Semantic Deviation Transformation: A Mathematical Framework for Analyzing Dynamic Multi-Variable Systems

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Abstract: The purpose of this work is to introduce a new mathematical operator, the Semantic Deviation Transformation (SDT), designed to study how multi-variable systems evolve over time and how their internal relationships change relative to a reference state. Many natural and engineered systems—such as environmental conditions, biomedical signals, and multi-sensor measurements—cannot be understood by examining isolated values. Instead, their information emerges from the interaction between variables and the temporal behavior of these interactions. The SDT provides a structured way to extract a single information value from raw data by measuring the deviation between a system's instantaneous interaction and its reference pattern, then aggregating these deviations over time. This transformation offers a general, flexible framework that can be applied to temperature-humidity systems, signal processing, ECG analysis, and any domain where variables interact dynamically. ABDALKADER ALKHATIB, BME,MBA abdalkader00@gmail.com

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