Anomalies, singularities, and catastrophes in C3ISR systems

Abstract

In this paper, we provide topological visualization of Digital Decision Support (DDS) tools, both linear and non-linear, the latter ones related to bifurcations and/or catastrophes, including such non-linear phenomena as hysteresis, or sudden jump/drop of state variable (amplitude). As a principal example, we discuss non-linear oscillator catastrophes with applications in: physics, optics, electronics, mechanics, decision process, and others. INTRODUCTIONDigital Decision Generation tools, or, rather Digital Decision Support (DDS) tools [1] are important software components of C3ISR systems and technologies. In this paper, we propose a new approach to extraction of non-linear events based on topologic visualization of essential variables and anomalous events in binary event (object) space [2] , called by us DDS tools.Any successful predictive analysis in machine/human learning [3] and/or cybersensor [4] fields should include extraction of non-linear and/or anomalous events [1][2][3] such as mathematical catastrophes [5] as precursors, for example.Catastrophes [5] are types of bifurcations [5] , or discrete singularities in topological manifold continuum, constructed from so-called essential variables, including control variables (cause) and state variables (effect). In this paper, we discuss only corank-one catastrophes [5] , such as: fold, cusp, butterfly, etc., with single state variable, z, while control variables are: x, y, etc.In general, DTS (Digital Topologic Singularities) can be categorized within three (3) major types: Threshold DTS, such as avionics of-the-expectation (OTE) incidents, a kind of flagging; Linear DTS (function's maxima, minima, inflection points, etc.); and non-linear DTS (e.g., catastrophes). In this paper, we mostly discuss the third DTS category, as well as compare them with the linear DTS, within heuristic machine learning, idealization, and abstraction. The basic flow chart of DDS includes: regression (noise extraction), smoothing, and 2D "analogization" of discrete experimental data; generation of 2D parametric curves: parametrization-to-continuum (PtC) of these curves into surface continuum (i.e., 3D "analogization"); and, discretization (or, quantization) into non-linear DTS (catastrophes), for example, in this strange discrete → analog → discrete heuristic process.In this paper, we discuss topologic visualization of singularities and anomalies, in the form of: curves, surfaces, spaces, sub-spaces, cross-sections, and projections, in 3D, 4D, and higher space. However, for the sake of clarity, we focus on Sensors, and Command, Control, Communications, and Intelligence (C3I) Technologies for Homeland Security, Defense, and Law Enforcement XIV, edited by Edward M. Carapezza, Proc. of SPIE Vol. 9456, 94560V · © 2015 SPIE · CCC code: 0277-786X/15/$18 ·