SYSTEM BEHAVIOR
Dynamic systems
Interpret changes across related measurements to help your team understand what is shifting and where closer investigation may be useful.
Explore the weather demoDATA ANALYSIS & SYSTEMS RESEARCH
We help you interpret complex datasets, understand how variables change over time, and decide what comes next.

Understand the system.
Examine the change.
INTERACTIVE DEMONSTRATION
Choose an example. Move through the data. See what changes.
BEYOND A SINGLE SIGNAL
Compare 48 synthetic weather variables and selected relationships. A single chart cannot capture every change in a high-dimensional system.
MULTIVARIABLE WORKSPACE
Each cell is a rolling mean change, in that variable's baseline standard deviations. These individual summaries do not show changes in relationships. A small value here can coexist with a larger relationship component above.
| Sensor group | Temperature | Pressure | Humidity | Wind |
|---|
Educational simulation. This simplified index illustrates selected changes; it is not a forecast or the proprietary research software.
The first 32 observations establish a baseline for 48 variables: temperature, pressure, humidity, and wind across 12 simulated sensor groups. Each new 16-observation window is compared with that baseline, starting at observation 48.
The mean component is the root-mean-square change in all 48 standardized channel averages. The relationship component measures changes in the 12 within-group temperature/humidity correlations. The combined index is the square root of the sum of their squares. This selected-pair summary does not capture every possible high-dimensional change.
In the relationship scenario, the generating relationship changes at observation 65 while individual generating means and scales stay the same. Sample averages still fluctuate. The drift scenario changes several averages; the stable scenario adds no intentional change.
Three consecutive windows above the chosen threshold record a review trigger. High, balanced, and low use 0.45, 0.60, and 0.85 index units. These are illustrative settings, not calibrated probabilities or significance levels. Only observations up to the timeline position are analyzed. The datasets are fixed synthetic examples, not validation results.
Follow battery response and airframe vibration during a simulated flight. Compare changes in the measurements with the flight log, then examine the inspection record.
DRONE TECH
The reference accounts for changing load. Review markers identify persistent departures.
| Seen during flight | Found after landing |
|---|---|
Educational simulation. All measurements, events, and inspection findings are invented for this example. Real analysis needs synchronized telemetry, flight context, and independent checks.
The example uses a fixed 12-minute flight, sampled every six seconds. The reference voltage includes a gradual discharge trend and current-related voltage drop. The vibration reference also changes with load. A climb and turn occur in both flights.
The changing flight adds electrical resistance from 06:24 and a sustained vibration increase from 08:24. Neither event label is an input to the detector. Five-sample average departures must exceed the selected threshold for three consecutive windows. Only samples up to the selected time are used.
High, balanced, and low thresholds are 0.25, 0.40, and 0.65 volts for additional voltage drop, and 0.06, 0.10, and 0.14 g RMS for vibration above the reference. These are illustrative settings, not aircraft operating limits. Temperature is shown for context and does not drive the review marker.
The later inspection is a separate fictional record used to compare timing and possible explanations. Agreement in this example does not establish causation or validated detection accuracy.
Background: PX4 battery load compensation and ArduPilot vibration analysis.
OBSERVATION WORKSPACE
Educational simulation. Synthetic data and a simple baseline comparison illustrate the workflow; this is not the proprietary research software.
The first 24 observations establish a baseline mean and standard deviation. The detector then compares each 8-observation moving average with that baseline. Three consecutive averages beyond the selected threshold trigger a review marker.
High sensitivity uses 1.4 baseline standard deviations, balanced uses 2.2, and low uses 3.2. Higher sensitivity reacts to smaller changes. This simplified example does not model real-world false-positive rates, dependencies, or changing baselines.
Only observations up to the selected timeline position are analyzed. The reported deviation is the current moving average's distance from the baseline, measured in baseline standard deviations.
THE TECHNOLOGY
We use Bayesian statistics and other models to examine patterns, weigh evidence, and make uncertainty explicit. Findings are interpreted in the context of your question, the available data, and the assumptions behind each model.
Algorithm development, dataset testing, and strong coding principles support the analysis. We compare accuracy and runtime and refine implementations to reduce execution time.
Discuss methodology and evaluationAREAS OF FOCUS
Potential uses to test against your data and workflow.
SYSTEM BEHAVIOR
Interpret changes across related measurements to help your team understand what is shifting and where closer investigation may be useful.
Explore the weather demoPATTERN ANALYSIS
Examine transaction and activity patterns in context to help analysts decide what warrants further review.
Discuss fraud analysisSECURITY RESEARCH
Assess changes in network or system behavior alongside existing evidence to inform an investigation and its next steps.
Discuss cybersecurityABOUT MAPPING DYNAMICS
Founder & Lead Developer
Interested in learning?
Learn with Mapping Our Thoughts (opens in a new tab)Antonio leads Mapping Dynamics' research and software development, connecting mathematical theory with the behavior of real systems.
His background includes elliptic-curve cryptography and software development. The work starts with a question, examines the assumptions, and makes the reasoning behind an interpretation clear.
QUESTIONS BEFORE COMMITMENT
Tell us what you need to understand, what data you have, and your timeline.
We then agree on the scope, approach, and any practical constraints before the work begins.
A review signal flags a change from a reference pattern. It points to something worth investigating.
It does not explain the cause or confirm fraud or a security incident. Some changes may also fall outside the measurements being reviewed.
Yes. Start with a brief description of your data and the question you want it to answer.
We agree on access and handling before any records are shared. This site does not accept uploads or live data feeds.
Our software undergoes ongoing testing across different datasets and analytical problems.
Each new problem helps us identify limitations, refine our tools, and strengthen how we evaluate results.
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