Hybrid Evaluation of Lifecycle and Impact of Outstanding Science

The HELIOS Model (Hybrid Evaluation of Lifecycle and Impact of Outstanding Science) is a comprehensive framework designed to evaluate the maturity of emerging technologies by integrating multiple key indicators. The model combines data from R&D investment, scientific publications, patents, adoption levels, and regulatory frameworks to position each technology within its lifecycle phase.

Overview

HELIOS provides a composite index that simultaneously reflects both the state of scientific development (research impact) and technological advancement (diffusion and investment) of a technology. This hybrid approach draws inspiration from established frameworks such as NASA's Technology readiness level (TRL) and Rogers' adoption categories, which link technological evolution with user acceptance.

In the HELIOS framework, each variable indicates a complementary aspect of maturity: sustained growth in investment and publications typically precedes phases of technological expansion, while an elaborate regulatory environment points to a more consolidated technology.

Mathematical formulation

The HELIOS index is calculated as a weighted average of five normalized variables (I, P, Pt, A, R) representing investment, publications, patents, adoption, and regulation, each scaled to the range [0,1]:

${\text{HELIOS}}=w_{I}I+w_{P}P+w_{Pt}Pt+w_{A}A+w_{R}R$

Where the weights sum to 1. A typical weight distribution might be:

• Investment (w_I): 0.25
• Publications (w_P): 0.25
• Patents (w_Pt): 0.20
• Adoption (w_A): 0.25
• Regulation (w_R): 0.05

The resulting HELIOS value ranges from 0 (very early-stage technology) to 1 (high maturity).

Scoring criteria and normalization

Each key variable is measured using standardized criteria and scales:

Investment (R&D)

Annual investment amount (public + private) in USD, normalized by dividing by the highest recorded level or sectoral target. Typical scoring ranges:

• 0: Minimal investment
• 0.2: Low investment
• 0.5: Moderate investment
• 1.0: Very high investment

Scientific publications

Number of academic articles in the related discipline per year, normalized against historical maximum. Example ranges:

• 0–10 articles: 0–0.2
• 11–50 articles: 0.2–0.5
• 51–200 articles: 0.5–0.8
• >200 articles: 0.8–1.0

Patents

Number of patent families published annually in the field. Similar normalization to publications:

• 0–50 patents: 0–0.3
• 51–200 patents: 0.3–0.6
• 201–500 patents: 0.6–0.9
• >500 patents: 0.9–1.0

Adoption

Degree of technology implementation or usage, estimated as market penetration following the diffusion of innovations model:

• <1%: ~0
• 1–10%: 0.1–0.3
• 10–50%: 0.3–0.7
• >50%: 0.7–1.0

Regulation

Maturity level of legal frameworks and standards, qualitatively assessed:

• 0: No regulation
• 0.5: Partial regulations
• 1.0: Complete and harmonized regulation

Visual representation

The current state of the five variables can be represented graphically using a radar chart, where each dimension (investment, publications, patents, adoption, regulation) is measured from 0 to 1. The resulting surface reflects the technology maturity profile. Additionally, the typical Sigmoid function (S-Curve) illustrates the overall maturity trajectory: its maximum slope indicates the inflection point (rapid growth phase) and the final saturation level marks complete maturity.

Variables and Scoring

Variable	Metric	Normalization	Typical Weight
Investment (I)	Annual R&D spend (USD)	I/Imax	0.25
Publications (P)	Articles per year	P/Pmax	0.25
Patents (Pt)	Patent families per year	Pt/Ptmax	0.20
Adoption (A)	% market penetration	tiered scale	0.25
Regulation (R)	Quality of legal standards	tiered scale	0.05

Practical example: Quantum computing

To illustrate HELIOS, consider quantum computing with recent data:

• Investment (I = 0.8): The sector has attracted billions of dollars, with McKinsey & Company estimating the global quantum market could reach $100 billion within ten years.
• Publications (P ≈ 0.9): The field has grown exponentially with increasing literature output.
• Patents (Pt ≈ 0.8): Reports show thousands of new families annually (e.g., 3,795 in 2023 vs 1,899 in 2020).
• Adoption (A = 0.3): Commercial adoption remains modest, mainly prototypes and cloud services.
• Regulation (R ≈ 0.4): Emerging regulatory framework, including U.S. export controls implemented in 2024.

Using suggested weights:

${\text{HELIOS}}=0.25(0.8)+0.25(0.9)+0.20(0.8)+0.25(0.3)+0.05(0.4)\approx 0.65$

A value of ~0.65 indicates an early growth stage, consistent with rapid expansion in patents and investment but limited adoption. This suggests quantum computing is still far from saturation, with the S-curve's increasing slope indicating that the mass adoption tipping point may be approaching.

Applications and interpretation

HELIOS values near 0.5–0.7 correspond to technologies in the development/early adoption phase, while indices close to 1 indicate maturity or stagnation. The model enables:

• Comparative analysis between different technologies
• Assessment of technology trajectory and lifecycle positioning
• Strategic decision-making for R&D investment and policy
• Technology forecasting and planning

Enhanced HELIOS model

The original HELIOS model was a linear evaluation tool, based on normalization and fixed weights, to assess the lifecycle and impact of scientific and technological developments.

The enhanced version extends its scope with non-linear normalization (e.g., sigmoid functions), S-curve growth models for forecasting (investment, publications, patents, adoption, regulation), and dynamic weights across lifecycle phases. It also applies non-linear aggregation (e.g., Choquet integral, OWA operator) to capture synergies and redundancies, and integrates Uncertainty quantification methods such as Monte Carlo simulations.

These upgrades turn HELIOS into a probabilistic forecasting framework, able to detect inflection points and support strategic planning, R&D investment, and policy-making in emerging technologies.

See also

• Technology readiness level
• Diffusion of innovations
• Innovation management
• Technology assessment
• Technology forecasting
• Sigmoid function
• Lazy user model
• Shifted Gompertz distribution

External links

• NASA Technology Readiness Levels
• Global Innovation Index - WIPO
• Garbayo, Eduardo (2025). "HELIOS -- Hybrid Evaluation of Lifecycle and Impact of Outstanding Science v-2.0". arXiv:2508.21329 [physics.soc-ph].
• Predictive models concocted to anticipate the union technology complaint
• HELIOS, Concept and Purpose
• HELIOS Model, Hybrid Evaluation of Lifecycle and Impact