HELIOS 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.

HELIOS ^[1] 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.^[2]

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.

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]:

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

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).

Each key variable is measured using standardized criteria and scales:

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

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

Number of patent families published annually in the field. Similar normalization to publications:^[3]

• 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

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

Maturity level of legal frameworks and standards, qualitatively assessed:

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

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.

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.^[4]
• 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).^[5]
• 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.^[6]

Using suggested weights:

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

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.

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

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.^[7]

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

• 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