Use cases

Our API provides scripts that can be used to implement Spherion solutions in various scenarios where uncertainty exists, and a probabilistic approach is necessary.

The potential use of Spherion Metrics in mapping the risk of meteor and other celestial body collisions with Earth is a highly relevant and appropriate application, considering the system’s core capabilities.

Modeling Orbital Uncertainty: 

The trajectories of meteors, asteroids, and comets are never known with absolute certainty. Observational data always carry errors, and gravitational perturbations from other celestial bodies introduce even more unpredictability. 

Spherion Metrics excels at explicitly encoding these uncertainties. Instead of presenting a single predicted trajectory, Spherion can depict a probabilistic cone of potential trajectories for a celestial body. Spherion’s overlapping zones would illustrate the probability distribution of the object’s future position. The potential use of Spherion Metrics in mapping the risk of meteors and other celestial bodies colliding with Earth is a highly relevant and appropriate application, considering the system’s core capabilities.

Modeling Orbital Uncertainty: 

The trajectories of meteors, asteroids, and comets are never known with absolute certainty. Observational data always carry errors, and gravitational perturbations from other celestial bodies introduce even more unpredictability. Spherion Metrics excels at explicitly encoding these uncertainties. Instead of presenting a single predicted trajectory, Spherion can depict a probabilistic cone of potential trajectories for a celestial body. Spherion’s overlapping zones would illustrate the probability distribution of the object’s future position.

Our API provides scripts that can be used to implement Spherion solutions in various scenarios where uncertainty exists, and a probabilistic approach is necessary.

Tumor Volumetry with Uncertainty
Instead of a single, rigid, three-dimensional reconstruction of a tumor, the Spherion Metric could generate a probabilistic map of the tumor. The tumor's core, where malignancy is certain, would be depicted by highly resolved Spherion zones. As one moves toward the periphery, overlapping Spherion hemispheres and circles would explicitly encode the probability of tumor cell presence, reflecting the uncertainty of the exact boundary. This enables clinicians to visualize not only the tumor's location, but also the level of confidence regarding its presence in a specific region.

Hierarchical accuracy for clinical decisions

◦ Diagnostic triage (lower resolution): 

At lower resolution, clinicians can swiftly evaluate the overall probabilistic distribution of a lesion within an organ, which is useful for initial triage and identifying potential areas of concern.

◦ Surgical Planning and Radiation Therapy (Higher Resolution): 

For precise interventions, Spherion can be refined to higher resolutions. Surgeons can identify the “most likely” tumor margins based on the Spherion high probability zones, as well as be aware of “possible” microscopic extensions (lower probability zones) that traditional methods may miss. This enables more informed decisions about resection margins or radiation field boundaries, balancing tumor removal with the preservation of healthy tissue.

◦ Targeted Biopsy Guidance:

This is where Spherion can provide significant value. Imaging data (e.g., positron emission tomography (PET) scans showing metabolic activity) can be integrated into the Spherion model. The system can then highlight specific Spherion zones that are most likely to contain aggressive or viable tumor cells, even if they are small or located on the periphery of the main mass. This would guide the surgeon or radiologist in precisely targeting the biopsy needle at the most informative part of the tumor, potentially improving diagnostic yield and informing treatment strategies.

◦ Monitoring Response to Treatment

Over time, follow-up scans could enhance the Spherion model. Effective treatment would show a reduction in high-probability Spherion zones and a decrease in uncertainty at the margins. Recurrence or progression would be indicated by the expansion of Spherion zones and increasing uncertainty in new areas, providing a more dynamic and informative assessment of treatment efficacy than volume measurements alone.

This application showcases Spherion’s capability to model spatial uncertainty in an essential domain, providing a more comprehensive and potentially more accurate method for making diagnostic and therapeutic decisions in oncology.

Problem: 

Tracking the spread of air pollutants from a source (e.g., a factory smokestack, a chemical spill, or a volcanic eruption) is challenging due to variable wind patterns, complex atmospheric conditions, and topographical features. These factors introduce significant uncertainty in predicting pollutant concentrations and dispersion trajectories. Traditional models often struggle to adapt to these uncertainties in real time or to provide clear, hierarchical representations of affected areas with varying levels of accuracy.
Application of the Spherion metric: 

Spherion can model the probabilistic plume of pollutants. Source representation: The pollutant source can be modeled as a Spherion point or a small Spherion zone, with initial uncertainty reflecting measurement errors or variations in emission rates. Uncertainty-Aware Dispersion: As the pollutant disperses, atmospheric models—considering wind speed, direction, temperature, and humidity—would influence the expansion and displacement of Spherion zones. Instead of defining a precise, rigid plume, Spherion represents the spatial distribution of the pollutant as a series of hierarchically defined, overlapping spheres, where the density or color of the spheres indicates the probability of a given pollutant concentration in that region.

Hierarchical Monitoring: Environmental agencies can leverage the hierarchical structure of Spherion Metrics to:  

Broad Overview (Lower Resolution): 

Observe a large-scale, high-level probability distribution of pollutants across a wide geographic area, swiftly identifying potentially affected regions.  

Detailed Analysis (Higher Resolution): 

Focus on specific areas of concern to examine more detailed, granular Spherion subdivisions, offering a more precise probabilistic assessment of pollutant levels for localized risk evaluations (e.g., near residential areas, schools, or agricultural sectors).

Real Time Adaptation: 

As new weather data or sensor readings become available, the Spherion model can dynamically adjust its sphere subdivisions and overlay regions to reflect updated uncertainties in pollutant movement, offering a real-time, adaptive view of the environmental threat. 

Integration into Decision Making: 

This uncertainty-aware spatial model can inform emergency responders about areas with a higher likelihood of contamination, guiding decisions on evacuations, public health alerts, and resource deployment with a clear understanding of inherent uncertainties.

This application utilizes Spherion's capability to model spatial relationships with explicit uncertainty, its hierarchical scalability, and its potential for integration with real-time data, offering a more nuanced and adaptive approach to environmental monitoring compared to deterministic models.