Multi-Scale Sampling Outline Introduction Information technology challenges Example: light patterns in forest Greg Pottie

Example: Light Pattern Sampling Photosynthesis begins above some (species-specific) incident light intensity threshold, and eventually saturates –Pattern of light levels thus conveys more useful information than simple average of intensity Do not necessarily need to reconstruct the field Selected statistics may be sufficient –E.g. histograms of intensity levels, characterization of light level dynamics Natural scenes are very complicated –Shadows from many levels

Some Early NIMS PAR Measurements Large variations over short distances –Pure static network will require unreasonable density for field reconstruction Pure mobile network will give misleading results with respect to rapid dynamics (e.g. branches blowing in wind) Some type of hybrid strategy suggested

Adaptive Sampling Strategies Over-deploy: focus on scheduling which nodes are on at a given time Actuate: work with smaller node densities, but allow nodes to move to respond to environmental dynamics Our apps (Terrestrial, Aquatic, Contaminant) are at unprecedented scales and highly dynamic: over-deployment is not an option –Always undersampled with respect to some phenomenon –Focus on infrastructure supported mobility –Passive supports (tethers, buoyancy) –Small number of moving nodes Many approaches/experiments explored in past two years

Speedup using Static and Mobile Nodes t=1 t=2 t=3 Static nodes act as triggers Network of static nodes ‘allocates’ tasks to mobile nodes

Sampling Lattice/deterministic pattern Gradient methods (e.g. Newton, LMS) Simulated annealing (guided walks) Multi-scale or multi-dwell Bisection/quad algorithms (decision trees with multiple depths) Random walk Sampling strategy depends on physical model, objectives, and available resources E.g., finding global max or min of a field depends on smoothness: Smooth Rough Similar stacks can be constructed for other sampling objectives (e.g., reconstruction, gathering statistics)

Multiscale Approach Goal is optimization of the hierarchical system –Not merely optimization of devices or any given layer –Models, devices, algorithms require co-design Context-driven algorithms –No single algorithm/device is best in all situations –Context is the state of the next level in the hierarchy; choose resources to apply when drilling down to next level according to this state –Probabilistic constraints and algorithms lead to more new optimizations Examples: adaptive and multi-scale sampling

Optimization Paradigm Humans State Detection Algorithms for each state Minimize involvement in routine tasks; employ for difficult cognitive tasks State of next model in hierarchy determines which algorithmic suite to use Can have multiple algorithms, possibly hierarchically arranged Play probability game to minimize costs of higher level reasoning; employ hierarchy of algorithmic approaches

Multi-level Processing Goal: construction of tree of (re-usable) algorithms and models relating physical structure of forest canopy to light levels on forest floor, and consequences for plant growth. Physical Model: –Fixed elements: trunks, major branches, topography (deterministic) –Variable elements: branches, leaves, sun position, clouds (statistical) Algorithmic Set: –Search algorithms to create maps of canopy and ground patterns; complexity and choice will vary spatially –Higher level reasoning to relate data to science question, determine model parameters (e.g., Bayes, rule-based, formal optimizations)

Physical Models Models apply at different levels of abstraction –Abstraction level(s) much match query Example: information from sources –Attenuation with distance from source –Statistical description (e.g., Correlations in time/space/transform domain, source and environmental dynamics) –Disk model –Statistical aggregations (e.g., flows on graph representing network) Model depends also on sensor data –Different statistics at different spatial scales and for different sensing modes –Data set affects number of viable hypotheses Feasibility depends on algorithmic availability –Need computationally effective suite

Model Uncertainty in Sensor Networks How much information is required to trust a model? Approach: information theoretic analysis of benefits of redundancy and auditing in model creation Will be backed up by simulations and experiments In how many locations must a field be sampled (by combination of static and mobile nodes) to determine it is caused by one (or more) point sources?

Data Integrity Multiple nodes observe source, exchange reputation information, and then interact with mobile audit node How can we trust the data produced by a sensor network? Approaches –Redundant deployment –Mobile auditors –Hybrid schemes Components –Reputation systems –Statistical analysis of information flows

Multi-scale sampling A homogeneous screen is placed to create a reflection Er proportional to incident light Ec. Camera captures the reflection on its CCD The image pixel intensity is transformed to Er using camera’s characteristic curve. Sensors with different modes and spatial resolutions –E.g. NIMS PAR sensor and camera –PAR measures local incident intensity –Camera measures relative reflected intensity Provides better spatial and temporal resolution, at cost of requiring careful calibration Analogous to remote sensing on local scales

Conclusion multi-layered systems provide major opportunities –Overall complexity can be significantly reduced, from both hardware and software perspective –Re-use of components in a variety of settings Multi-layered systems present many research challenges –Fundamental research questions in model construction, data and model uncertainty, information flows among layers, and large-scale systems design/optimization –Necessary to pursue mix of lab and field experiments to ensure realism in problems and generality of results