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Loveland, CO, United States

Calderon C.P.,Numerica Corporation
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics | Year: 2013

Several single-molecule studies aim to reliably extract parameters characterizing molecular confinement or transient kinetic trapping from experimental observations. Pioneering works from single-particle tracking (SPT) in membrane diffusion studies appealed to mean square displacement (MSD) tools for extracting diffusivity and other parameters quantifying the degree of confinement. More recently, the practical utility of systematically treating multiple noise sources (including noise induced by random photon counts) through likelihood techniques has been more broadly realized in the SPT community. However, bias induced by finite-time-series sample sizes (unavoidable in practice) has not received great attention. Mitigating parameter bias induced by finite sampling is important to any scientific endeavor aiming for high accuracy, but correcting for bias is also often an important step in the construction of optimal parameter estimates. In this article, it is demonstrated how a popular model of confinement can be corrected for finite-sample bias in situations where the underlying data exhibit Brownian diffusion and observations are measured with non-negligible experimental noise (e.g., noise induced by finite photon counts). The work of Tang and Chen is extended to correct for bias in the estimated "corral radius" (a parameter commonly used to quantify confinement in SPT studies) in the presence of measurement noise. It is shown that the approach presented is capable of reliably extracting the corral radius using only hundreds of discretely sampled observations in situations where other methods (including MSD and Bayesian techniques) would encounter serious difficulties. The ability to accurately statistically characterize transient confinement suggests additional techniques for quantifying confined and/or hop diffusion in complex environments. © 2013 American Physical Society. Source


Grant
Agency: Department of Defense | Branch: Navy | Program: SBIR | Phase: Phase II | Award Amount: 499.35K | Year: 2015

The Department of Defense (DoD) is supported by a vast global network of computers, sensors, and equipment that is continually at risk of being breached by adversaries. Such cyber elements comprise an important part of the DoDs military readiness and the loss or degradation of such elements would reduce key advantages in communication, intelligence, and organization. Despite heavy investments in security and cyber defense, the sheer ubiquity and interconnectedness of DoD equipment leave open the possibility of intrusion through a myriad of means including advanced persistent threats (APTs). Such threats take many forms, including Trojans, back-doors in embedded systems, worms, spear-phishing, and viruses, all of which could prove detrimental to the war fighter if not discovered. As part of our work we have demonstrated several novel ideas for detecting APTs based upon modern ideas in space-time signal processing, multiple hypothesis testing, and robust principal component analysis. In particular, previous results by Numerica have proven especially pertinent to APT detection since these algorithms have been demonstrated to scale to millions of data streams, can fuse data from a variety of input types, and have quite advantageous sparsity properties for visualization and analytics.


Grant
Agency: Department of Defense | Branch: Navy | Program: SBIR | Phase: Phase II | Award Amount: 749.99K | Year: 2014

U.S. intelligence, reconnaissance, and surveillance (ISR) platforms employ SIGINT sensors for target platform detection, identification and location. Many receivers are narrowband and are scanned over the RF spectrum (e.g., 2-18 GHz) in search of RF emitters of interest. With the rapid proliferation of RF technology, the signal spectrum has become complex and congested placing a burden on the SIGINT receiver to keep up with its surveillance and data processing requirements. However, the receiver must maintain a high probability of intercept for critical emitters. The objective of this SBIR topic was to develop methods for efficient SIGINT receiver data collection and processing. This proposed Phase II program will develop and demonstrate a mathematical optimization algorithm that will generate a receiver frequency band scan schedule that maximizes the receiver's resource usage. The solution is developed to specifically address the intercept of modern, agile emitters. An advanced software prototype that implements the optimization algorithm will be developed. Work is planned to integrate the software system with the ALQ-217 receiver. Demonstrations using representative scenarios will be used to compare the new scan schedule optimization algorithm with a baseline to assess the performance advantages.


Grant
Agency: Department of Defense | Branch: Missile Defense Agency | Program: SBIR | Phase: Phase I | Award Amount: 124.99K | Year: 2015

The performance of methods for track refinement from break-up events involving ballistic missiles may be degraded by certain unexpected off-nominal behaviors. For example, if the parent object is a rotating rigid body, it possesses rotational kinetic energy that could be released as translational kinetic energy during a separation event. The conversion of rotational energy to translational energy can result in unexpected velocities for the separation objects. To accommodate this off-nominal behavior in the track refinement procedure, we propose a solution founded on a model of the underlying physics of rotating bodies. The value of our approach will be demonstrated during the Phase I effort using Monte-Carlo simulations of off-nominal break-up events. Approved for Public Release 14-MDA-8047 (14 Nov 14)


Grant
Agency: Department of Defense | Branch: Air Force | Program: SBIR | Phase: Phase I | Award Amount: 150.00K | Year: 2015

ABSTRACT:The United States Air Force must increasingly provide supplies and munitions via airdrop to ground forces spread diffusely over large areas amid hostile enemy-held terrain. The calculation of the airdrop release point is crucial for ensuring safe and accurate delivery to designated landing sites. Wind and parafoil models have insufficient fidelity to accurately predict the landing location from a given release point. We propose a machine learning approach using Gaussian process regression to assimilate historical data of previous trajectories to more accurately learn the predicted landing locations. Having learned more accurately the mapping from release point to landing site, the optimal release point is then selected. Our approach then recalculates small adjustments to the aircraft navigation to achieve the optimal aircraft approach trajectory subject to constraints of a pre-specified flight corridor. The Gaussian process approach provides a unified holistic approach rigorous mathematical framework for probabilistic machine learning that allows the data to speak for itself while imposing very few assumptions. Moreover, we propose a Cramer-Rao bound analysis to determine if an improvement in air drop accuracy can indeed be supported by the data. BENEFIT:The proposed machine learning approach will allow the Air Force to utilize historical trajectory data to improve the accuracy of predicted airdrop landing locations. The process will ensure that supplies and munitions are delivered more accurately and with greater certainty leading to less waste and fewer payloads going astray into enemy held terrain. The approach also provides for optimal navigation updates for the delivery aircraft subject to constraints on terrain and designated safety corridors.The benefits are not restricted to military applications only the same approach will provide improved delivery of humanitarian aid and supplies throughout the world. Numericas intended commercialization is to integrate the approach into the existing Joint Program Airdrop System. Numerica will work with prime contractors and suppliers of airdrop equipment to commercialize the machine learning algorithms to improve commercial airdrop applications. Beyond airdrop applications, improved model predictions via machine learning meets an emerging need in many industries including cyber-security, air traffic safety, and civilian policing.

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