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At least 307 records · Page 17

A Markovian model for assessment of personnel hiring plans

As a result of the current economic environment, many organizations are having to operate with fewer resources. In the manpower area, these constraints have forced organizations to operate within well-defined hiring plans. Exceeding personnel ceilings is in most cases an intolerable situation. A mathematical model, based on the theory of Markov processes, is presented which can be used to assess the chances of success of personnel hiring plans. The model considers a plan to be successful if the final population size, at the end of the planning period, lies within a range specified by management. Although this model was developed to assess personnel hiring plans at the Goddard Space Flight Center, it is directly applicable wherever personnel hiring plans are used.

Katz, L. G.↗

Mapping the Milky Way Galaxy with LISA

Gravitational wave detectors in the mHz band (such as the Laser Interferometer Space Antenna, or LISA) will observe thousands of compact binaries in the galaxy which can be used to better understand the structure of the Milky Way. To test the effectiveness of LISA to measure the distribution of the galaxy, we simulated the Close White Dwarf Binary (CWDB) gravitational wave sky using different models for the Milky Way. To do so, we have developed a galaxy density distribution modeling code based on the Markov Chain Monte Carlo method. The code uses different distributions to construct realizations of the galaxy. We then use the Fisher Information Matrix to estimate the variance and covariance of the recovered parameters for each detected CWDB. This is the first step toward characterizing the capabilities of space-based gravitational wave detectors to constrain models for galactic structure, such as the size and orientation of the bar in the center of the Milky Way

McKinnon, Jose A.↗

Improved image decompression for reduced transform coding artifacts

The perceived quality of images reconstructed from low bit rate compression is severely degraded by the appearance of transform coding artifacts. This paper proposes a method for producing higher quality reconstructed images based on a stochastic model for the image data. Quantization (scalar or vector) partitions the transform coefficient space and maps all points in a partition cell to a representative reconstruction point, usually taken as the centroid of the cell. The proposed image estimation technique selects the reconstruction point within the quantization partition cell which results in a reconstructed image which best fits a non-Gaussian Markov random field (MRF) image model. This approach results in a convex constrained optimization problem which can be solved iteratively. At each iteration, the gradient projection method is used to update the estimate based on the image model. In the transform domain, the resulting coefficient reconstruction points are projected to the particular quantization partition cells defined by the compressed image. Experimental results will be shown for images compressed using scalar quantization of block DCT and using vector quantization of subband wavelet transform. The proposed image decompression provides a reconstructed image with reduced visibility of transform coding artifacts and superior perceived quality.

Orourke, Thomas P.↗

Optimal maintenance center inventories for fault-tolerant repairable systems

A probabilistic approach is taken to determine the optimal repairable parts inventory for a maintenance center, servicing machines which contain several m-out-of-n systems of different parts, with a constraint on the total inventory investment. A model, based on the discrete Markov process, accounts for a typical ultrareliable avionics system, such as one presently being developed by NASA. The dynamic programming algorithm for minimizing the stockout and holding costs is applied to an exemplary maintenance center, and solutions for single-item and multi-item cases are given. The computational burden is noted to be reasonable and a computer program is used to generate optimal solutions.

Lawrence, S. H.↗

Stochastic charging of dust grains in planetary rings: Diffusion rates and their effects on Lorentz resonances

Dust grains in planetary rings acquire stochastically fluctuating electric charges as they orbit through any corotating magnetospheric plasma. Here we investigate the nature of this stochastic charging and calculate its effect on the Lorentz resonance (LR). First we model grain charging as a Markov process, where the transition probabilities are identified as the ensemble-averaged charging fluxes due to plasma pickup and photoemission. We determine the distribution function P(t;N), giving the probability that a grain has N excess charges at time t. The autocorrelation function tau(sub q) for the strochastic charge process can be approximated by a Fokker-Planck treatment of the evolution equations for P(t; N). We calculate the mean square response to the stochastic fluctuations in the Lorentz force. We find that transport in phase space is very small compared to the resonant increase in amplitudes due to the mean charge, over the timescale that the oscillator is resonantly pumped up. Therefore the stochastic charge variations cannot break the resonant interaction; locally, the Lorentz resonance is a robust mechanism for the shaping of etheral dust ring systems. Slightly stronger bounds on plasma parameters are required when we consider the longer transit times between Lorentz resonances.

Schaffer, L.↗

MMPP Traffic Generator for the Testing of the SCAR 2 Fast Packet Switch

A prototype MWP Traffic Generator (TG) has been designed for testing of the COMSAT-supplied SCAR II Fast Packet Switch. By generating packets distributed according to a Markov-Modulated Poisson Process (MMPP) model. it allows the assessment of the switch performance under traffic conditions that are more realistic than could be generated using the COMSAT-supplied Traffic Generator Module. The MMPP model is widely believed to model accurately real-world superimposed voice and data communications traffic. The TG was designed to be as much as possible of a "drop-in" replacement for the COMSAT Traffic Generator Module. The latter fit on two Altera EPM7256EGC 192-pin CPLDs and produced traffic for one switch input port. No board changes are necessary because it has been partitioned to use the existing board traces. The TG, consisting of parts "TGDATPROC" and "TGRAMCTL" must merely be reprogrammed into the Altera devices of the same name. However, the 040 controller software must be modified to provide TG initialization data. This data will be given in Section II.

Chren, William A., Jr.↗

Use of Inverse Reinforcement Learning for Identity Prediction

We adopt Markov Decision Processes (MDP) to model sequential decision problems, which have the characteristic that the current decision made by a human decision maker has an uncertain impact on future opportunity. We hypothesize that the individuality of decision makers can be modeled as differences in the reward function under a common MDP model. A machine learning technique, Inverse Reinforcement Learning (IRL), was used to learn an individual's reward function based on limited observation of his or her decision choices. This work serves as an initial investigation for using IRL to analyze decision making, conducted through a human experiment in a cyber shopping environment. Specifically, the ability to determine the demographic identity of users is conducted through prediction analysis and supervised learning. The results show that IRL can be used to correctly identify participants, at a rate of 68% for gender and 66% for one of three college major categories.

Hayes, Roy↗

The Photochemical Reflectance Index from Directional Cornfield Reflectances: Observations and Simulations

The two-layer Markov chain Analytical Canopy Reflectance Model (ACRM) was linked with in situ hyperspectral leaf optical properties to simulate the Photochemical Reflectance Index (PRI) for a corn crop canopy at three different growth stages. This is an extended study after a successful demonstration of PRI simulations for a cornfield previously conducted at an early vegetative growth stage. Consistent with previous in situ studies, sunlit leaves exhibited lower PRI values than shaded leaves. Since sunlit (shaded) foliage dominates the canopy in the reflectance hotspot (coldspot), the canopy PRI derived from field hyperspectral observations displayed sensitivity to both view zenith angle and relative azimuth angle at all growth stages. Consequently, sunlit and shaded canopy sectors were most differentiated when viewed along the azimuth matching the solar principal plane. These directional PRI responses associated with sunlit/shaded foliage were successfully reproduced by the ACRM. As before, the simulated PRI values from the current study were closer to in situ values when both sunlit and shaded leaves were utilized as model input data in a two-layer mode, instead of a one-layer mode with sunlit leaves only. Model performance as judged by correlation between in situ and simulated values was strongest for the mature corn crop (r = 0.87, RMSE = 0.0048), followed by the early vegetative stage (r = 0.78; RMSE = 0.0051) and the early senescent stage (r = 0.65; RMSE = 0.0104). Since the benefit of including shaded leaves in the scheme varied across different growth stages, a further analysis was conducted to investigate how variable fractions of sunlit/shaded leaves affect the canopy PRI values expected for a cornfield, with implications for 20 remote sensing monitoring options. Simulations of the sunlit to shaded canopy ratio near 50/50 +/- 10 (e.g., 60/40) matching field observations at all growth stages were examined. Our results suggest in the importance of the sunlit/shaded fraction and canopy structure in understanding and interpreting PRI.

Cheng, Yen-Ben↗

Deep Space Optical Link ARQ Performance Analysis

Substantial advancements have been made toward the use of optical communications for deep space exploration missions, promising a much higher volume of data to be communicated in comparison with present -day Radio Frequency (RF) based systems. One or more ground-based optical terminals are assumed to communicate with the spacecraft. Both short-term and long-term link outages will arise due to weather at the ground station(s), space platform pointing stability, and other effects. To mitigate these outages, an Automatic Repeat Query (ARQ) retransmission method is assumed, together with a reliable back channel for acknowledgement traffic. Specifically, the Licklider Transmission Protocol (LTP) is used, which is a component of the Disruption-Tolerant Networking (DTN) protocol suite that is well suited for high bandwidth-delay product links subject to disruptions. We provide an analysis of envisioned deep space mission scenarios and quantify buffering, latency and throughput performance, using a simulation in which long-term weather effects are modeled with a Gilbert -Elliot Markov chain, short-term outages occur as a Bernoulli process, and scheduled outages arising from geometric visibility or operational constraints are represented. We find that both short- and long-term effects impact throughput, but long-term weather effects dominate buffer sizing and overflow losses as well as latency performance.

optical space communications↗

Energy-Optimized Path Planning for Uas in Varying Winds Via Reinforcement Learning

In this paper we propose a reinforcement learning (RL) algorithm for path planning of Unmanned Aviation Vehicles (UAVs) under varying wind conditions. Solutions to UAV path planning problems are becoming increasingly necessary as autonomous UAVs continue to enter commercial and government spaces. Path-planning is inherently challenging, as UAVs need to account for dynamically changing flying conditions such as weather, obstacle or no-fly zones, degraded vehicle health, and off-nominal battery power consumption. Machine learning methods such as reinforcement learning (RL) have the potential to revolutionize how vehicles navigate in such uncertain environments. In this study, we compute UAV trajectories from a pre-determined starting position to a target cell within a 7X7 grid environment by optimizing parameters for mission assurance and safety limits in addition to the energy consumption and operation time. The UAV navigates the grid by taking actions to move in any of the eight cardinal and inter-cardinal directions, under constant thrust profile. The resultant UAV state is sampled from a probability distribution which accounts for the UAV’s action, local wind velocity, and the presence of obstacles or boundaries. As the unmanned airspace gets more complex due to multiple vehicles and environmental uncertainties, trade-offs between energy consumption, operation time, risk tolerance, and mission assurance need to be made. Our Markov Decision Process (MDP) environment model can capture any combination of these in the optimization objective, making it novel compared to other work in the field.

trajectory planning↗

Semi-Markov Unreliability Range Evaluator

Semi-Markov Unreliability Range Evaluator, SURE, computer program is software tool for analysis of reconfigurable, fault-tolerant systems. Traditional reliability analyses based on aggregates of fault-handling and fault-occurrence models. SURE provides efficient means for calculating accurate upper and lower bounds for probabilities of death states for large class of semi-Markov mathematical models, and not merely those reduced to critical-pair architectures.

Butler, Ricky W.↗

Wheat forecast economics effect study

A model to assess the value of improved information regarding the inventories, productions, exports, and imports of crop on a worldwide basis is discussed. A previously proposed model is interpreted in a stochastic control setting and the underlying assumptions of the model are revealed. In solving the stochastic optimization problem, the Markov programming approach is much more powerful and exact as compared to the dynamic programming-simulation approach of the original model. The convergence of a dual variable Markov programming algorithm is shown to be fast and efficient. A computer program for the general model of multicountry-multiperiod is developed. As an example, the case of one country-two periods is treated and the results are presented in detail. A comparison with the original model results reveals certain interesting aspects of the algorithms and the dependence of the value of information on the incremental cost function.

Mehra, R. K.↗

Probabilistic Calibration of Expensive Models using Efficiently Trained Surrogates

Calibration of computational models in the presence of uncertainty is often cast as a Bayesian inference problem and solved via sampling methods, e.g., Markov chain Monte Carlo. When the computational model is expensive, this task becomes intractable due to the large number of samples required to accurately estimate the posterior distribution of the calibration parameters. A popular solution to this problem is to use machine learning to develop a faster-to-evaluate, lower-fidelity substitute for the original model to serve as a surrogate while solving the inference problem. Although considered an offline cost, generating training data to construct this surrogate model can still be an expensive task in practice. An active learning algorithm is presented that focuses training on improving surrogate accuracy specifically in and around the bulk of the posterior distribution, as this is where the model is exercised during calibration. Candidate samples are drawn from families of distributions related to an approximation of the posterior. The sample maximizing predictive variance is then selected for evaluation by the original computational model, yielding a label for the training point. Iterating this approach increases efficiency relative to space filling designs (e.g., Latin hypercube sampling) by avoiding low probability points. Practical considerations are discussed, including the benefits of using a sequential Monte Carlo sampling approach, convergence heuristics, and the importance of both exploration and exploitation given that the true posterior is unknown a priori.

uncertainty quantification↗

Estimating the Properties of Hard X-Ray Solar Flares by Constraining Model Parameters

We wish to better constrain the properties of solar flares by exploring how parameterized models of solar flares interact with uncertainty estimation methods. We compare four different methods of calculating uncertainty estimates in fitting parameterized models to Ramaty High Energy Solar Spectroscopic Imager X-ray spectra, considering only statistical sources of error. Three of the four methods are based on estimating the scale-size of the minimum in a hypersurface formed by the weighted sum of the squares of the differences between the model fit and the data as a function of the fit parameters, and are implemented as commonly practiced. The fourth method is also based on the difference between the data and the model, but instead uses Bayesian data analysis and Markov chain Monte Carlo (MCMC) techniques to calculate an uncertainty estimate. Two flare spectra are modeled: one from the Geostationary Operational Environmental Satellite X1.3 class flare of 2005 January 19, and the other from the X4.8 flare of 2002 July 23.We find that the four methods give approximately the same uncertainty estimates for the 2005 January 19 spectral fit parameters, but lead to very different uncertainty estimates for the 2002 July 23 spectral fit. This is because each method implements different analyses of the hypersurface, yielding method-dependent results that can differ greatly depending on the shape of the hypersurface. The hypersurface arising from the 2005 January 19 analysis is consistent with a normal distribution; therefore, the assumptions behind the three non- Bayesian uncertainty estimation methods are satisfied and similar estimates are found. The 2002 July 23 analysis shows that the hypersurface is not consistent with a normal distribution, indicating that the assumptions behind the three non-Bayesian uncertainty estimation methods are not satisfied, leading to differing estimates of the uncertainty. We find that the shape of the hypersurface is crucial in understanding the output from each uncertainty estimation technique, and that a crucial factor determining the shape of hypersurface is the location of the low-energy cutoff relative to energies where the thermal emission dominates. The Bayesian/MCMC approach also allows us to provide detailed information on probable values of the low-energy cutoff, Ec, a crucial parameter in defining the energy content of the flare-accelerated electrons. We show that for the 2002 July 23 flare data, there is a 95% probability that Ec lies below approximately 40 keV, and a 68% probability that it lies in the range 7-36 keV. Further, the low-energy cutoff is more likely to be in the range 25-35 keV than in any other 10 keV wide energy range. The low-energy cutoff for the 2005 January 19 flare is more tightly constrained to 107 +/- 4 keV with 68% probability.

X-rays↗

Spectral Bio-indicator Simulations for Tracking Photosynthetic Activities in a Corn Field

Accurate assessment of vegetation canopy optical properties plays a critical role in monitoring natural and managed ecosystems under environmental changes. In this context, radiative transfer (RT) models simulating vegetation canopy reflectance have been demonstrated to be a powerful tool for understanding and estimating spectral bio-indicators. In this study, two narrow band spectroradiometers were utilized to acquire observations over corn canopies for two summers. These in situ spectral data were then used to validate a two-layer Markov chain-based canopy reflectance model for simulating the Photochemical Reflectance Index (PRI), which has been widely used in recent vegetation photosynthetic light use efficiency (LUE) studies. The in situ PRI derived from narrow band hyperspectral reflectance exhibited clear responses to: 1) viewing geometry which affects the asset of light environment; and 2) seasonal variation corresponding to the growth stage. The RT model (ACRM) successfully simulated the responses to the variable viewing geometry. The best simulations were obtained when the model was set to run in the two layer mode using the sunlit leaves as the upper layer and shaded leaves as the lower layer. Simulated PRI values yielded much better correlations to in situ observations when the cornfield was dominated by green foliage during the early growth, vegetative and reproductive stages (r = 0.78 to 0.86) than in the later senescent stage (r = 0.65). Further sensitivity analyses were conducted to show the important influences of leaf area index (LAI) and the sunlit/shaded ratio on PRI observations.

Cheng, Yen-Ben↗

Discrete Deterministic and Stochastic Petri Nets

Petri nets augmented with timing specifications gained a wide acceptance in the area of performance and reliability evaluation of complex systems exhibiting concurrency, synchronization, and conflicts. The state space of time-extended Petri nets is mapped onto its basic underlying stochastic process, which can be shown to be Markovian under the assumption of exponentially distributed firing times. The integration of exponentially and non-exponentially distributed timing is still one of the major problems for the analysis and was first attacked for continuous time Petri nets at the cost of structural or analytical restrictions. We propose a discrete deterministic and stochastic Petri net (DDSPN) formalism with no imposed structural or analytical restrictions where transitions can fire either in zero time or according to arbitrary firing times that can be represented as the time to absorption in a finite absorbing discrete time Markov chain (DTMC). Exponentially distributed firing times are then approximated arbitrarily well by geometric distributions. Deterministic firing times are a special case of the geometric distribution. The underlying stochastic process of a DDSPN is then also a DTMC, from which the transient and stationary solution can be obtained by standard techniques. A comprehensive algorithm and some state space reduction techniques for the analysis of DDSPNs are presented comprising the automatic detection of conflicts and confusions, which removes a major obstacle for the analysis of discrete time models.

MATHEMATICAL MODELS↗