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Mean-Field-Type Game Theory with Rosenblatt Noise
Authors:
Hamidou Tembine,
Tyrone E. Duncan,
Bozenna Pasik-Duncan
Abstract:
We study the integration of Rosenblatt noise into stochastic systems, control theory, and mean-field-type game theory, addressing the limitations of traditional Gaussian and Markovian models. Empirical evidence from various domains, including water demand, e-commerce, power grid operations, wireless channels, and agricultural supply chains, demonstrates the prevalence of non-Gaussian characteristi…
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We study the integration of Rosenblatt noise into stochastic systems, control theory, and mean-field-type game theory, addressing the limitations of traditional Gaussian and Markovian models. Empirical evidence from various domains, including water demand, e-commerce, power grid operations, wireless channels, and agricultural supply chains, demonstrates the prevalence of non-Gaussian characteristics such as skews, heavy tails and strong long-range dependencies. The Rosenblatt process, a non-Gaussian non-Markovian, self-similar process, offers a baseline framework for capturing some the behaviors observed in real data. We develop novel stochastic calculus formulas for Rosenblatt processes, apply these to dynamical systems, and analyze optimal control problems, revealing the suboptimality of traditional noise approximation methods. We extend game-theoretic analysis to environments driven by Rosenblatt noise, establishing conditions for saddle-point equilibria in zero-sum games and identifying state-feedback Nash equilibria in non-zero-sum games. Our findings underscore the importance of incorporating non-Gaussian noise into predictive analytics and control strategies, enhancing the accuracy and robustness of models in real-world applications. These findings represent a significant advancement in mean-field-type game theory with variance-awareness, offering new insights and tools for managing interactive systems influenced by Rosenblatt noise.
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Submitted 29 May, 2025;
originally announced June 2025.
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Rapid Automated Mapping of Clouds on Titan With Instance Segmentation
Authors:
Zachary Yahn,
Douglas M Trent,
Ethan Duncan,
Benoît Seignovert,
John Santerre,
Conor Nixon
Abstract:
Despite widespread adoption of deep learning models to address a variety of computer vision tasks, planetary science has yet to see extensive utilization of such tools to address its unique problems. On Titan, the largest moon of Saturn, tracking seasonal trends and weather patterns of clouds provides crucial insights into one of the most complex climates in the Solar System, yet much of the avail…
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Despite widespread adoption of deep learning models to address a variety of computer vision tasks, planetary science has yet to see extensive utilization of such tools to address its unique problems. On Titan, the largest moon of Saturn, tracking seasonal trends and weather patterns of clouds provides crucial insights into one of the most complex climates in the Solar System, yet much of the available image data are still analyzed in a conventional way. In this work, we apply a Mask R-CNN trained via transfer learning to perform instance segmentation of clouds in Titan images acquired by the Cassini spacecraft - a previously unexplored approach to a big data problem in planetary science. We demonstrate that an automated technique can provide quantitative measures for clouds, such as areas and centroids, that may otherwise be prohibitively time-intensive to produce by human mapping. Furthermore, despite Titan specific challenges, our approach yields accuracy comparable to contemporary cloud identification studies on Earth and other worlds. We compare the efficiencies of human-driven versus algorithmic approaches, showing that transfer learning provides speed-ups that may open new horizons for data investigation for Titan. Moreover, we suggest that such approaches have broad potential for application to similar problems in planetary science where they are currently under-utilized. Future planned missions to the planets and remote sensing initiatives for the Earth promise to provide a deluge of image data in the coming years that will benefit strongly from leveraging machine learning approaches to perform the analysis.
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Submitted 8 January, 2025;
originally announced January 2025.
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Feature Extraction and Classification from Planetary Science Datasets enabled by Machine Learning
Authors:
Conor Nixon,
Zachary Yahn,
Ethan Duncan,
Ian Neidel,
Alyssa Mills,
Benoît Seignovert,
Andrew Larsen,
Kathryn Gansler,
Charles Liles,
Catherine Walker,
Douglas Trent,
John Santerre
Abstract:
In this paper we present two examples of recent investigations that we have undertaken, applying Machine Learning (ML) neural networks (NN) to image datasets from outer planet missions to achieve feature recognition. Our first investigation was to recognize ice blocks (also known as rafts, plates, polygons) in the chaos regions of fractured ice on Europa. We used a transfer learning approach, addi…
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In this paper we present two examples of recent investigations that we have undertaken, applying Machine Learning (ML) neural networks (NN) to image datasets from outer planet missions to achieve feature recognition. Our first investigation was to recognize ice blocks (also known as rafts, plates, polygons) in the chaos regions of fractured ice on Europa. We used a transfer learning approach, adding and training new layers to an industry-standard Mask R-CNN (Region-based Convolutional Neural Network) to recognize labeled blocks in a training dataset. Subsequently, the updated model was tested against a new dataset, achieving 68% precision. In a different application, we applied the Mask R-CNN to recognize clouds on Titan, again through updated training followed by testing against new data, with a precision of 95% over 369 images. We evaluate the relative successes of our techniques and suggest how training and recognition could be further improved. The new approaches we have used for planetary datasets can further be applied to similar recognition tasks on other planets, including Earth. For imagery of outer planets in particular, the technique holds the possibility of greatly reducing the volume of returned data, via onboard identification of the most interesting image subsets, or by returning only differential data (images where changes have occurred) greatly enhancing the information content of the final data stream.
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Submitted 26 October, 2023;
originally announced October 2023.
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Communication Layer Security in Smart Farming: A Survey on Wireless Technologies
Authors:
Hossein Mohammadi Rouzbahani,
Hadis Karimipour,
Evan Fraser,
Ali Dehghantanha,
Emily Duncan,
Arthur Green,
Conchobhair Russell
Abstract:
Human population growth has driven rising demand for food that has, in turn, imposed huge impacts on the environment. In an effort to reconcile our need to produce more sustenance while also protecting the ecosystems of the world, farming is becoming more reliant on smart tools and communication technologies. Developing a smart farming framework allows farmers to make more efficient use of inputs,…
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Human population growth has driven rising demand for food that has, in turn, imposed huge impacts on the environment. In an effort to reconcile our need to produce more sustenance while also protecting the ecosystems of the world, farming is becoming more reliant on smart tools and communication technologies. Developing a smart farming framework allows farmers to make more efficient use of inputs, thus protecting water quality and biodiversity habitat. Internet of Things (IoT), which has revolutionized every sphere of the economy, is being applied to agriculture by connecting on-farm devices and providing real-time monitoring of everything from environmental conditions to market signals through to animal health data. However, utilizing IoT means farming networks are now vulnerable to malicious activities, mostly when wireless communications are highly employed. With that in mind, this research aims to review different utilized communication technologies in smart farming. Moreover, possible cyber attacks are investigated to discover the vulnerabilities of communication technologies considering the most frequent cyber-attacks that have been happened.
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Submitted 3 March, 2022;
originally announced March 2022.
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Matrix-Valued Mean-Field-Type Games: Risk-Sensitive, Adversarial, and Risk-Neutral Linear-Quadratic Case
Authors:
Julian Barreiro-Gomez,
Tyrone E. Duncan,
Hamidou Tembine
Abstract:
In this paper we study a class of matrix-valued linear-quadratic mean-field-type games for both the risk-neutral, risk-sensitive and robust cases. Non-cooperation, full cooperation and adversarial between teams are treated. We provide a semi-explicit solution for both problems by means of a direct method. The state dynamics is described by a matrix-valued linear jump-diffusion-regime switching sys…
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In this paper we study a class of matrix-valued linear-quadratic mean-field-type games for both the risk-neutral, risk-sensitive and robust cases. Non-cooperation, full cooperation and adversarial between teams are treated. We provide a semi-explicit solution for both problems by means of a direct method. The state dynamics is described by a matrix-valued linear jump-diffusion-regime switching system of conditional mean-field type where the conditioning is with respect to common noise which is a regime switching process. The optimal strategies are in a state-and-conditional mean-field feedback form. Semi-explicit solutions of equilibrium costs and strategies are also provided for the full cooperative, adversarial teams, risk-sensitive full cooperative and risk-sensitive adversarial team cases. It is shown that full cooperation increases the well-posedness domain under risk-sensitive decision-makers by means of population risk-sharing. Finally, relationship between risk-sensitivity and robustness are established in the mean-field type context.
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Submitted 5 June, 2019; v1 submitted 23 April, 2019;
originally announced April 2019.
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Semi-Explicit Solutions to some Non-Linear Non-Quadratic Mean-Field-Type Games: A Direct Method
Authors:
Julian Barreiro-Gomez,
Tyrone E. Duncan,
Bozenna Pasik-Duncan,
Hamidou Tembine
Abstract:
This article examines mean-field-type game problems by means of a direct method. We provide various solvable examples beyond the classical linear-quadratic game problems. These include quadratic-quadratic games and games with power, logarithmic, sine square, hyperbolic sine square payoffs. Non-linear state dynamics such as log-state, control-dependent regime switching, quadratic state, cotangent s…
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This article examines mean-field-type game problems by means of a direct method. We provide various solvable examples beyond the classical linear-quadratic game problems. These include quadratic-quadratic games and games with power, logarithmic, sine square, hyperbolic sine square payoffs. Non-linear state dynamics such as log-state, control-dependent regime switching, quadratic state, cotangent state and hyperbolic cotangent state are considered. We identify equilibrium strategies and equilibrium payoffs in state-and-conditional mean-field type feedback form. It is shown that a simple direct method can be used to solve broader classes of non-quadratic mean-field-type games under jump-diffusion-regime switching Gauss-Volterra processes which include fractional Brownian motions and multi-fractional Brownian motions. We provide semi-explicit solutions to the fully cooperative, noncooperative nonzero-sum, and adversarial game problems.
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Submitted 21 April, 2019; v1 submitted 17 December, 2018;
originally announced December 2018.
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Segmenting root systems in X-ray computed tomography images using level sets
Authors:
Amy Tabb,
Keith E. Duncan,
Christopher N. Topp
Abstract:
The segmentation of plant roots from soil and other growing media in X-ray computed tomography images is needed to effectively study the root system architecture without excavation. However, segmentation is a challenging problem in this context because the root and non-root regions share similar features. In this paper, we describe a method based on level sets and specifically adapted for this seg…
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The segmentation of plant roots from soil and other growing media in X-ray computed tomography images is needed to effectively study the root system architecture without excavation. However, segmentation is a challenging problem in this context because the root and non-root regions share similar features. In this paper, we describe a method based on level sets and specifically adapted for this segmentation problem. In particular, we deal with the issues of using a level sets approach on large image volumes for root segmentation, and track active regions of the front using an occupancy grid. This method allows for straightforward modifications to a narrow-band algorithm such that excessive forward and backward movements of the front can be avoided, distance map computations in a narrow band context can be done in linear time through modification of Meijster et al.'s distance transform algorithm, and regions of the image volume are iteratively used to estimate distributions for root versus non-root classes. Results are shown of three plant species of different maturity levels, grown in three different media. Our method compares favorably to a state-of-the-art method for root segmentation in X-ray CT image volumes.
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Submitted 17 September, 2018;
originally announced September 2018.