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1. Title: Erasures and Recovery: Optimal K-Dual Frames in Redundant Systems
1. Title: Erasures and Recovery: Optimal K-Dual Frames in Redundant Systems
[Paper ID: ICPAM-DS-26-AM0001]
[Paper ID: ICPAM-DS-26-AM0001]
Presenter: Shankhadeep Mondal (Joint work with Dr. Deguang Han and Dr. R. N. Mohapatra)
Presenter: Shankhadeep Mondal (Joint work with Dr. Deguang Han and Dr. R. N. Mohapatra)
Abstract: Frames provide redundant representations that are inherently robust to data loss, making them fundamental tools in signal processing and related applications. In practical transmission systems, however, the loss of frame coefficients—known as erasures—can significantly affect reconstruction accuracy. This talk investigates optimal reconstruction strategies for K-frames in the presence of erasures, where reconstruction is constrained to the range of a bounded linear operator K. We introduce and analyze optimal K-dual frames and K-dual pairs under deterministic and probabilistic erasure models. Optimality is measured using operator-theoretic quantities, including the operator norm and the spectral radius of the associated error operators. For single and multiple erasures, we characterize when a K-dual minimizes the worst-case reconstruction error and identify conditions under which the canonical K-dual is optimal or uniquely optimal. In addition, we introduce the notions of uniform and higher-order uniform K-dual pairs, which play a key role in spectral optimality for multiple erasures. Explicit bounds for recon struction error are derived in terms of trace and spectral data of the operator K, and examples are provided to illustrate both uniqueness and non-uniqueness phenomena. These results extend classical frame-theoretic robustness principles to the broader setting of K-frames and provide a unified framework for stable reconstruction under structured data loss.
Abstract: Frames provide redundant representations that are inherently robust to data loss, making them fundamental tools in signal processing and related applications. In practical transmission systems, however, the loss of frame coefficients—known as erasures—can significantly affect reconstruction accuracy. This talk investigates optimal reconstruction strategies for K-frames in the presence of erasures, where reconstruction is constrained to the range of a bounded linear operator K. We introduce and analyze optimal K-dual frames and K-dual pairs under deterministic and probabilistic erasure models. Optimality is measured using operator-theoretic quantities, including the operator norm and the spectral radius of the associated error operators. For single and multiple erasures, we characterize when a K-dual minimizes the worst-case reconstruction error and identify conditions under which the canonical K-dual is optimal or uniquely optimal. In addition, we introduce the notions of uniform and higher-order uniform K-dual pairs, which play a key role in spectral optimality for multiple erasures. Explicit bounds for recon struction error are derived in terms of trace and spectral data of the operator K, and examples are provided to illustrate both uniqueness and non-uniqueness phenomena. These results extend classical frame-theoretic robustness principles to the broader setting of K-frames and provide a unified framework for stable reconstruction under structured data loss.
2. Title: Dynamics of a two-stage epidemiological model with post-infection mortality and transmission heterogeneity
2. Title: Dynamics of a two-stage epidemiological model with post-infection mortality and transmission heterogeneity
[Paper ID: ICPAM-DS-26-AM0002]
[Paper ID: ICPAM-DS-26-AM0002]
Presenter: B Sagar Email: b.sagar@ucf.edu Co-Author: Zhisheng Shuai
Presenter: B Sagar Email: b.sagar@ucf.edu Co-Author: Zhisheng Shuai
School of Data, Mathematical, and Statistical Sciences, University of Central Florida, Orlando, FL. 32826
School of Data, Mathematical, and Statistical Sciences, University of Central Florida, Orlando, FL. 32826
Abstract: We formulate a two-stage epidemiological model that incorporates key post-infection features, including reinfection and post-infection mortality (PIM). The model emphasizes the role of transmission heterogeneity in shaping disease dynamics, influencing both endemic levels and oscillatory behaviors. Numerical simulations show that late-stage hyper-infectivity leads to higher endemic infection levels with long-period oscillations, while early-stage hyper-infectivity results in lower infection levels with shorter-period oscillations.
Abstract: We formulate a two-stage epidemiological model that incorporates key post-infection features, including reinfection and post-infection mortality (PIM). The model emphasizes the role of transmission heterogeneity in shaping disease dynamics, influencing both endemic levels and oscillatory behaviors. Numerical simulations show that late-stage hyper-infectivity leads to higher endemic infection levels with long-period oscillations, while early-stage hyper-infectivity results in lower infection levels with shorter-period oscillations.
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