Blazar observations above 60 GeV: the Influence of CELESTE's Energy Scale on the Study of Flares and Spectra

The CELESTE atmospheric Cherenkov detector ran until June 2004. It has observed the blazars Mrk 421, 1ES 1426+428 and Mrk 501. We significantly improved our understanding of the atmosphere using a LIDAR, and of the optical throughput of the detector using stellar photometry. The new data analysis provides better background rejection. We present our light curve for Mrk 421 for the 2002-2004 season and a comparison with X-ray data and the 2004 observation of 1ES 1426+428. The new analysis will allow a more sensitive search for a signal from Mrk 501.Comment: 7 pages, 7 figures, proc. of the 35th COSPAR Scientific Assembly held in Paris, France, July 200

Modeling and Predicting Epidemic Spread: A Gaussian Process Regression Approach

Modeling and prediction of epidemic spread are critical to assist in policy-making for mitigation. Therefore, we present a new method based on Gaussian Process Regression to model and predict epidemics, and it quantifies prediction confidence through variance and high probability error bounds. Gaussian Process Regression excels in using small datasets and providing uncertainty bounds, and both of these properties are critical in modeling and predicting epidemic spreading processes with limited data. However, the derivation of formal uncertainty bounds remains lacking when using Gaussian Process Regression in the setting of epidemics, which limits its usefulness in guiding mitigation efforts. Therefore, in this work, we develop a novel bound on the variance of the prediction that quantifies the impact of the epidemic data on the predictions we make. Further, we develop a high probability error bound on the prediction, and we quantify how the epidemic spread, the infection data, and the length of the prediction horizon all affect this error bound. We also show that the error stays below a certain threshold based on the length of the prediction horizon. To illustrate this framework, we leverage Gaussian Process Regression to model and predict COVID-19 using real-world infection data from the United Kingdom

Adaptive Identification of SIS Models

Effective containment of spreading processes such as epidemics requires accurate knowledge of several key parameters that govern their dynamics. In this work, we first show that the problem of identifying the underlying parameters of epidemiological spreading processes is often ill-conditioned and lacks the persistence of excitation required for the convergence of adaptive learning schemes. To tackle this challenge, we leverage a relaxed property called initial excitation combined with a recursive least squares algorithm to design an online adaptive identifier to learn the parameters of the susceptible-infected-susceptible (SIS) epidemic model from the knowledge of its states. We prove that the iterates generated by the proposed algorithm minimize an auxiliary weighted least squares cost function. We illustrate the convergence of the error of the estimated epidemic parameters via several numerical case studies and compare it with results obtained using conventional approaches

Feedback Design for Devising Optimal Epidemic Control Policies

For reliable epidemic monitoring and control, this paper proposes a feedback mechanism design to effectively cope with data and model uncertainties. Using past epidemiological data, we describe methods to estimate the parameters of general epidemic models. Because the data could be noisy, the estimated parameters may not be accurate. Therefore, under uncertain parameters and noisy measurements, we provide an observer design method for robust state estimation. Then, using the estimated model and state, we devise optimal control policies by minimizing a predicted cost functional. Finally, the effectiveness of the proposed method is demonstrated through its implementation on a modified SIR epidemic model