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2026-01-16 (Piątek)
Zapraszamy do sali 1.02, ul. Pasteura 5 o godzinie 12:15 
Masaru Hitomi (Tohoku University, Japan)Statistical-Mechanical Analysis of Typical Performance in the Maximum Entropy Method
The Maximum Entropy Method (MEM) is a reconstruction technique that utilizes prior information known as the default model to infer the true data from observed data. Since its proposal in the context of geology [1], this method has been successfully applied across a wide range of fields, including astronomy, computational physics, signal processing, and linguistics [2, 3].In recent years, however, estimation methods that focus on the sparsity of data, such as sparse estimation and compressed sensing[4], have gained attention and are being increasingly applied in various disciplines. These methods, particularly in the context of statistical mechanics, benefit from the replica method, which provides theoretical guarantees for the accuracy of their estimates.
In contrast, MEM, despite its long history and broad applicability, has been empirically known to depend on the choice of the default model for reconstruction. However, its reconstruction accuracy has not been systematically evaluated.
In this talk, I will reveal how the reconstruction accuracy of MEM depends on the default model using a statistical mechanics approach [5]. I show that, for certain default models, a phase transition occurs between successful and unsuccessful reconstructions. Furthermore, by comparing MEM with other reconstruction methods, I also discuss the limitations and potential of MEM in practical applications.
Finally, I will briefly introduce my previous research on large-angle twisted bilayer graphene, which forms the background of my work, and outline several topics I would like to explore during my stay in Warszawa.
[1] J. P. Burg, 37th Annual International Meeting, Soc. of Explor. Geophys. 31 (1967).
[2] R. T. Lacoss, Geophysics 36 881-675 (1971).
[3] R. N. Silver, D. S. Silia, J. E. Gubernatis, Phys. Rev. B 411 2380 (1990).
[4] D. Donoho, IEEE Trans. on Inf. Theo. 52 1289 (2006).
[5] M. Hitomi, M. Ohzeki, Phys. Rev. Research 7 04309 (2925).
In contrast, MEM, despite its long history and broad applicability, has been empirically known to depend on the choice of the default model for reconstruction. However, its reconstruction accuracy has not been systematically evaluated.
In this talk, I will reveal how the reconstruction accuracy of MEM depends on the default model using a statistical mechanics approach [5]. I show that, for certain default models, a phase transition occurs between successful and unsuccessful reconstructions. Furthermore, by comparing MEM with other reconstruction methods, I also discuss the limitations and potential of MEM in practical applications.
Finally, I will briefly introduce my previous research on large-angle twisted bilayer graphene, which forms the background of my work, and outline several topics I would like to explore during my stay in Warszawa.
[1] J. P. Burg, 37th Annual International Meeting, Soc. of Explor. Geophys. 31 (1967).
[2] R. T. Lacoss, Geophysics 36 881-675 (1971).
[3] R. N. Silver, D. S. Silia, J. E. Gubernatis, Phys. Rev. B 411 2380 (1990).
[4] D. Donoho, IEEE Trans. on Inf. Theo. 52 1289 (2006).
[5] M. Hitomi, M. Ohzeki, Phys. Rev. Research 7 04309 (2925).