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Archisman Bhattacharjee

Publications and source records attributed to Archisman Bhattacharjee.

2 recordsLinked to original sources

Exceptional Sets for Certain ${}_2F_1$ Hypergeometric Functions

For $a,b,c \in \mathbb{Q}$, the exceptional set associated to the Gauss hypergeometric function $_2F_1(a,b,c;z)$ is defined by $E(a,b,c) := \{ z \in \overline{\mathbb{Q}} \mid {}_2F_1(a,b,c;z) \in \overline{\mathbb{Q}} \}.$ In this paper, the exceptional sets $E(a,b,c)$ are determined explicitly for each $_2F_1(a,b,c;z)$ whose monodromy group is an arithmetic triangle group in Takeuchi's class I. The description is obtained via hypergeometric-modular identities together with transcendence results for periods of abelian varieties due to W\"ustholz, and classical result of Schneider on algebraic values of $j$-invariant of elliptic curves with complex multiplication.

math.NT

Coherent Spectral Feature Extraction Using Symmetric Autoencoders

Hyperspectral data acquired through remote sensing are invaluable for environmental and resource studies. While rich in spectral information, various complexities such as environmental conditions, material properties, and sensor characteristics can cause significant variability even among pixels belonging to the same material class. This variability poses nuisance for accurate land-cover classification and analysis. Focusing on the spectral domain, we utilize an autoencoder architecture called the symmetric autoencoder (SymAE), which leverages permutation invariant representation and stochastic regularization in tandem to disentangle class-invariant 'coherent' features from variability-causing 'nuisance' features on a pixel-by-pixel basis. This disentanglement is achieved through a purely data-driven process, without the need for hand-crafted modeling, noise distribution priors, or reference 'clean signals'. Additionally, SymAE can generate virtual spectra through manipulations in latent space. Using AVIRIS instrument data, we demonstrate these virtual spectra, offering insights on the disentanglement. Extensive experiments across six benchmark hyperspectral datasets show that coherent features extracted by SymAE can be used to achieve state-of-the-art pixel-based classification. Furthermore, we leverage these coherent features to enhance the performance of some leading spectral-spatial HSI classification methods. Our approach especially shows improvement in scenarios where training and test sets are disjoint, a common challenge in real-world applications where existing methods often struggle to maintain relatively high performance.

physics.geo-ph