相关论文: On Splitting Invariants and Sign Conventions in En…

In the theory of endoscopy appears transfer factors. They were defined by Langlands and Shelstad in the ordinary case and by Kottwitz and Shelstad in the twisted case. The definition is abstract. For classical groups, we compute explicitely…

The standard theory of endoscopy for real groups has two parallel formulations. The original formulation of Langlands and Shelstad relies on methods in harmonic analysis. The subsequent formulation of Adams, Barbasch and Vogan relies on…

To a maximal torus in a quasi-split semi-simple simply-connected group over a local field of characteristic 0, Langlands and Shelstad construct a cohomological invariant called the splitting invariant, which is an important component of…

Twisted Alexander invariants of knots are well-defined up to multiplication of units. We get rid of this multiplicative ambiguity via a combinatorial method and define normalized twisted Alexander invariants. We then show that the…

The Langlands-Shelstad transfer factor is a function defined on some reductive groups over a p-adic field. Near the origin of the group, it may be viewed as a function on the Lie algebra. For classical groups, its values have the form q^c…

We establish endoscopic and stable trace formulas whose discrete spectral terms are weighted by automorphic $L$-functions, by the use of basic functions that are incorporated into the global spectral and geometric coefficients. This is a…

We extend the local Langlands conjectures to a certain class of disconnected groups, allowing non-abelian component groups, and recast in this language some aspects of twisted endoscopy. We further introduce normalized twisted transfer…

Over the years, the Invariant Scattering Transform (IST) technique has become popular for medical image analysis, including using wavelet transform computation using Convolutional Neural Networks (CNN) to capture patterns' scale and…

We introduce the notion of the descent set polynomial as an alternative way of encoding the sizes of descent classes of permutations. Descent set polynomials exhibit interesting factorization patterns. We explore the question of when…

While several instances of shifted convolution problems for GL(3) x GL(2) have been solved, the case where one factor is the classical divisor function and one factor is a GL(3) Fourier coefficient has remained open. We solve this case in…

The Z Transform is a mathematical operation in signal processing, which gives a tractable way to solve linear, constant-coefficient difference equations. Based on the classical Z transform and inspired by the thought of sliding DFT, a new…

Crafting adversarial examples can be formulated as an optimization problem. While sign-based optimizers such as I-FGSM and MI-FGSM have become the de facto standard for the induced optimization problems, there still exist several unsolved…

The modern way to understand symmetries of a quantum field theory is via its topological defects in various dimensions. In this contribution to the proceedings we focus on line defects in 2d QFT and we point out that topological defects…

In this paper we propose a method for transfer learning of endoscopic images. For transferring between features obtained from images taken by different (old and new) endoscopes, we extend the Max-Margin Domain Transfer (MMDT) proposed by…

This work extends the factorization method to the inverse scattering problem of reconstructing the shape and location of an absorbing penetrable scatterer embedded in a thin infinite elastic (Kirchhoff--Love) plate. With the assumption that…

Langlands' functoriality principle predicts deep relations between the local and automorphic spectra of different reductive groups. This has been generalized by the relative Langlands program to include spherical varieties, among which…

Background: Spatial transcriptomics have emerged as a powerful tool in biomedical research because of its ability to capture both the spatial contexts and abundance of the complete RNA transcript profile in organs of interest. However,…

We investigate distributed source coding of two correlated sources X and Y where messages are passed to a decoder in a cascade fashion. The encoder of X sends a message at rate R_1 to the encoder of Y. The encoder of Y then sends a message…

Manual medical image segmentation is subjective and suffers from annotator-related bias, which can be mimicked or amplified by deep learning methods. Recently, researchers have suggested that such bias is the combination of the annotator…

The Alexander polynomial of a knot has been generalized in three different ways to give twisted invariants. The resulting invariants are usually referred to as twisted Alexander polynomials, higher-order Alexander polynomials and…