no code implementations • 3 May 2023 • Gideon Yoffe, Axel Bühler, Nachum Dershowitz, Israel Finkelstein, Eli Piasetzky, Thomas Römer, Barak Sober

We present a pipeline for a statistical textual exploration, offering a stylometry-based explanation and statistical validation of a hypothesized partition of a text.

no code implementations • 7 Sep 2022 • Boris Shustin, Haim Avron, Barak Sober

In case some of the components are given analytically (e. g., if the cost function and its gradient are given explicitly, or if the tangent spaces can be computed), the algorithm can be easily adapted to use the accurate expressions instead of the approximations.

no code implementations • 23 Jan 2022 • Wei Pu, Jun-Jie Huang, Barak Sober, Nathan Daly, Catherine Higgitt, Ingrid Daubechies, Pier Luigi Dragotti, Miguel Rodigues

In this paper, we focus on X-ray images of paintings with concealed sub-surface designs (e. g., deriving from reuse of the painting support or revision of a composition by the artist), which include contributions from both the surface painting and the concealed features.

no code implementations • 28 Jul 2021 • Ingrid Daubechies, Ronald DeVore, Nadav Dym, Shira Faigenbaum-Golovin, Shahar Z. Kovalsky, Kung-Ching Lin, Josiah Park, Guergana Petrova, Barak Sober

Namely, we show that refinable functions are approximated by the outputs of deep ReLU networks with a fixed width and increasing depth with accuracy exponential in terms of their number of parameters.

1 code implementation • 11 May 2021 • Yariv Aizenbud, Barak Sober

Assuming that the data was sampled uniformly from a tubular neighborhood of $\mathcal{M}\in \mathcal{C}^k$, a compact manifold without boundary, we present an algorithm that takes a point $r$ from the tubular neighborhood and outputs $\hat p_n\in \mathbb{R}^D$, and $\widehat{T_{\hat p_n}\mathcal{M}}$ an element in the Grassmanian $Gr(d, D)$.

no code implementations • 16 Sep 2020 • Wei Pu, Barak Sober, Nathan Daly, Zahra Sabetsarvestani, Catherine Higgitt, Ingrid Daubechies, Miguel R. D. Rodrigues

These features are then used to (1) reproduce both of the original RGB images, (2) reconstruct the hypothetical separated X-ray images, and (3) regenerate the mixed X-ray image.

no code implementations • 20 Jul 2020 • Barak Sober, Robert Ravier, Ingrid Daubechies

In this paper, we investigate the convergence of such approximations made by Manifold Moving Least-Squares (Manifold-MLS), a method that constructs an approximating manifold $\mathcal{M}^h$ using information from a given point cloud that was developed by Sober \& Levin in 2019.

no code implementations • 27 May 2019 • Nadav Dym, Barak Sober, Ingrid Daubechies

The combination of this phenomenon with the capacity, demonstrated here, of DNNs to efficiently approximate IFS may contribute to the success of DNNs, particularly striking for image processing tasks, as well as suggest new algorithms for representing self similarities in images based on the DNN mechanism.

no code implementations • 2 Nov 2017 • Barak Sober, Yariv Aizenbud, David Levin

The resulting approximant is shown to be a function defined over a neighborhood of a manifold, approximating the originally sampled manifold.

no code implementations • 22 Jun 2016 • Barak Sober, David Levin

We assume that the data points are located "near" the lower dimensional manifold and suggest a non-linear moving least-squares projection on an approximating $d$-dimensional manifold.

no code implementations • 23 Feb 2016 • Barak Sober, David Levin

This work suggests a new variational approach to the task of computer aided restoration of incomplete characters, residing in a highly noisy document.

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