Research

Manifold Approximation

Manifold-MLS - Enhancing the Moving Least-Squares (MLS) mechanism to approximate low dimensional manifolds embedded in a high dimensional space.

Working with researches from Tel-Aviv University and Duke University Dr. Sober and his associates created a framework, which enables researches to operate directly on a sampled manifold instead of performing dimension reduction. The framework uses only the manifold dimensions and assumes no other knowledge of the manifold. The approximations are shown to be smooth and have optimal approximation order. Using this framework one can reconstruct geodesic distances.

Similar to local polynomial regression (i.e., Moving Least-Squares for function approximation) under certain assumptions regarding the noise distribution it can be demostrated that the algorithm converges in probability when the sample size reaches infinity.

In the process of these investigations, we have encountered a fascinating connection between least-squares linear regression and Principal Component Analysis.

Computerized Paleography

Studying the development of ancient Hebrew writing dating to First Temple Period, Dr. Sober collaborates with an interdisciplinary team of researchers tackling various questions related to the subject.

The team's most prominent findings include:

• Finding an empirical evidence of high literacy rates in the Kingdom of Judah on the eve of the Babylonian conquest and destruction of Jerusalem.
  publication: 10.1073/pnas.1522200113

• Showing negative evidence to the dissemination of writing skills 200 years earlier in the northern kingdom of Israel.
  publication: in preperation.

• the discovery of a hitherto unknown inscription on the opposite side of an existing inscription. The existing insctiption was stored for more than fifty yearsin Israel Museum.
  publication: 10.1371/journal.pone.0178400

Researchers:
    Israel Finkelstein - Tel Aviv University
    David Levin - Tel Aviv University
    Murray Moinester - Tel Aviv University
    Nadav Na'aman - Tel Aviv University
    Eliezer Piasetzky - Tel Aviv University
    Christopher A. Rollston - George Washington University
    Benjamin Sass - Tel Aviv University
    Eli Turkel - Tel Aviv University
    Michael Cordonsky - Tel Aviv University
    Barak Sober - Hebrew University of Jerusalem
    Anat Mendel - Tel Aviv University
    Arie Shaus - Tel Aviv University
    Sira Faigenbaum-Golovin - Tel Aviv University
    Eythan Levy - Tel Aviv University
    Ma'ayan Mor - Tel Aviv University

 project homepage

Machine Learning in Art Investigationy

X-ray imaging plays a crucial role in the process of understanding the way a painting was created as well as locating areas that need to undergo restoration of preservation. However, X-ray images of artworks, contain a mixture of signals originating from overlaid pictures or artworks painted on both sides of the canvas.

Participating in the ARTICT project, led by researchers from the University College of London, the British Library and the Imperial College London, we developed a self-supervised deep neural network capable of learning and separating these mixed signals. Applying this network to two panels of the Ghent Altarpiece, our results show spectacular improvement over previous attempts.
Publication: 

10.1126/sciadv.aaw7416

To assist the conservation work process, we had to scale up the algorithmic capabilities and devise a more efficient neural-network architecture.
Publications: 

10.1109/ICASSP40776.2020.9054651  

10.1109/TIP.2023.3275872

We are currently working in collaboration with the Belgian Royal Institute for Cultural Heritage (KIK-IRPA) on applying these methodologies on problematic areas of the Ghent Altarpiece.

Researchers:
    Miguel Rodrigues - University College London
    Pier Luigi Dragotti - Imperial College London
    Catherine Higgitt - National Gallery, London
    David Peggie - National Gallery, London
    Ingrid Daubechies - Duke University
    Barak Sober - The Hebrew University, Jerusalem
    Cerys Jones - University College London
    Junjie Huang - Imperial College London
    Nathan Daly - National Gallery, London
    Wei Pu - University College London
    Chao Zhou - University College London
    Maria Villafane - Imperial College London
    Su Yan - Imperial College London

project homepage

Statistical Language Research in Biblical Hebrew

In this multidisciplinary effort, a team of world renowned scholars from the fields biblical studies, archaeology, compter science and statistics is attempting to establish an innovative, statistically-rigourous paradigm of exploring hypothesized partitions of texts. The study focuses on the exploring the literary uniqueness of priestly source -- a widely accepted distinct consituent of the pentatuech (Torah).

Researchers:
    Axel Bühler - Université de Genève
    Nachum Dershowitz - Tel Aviv University
    Israel Finkelstein - Tel Aviv and Haifa Universities
    Eli Piasetzky - Tel Aviv University
    Thomas Römer - Collège de France
    Barak Sober - The Hebrew University, Jerusalem
    Gideon Yoffe - The Hebrew University, Jerusalem

Publications:

Yoffe, G., Bühler, A., Dershowitz, N., Finkelstein, I., Piasetzky, E., Römer, T. & Sober, B. (2023). A statistical exploration of text partition into constituents: The case of the priestly source in the books of Genesis and Exodus. arXiv:2305.02170 .
Accepted for publication in: Findings of the Association for Computational Linguistics 2023.        
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