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Zhiruo Zhou studied Johann Friedrich Pfaff and shared her study with MCL members in the pre-seminar sharing on Mar 6th, 2023. Johann Friedrich Pfaff was born 22 December 1765 in Stuttgart, Württemberg (now Germany), and died 21 April 1825 in Halle, Saxony (now Germany). He was an influential German mathematician and well known for his work on systems of partial differential equations.

Johann Friedrich was the second son in the family and had six brothers. Although he was probably the one that gained the most fame among his siblings, his brothers were also talented in various fields. His youngest brother Johann Wilhelm Pfaff was a mathematician, and his second youngest brother Christoph Heinrich Pfaff had experiences working on chemistry, medicine, pharmacy and electricity on animals.

Johann Friedrich was born in a family with the tradition of working for the government and therefore took the school named Hohe Karlsschule to receive training for government officials’ sons when he was nine years old. He spent around eleven years there and left when he had completed studies in law which was supposed to be a fitting subject for a civil servant. Driven by the interest in mathematics and encouragement from academy, Johann Friedrich decided to move toward scientific topics and studied mathematics and physics at the University of Göttingen for two years. Then he moved to Berlin to study astronomy and wrote his first paper on astronomy there.

In 1788, Johann Friedrich accepted the election as a professor of mathematics at the University of Helmstedt and stay there until 1810. He spent a lot of efforts on teaching and increasing the number of students of mathematics. He met the student Gauss there and had a good relationship with Gauss. However, [...]

Knowledge graph embedding has been intensively studied in recent years. TransE, RotatE, and PairRE are the most representative and effective among distance-based KG embeddings that make use of simple translation, rotation, and scaling operations respectively to represent relations between entities. These models use simple geometric transformations yet achieve relatively good performance in link prediction. However, it is unclear how to leverage the strength of these individual operations and produce a better embedding model. It turns out that we can treat each operation as a basic building block, from which we can build the most effective KG embedding scoring functions. The composition of geometric operators is a well-established tool for image manipulation. It is natural to apply the same strategy to combine translation, rotation, and scaling operators in the 3D space. Our previous work CompoundE has demonstrated that the composition of affine operations can be an effective strategy in designing KG embedding. We are interested to know whether we can achieve even better results by cascading 3D operators.

We propose to extend our previous work by including more affine operations other than only translation, rotation, and scaling in our framework, and moving from 2D transformations to 3D transformations. In addition, we propose to enhance our CompoundE by addressing two critical issues. First, although Compounding operations lead to plenty of model variants, it is still unclear how to systematically search for a scoring function that performs the best for an individual dataset. We propose to use beam search to gradually build more complex scoring functions from simple but effective variants. To speed up the model tuning during the search, we use the pre-trained entity embedding from base models as initialization. Second, although ensemble learning is a popular [...]

Hongyu Fu studied Karl Christian von Langsdorf and shared his study with MCL members in the pre-seminar sharing on February 6th, 2023. Karl Christian von Langsdorf, also known as Carl Christian von Langsdorff, was born 18 May 1757 in Nauheim, and died 10 June 1834 in Heidelberg. He was a German Mathematician, Geologist, Natural scientist and Saltwork Engineer. He is mostly well-known for his specialist in the area of saltworks engineering, and his subject to the 15-year-old Georg Ohm to a thorough examination of his knowledge of mathematics.

Karl Christian von Langsdorf’s father was Georg Melchior Langsdorff, who worked as saltworks archivist and master of the bursary in Nauheim, German. He finished his Gymnasium (secondary school) in Idstein 1773, and went to University of Göttingen to study with Abraham Gotthelf Kästner concerning Philosophy Law Mathematics in 1774, then he went to University of Giessen during 1776 – 1777. He finished his doctorate in 1781 in Erfurt, and then decided against academic career due to his health reasons.

Karl Christian von Langsdorf explored his early career in saltworks. Before his graduation, he  interned at the saltworks in Salzhausen, and devoted himself in Nidda, Hesse to the study of saltworks. After his graduation, he pursued a career in administration and became Rentmeister and land judge in Mülheim an der Ruhr. In 1784, he was active as a saltworks inspector in Gerabronn.

The academic career of Karl Christian von Langsdorf begins in 1798, he was given a full professorship in mechanical engineering at Erlangen, where he subjected the 15-year-old Georg Ohm to a thorough examination of his knowledge of mathematics. During 1803 – 1806, he taught mathematics and technology at Vilnius University in Russia, and returned with the aristocratic descriptor [...]

Usually, the early learning-based point cloud classification methods were developed under the assumption that all point clouds in the dataset are well aligned with the canonical axes. In such scenarios, the 3D Cartesian point coordinates were to learn features. As a consequence, when input point clouds were not aligned, the classification performance dropped significantly. The same assumption holds true in the PointHop and PointHop++ methods proposed by MCL.

In our work SO(3)-Invariant PointHop (or S3I-PointHop in short), we analyze the reason for failure of PointHop due to pose variations, and solve the problem by replacing its pose dependent modules with rotation invariant counterparts. Furthermore, we significantly simplify the PointHop pipeline by using only one single hop along with multiple spatial aggregation techniques. We begin by aligning the point cloud to its three principal axes. This offers a coarse alignment and comes with several ambiguities such as due to eigen vector sign and object asymmetries. The feature extraction process consists of constructing local and global point features. The geometric features are derived from distances and angles in a local point cloud neighborhood. Similarly, the covariance features are found by performing eigen decomposition of the local covariance matrix. The geometric and covariance features form the set of local features. The global features comprise of omni-directional octant features of points in the 3D space similar to PointHop. Later, the Saab transform is conducted.

For aggregating the local and global point features into a global shape feature, conical and spherical aggregation is proposed. For conical aggregation, along each positive and negative principal axes, cones with tip at the origin and at unit distance along the axis are constructed. Then, only the features of points lying inside the respective cones are [...]

Videos captured under low light conditions are often noisy and of poor visibility. Low-light video enhancement aims to improve viewers’ experience by increasing brightness, suppressing noise, and amplifying detailed texture.  The performance of computer vision tasks such as object tracking and face recognition can be severely affected under low-light noisy environments.  Hence, low-light video enhancement is needed to ensure the robustness of computer vision systems. Besides, the technology is highly demanded in consumer electronics such as video capturing by smart phones.

A self-supervised adaptive low-light video enhancement (SALVE) method is proposed in this work. SALVE first conducts an effective Retinex-based low-light image enhancement on a few key frames of an input low-light video. Next, it learns mappings from the low- to enhanced-light frames via Ridge regression.  Finally, it uses these mappings to enhance the remaining frames in the input video. SALVE is a hybrid method that combines components from a traditional Retinex-based image enhancement method and a learning-based method. The former component leads to a robust solution which is easily adaptive to new real-world environments. The latter component offers a fast, computationally inexpensive and temporally consistent solution. We conduct extensive experiments to show the superior performance of SALVE. Our user study shows that 87% of participants prefer SALVE over prior work.

First figure shows an overview of the proposed SALVE method.  For intra-coded frames (I frames), it estimates an illumination component and a reflectance component using the NATLE method.  For inter-coded frames (P/B frames), it predicts these components using a ridge regression learned from the last raw and enhanced I frame pairs.

Second figure shows a quantitative comparison table between our low-light video enhancement method and prior work. To further demonstrate the effectiveness of our method, we [...]