Approximating Word Ranking and Negative Sampling for Word Embedding

CBOW (Continuous Bag-Of-Words) is one of the most commonly used techniques to generate word embeddings in various NLP tasks. However, it fails to reach the optimal performance due to uniform involvements of positive words and a simple sampling distribution of negative words. To resolve these issues, we propose OptRank to optimize word ranking and approximate negative sampling for bettering word embedding. Specifically, we first formalize word embedding as a ranking problem. Then, we weigh the positive words by their ranks such that highly ranked words have more importance, and adopt a dynamic sampling strategy to select informative negative words. In addition, an approximation method is designed to efficiently compute word ranks. Empirical experiments show that OptRank consistently outperforms its counterparts on a benchmark dataset with different sampling scales, especially when the sampled subset is small. The code and datasets can be obtained from https://github.com/ouououououou/OptRank

Design of a lab scale direct-filtration system and its application in process lab

The Environmental Process and Simulation Center (EPSC) at Michigan Technological University started accommodating laboratories for an Environmental Engineering senior level class CEE 4509 Environmental Process and Simulation Laboratory since 2004. Even though the five units that exist in EPSC provide the students opportunities to have hands-on experiences with a wide range of water/wastewater treatment technologies, a key module was still missing for the student to experience a full cycle of treatment. This project fabricated a direct-filtration pilot system in EPSC and generated a laboratory manual for education purpose. Engineering applications such as clean bed head loss calculation, backwash flowrate determination, multimedia density calculation and run length prediction are included in the laboratory manual. The system was tested for one semester and modifications have been made both to the direct filtration unit and the laboratory manual. Future work is also proposed to further refine the module

Conformal isoparametric spacelike hypersurfaces in conformal spaces Q⁴₁ and Q⁵₁

We study the conformal geometry of conformal spacelike hypersurfaces in the conformal spaces Q⁴₁ and Q⁵₁. We obtain a complete classification of conformal isoparametric spacelike hypersurfaces in Q⁴₁ and Q⁵₁.Вивчено конформну геометрiю конформних простороподiбних гiперповерхонь у конформних просторах Q⁴₁ and Q⁵₁. Отримано повну класифiкацiю конформних iзопараметричних простороподiбних гiперповерхонь у Q⁴₁ та Q⁵₁

Manipulation of Abro1 Localization in U2OS Cells

https://openworks.mdanderson.org/sumexp22/1142/thumbnail.jp

The Existence of Hamilton Cycle in n-Balanced k-Partite Graphs

Let $G_{k,n}$ be the $n$-balanced $k$-partite graph, whose vertex set can be partitioned into $k$ parts, each has $n$ vertices. In this paper, we prove that if $k \geq 2,n \geq 1$, for the edge set $E(G)$ of $G_{k,n}$ $$|E(G)| \geq\left\{\begin{array}{cc} 1 & \text { if } k=2, n=1 n^{2} C_{k}^{2}-(k-1) n+2 & \text { other } \end{array}\right.$$ then $G_{k,n}$ is hamiltonian. And the result may be the best