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1. Isometric fows of G2-structures

   Grigorian, Sergey (January 2022, Trends in mathematics)

   Cerejeiras, P.; Reissig, M; Sabadini, I; Toft, J. (Ed.)

   We survey recent progress in the study of flows of isometric G2- structures on seven-dimensional manifolds, that is, flows that preserve the metric, while modifying the G2-structure. In particular, heat flows of isometric G2-structures have been recently studied from several different perspectives, in particular in terms of 3-forms, octonions, vector fields, and geometric structures. We will give an overview of each approach, the results obtained, and compare the different perspectives. 

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2. Exploiting Inter-Flow Relationship for Coflow Placement in Datacenters

   https://doi.org/10.1145/3106989.3107004  

   Huang, Xin Sunny; Ng, T. S. (January 2017, APNet'17 Proceedings of the First Asia-Pacific Workshop on Networking)

   A crucial challenge for data-parallel clusters is achieving high application-level communication efficiency for structured traffic flows (a.k.a. Coflows) from distributed data processing applications. A range of recent works focus on designing network scheduling algorithms with predetermined Coflow placement, i.e. the endpoints of subflows within a Coflow are preset. However, the underlying Coflow placement problem and its decisive impact on scheduling efficiency have long been overlooked. It is hard to find good placements for Coflows. At the intra-Coflow level, constituent flows are related and therefore their placement decisions are dependent. Thus, strategies extended from flow-by-flow placement is sub-optimal due to negligence of the inter-flow relationship in a Coflow. At the inter-Coflow level, placing a new Coflow may introduce contentions with existing Coflows, which changes communication efficiency. This paper is the first to study the Coflow placement problem with careful considerations of the inter-flow relationship in Coflows. We formulate the Coflow placement problem and propose a Coflow placement algorithm. Under realistic traffic in various settings, our algorithm reduces the average completion time for Coflows by up to 26%. 

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3. Ring-Opening Metathesis Polymerization of the Dewar Isomer of 1,2-Azaborinine, a B–N Isostere of Benzene

   https://doi.org/10.1021/acsmacrolett.3c00601  

   Lin, Huina; Yang, Xinyu; Liu, Shih-Yuan; Jäkle, Frieder (December 2023, ACS Macro Letters)

   The successful polymerization of the Dewar isomer of an azaborinine heterocycle is reported. Controlled ring-opening metathesis polymerization was accomplished with Grubbs and Hoveya−Grubbs second generation catalysts (G2, HG2), as well as a Z-selective Ru catalyst (HGM2001). The structure of the polymers containing 4-membered B−N heterocycles was verified by GPC and multinuclear and 2D NMR. Differences in stereochemistry of polymers derived from G2/HG2 versus the Z-selective catalyst HGM2001 were substantiated by 2D NOESY, FT-IR, and Raman analyses. The incorporation of B−N heterocycles into these polymer structures is promising as a route to functional polymers that contain polar side groups. 

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4. Numerical approximations of the Allen-Cahn-Ohta-Kawasaki equation with modified physics-informed neural networks (PINNs)

   Xu, Jingjing; Zhao, Jia; Zhao, Yanxiang (January 2023, International journal of numerical analysis and modeling)

   The physics-informed neural networks (PINNs) has been widely utilized to numerically approximate PDE problems. While PINNs has achieved good results in producing solutions for many partial differential equations, studies have shown that it does not perform well on phase field models. In this paper, we partially address this issue by introducing a modified physics-informed neural networks. In particular, they are used to numerically approximate Allen- Cahn-Ohta-Kawasaki (ACOK) equation with a volume constraint. Technically, the inverse of Laplacian in the ACOK model presents many challenges to the baseline PINNs. To take the zero- mean condition of the inverse of Laplacian, as well as the volume constraint, into consideration, we also introduce a separate neural network, which takes the second set of sampling points in the approximation process. Numerical results are shown to demonstrate the effectiveness of the modified PINNs. An additional benefit of this research is that the modified PINNs can also be applied to learn more general nonlocal phase-field models, even with an unknown nonlocal kernel. 

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5. On High-Dimensional Graph Learning Under Total Positivity

   https://doi.org/10.1109/IEEECONF53345.2021.9723191  

   Tugnait, Jitendra K. (October 2021, 22021 55th Asilomar Conference on Signals, Systems, and Computers)

   We consider the problem of estimating the structure of an undirected weighted sparse graphical model of multivariate data under the assumption that the underlying distribution is multivariate totally positive of order 2, or equivalently, all partial correlations are non-negative. Total positivity holds in several applications. The problem of Gaussian graphical model learning has been widely studied without the total positivity assumption where the problem can be formulated as estimation of the sparse precision matrix that encodes conditional dependence between random variables associated with the graph nodes. An approach that imposes total positivity is to assume that the precision matrix obeys the Laplacian constraints which include constraining the off-diagonal elements of the precision matrix to be non-positive. In this paper we investigate modifications to widely used penalized log-likelihood approaches to enforce total positivity but not the Laplacian structure. An alternating direction method of multipliers (ADMM) algorithm is presented for constrained optimization under total positivity and lasso as well as adaptive lasso penalties. Numerical results based on synthetic data show that the proposed constrained adaptive lasso approach significantly outperforms existing Laplacian-based approaches, both statistical and smoothness-based non-statistical. 

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