Dynamics of Defects in Field-Induced Skyrmion Lattice Melting

TP4 project: My work is mainly to achieve the identification, segmentation and tracking of defects and analyze their dynamics. In detail, the positions, the motion tracks, life expectancy, velocity distribution, etc. We will determine these observables among 488 frames while experimentally the field is ramped continuously from about 600 Oe to 1200 Oe

GPU Scheduler for De Novo Genome Assembly with Multiple MPI Processes

$\textit{De Novo}$ Genome assembly is one of the most important tasks in computational biology. ELBA is the state-of-the-art distributed-memory parallel algorithm for overlap detection and layout simplification steps of $\textit{De Novo}$ genome assembly but exists a performance bottleneck in pairwise alignment. In this work, we introduce 3 GPU schedulers for ELBA to accommodate multiple MPI processes and multiple GPUs. The GPU schedulers enable multiple MPI processes to perform computation on GPUs in a round-robin fashion. Both strong and weak scaling experiments show that 3 schedulers are able to significantly improve the performance of baseline while there is a trade-off between parallelism and GPU scheduler overhead. For the best performance implementation, the one-to-one scheduler achieves $\sim$7-8$\times$ speed-up using 25 MPI processes compared with the baseline vanilla ELBA GPU scheduler

Uniformly convex neural networks and non-stationary iterated network Tikhonov (iNETT) method

We propose a non-stationary iterated network Tikhonov (iNETT) method for the solution of ill-posed inverse problems. The iNETT employs deep neural networks to build a data-driven regularizer, and it avoids the difficult task of estimating the optimal regularization parameter. To achieve the theoretical convergence of iNETT, we introduce uniformly convex neural networks to build the data-driven regularizer. Rigorous theories and detailed algorithms are proposed for the construction of convex and uniformly convex neural networks. In particular, given a general neural network architecture, we prescribe sufficient conditions to achieve a trained neural network which is component-wise convex or uniformly convex; moreover, we provide concrete examples of realizing convexity and uniform convexity in the modern U-net architecture. With the tools of convex and uniformly convex neural networks, the iNETT algorithm is developed and a rigorous convergence analysis is provided. Lastly, we show applications of the iNETT algorithm in 2D computerized tomography, where numerical examples illustrate the efficacy of the proposed algorithm

DFedADMM: Dual Constraints Controlled Model Inconsistency for Decentralized Federated Learning

To address the communication burden issues associated with federated learning (FL), decentralized federated learning (DFL) discards the central server and establishes a decentralized communication network, where each client communicates only with neighboring clients. However, existing DFL methods still suffer from two major challenges: local inconsistency and local heterogeneous overfitting, which have not been fundamentally addressed by existing DFL methods. To tackle these issues, we propose novel DFL algorithms, DFedADMM and its enhanced version DFedADMM-SAM, to enhance the performance of DFL. The DFedADMM algorithm employs primal-dual optimization (ADMM) by utilizing dual variables to control the model inconsistency raised from the decentralized heterogeneous data distributions. The DFedADMM-SAM algorithm further improves on DFedADMM by employing a Sharpness-Aware Minimization (SAM) optimizer, which uses gradient perturbations to generate locally flat models and searches for models with uniformly low loss values to mitigate local heterogeneous overfitting. Theoretically, we derive convergence rates of $\small \mathcal{O}\Big(\frac{1}{\sqrt{KT}}+\frac{1}{KT(1-\psi)^2}\Big)$ and $\small \mathcal{O}\Big(\frac{1}{\sqrt{KT}}+\frac{1}{KT(1-\psi)^2}+ \frac{1}{T^{3/2}K^{1/2}}\Big)$ in the non-convex setting for DFedADMM and DFedADMM-SAM, respectively, where $1 - \psi$ represents the spectral gap of the gossip matrix. Empirically, extensive experiments on MNIST, CIFAR10 and CIFAR100 datesets demonstrate that our algorithms exhibit superior performance in terms of both generalization and convergence speed compared to existing state-of-the-art (SOTA) optimizers in DFL.Comment: 24 page

Fast Algorithms for Separable Linear Programs

In numerical linear algebra, considerable effort has been devoted to obtaining faster algorithms for linear systems whose underlying matrices exhibit structural properties. A prominent success story is the method of generalized nested dissection~[Lipton-Rose-Tarjan'79] for separable matrices. On the other hand, the majority of recent developments in the design of efficient linear program (LP) solves do not leverage the ideas underlying these faster linear system solvers nor consider the separable structure of the constraint matrix. We give a faster algorithm for separable linear programs. Specifically, we consider LPs of the form $\min_{\mathbf{A}\mathbf{x}=\mathbf{b}, \mathbf{l}\leq\mathbf{x}\leq\mathbf{u}} \mathbf{c}^\top\mathbf{x}$, where the graphical support of the constraint matrix $\mathbf{A} \in \mathbb{R}^{n\times m}$ is $O(n^\alpha)$-separable. These include flow problems on planar graphs and low treewidth matrices among others. We present an $\tilde{O}((m+m^{1/2 + 2\alpha}) \log(1/\epsilon))$ time algorithm for these LPs, where $\epsilon$ is the relative accuracy of the solution. Our new solver has two important implications: for the $k$-multicommodity flow problem on planar graphs, we obtain an algorithm running in $\tilde{O}(k^{5/2} m^{3/2})$ time in the high accuracy regime; and when the support of $\mathbf{A}$ is $O(n^\alpha)$-separable with $\alpha \leq 1/4$, our algorithm runs in $\tilde{O}(m)$ time, which is nearly optimal. The latter significantly improves upon the natural approach of combining interior point methods and nested dissection, whose time complexity is lower bounded by $\Omega(\sqrt{m}(m+m^{\alpha\omega}))=\Omega(m^{3/2})$, where $\omega$ is the matrix multiplication constant. Lastly, in the setting of low-treewidth LPs, we recover the results of [DLY,STOC21] and [GS,22] with significantly simpler data structure machinery.Comment: 55 pages. To appear at SODA 202

Spraying exogenous hormones alleviate impact of weak-light on yield by improving leaf carbon and nitrogen metabolism in fresh waxy maize

Insufficient light during the growth periods has become one of the main factors restricting maize yield with global climate change. Exogenous hormones application is a feasible measure to alleviate abiotic stresses on crop productivity. In this study, a field trial was conducted to investigate the effects of spraying exogenous hormones on yield, dry matter (DM) and nitrogen (N) accumulation, leaf carbon and N metabolism of fresh waxy maize under weak-light stress in 2021 and 2022. Five treatments including natural light (CK), weak-light after pollination (Z), spraying water (ZP1), exogenous Phytase Q9 (ZP2) and 6-benzyladenine (ZP3) under weak-light after pollination were set up using two hybrids suyunuo5 (SYN5) and jingkenuo2000 (JKN2000). Results showed that weak-light stress significantly reduced the average fresh ear yield (49.8%), fresh grain yield (47.9%), DM (53.3%) and N accumulation (59.9%), and increased grain moisture content. The net photosynthetic rate (Pn), transpiration rate (Tr) of ear leaf after pollination decreased under Z. Furthermore, weak-light decreased the activities of RuBPCase and PEPCase, nitrate reductase (NR), glutamine synthetase (GS), glutamate synthase (GOGAT), superoxide dismutase (SOD), catalase (CAT) and peroxidase (POD) in ear leaves, and increased malondialdehyde (MDA) accumulation. And the decrease was greater on JKN2000. While ZP2 and ZP3 treatments increased the fresh ear yield (17.8%, 25.3%), fresh grain yield (17.2%, 29.5%), DM (35.8%, 44.6%) and N (42.5%, 52.4%) accumulation, and decreased grain moisture content compared with Z. The Pn, Tr increased under ZP2 and ZP3. Moreover, the ZP2 and ZP3 treatments improved the activities of RuBPCase, PEPCase; NR, GS, GOGAT; SOD, CAT, POD in ear leaves, and decreased MDA content during grain filling stage. The results also showed the mitigative effect of ZP3 was greater than ZP2, and the improvement effect was more significant on JKN2000