Measuring growth rates of apple fruitlets is important because it allows apple growers to determine when to apply chemical thinners to their crops to optimize yield. The current practice of obtaining growth rates involves using calipers to record sizes of fruitlets across multiple days. Due to the number of fruitlets needed to be sized, this method is laborious, time-consuming, and prone to human error. In this paper, we present a computer vision approach to measure the sizes and growth rates of apple fruitlets. With images collected by a hand-held stereo camera, our system detects, segments, and fits ellipses to fruitlets to measure their diameters. To measure growth rates, we utilize an Attentional Graph Neural Network to associate fruitlets across different days. We provide quantitative results on data collected in an apple orchard, and demonstrate that our system is able to predict abscise rates within 3% of the current method with a 7 times improvement in speed, while requiring significantly less manual effort. Moreover, we provide results on images captured by a robotic system in the field, and discuss the next steps to make the process fully autonomous.

休眠季节葡萄树修剪需要熟练的季节性工人，这在冬季变得越来越缺乏。随着在短期季节性招聘文化和低工资的短期季节性招聘文化和低工资的时间内，随着工人更少的葡萄藤，葡萄藤往往被修剪不一致地导致葡萄化物不平衡。除此之外，目前现有的机械方法无法选择性地修剪葡萄园和手动后续操作，通常需要进一步提高生产成本。在本文中，我们展示了崎岖，全自治机器人的设计和田间评估，用于休眠季节葡萄园的端到最终修剪。该设计的设计包括新颖的相机系统，运动冗余机械手，地面机器人和在感知系统中的新颖算法。所提出的研究原型机器人系统能够在213秒/葡萄藤中完全从两侧刺激一排藤蔓，总修枝精度为87％。与机械预灌浆试验相比，商业葡萄园中自治系统的初始现场测试显示出休眠季节修剪的显着变化。在手稿中描述了设计方法，系统组件，经验教训，未来增强以及简要的经济分析。

Kernel matrices, as well as weighted graphs represented by them, are ubiquitous objects in machine learning, statistics and other related fields. The main drawback of using kernel methods (learning and inference using kernel matrices) is efficiency -- given $n$ input points, most kernel-based algorithms need to materialize the full $n \times n$ kernel matrix before performing any subsequent computation, thus incurring $\Omega(n^2)$ runtime. Breaking this quadratic barrier for various problems has therefore, been a subject of extensive research efforts. We break the quadratic barrier and obtain $\textit{subquadratic}$ time algorithms for several fundamental linear-algebraic and graph processing primitives, including approximating the top eigenvalue and eigenvector, spectral sparsification, solving linear systems, local clustering, low-rank approximation, arboricity estimation and counting weighted triangles. We build on the recent Kernel Density Estimation framework, which (after preprocessing in time subquadratic in $n$) can return estimates of row/column sums of the kernel matrix. In particular, we develop efficient reductions from $\textit{weighted vertex}$ and $\textit{weighted edge sampling}$ on kernel graphs, $\textit{simulating random walks}$ on kernel graphs, and $\textit{importance sampling}$ on matrices to Kernel Density Estimation and show that we can generate samples from these distributions in $\textit{sublinear}$ (in the support of the distribution) time. Our reductions are the central ingredient in each of our applications and we believe they may be of independent interest. We empirically demonstrate the efficacy of our algorithms on low-rank approximation (LRA) and spectral sparsification, where we observe a $\textbf{9x}$ decrease in the number of kernel evaluations over baselines for LRA and a $\textbf{41x}$ reduction in the graph size for spectral sparsification.

Recent work shows that the expressive power of Graph Neural Networks (GNNs) in distinguishing non-isomorphic graphs is exactly the same as that of the Weisfeiler-Lehman (WL) graph test. In particular, they show that the WL test can be simulated by GNNs. However, those simulations involve neural networks for the 'combine' function of size polynomial or even exponential in the number of graph nodes $n$, as well as feature vectors of length linear in $n$. We present an improved simulation of the WL test on GNNs with \emph{exponentially} lower complexity. In particular, the neural network implementing the combine function in each node has only a polylogarithmic number of parameters in $n$, and the feature vectors exchanged by the nodes of GNN consists of only $O(\log n)$ bits. We also give logarithmic lower bounds for the feature vector length and the size of the neural networks, showing the (near)-optimality of our construction.

SemideFinite编程（SDP）是一个统一的框架，可以概括线性编程和四二次二次编程，同时在理论和实践中也产生有效的求解器。但是，当覆盖SDP的约束以在线方式到达时，存在近似最佳解决方案的已知结果。在本文中，我们研究了在线涵盖线性和半决赛程序，其中通过可能错误的预测指标的建议增强了算法。我们表明，如果预测变量是准确的，我们可以有效地绕过这些不可能的结果，并在最佳解决方案（即一致性）上实现恒定因素近似值。另一方面，如果预测变量不准确，在某些技术条件下，我们取得的结果既匹配经典的最佳上限和紧密的下限，则达到恒定因素，即稳健性。更广泛地，我们引入了一个框架，该框架既扩展了（1）由Bamas，Maggiori和Svensson（Neurips 2020）研究的机器学习预测变量增加的在线套装问题，以及（2）在线覆盖SDP问题，由SDP问题发起。 Elad，Kale和Naor（ICALP 2016）。具体而言，我们获得了一般的在线学习算法，用于涵盖具有分数建议和约束的线性程序，并启动学习启发算法以涵盖SDP问题的研究。我们的技术基于Buchbinder和NAOR的原始二次框架（操作研究的数学，34，2009），并且可以进一步调整以处理变量位于有限区域的约束，即框约束。

我们探索稀疏优化问题的算法和局限性，例如稀疏线性回归和稳健的线性回归。稀疏线性回归问题的目的是确定少数关键特征，而强大的线性回归问题的目标是确定少量错误的测量值。具体而言，稀疏线性回归问题寻求$ k $ -sparse vector $ x \ in \ mathbb {r}^d $以最小化$ \ | ax-b \ | _2 $，给定输入矩阵$ a \ in \ mathbb in \ mathbb {r}^{n \ times d} $和一个目标向量$ b \ in \ mathbb {r}^n $，而强大的线性回归问题寻求一个$ s $ s $，最多可以忽略$ k $行和a向量$ x $最小化$ \ |（ax-b）_s \ | _2 $。我们首先显示了在[OWZ15]工作上稳健回归构建的近似近似值的双晶格，这意味着稀疏回归的结果相似。我们通过减少$ k $ clique的猜想，进一步显示出稳健回归的精细颗粒硬度。在正面，我们给出了一种鲁棒回归的算法，该算法可实现任意准确的添加误差，并使用运行时与从细粒硬度结果中的下界紧密匹配的运行时，以及与类似运行时稀疏回归的算法。我们的上限和下限都依赖于从鲁棒线性回归到我们引入的稀疏回归的一般减少。我们的算法受到3SUM问题的启发，使用大约最近的邻居数据结构，并且可能具有独立的兴趣来解决稀疏优化问题。例如，我们证明我们的技术也可以用于研究稀疏的PCA问题。