Cuspidal机器人是具有至少两种逆运动溶液的机器人，可以通过无奇异路径连接。过去已经研究了普通3R机器人的尖锐性，但是将研究扩展到六度自由的机器人可能是一个具有挑战性的问题。许多机器人可以与真实代数集一起建模为多项式图，以便将尖的概念扩展到这些数据。在本文中，我们设计了一种算法，该算法在输入$ n $不确定的多项式地图上，而$ s $多项式在相同的不确定的情况下描述了一个真实的代数$ d $，请确定地图限制的限制性正在考虑的实际代数设定。此外，如果$ d $和$ \ \ tau $分别是输入多项式系数的最高学位和界限，则该算法在$ \ tau $中以$ \ tau $和$（$（ （s+d）d）^{o（n^2）} $。它依赖于计算机代数中的许多高级算法，这些算法在真实代数集和多项式图的关键基因座上使用高级方法。据我们所知，这是第一种从一般角度解决尖锐性问题的算法。

Linear partial differential equations (PDEs) are an important, widely applied class of mechanistic models, describing physical processes such as heat transfer, electromagnetism, and wave propagation. In practice, specialized numerical methods based on discretization are used to solve PDEs. They generally use an estimate of the unknown model parameters and, if available, physical measurements for initialization. Such solvers are often embedded into larger scientific models or analyses with a downstream application such that error quantification plays a key role. However, by entirely ignoring parameter and measurement uncertainty, classical PDE solvers may fail to produce consistent estimates of their inherent approximation error. In this work, we approach this problem in a principled fashion by interpreting solving linear PDEs as physics-informed Gaussian process (GP) regression. Our framework is based on a key generalization of a widely-applied theorem for conditioning GPs on a finite number of direct observations to observations made via an arbitrary bounded linear operator. Crucially, this probabilistic viewpoint allows to (1) quantify the inherent discretization error; (2) propagate uncertainty about the model parameters to the solution; and (3) condition on noisy measurements. Demonstrating the strength of this formulation, we prove that it strictly generalizes methods of weighted residuals, a central class of PDE solvers including collocation, finite volume, pseudospectral, and (generalized) Galerkin methods such as finite element and spectral methods. This class can thus be directly equipped with a structured error estimate and the capability to incorporate uncertain model parameters and observations. In summary, our results enable the seamless integration of mechanistic models as modular building blocks into probabilistic models.

Over the past decade, neural networks have been successful at making predictions from biological sequences, especially in the context of regulatory genomics. As in other fields of deep learning, tools have been devised to extract features such as sequence motifs that can explain the predictions made by a trained network. Here we intend to go beyond explainable machine learning and introduce SEISM, a selective inference procedure to test the association between these extracted features and the predicted phenotype. In particular, we discuss how training a one-layer convolutional network is formally equivalent to selecting motifs maximizing some association score. We adapt existing sampling-based selective inference procedures by quantizing this selection over an infinite set to a large but finite grid. Finally, we show that sampling under a specific choice of parameters is sufficient to characterize the composite null hypothesis typically used for selective inference-a result that goes well beyond our particular framework. We illustrate the behavior of our method in terms of calibration, power and speed and discuss its power/speed trade-off with a simpler data-split strategy. SEISM paves the way to an easier analysis of neural networks used in regulatory genomics, and to more powerful methods for genome wide association studies (GWAS).

In intensively managed forests in Europe, where forests are divided into stands of small size and may show heterogeneity within stands, a high spatial resolution (10 - 20 meters) is arguably needed to capture the differences in canopy height. In this work, we developed a deep learning model based on multi-stream remote sensing measurements to create a high-resolution canopy height map over the "Landes de Gascogne" forest in France, a large maritime pine plantation of 13,000 km$^2$ with flat terrain and intensive management. This area is characterized by even-aged and mono-specific stands, of a typical length of a few hundred meters, harvested every 35 to 50 years. Our deep learning U-Net model uses multi-band images from Sentinel-1 and Sentinel-2 with composite time averages as input to predict tree height derived from GEDI waveforms. The evaluation is performed with external validation data from forest inventory plots and a stereo 3D reconstruction model based on Skysat imagery available at specific locations. We trained seven different U-net models based on a combination of Sentinel-1 and Sentinel-2 bands to evaluate the importance of each instrument in the dominant height retrieval. The model outputs allow us to generate a 10 m resolution canopy height map of the whole "Landes de Gascogne" forest area for 2020 with a mean absolute error of 2.02 m on the Test dataset. The best predictions were obtained using all available satellite layers from Sentinel-1 and Sentinel-2 but using only one satellite source also provided good predictions. For all validation datasets in coniferous forests, our model showed better metrics than previous canopy height models available in the same region.

Knowledge Distillation (KD) is a commonly used technique for improving the generalization of compact Pre-trained Language Models (PLMs) on downstream tasks. However, such methods impose the additional burden of training a separate teacher model for every new dataset. Alternatively, one may directly work on the improvement of the optimization procedure of the compact model toward better generalization. Recent works observe that the flatness of the local minimum correlates well with better generalization. In this work, we adapt Stochastic Weight Averaging (SWA), a method encouraging convergence to a flatter minimum, to fine-tuning PLMs. We conduct extensive experiments on various NLP tasks (text classification, question answering, and generation) and different model architectures and demonstrate that our adaptation improves the generalization without extra computation cost. Moreover, we observe that this simple optimization technique is able to outperform the state-of-the-art KD methods for compact models.

This work addresses the problems of (a) designing utilization measurements of trained artificial intelligence (AI) models and (b) explaining how training data are encoded in AI models based on those measurements. The problems are motivated by the lack of explainability of AI models in security and safety critical applications, such as the use of AI models for classification of traffic signs in self-driving cars. We approach the problems by introducing theoretical underpinnings of AI model utilization measurement and understanding patterns in utilization-based class encodings of traffic signs at the level of computation graphs (AI models), subgraphs, and graph nodes. Conceptually, utilization is defined at each graph node (computation unit) of an AI model based on the number and distribution of unique outputs in the space of all possible outputs (tensor-states). In this work, utilization measurements are extracted from AI models, which include poisoned and clean AI models. In contrast to clean AI models, the poisoned AI models were trained with traffic sign images containing systematic, physically realizable, traffic sign modifications (i.e., triggers) to change a correct class label to another label in a presence of such a trigger. We analyze class encodings of such clean and poisoned AI models, and conclude with implications for trojan injection and detection.

White matter bundle segmentation is a cornerstone of modern tractography to study the brain's structural connectivity in domains such as neurological disorders, neurosurgery, and aging. In this study, we present FIESTA (FIber gEneration and bundle Segmentation in Tractography using Autoencoders), a reliable and robust, fully automated, and easily semi-automatically calibrated pipeline based on deep autoencoders that can dissect and fully populate WM bundles. Our framework allows the transition from one anatomical bundle definition to another with marginal calibrating time. This pipeline is built upon FINTA, CINTA, and GESTA methods that demonstrated how autoencoders can be used successfully for streamline filtering, bundling, and streamline generation in tractography. Our proposed method improves bundling coverage by recovering hard-to-track bundles with generative sampling through the latent space seeding of the subject bundle and the atlas bundle. A latent space of streamlines is learned using autoencoder-based modeling combined with contrastive learning. Using an atlas of bundles in standard space (MNI), our proposed method segments new tractograms using the autoencoder latent distance between each tractogram streamline and its closest neighbor bundle in the atlas of bundles. Intra-subject bundle reliability is improved by recovering hard-to-track streamlines, using the autoencoder to generate new streamlines that increase each bundle's spatial coverage while remaining anatomically meaningful. Results show that our method is more reliable than state-of-the-art automated virtual dissection methods such as RecoBundles, RecoBundlesX, TractSeg, White Matter Analysis and XTRACT. Overall, these results show that our framework improves the practicality and usability of current state-of-the-art bundling framework

There are many potential benefits to news readers accessing diverse sources. Modern news aggregators do the hard work of organizing the news, offering readers a plethora of source options, but choosing which source to read remains challenging. We propose a new framework to assist readers in identifying source differences and gaining an understanding of news coverage diversity. The framework is based on the generation of Discord Questions: questions with a diverse answer pool, explicitly illustrating source differences. To assemble a prototype of the framework, we focus on two components: (1) discord question generation, the task of generating questions answered differently by sources, for which we propose an automatic scoring method, and create a model that improves performance from current question generation (QG) methods by 5%, (2) answer consolidation, the task of grouping answers to a question that are semantically similar, for which we collect data and repurpose a method that achieves 81% balanced accuracy on our realistic test set. We illustrate the framework's feasibility through a prototype interface. Even though model performance at discord QG still lags human performance by more than 15%, generated questions are judged to be more interesting than factoid questions and can reveal differences in the level of detail, sentiment, and reasoning of sources in news coverage.

In a fissile material, the inherent multiplicity of neutrons born through induced fissions leads to correlations in their detection statistics. The correlations between neutrons can be used to trace back some characteristics of the fissile material. This technique known as neutron noise analysis has applications in nuclear safeguards or waste identification. It provides a non-destructive examination method for an unknown fissile material. This is an example of an inverse problem where the cause is inferred from observations of the consequences. However, neutron correlation measurements are often noisy because of the stochastic nature of the underlying processes. This makes the resolution of the inverse problem more complex since the measurements are strongly dependent on the material characteristics. A minor change in the material properties can lead to very different outputs. Such an inverse problem is said to be ill-posed. For an ill-posed inverse problem the inverse uncertainty quantification is crucial. Indeed, seemingly low noise in the data can lead to strong uncertainties in the estimation of the material properties. Moreover, the analytical framework commonly used to describe neutron correlations relies on strong physical assumptions and is thus inherently biased. This paper addresses dual goals. Firstly, surrogate models are used to improve neutron correlations predictions and quantify the errors on those predictions. Then, the inverse uncertainty quantification is performed to include the impact of measurement error alongside the residual model bias.

In this research work, we have demonstrated the application of Mask-RCNN (Regional Convolutional Neural Network), a deep-learning algorithm for computer vision and specifically object detection, to semiconductor defect inspection domain. Stochastic defect detection and classification during semiconductor manufacturing has grown to be a challenging task as we continuously shrink circuit pattern dimensions (e.g., for pitches less than 32 nm). Defect inspection and analysis by state-of-the-art optical and e-beam inspection tools is generally driven by some rule-based techniques, which in turn often causes to misclassification and thereby necessitating human expert intervention. In this work, we have revisited and extended our previous deep learning-based defect classification and detection method towards improved defect instance segmentation in SEM images with precise extent of defect as well as generating a mask for each defect category/instance. This also enables to extract and calibrate each segmented mask and quantify the pixels that make up each mask, which in turn enables us to count each categorical defect instances as well as to calculate the surface area in terms of pixels. We are aiming at detecting and segmenting different types of inter-class stochastic defect patterns such as bridge, break, and line collapse as well as to differentiate accurately between intra-class multi-categorical defect bridge scenarios (as thin/single/multi-line/horizontal/non-horizontal) for aggressive pitches as well as thin resists (High NA applications). Our proposed approach demonstrates its effectiveness both quantitatively and qualitatively.