We introduce the notion of the Lie derivative in the context of dual quaternions that represent rigid motions and twists. First we define the wrench in terms of dual quaternions. Then we show how the Lie derivative helps understand how actuators affect an end effector in parallel robots, and make it explicit in the two cases case of Stewart Platforms, and cable-driven parallel robots. We also show how to use Lie derivatives with the Newton-Raphson Method to solve the forward kinematic problem for over constrained parallel actuators. Finally, we derive the equations of motion of the end effector in dual quaternion form, which include the effect of inertia from the actuators.
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Tracking ripening tomatoes is time consuming and labor intensive. Artificial intelligence technologies combined with those of computer vision can help users optimize the process of monitoring the ripening status of plants. To this end, we have proposed a tomato ripening monitoring approach based on deep learning in complex scenes. The objective is to detect mature tomatoes and harvest them in a timely manner. The proposed approach is declined in two parts. Firstly, the images of the scene are transmitted to the pre-processing layer. This process allows the detection of areas of interest (area of the image containing tomatoes). Then, these images are used as input to the maturity detection layer. This layer, based on a deep neural network learning algorithm, classifies the tomato thumbnails provided to it in one of the following five categories: green, brittle, pink, pale red, mature red. The experiments are based on images collected from the internet gathered through searches using tomato state across diverse languages including English, German, French, and Spanish. The experimental results of the maturity detection layer on a dataset composed of images of tomatoes taken under the extreme conditions, gave a good classification rate.
Bias correction can often improve the finite sample performance of estimators. We show that the choice of bias correction method has no effect on the higher-order variance of semiparametrically efficient parametric estimators, so long as the estimate of the bias is asymptotically linear. It is also shown that bootstrap, jackknife, and analytical bias estimates are asymptotically linear for estimators with higher-order expansions of a standard form. In particular, we find that for a variety of estimators the straightforward bootstrap bias correction gives the same higher-order variance as more complicated analytical or jackknife bias corrections. In contrast, bias corrections that do not estimate the bias at the parametric rate, such as the split-sample jackknife, result in larger higher-order variances in the i.i.d. setting we focus on. For both a cross-sectional MLE and a panel model with individual fixed effects, we show that the split-sample jackknife has a higher-order variance term that is twice as large as that of the `leave-one-out' jackknife.
Reservoir Computing (RC) has become popular in recent years due to its fast and efficient computational capabilities. Standard RC has been shown to be equivalent in the asymptotic limit to Recurrent Kernels, which helps in analyzing its expressive power. However, many well-established RC paradigms, such as Leaky RC, Sparse RC, and Deep RC, are yet to be analyzed in such a way. This study aims to fill this gap by providing an empirical analysis of the equivalence of specific RC architectures with their corresponding Recurrent Kernel formulation. We conduct a convergence study by varying the activation function implemented in each architecture. Our study also sheds light on the role of sparse connections in RC architectures and propose an optimal sparsity level that depends on the reservoir size. Furthermore, our systematic analysis shows that in Deep RC models, convergence is better achieved with successive reservoirs of decreasing sizes.
We present a pipeline for unbiased and robust multimodal registration of neuroimaging modalities with minimal pre-processing. While typical multimodal studies need to use multiple independent processing pipelines, with diverse options and hyperparameters, we propose a single and structured framework to jointly process different image modalities. The use of state-of-the-art learning-based techniques enables fast inferences, which makes the presented method suitable for large-scale and/or multi-cohort datasets with a diverse number of modalities per session. The pipeline currently works with structural MRI, resting state fMRI and amyloid PET images. We show the predictive power of the derived biomarkers using in a case-control study and study the cross-modal relationship between different image modalities. The code can be found in https: //github.com/acasamitjana/JUMP.
Bayesian inversions followed by estimations of rare event probabilities are often needed to analyse groundwater hazards. Instead of focusing on the posterior distribution of model parameters, the main interest lies then in the distribution of a specific quantity of interest contingent upon these parameters. To address the associated methodological challenges, we introduce a two-stage Sequential Monte Carlo approach. In the first stage, it generates particles that approximate the posterior distribution; in the second stage, it employs subset sampling techniques to assess the probability of the rare event of interest. By considering two hydrogeological problems of increasing complexity, we showcase the efficiency and accuracy of the resulting PostRisk-SMC method for rare event probability estimation related to groundwater hazards. We compare the performance of the PostRisk-SMC method with a traditional Monte Carlo approach that relies on Markov chain Monte Carlo samples. We showcase that our estimates align with those of the traditional method, but the coefficients of variation are notably lower for the same computational budget when targeting more rare events. Furthermore, we highlight that the PostRisk-SMC method allows estimating rare event probabilities approaching one in a billion using less than one hundred thousand forward simulations. Even if the presented examples are related to groundwater hazards, the methodology is well-suited for addressing a wide range of topics in the geosciences and beyond.
Depth perception in volumetric visualization plays a crucial role in the understanding and interpretation of volumetric data. Numerous visualization techniques, many of which rely on physically based optical effects, promise to improve depth perception but often do so without considering camera movement or the content of the volume. As a result, the findings from previous studies may not be directly applicable to crowded volumes, where a large number of contained structures disrupts spatial perception. Crowded volumes therefore require special analysis and visualization tools with sparsification capabilities. Interactivity is an integral part of visualizing and exploring crowded spaces, but has received little attention in previous studies. To address this gap, we conducted a study to assess the impact of different rendering techniques on depth perception in crowded volumes, with a particular focus on the effects of camera movement. The results show that depth perception considering camera motion depends much more on the content of the volume than on the chosen visualization technique. Furthermore, we found that traditional rendering techniques, which have often performed poorly in previous studies, showed comparable performance to physically based methods in our study.
Hamiltonian Monte Carlo (HMC) is a powerful tool for Bayesian statistical inference due to its potential to rapidly explore high dimensional state space, avoiding the random walk behavior typical of many Markov Chain Monte Carlo samplers. The proper choice of the integrator of the Hamiltonian dynamics is key to the efficiency of HMC. It is becoming increasingly clear that multi-stage splitting integrators are a good alternative to the Verlet method, traditionally used in HMC. Here we propose a principled way of finding optimal, problem-specific integration schemes (in terms of the best conservation of energy for harmonic forces/Gaussian targets) within the families of 2- and 3-stage splitting integrators. The method, which we call Adaptive Integration Approach for statistics, or s-AIA, uses a multivariate Gaussian model and simulation data obtained at the HMC burn-in stage to identify a system-specific dimensional stability interval and assigns the most appropriate 2-/3-stage integrator for any user-chosen simulation step size within that interval. s-AIA has been implemented in the in-house software package HaiCS without introducing computational overheads in the simulations. The efficiency of the s-AIA integrators and their impact on the HMC accuracy, sampling performance and convergence are discussed in comparison with known fixed-parameter multi-stage splitting integrators (including Verlet). Numerical experiments on well-known statistical models show that the adaptive schemes reach the best possible performance within the family of 2-, 3-stage splitting schemes.
Semi-structured explanation depicts the implicit process of a reasoner with an explicit representation. This explanation highlights how available information in a specific query is utilised and supplemented with information a reasoner produces from its internal weights towards generating an answer. Despite the recent improvements in generative capabilities of language models, producing structured explanations to verify a model's true reasoning capabilities remains a challenge. This issue is particularly pronounced for not-so-large LMs (e.g., FLAN-T5-XXL). In this work, we first underscore the limitations of supervised fine-tuning (SFT) in tackling this challenge, and then introduce a carefully crafted reward engineering method in reinforcement learning (RL) to better address this problem. We investigate multiple reward aggregation methods and provide a detailed discussion which sheds light on the promising potential of RL for future research. Our proposed method on two semi-structured explanation generation benchmarks (ExplaGraph and COPA-SSE) achieves new state-of-the-art results.
Human-in-the-loop aims to train an accurate prediction model with minimum cost by integrating human knowledge and experience. Humans can provide training data for machine learning applications and directly accomplish some tasks that are hard for computers in the pipeline with the help of machine-based approaches. In this paper, we survey existing works on human-in-the-loop from a data perspective and classify them into three categories with a progressive relationship: (1) the work of improving model performance from data processing, (2) the work of improving model performance through interventional model training, and (3) the design of the system independent human-in-the-loop. Using the above categorization, we summarize major approaches in the field, along with their technical strengths/ weaknesses, we have simple classification and discussion in natural language processing, computer vision, and others. Besides, we provide some open challenges and opportunities. This survey intends to provide a high-level summarization for human-in-the-loop and motivates interested readers to consider approaches for designing effective human-in-the-loop solutions.
Although measuring held-out accuracy has been the primary approach to evaluate generalization, it often overestimates the performance of NLP models, while alternative approaches for evaluating models either focus on individual tasks or on specific behaviors. Inspired by principles of behavioral testing in software engineering, we introduce CheckList, a task-agnostic methodology for testing NLP models. CheckList includes a matrix of general linguistic capabilities and test types that facilitate comprehensive test ideation, as well as a software tool to generate a large and diverse number of test cases quickly. We illustrate the utility of CheckList with tests for three tasks, identifying critical failures in both commercial and state-of-art models. In a user study, a team responsible for a commercial sentiment analysis model found new and actionable bugs in an extensively tested model. In another user study, NLP practitioners with CheckList created twice as many tests, and found almost three times as many bugs as users without it.
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