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Nonlinear tracking control enabling a dynamical system to track a desired trajectory is fundamental to robotics, serving a wide range of civil and defense applications. In control engineering, designing tracking control requires complete knowledge of the system model and equations. We develop a model-free, machine-learning framework to control a two-arm robotic manipulator using only partially observed states, where the controller is realized by reservoir computing. Stochastic input is exploited for training, which consists of the observed partial state vector as the first and its immediate future as the second component so that the neural machine regards the latter as the future state of the former. In the testing (deployment) phase, the immediate-future component is replaced by the desired observational vector from the reference trajectory. We demonstrate the effectiveness of the control framework using a variety of periodic and chaotic signals, and establish its robustness against measurement noise, disturbances, and uncertainties.

Point source localisation is generally modelled as a Lasso-type problem on measures. However, optimisation methods in non-Hilbert spaces, such as the space of Radon measures, are much less developed than in Hilbert spaces. Most numerical algorithms for point source localisation are based on the Frank-Wolfe conditional gradient method, for which ad hoc convergence theory is developed. We develop extensions of proximal-type methods to spaces of measures. This includes forward-backward splitting, its inertial version, and primal-dual proximal splitting. Their convergence proofs follow standard patterns. We demonstrate their numerical efficacy.

Assessing and comparing the security level of different voting systems is non-trivial as the technical means provided for and societal assumptions made about various systems differ significantly. However, trust assumptions concerning the involved parties are present for all voting systems and can be used as a basis for comparison. This paper discusses eight concrete voting systems with different properties, 12 types of parties involved, and seven general security goals set for voting. The emerging trust relations are assessed for their criticality, and the result is used for comparison of the considered systems.

Nonparametric varying coefficient (NVC) models are useful for modeling time-varying effects on responses that are measured repeatedly for the same subjects. When the number of covariates is moderate or large, it is desirable to perform variable selection from the varying coefficient functions. However, existing methods for variable selection in NVC models either fail to account for within-subject correlations or require the practitioner to specify a parametric form for the correlation structure. In this paper, we introduce the nonparametric varying coefficient spike-and-slab lasso (NVC-SSL) for Bayesian high-dimensional NVC models. Through the introduction of functional random effects, our method allows for flexible modeling of within-subject correlations without needing to specify a parametric covariance function. We further propose several scalable optimization and Markov chain Monte Carlo (MCMC) algorithms. For variable selection, we propose an Expectation Conditional Maximization (ECM) algorithm to rapidly obtain maximum a posteriori (MAP) estimates. Our ECM algorithm scales linearly in the total number of observations $N$ and the number of covariates $p$. For uncertainty quantification, we introduce an approximate MCMC algorithm that also scales linearly in both $N$ and $p$. We demonstrate the scalability, variable selection performance, and inferential capabilities of our method through simulations and a real data application. These algorithms are implemented in the publicly available R package NVCSSL on the Comprehensive R Archive Network.

Recent span-based joint extraction models have demonstrated significant advantages in both entity recognition and relation extraction. These models treat text spans as candidate entities, and span pairs as candidate relationship tuples, achieving state-of-the-art results on datasets like ADE. However, these models encounter a significant number of non-entity spans or irrelevant span pairs during the tasks, impairing model performance significantly. To address this issue, this paper introduces a span-based multitask entity-relation joint extraction model. This approach employs the multitask learning to alleviate the impact of negative samples on entity and relation classifiers. Additionally, we leverage the Intersection over Union(IoU) concept to introduce the positional information into the entity classifier, achieving a span boundary detection. Furthermore, by incorporating the entity Logits predicted by the entity classifier into the embedded representation of entity pairs, the semantic input for the relation classifier is enriched. Experimental results demonstrate that our proposed SpERT.MT model can effectively mitigate the adverse effects of excessive negative samples on the model performance. Furthermore, the model demonstrated commendable F1 scores of 73.61\%, 53.72\%, and 83.72\% on three widely employed public datasets, namely CoNLL04, SciERC, and ADE, respectively.

When faced with a constant target density, geodesic slice sampling on the sphere simplifies to a geodesic random walk. We prove that this random walk is Wasserstein contractive and that its contraction rate stabilizes with increasing dimension instead of deteriorating arbitrarily far. This demonstrates that the performance of geodesic slice sampling on the sphere can be entirely robust against dimension-increases, which had not been known before. Our result is also of interest due to its implications regarding the potential for dimension-independent performance by Gibbsian polar slice sampling, which is an MCMC method on $\mathbb{R}^d$ that implicitly uses geodesic slice sampling on the sphere within its transition mechanism.

Complex networks are used to model many real-world systems. However, the dimensionality of these systems can make them challenging to analyze. Dimensionality reduction techniques like POD can be used in such cases. However, these models are susceptible to perturbations in the input data. We propose an algorithmic framework that combines techniques from pattern recognition (PR) and stochastic filtering theory to enhance the output of such models. The results of our study show that our method can improve the accuracy of the surrogate model under perturbed inputs. Deep Neural Networks (DNNs) are susceptible to adversarial attacks. However, recent research has revealed that Neural Ordinary Differential Equations (neural ODEs) exhibit robustness in specific applications. We benchmark our algorithmic framework with the neural ODE-based approach as a reference.

This work uses the entropy-regularised relaxed stochastic control perspective as a principled framework for designing reinforcement learning (RL) algorithms. Herein agent interacts with the environment by generating noisy controls distributed according to the optimal relaxed policy. The noisy policies on the one hand, explore the space and hence facilitate learning but, on the other hand, introduce bias by assigning a positive probability to non-optimal actions. This exploration-exploitation trade-off is determined by the strength of entropy regularisation. We study algorithms resulting from two entropy regularisation formulations: the exploratory control approach, where entropy is added to the cost objective, and the proximal policy update approach, where entropy penalises policy divergence between consecutive episodes. We focus on the finite horizon continuous-time linear-quadratic (LQ) RL problem, where a linear dynamics with unknown drift coefficients is controlled subject to quadratic costs. In this setting, both algorithms yield a Gaussian relaxed policy. We quantify the precise difference between the value functions of a Gaussian policy and its noisy evaluation and show that the execution noise must be independent across time. By tuning the frequency of sampling from relaxed policies and the parameter governing the strength of entropy regularisation, we prove that the regret, for both learning algorithms, is of the order $\mathcal{O}(\sqrt{N}) $ (up to a logarithmic factor) over $N$ episodes, matching the best known result from the literature.

Graph-centric artificial intelligence (graph AI) has achieved remarkable success in modeling interacting systems prevalent in nature, from dynamical systems in biology to particle physics. The increasing heterogeneity of data calls for graph neural architectures that can combine multiple inductive biases. However, combining data from various sources is challenging because appropriate inductive bias may vary by data modality. Multimodal learning methods fuse multiple data modalities while leveraging cross-modal dependencies to address this challenge. Here, we survey 140 studies in graph-centric AI and realize that diverse data types are increasingly brought together using graphs and fed into sophisticated multimodal models. These models stratify into image-, language-, and knowledge-grounded multimodal learning. We put forward an algorithmic blueprint for multimodal graph learning based on this categorization. The blueprint serves as a way to group state-of-the-art architectures that treat multimodal data by choosing appropriately four different components. This effort can pave the way for standardizing the design of sophisticated multimodal architectures for highly complex real-world problems.

In large-scale systems there are fundamental challenges when centralised techniques are used for task allocation. The number of interactions is limited by resource constraints such as on computation, storage, and network communication. We can increase scalability by implementing the system as a distributed task-allocation system, sharing tasks across many agents. However, this also increases the resource cost of communications and synchronisation, and is difficult to scale. In this paper we present four algorithms to solve these problems. The combination of these algorithms enable each agent to improve their task allocation strategy through reinforcement learning, while changing how much they explore the system in response to how optimal they believe their current strategy is, given their past experience. We focus on distributed agent systems where the agents' behaviours are constrained by resource usage limits, limiting agents to local rather than system-wide knowledge. We evaluate these algorithms in a simulated environment where agents are given a task composed of multiple subtasks that must be allocated to other agents with differing capabilities, to then carry out those tasks. We also simulate real-life system effects such as networking instability. Our solution is shown to solve the task allocation problem to 6.7% of the theoretical optimal within the system configurations considered. It provides 5x better performance recovery over no-knowledge retention approaches when system connectivity is impacted, and is tested against systems up to 100 agents with less than a 9% impact on the algorithms' performance.