Increasing global digitalization is changing the everyday language skills required to participate in society, to carry out professional activities, and to take advantage of educational opportunities. As a result, new linguistic and digital competences are required for migrants. At the same time, digitalization offers new potential for learner-oriented language learning. In this article, we compare the results of two studies on teachers of adult multilingual migrant learners. These teachers instruct learners at different levels of literacy and with varied prior formal learning experiences. Both studies are situated in the German education system. The results illustrate how teachers and learners can work together using digital technologies to promote language learning. We explore the opportunities for effective, multilingual, and motivating language learning, as well as the challenges faced by learners and teachers, pointing to the need for further training in digital technology for both groups.

This paper introduces two enhanced control approaches to improve the performance of parallel manipulators, addressing their inherent nonlinear dynamics and complex structure. The first approach results in a hybrid control system in joint space, integrating acceleration-based control, sliding mode, and disturbance observer techniques. The control system is designed to correct tracking errors and compensate for generalized disturbances, thus improving accuracy in tracking reference positions. The second approach merges the joint-space and task-space formulations, implementing proportional-derivative controllers in task space to manage the end-effector positions while maintaining safe operational configurations. The stability of the proposed controllers is demonstrated through Lyapunov analysis, while their performance is validated through comprehensive simulations and real-time experiments.

Continuous-time batch state estimation using Gaussian processes is an efficient approach to estimate the trajectories of robots over time. In the past, relatively simple physics-motivated priors have been considered for such approaches, using assumptions such as constant velocity or acceleration. This paper presents an approach to incorporating exogenous control inputs, such as velocity or acceleration commands, into the continuous Gaussian process state estimation framework. It is shown that this approach generalizes across different domains in robotics, making it applicable to both the estimation of continuous-time trajectories for mobile robots and the estimation of quasi-static continuum-robot shapes. Results show that incorporating control inputs leads to more informed priors, potentially requiring less measurements and estimation nodes to obtain accurate estimates. This makes the approach particularly useful in situations in which limited sensing is available. For example, in a mobile robot localization experiment with sparse landmark distance measurements and frequent odometry control inputs, our approach provides accurate trajectory estimates with root-mean-square errors around 3-4 cm and 4-5 degrees, even with time intervals up to five seconds between discrete estimation nodes, which significantly reduces computation time.

We explore general notions of consistency. These notions are sentences $\mathcal {C}_{\alpha }$ (they depend on numerations $\alpha $ of a certain theory) that generalize the usual features of consistency statements. The following forms of consistency fit the definition of general notions of consistency (${\texttt {Pr}}_{\alpha }$ denotes the provability predicate for the numeration $\alpha $): $\neg {\texttt {Pr}}_{\alpha }(\ulcorner \perp \urcorner )$, $\omega \text {-}{\texttt {Con}}_{\alpha }$ (the formalized $\omega $-consistency), $\neg {\texttt {Pr}}_{\alpha }(\ulcorner {\texttt {Pr}}_{\alpha }(\ulcorner \cdots {\texttt {Pr}}_{\alpha }(\ulcorner \perp \urcorner )\cdots \urcorner )\urcorner )$, and $n\text {-}{\texttt {Con}}_{\alpha }$ (the formalized n-consistency of Kreisel).

We generalize the former notions of consistency while maintaining two important features, to wit: Gödel’s Second Incompleteness Theorem, i.e., (with $\xi $ some standard $\Delta _0(T)$-numeration of the axioms of T), and a result by Feferman that guarantees the existence of a numeration $\tau $ such that $T\vdash \mathcal {C}_\tau $.

We encompass slow consistency into our framework. To show how transversal and natural our approach is, we create a notion of provability from a given $\mathcal {C}_{\alpha }$, we call it $\mathcal {P}_{\mathcal {C}_{\alpha }}$, and we present sufficient conditions on $\mathcal {C}_{\alpha }$ for the notion $\mathcal {P}_{\mathcal {C}_{\alpha }}$ to satisfy the standard derivability conditions. Moreover, we also develop a notion of interpretability from a given $\mathcal {C}_{\alpha }$, we call it $\rhd _{\mathcal {C}_{\alpha }}$, and we study some of its properties. All these new notions—of provability and interpretability—serve primarily to emphasize the naturalness of our notions, not necessarily to give insights on these topics.

Functional programmers have many things for which to thank the late David Turner: design decisions he made in his languages SASL, KRC, and Miranda over the last 50 years are still influential and inspirational now. In particular, Turner was a strong advocate of lazy evaluation and of list comprehensions. As an illustration of these techniques, he popularized a one-line recursive “sieve” to generate the infinite list of prime numbers.

Turner called this algorithm The Sieve of Eratosthenes. In a lovely paper called “The Genuine Sieve of Eratosthenes”, Melissa O’Neill argued that Turner’s program is not in fact a faithful implementation of the algorithm, and gave a detailed presentation using priority queues of the real thing. She included a variation by Richard Bird, which uses only lists but makes clever use of circular programming. Bird describes his circular program again in his textbook “Thinking Functionally with Haskell”, and sets its proof of correctness as an exercise. In particular, why is this circular program productive? Unfortunately, Bird’s hint for a solution is incorrect. So what should a proof look like?

One of the last projects Turner worked on was the notion of “Total Functional Programming”. He observed that most programs are already structurally recursive or corecursive, therefore guaranteed respectively terminating or productive; he conjectured that “with more practice we will find this is always true”. We explore Bird’s circular Sieve of Eratosthenes as a challenge problem for Turner’s Total Functional Programming.

In the last two decades the study of random instances of constraint satisfaction problems (CSPs) has flourished across several disciplines, including computer science, mathematics and physics. The diversity of the developed methods, on the rigorous and non-rigorous side, has led to major advances regarding both the theoretical as well as the applied viewpoints. Based on a ceteris paribus approach in terms of the density evolution equations known from statistical physics, we focus on a specific prominent class of regular CSPs, the so-called occupation problems, and in particular on $r$-in-$k$ occupation problems. By now, out of these CSPs only the satisfiability threshold – the largest degree for which the problem admits asymptotically a solution – for the $1$-in-$k$ occupation problem has been rigorously established. Here we determine the satisfiability threshold of the $2$-in-$k$ occupation problem for all $k$. In the proof we exploit the connection of an associated optimization problem regarding the overlap of satisfying assignments to a fixed point problem inspired by belief propagation, a message passing algorithm developed for solving such CSPs.

The safety of human-collaborative operations with robots depends on monitoring the external torque of the robot, in which there are toque sensor-based and torque sensor-free methods. Economically, the classic method for estimating joint external torque is the first-order momentum observer (MOB) based on a physic model without torque sensors. However, uncertainties in the dynamic model, which encompasses parameters identification error and joint friction, affect the torque estimation accuracy. To address this issue, this paper proposes using the backpropagation neural network (BPNN) method to estimate joint external torque without the delicate physical model by utilizing the powerful machine learning ability to handle the uncertainties of the MOB method and improve the accuracy of torque estimation. Using data obtained from the torque sensor to train the BPNN to build up a digital torque model, the trained BPNN can perceive force in practical applications without relying on the torque sensor. In the end, by contrast to the classic first-order MOB, the result demonstrates that BPNN achieves higher estimation accuracy compared to the MOB.

Motion primitives play an important role in motion planning for autonomous vehicles, as they effectively address the sampling challenges inherent in nonholonomic motion planning. Employing motion primitives (MPs) is a widely accepted approach in nonholonomic motion planning based on sampling. This study specifically addresses the problem of learning from human-driving data to create human-like trajectories from predefined start-to-end states, which then serve as MP within the sampling-based nonholonomic motion planning framework. In this paper, we propose a deep learning-based method for generating MP that capture human-driving trajectory data features. By processing human-driving trajectory data, we create a Motion Primitive dataset that uniformly covers typical urban driving scenarios. Based on this dataset, a vehicle model long short-term memory neural network model is constructed to learn the features of the human-driving trajectory data. Finally, a framework for the generation of MP for practical applications is given based on this neural network. Our experiments, which focus on the dataset, the MMP generation network, and the generation process, demonstrate that our method significantly improves the training efficacy of the MP generation network. Additionally, the MP generated by our method exhibit higher accuracy compared to traditional methods.