Measure of uncertainty in past lifetime distribution plays an important role in the context of information theory, forensic science and other related fields. In the present work, we propose non-parametric kernel type estimator for generalized past entropy function, which was introduced by Gupta and Nanda [9], under $\alpha$-mixing sample. The resulting estimator is shown to be weak and strong consistent and asymptotically normally distributed under certain regularity conditions. The performance of the estimator is validated through simulation study and a real data set.

Anxiety about nuclear war emerged after the 1945 atomic bombings of Japan and has risen and fallen over the following decades. It is grounded in future thinking shaped by narrative form and function in policy discussions and especially in film and television. These media have repeatedly drawn on three basic narrative templates organised around three different endings: destruction, judgement, and renewal; human extinction; and permanent and irreversible societal collapse. Several film and television productions are used to illustrate the internal organisation of these narrative templates and to examine how both nuclear fear and nuclear anxiety are involved.

Linear Temporal Logic (LTL) offers a formal way of specifying complex objectives for Cyber-Physical Systems (CPS). In the presence of uncertain dynamics, the planning for an LTL objective can be solved by model-free reinforcement learning (RL). Surrogate rewards for LTL objectives are commonly utilized in model-free RL for LTL objectives. In a widely adopted surrogate reward approach, two discount factors are used to ensure that the expected return (i.e., the cumulative reward) approximates the satisfaction probability of the LTL objective. The expected return then can be estimated by methods using the Bellman updates such as RL. However, the uniqueness of the solution to the Bellman equation with two discount factors has not been explicitly discussed. We demonstrate, through an example, that when one of the discount factors is set to one, as allowed in many previous works, the Bellman equation may have multiple solutions, leading to an inaccurate evaluation of the expected return. To address this issue, we propose a condition that ensures the Bellman equation has the expected return as its unique solution. Specifically, we require that the solutions for states within rejecting bottom strongly connected components (BSCCs) be zero. We prove that this condition guarantees the uniqueness of the solution, first for recurrent states (i.e., states within a BSCC) and then for transient states. Finally, we numerically validate our results through case studies.

Course-prerequisite networks (CPNs) are directed acyclic graphs that model complex academic curricula by representing courses as nodes and dependencies between them as directed links. These networks are indispensable tools for visualizing, studying, and understanding curricula. For example, CPNs can be used to detect important courses, improve advising, guide curriculum design, analyze graduation time distributions, and quantify the strength of knowledge flow between different university departments. However, most CPN analyses to date have focused only on micro- and meso-scale properties. To fill this gap, we define and study three new global CPN measures: breadth, depth, and flux. All three measures are invariant under transitive reduction and are based on the concept of topological stratification, which generalizes topological ordering in directed acyclic graphs. These measures can be used for macro-scale comparison of different CPNs. We illustrate the new measures numerically by applying them to three real and synthetic CPNs from three universities: the Cyprus University of Technology, the California Institute of Technology, and Johns Hopkins University. The CPN data analyzed in this paper are publicly available in a GitHub repository.

The main goal of this paper is to introduce a new model of evolvement of beliefs on networks. It generalizes the DeGroot model and describes the iterative process of establishing the consensus in isolated social networks in the case of nonlinear aggregation functions. Our main tools come from mean theory and graph theory. The case, when the root set of the network (influencers, news agencies, etc.) is ergodic is fully discussed. The other possibility, when the root contains more than one component, is partially discussed and it could be a motivation for further research.

This study focuses on the development and testing of SensHB.Q, a force-sensitive interface for driving omnidirectional motorized systems such as wheelchairs, precision agriculture rovers, hospital beds, mobile service robots, and heavy-duty platforms. As manual driving is still fundamental in transportation vehicles, the design of intuitive driving interfaces has a major impact on the user experience. Force-sensitive interfaces measure the forces and torques applied by the driver on a sensitive area of the device and then convert these force inputs into commands for the omnidirectional system. In this paper, the design of the SensHB.Q force-sensitive interface and the transfer function for converting force inputs into speed commands are presented. Experimental tests are then conducted to validate the effectiveness of this interface in controlling two omnidirectional motorized systems: MoviWE.Q electrically powered wheelchair and Agrimaro.Q rover for precision agriculture in greenhouses.

Large language models (LLMs) excel at understanding natural language but struggle with explicit commonsense reasoning. A recent trend of research suggests that the combination of LLM with robust symbolic reasoning systems can overcome this problem on story-based question answering (Q&A) tasks. In this setting, existing approaches typically depend on human expertise to manually craft the symbolic component. We argue, however, that this component can also be automatically learned from examples. In this work, we introduce LLM2LAS, a hybrid system that effectively combines the natural language understanding capabilities of LLMs, the rule induction power of the learning from answer sets (LAS) system ILASP, and the formal reasoning strengths of answer set programming (ASP). LLMs are used to extract semantic structures from text, which ILASP then transforms into interpretable logic rules. These rules allow an ASP solver to perform precise and consistent reasoning, enabling correct answers to previously unseen questions. Empirical results outline the strengths and weaknesses of our automatic approach for learning and reasoning in a story-based Q&A benchmark.

Hybrid prototyping (HP) – the combination of mixed prototyping media within a single product design – has shown potential to substantially reduce process cost and fabrication time. However, previous work has not considered how HP processes and fabrication should be aligned with designer intent or activity needs, how these may change the realised savings or good practice guidance for successful implementation. This work proposes three approaches for HP with Lego and additive manufacturing, targeted towards enabling mixed fidelity for prototype flexibility, parallelisation for rapid fabrication and component reuse to minimise material waste. It then establishes good practice guidance and proposes a HP method that accounts for practical and process constraints, then implemented through an automated hybridisation tool. Approaches are compared through a simulation study and a case study to establish relative benefit. Results show potential time and material savings of 56% and 76%, respectively, depending on the approach chosen, demonstrating the substantial and practical scope for savings that HP provides.