A linear equation $E$ is said to be sparse if there is $c\gt 0$ so that every subset of $[n]$ of size $n^{1-c}$ contains a solution of $E$ in distinct integers. The problem of characterising the sparse equations, first raised by Ruzsa in the 90s, is one of the most important open problems in additive combinatorics. We say that $E$ in $k$ variables is abundant if every subset of $[n]$ of size $\varepsilon n$ contains at least $\text{poly}(\varepsilon )\cdot n^{k-1}$ solutions of $E$. It is clear that every abundant $E$ is sparse, and Girão, Hurley, Illingworth, and Michel asked if the converse implication also holds. In this note, we show that this is the case for every $E$ in four variables. We further discuss a generalisation of this problem which applies to all linear equations.

In the field of laparoscopic surgery, research is currently focusing on the development of new robotic systems to assist practitioners in complex operations, improving the precision of their medical gestures. In this context, the performance of these robotic platforms can be conditioned by various factors, such as the robot’s accessibility and dexterity in the task workspace. In this paper, we present a new strategy for improving the kinematic and dynamic performance of a 7-degrees of freedom robot-assisted camera-holder system for laparoscopic surgery. This approach involves the simultaneous optimization of the robot base placement and the laparoscope mounting orientation. To do so, a general robot capability representation approach is implemented in an innovative multiobjective optimization algorithm. The obtained results are first evaluated in simulation and then validated experimentally by comparing the robot’s performances implementing both the existing and the optimized solution. The optimization result led to a 2% improvement in the accessibility index and a 14% enhancement in manipulability. Furthermore, the dynamic performance criteria resulted in a substantial 43% reduction in power consumption.

Pharmaceutical distribution routing problem is a key problem for pharmaceutical enterprises, since efficient schedules can enhance resource utilization and reduce operating costs. Meanwhile, it is a complicated combinatorial optimization problem. Existing research mainly focused on delivery route lengths or distribution costs minimization, while seldom considered customer priority and carbon emissions simultaneously. However, considering the customer priority and carbon emissions simultaneously will not only help to enhance customer satisfaction, but also help to reduce the carbon emissions. In this article, we consider the customer priority and carbon emission minimization simultaneously in the pharmaceutical distribution routing problem, the corresponding problem is named pharmaceutical distribution routing problem considering customer priority and carbon emissions. A corresponding mathematical model is formulated, the objectives of which are minimizing fixed cost, refrigeration cost, fuel consumption cost, carbon emission cost, and penalty cost for violating time windows. Moreover, a hybrid genetic algorithm (HGA) is proposed to solve the problem. The framework of the proposed HGA is genetic algorithm (GA), where an effective local search based on variable neighborhood search (VNS) is specially designed and incorporated to improve the intensification abilities. In the proposed HGA, crossover with adaptive probability and mutation with adaptive probability are utilized to enhance the algorithm performance. Finally, the proposed HGA is compared with four optimization algorithms, and experimental results have demonstrated the effectiveness of the HGA.

In practical applications, many robots equipped with embedded devices have limited computing capabilities. These limitations often hinder the performance of existing dynamic SLAM algorithms, especially when faced with occlusions or processor constraints. Such challenges lead to subpar positioning accuracy and efficiency. This paper introduces a novel lightweight dynamic SLAM algorithm designed primarily to mitigate the interference caused by moving object occlusions. Our proposed approach combines a deep learning object detection algorithm with a Kalman filter. This combination offers prior information about dynamic objects for each SLAM algorithm frame. Leveraging geometric techniques like RANSAC and the epipolar constraint, our method filters out dynamic feature points, focuses on static feature points for pose determination, and enhances the SLAM algorithm’s robustness in dynamic environments. We conducted experimental validations on the TUM public dataset, which demonstrated that our approach elevates positioning accuracy by approximately 54% and boosts the running speed by 75.47% in dynamic scenes.

The naive combination of polymorphic effects and polymorphic type assignment has been well known to break type safety. In the literature, there are two kinds of approaches to this problem: one is to restrict how effects are triggered and the other is to restrict how they are implemented. This work explores a new approach to ensuring the safety of the use of polymorphic effects in polymorphic type assignment. A novelty of our work is to restrict effect interfaces. To formalize our idea, we employ algebraic effects and handlers, where an effect interface is given by a set of operations coupled with type signatures. We propose signature restriction, a new notion to restrict the type signatures of operations and show that signature restriction ensures type safety of a language equipped with polymorphic effects and unrestricted polymorphic type assignment. We also develop a type-and-effect system to enable the use of both of the operations that satisfy and those that do not satisfy the signature restriction in a single program.

In this qualitative systematic meta-synthesis study, 57 studies from the international literature published between 2010 and 2024 on the use of voice-based artificially intelligent chatbots in English language learning were analyzed. The present study aimed to explore the most recent studies on this topic by investigating the theoretical frameworks, methodological and technological properties, user reports of chatbot usage experience, and pedagogical implementations. It sought to identify research and implementation trends for voice-based chatbots via qualitative data analysis methods. Based on the reviewed studies, this paper presents data-based pedagogical implications that align with the latest voice-based AI chatbot research trends.

A decoupling method is proposed for the elastic stiffness modeling of hybrid robots based on the rigidity principle, screw theory, strain energy, and Castigliano’s second theorem. It enables the decoupling of parallel and serial modules, as well as the individual contributions of each elastic component to the mechanism’s stiffness performance. The method is implemented as follows: (1) formulate limb constraint wrenches and corresponding limb stiffness matrix based on the screw theory and strain energy, (2) formulate the overall stiffness matrix of parallel and serial modules corresponding to end of the hybrid robots based on the rigidity principle, principle of virtual work, the wrench transfer formula, and strain energy methods, and (3) obtain and decouple the overall stiffness matrix and deflection of the robot based on the Castigliano’s second theorem. Finally, A planar hybrid structure and the 4SRRR + 6R hybrid robot are used as illustrative examples to implement the proposed method. The results indicate that selectively enhancing the stiffness performance of the mechanism is the most effective approach.

Suicide is a leading cause of death in the United States, particularly among adolescents. In recent years, suicidal ideation, attempts, and fatalities have increased. Systems maps can effectively represent complex issues such as suicide, thus providing decision-support tools for policymakers to identify and evaluate interventions. While network science has served to examine systems maps in fields such as obesity, there is limited research at the intersection of suicidology and network science. In this paper, we apply network science to a large causal map of adverse childhood experiences (ACEs) and suicide to address this gap. The National Center for Injury Prevention and Control (NCIPC) within the Centers for Disease Control and Prevention recently created a causal map that encapsulates ACEs and adolescent suicide in 361 concept nodes and 946 directed relationships. In this study, we examine this map and three similar models through three related questions: (Q1) how do existing network-based models of suicide differ in terms of node- and network-level characteristics? (Q2) Using the NCIPC model as a unifying framework, how do current suicide intervention strategies align with prevailing theories of suicide? (Q3) How can the use of network science on the NCIPC model guide suicide interventions?