This paper investigates the time N until a random walk first exceeds some specified barrier. Letting $X_i, i \geq 1,$ be a sequence of independent, identically distributed random variables with a log-concave density or probability mass function, we derive both lower and upper bounds on the probability $P(N \gt n),$ as well as bounds on the expected value $E[N].$ On barriers of the form $a + b \sqrt{k},$ where a is nonnegative, b is positive, and k is the number of steps, we provide additional bounds on $E[N].$

This paper offers a substantial improvement in the revision-theoretic approach to conditionals in theories of transparent truth. The main modifications are (i) a new limit rule; (ii) a modification of the extension to the continuum-valued case; and (iii) the suggestion of a variation on how universal quantification is handled, leading to more satisfactory laws of restricted quantification.

In our digital world, reusing data to inform: decisions, advance science, and improve people’s lives should be easier than ever. However, the reuse of data remains limited, complex, and challenging. Some of this complexity requires rethinking consent and public participation processes about it. First, to ensure the legitimacy of uses, including normative aspects like agency and data sovereignty. Second, to enhance data quality and mitigate risks, especially since data are proxies that can misrepresent realities or be oblivious to the original context or use purpose. Third, because data, both as a good and infrastructure, are the building blocks of both technologies and knowledge of public interest that can help societies work towards the well-being of their people and the environment. Using the case study of the European Health Data Space, we propose a multidimensional, polytopic framework with multiple intersections to democratising decision-making and improving the way in which meaningful participation and consent processes are conducted at various levels and from the point of view of institutions, regulations, and practices.

Two salient notions of sameness of theories are synonymy, aka definitional equivalence, and bi-interpretability. Of these two definitional equivalence is the strictest notion. In which cases can we infer synonymy from bi-interpretability? We study this question for the case of sequential theories. Our result is as follows. Suppose that two sequential theories are bi-interpretable and that the interpretations involved in the bi-interpretation are one-dimensional and identity preserving. Then, the theories are synonymous.

The crucial ingredient of our proof is a version of the Schröder–Bernstein theorem under very weak conditions. We think this last result has some independent interest.

We provide an example to show that this result is optimal. There are two finitely axiomatized sequential theories that are bi-interpretable but not synonymous, where precisely one of the interpretations involved in the bi-interpretation is not identity preserving.

In the context of dependent type theory, we show that coinductive predicates have an equivalent topological counterpart in terms of coinductively generated positivity relations, introduced by G. Sambin to represent closed subsets in point-free topology. Our work is complementary to a previous one with M. E. Maietti, where we showed that, in dependent type theory, the well-known concept of wellfounded trees has a topological counterpart in terms of proof-relevant inductively generated formal covers used to provide a predicative and constructive representation of complete suplattices. The proofs performed within Martin–Löf’s type theory and the Minimalist Foundation have been checked in the Agda proof assistant.

Simultaneous localization and mapping technology is the basis for multi-robot systems to complete navigation, path planning, and autonomous exploration in complex, dynamic, and Global Positioning System (GPS)-denied environments. This paper reviews the current status and progress of multi-robot simultaneous localization and mapping (SLAM) technology based on LiDAR. First, this paper studies the basic principles of LiDAR SLAM. It analyzes the system model construction of LiDAR SLAM, including the mobile robot coordinate system model, kinematic model, sensor model, map presentation, LiDAR SLAM framework, and classic algorithms. Then, this paper discusses the basic framework of collaborative SLAM, analyzes the key issues such as data association, loop closure detection, and global graph optimization in collaborative SLAM, and conducts a detailed literature review on the solutions to key problems in sub-fields of multi-robot SLAM such as frontier detection, task allocation, map fusion, and compares the advantages and disadvantages of various algorithms. Finally, this paper outlines the challenges and future research directions of multi-robot LiDAR SLAM.

In recent years, the deterioration of infrastructure facilities, such as bridges, has caused several problems. Currently, human inspectors conduct periodic inspections to identify damaged areas. However, this process is expensive and time-consuming. Therefore, robotic inspection has received significant attention. This study focused on magnet-wheeled inspection robots operating along complex multilevel paths. The movement from the bottom to the top surface of the flanges was particularly difficult, similar to that of an overhanging steel plate. As the motor drives the robot wheel, gravity and anti-torque interfere with the robot’s movement along its path. However, static analysis shows that the impact can be reduced depending on the robot’s posture relative to that of the flange. Therefore, a magnetic-wheeled robot with a posture-changing pushing mechanism is proposed. This study confirms that the proposed robot can travel along its path using a pushing mechanism while carrying a 1.0 kg weight. Therefore, the robot’s ability to conduct inspections while carrying heavy equipment, such as inspection devices, was confirmed.

Robots need a sense of touch to handle objects effectively, and force sensors provide a straightforward way to measure touch or physical contact. However, contact force data are typically sparse and difficult to analyze, as it only appears during contact and is often affected by noise. Therefore, many researchers have consequently relied on vision-based methods for robotic manipulation. However, vision has limitations, such as occlusions that block the camera’s view, making it ineffective or insufficient for dexterous tasks involving contact. This article presents a method for robotic systems operating under quasi-static conditions to perform contact-rich manipulation using only force/torque measurements. First, the interaction forces/torques between the manipulated object and its environment are collected in advance. A potential function is then constructed from the collected force/torque data using Gaussian process regression with derivatives. Next, we develop haptic dynamic movement primitives (Haptic DMPs) to generate robot trajectories. Unlike conventional DMPs, which primarily focus on kinematic aspects, our Haptic DMPs incorporate force-based interactions by integrating the constructed potential energy. The effectiveness of the proposed method is demonstrated through numerical tasks, including the classical peg-in-hole problem.

Human interactions in the online world comprise a combination of positive and negative exchanges. These diverse interactions can be captured using signed network representations, where edges take positive or negative weights to indicate the sentiment of the interaction between individuals. Signed networks offer valuable insights into online political polarization by capturing antagonistic interactions and ideological divides on social media platforms. This study analyzes polarization on Menéame, a Spanish social media platform that facilitates engagement with news stories through comments and voting. Using a dual-method approach—Signed Hamiltonian Eigenvector Embedding for Proximity for signed networks and Correspondence Analysis for unsigned networks—we investigate how including negative ties enhances the understanding of structural polarization levels across different conversation topics on the platform. While the unsigned Menéame network effectively delineates ideological communities, only by incorporating negative ties can we identify ideologically extreme users who engage in antagonistic behaviors: without them, the most extreme users remain indistinguishable from their less confrontational ideological peers.

We present ASP Chef Mustache, an extension of ASP Chef that enhances template-based rendering of answer set programming (ASP) solutions using a logic-less templating system inspired by Mustache. Our approach integrates data visualization frameworks such as Tabulator, Chart.js, and vis.js, enabling interactive representations of ASP interpretations as tables, charts, and graphs. Mustache queries in templates support advanced constructs for formatting, sorting, and multi-stage expansion, facilitating the generation of rich, structured outputs. We demonstrate the power of this framework through a series of use cases, including data analysis for the Italian VQR, visualization of blocking sets in graphs, and scheduling problems. The result is a versatile tool for bridging declarative problem solving and modern web-based visual analytics.