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We investigate numbers of faces of polytopes. We begin with the face numbers of 3-polytopes. The characterisation of $f$-vectors of $d$-polytopes ($d\ge 4$) is beyond our current means.In view of this, researchers have considered characterisations of the "projections" of the $f$-vectors, namely the proper subsequences of the $f$-vector; we review the existing results. Section 8.2 gives a proof of a theorem of Xue (2021) on the minimum number of faces of $d$-polytopes with at most $2d$ vertices, answering a conjecture of Grunbaum (2003). This is followed by results on the minimum number of faces of $d$-polytopes with more than $2d$ vertices. We then discuss the lower and upper bound theorems for simplicial polytopes, due to Barnette (1973) and McMullen (1970), respectively, and their extensions such as the $g$-conjecture of McMullen (1971), now the $g$-theorem. The proof of the lower bound theorem connects rigidity theory and the combinatorics polytopes. The chapter ends with a discussion of the flag vector of a polytope. This includes a result of Bayer and Billera (1985) on linear equations for flag vectors like the Dehn--Sommerville’s equations for simplicial polytopes.
The \textit{diameter} of a graph $G$, denoted $\diam G$, is the maximum distance between any two vertices in the graph. The \textit{diameter} of polyhedra is defined as the diameter of their graphs. While the chapter focusses on polytopes, polyhedra also feature in it.There is a connection between diameters of polyhedra and linear programming, and this is partially materialised through the \defn{Hirsch conjectures}, conjectures that relate the diameter of a polyhedra with its dimension and number of facets. We first show that the unbounded and monotonic versions of these conjectures are false (Section 7.2). Early on, Klee and Walkup (1967) realised that problems on the diameter of polyhedra can be reduced to problems on the diameter of simple polyhedra; this and other reductions are the focus of Section 7.3. We also present the counterexample of Santos (2012) for the bounded Hirsch conjecture. We then move to examine lower and upper bounds for the diameter of general polytopes and the diameter of specific polytopes. The final section is devoted to generalisations of polyhedra where diameters may be easier to compute or estimate.
Convex polytopes can be equivalently defined as bounded intersections of finitely many halfspaces in some $\R^{d}$ and as convex hulls of finitely many points in $\R^{d}$.A halfspace is defined by a linear inequality, and each nonempty closed convex set in $\R^{d}$ is the set of solutions of a system of possibly infinite linear inequalities.If we have a finite number of inequalities, the set is a \textit{polyhedron}.Polyhedra are therefore generalisations of polytopes and polyhedral cones. Many assertions in this chapter, such as the facial structure of polytopes, are derived from analogous assertions about polyhedra. We learn how to preprocess objects via projective transformations to simplify the solution of a problem. We then discuss common examples of polytopes. For the visualisation of low-dimensional polytopes, we study Schlegel diagrams, a special type of polytopal complex. We will also examine common results in polytope theory such as the Euler--Poincar\’e--Schl\"afli equation, and a theorem of Bruggesser and Mani (1971) on the existence of shelling orders.The chapter ends with Gale transforms, a useful device to study polytopes with small number of vertices.
In this article, we review the main results achieved by the research activities carried out at PRISMA Lab of the University of Naples Federico II where, for 35 years, an interdisciplinary team of experts developed robots that are ultimately useful to humans. We summarize the key contributions made in the last decade in the six research areas of dynamic manipulation and locomotion, aerial robotics, human-robot interaction, artificial intelligence and cognitive robotics, industrial robotics, and medical robotics. After a brief overview of each research field, the most significant methodologies and results are reported and discussed, highlighting their cross-disciplinary and translational aspects. Finally, the potential future research directions identified are discussed.
Collaborative robots are becoming intelligent assistants of human in industrial settings and daily lives. Dynamic model identification is an active topic for collaborative robots because it can provide effective ways to achieve precise control, fast collision detection and smooth lead-through programming. In this research, an improved iterative approach with a comprehensive friction model for dynamic model identification is proposed for collaborative robots when the joint velocity, temperature and load torque effects are considered. Experiments are conducted on the AUBO I5 collaborative robots. Two other existing identification algorithms are adopted to make comparison with the proposed approach. It is verified that the average error of the proposed I-IRLS algorithm is reduced by over 14% than that of the classical IRLS algorithm. The proposed I-IRLS method can be widely used in various application scenarios of collaborative robots.
In 2003, a new radio programme called Radioatelier was launched as part of the Czech Radio 3 – Vltava broadcast, the national public service art channel. It was aimed at presenting experimental radio forms, something completely unprecedented at that time. With 213 new commissions by December 2022, the programme entered its third decade of existence, having won a number of major radio art awards, while facing threats of impending programme cancellation in 2023. The present article is quite personal, offering generational insights of the producer, who was privileged enough to set goals and scope of the programme in its initial stages and who went on to co-exist with it for the following two decades. It also presents the complete list of sound compositions commissioned by Radioatelier between 2003 and 2022.
Now in its third edition, this textbook is a comprehensive introduction to the multidisciplinary field of mobile robotics, which lies at the intersection of artificial intelligence, computational vision, and traditional robotics. Written for advanced undergraduates and graduate students in computer science and engineering, the book covers algorithms for a range of strategies for locomotion, sensing, and reasoning. The new edition includes recent advances in robotics and intelligent machines, including coverage of human-robot interaction, robot ethics, and the application of advanced AI techniques to end-to-end robot control and specific computational tasks. This book also provides support for a number of algorithms using ROS 2, and includes a review of critical mathematical material and an extensive list of sample problems. Researchers as well as students in the field of mobile robotics will appreciate this comprehensive treatment of state-of-the-art methods and key technologies.
The present study aims to explore how pre- and in-service language teachers incorporate the cutting-edge technology of immersive virtual reality (iVR) into their teaching practice. Specifically, the study examined how their different knowledge levels and teaching experiences influenced their integration of technology by analyzing their performance-based tasks in microteaching in an iVR environment. This particular technology was selected for the study because it was expected to bring multiple pedagogical benefits to future foreign language learning classrooms, such as contextualized learning, increased learner motivation and interest, and enhanced interaction and communicative skill training. The study employed in-depth qualitative analysis. Data (lesson plans, screen recordings of microteaching episodes, and reflection papers) were collected from one preservice teacher training course and one in-service teacher training course at a Korean university. The study found a large gap between pre- and in-service teacher performance and identified the sources of the differences based on qualitative data analysis. The results showed that not only teachers’ technological knowledge but also their pedagogical knowledge of the use of technology and confidence in teaching affected technology integration. As technology integration has become more important in language education, the current study provided insight into how to better prepare teachers for future learners.
This paper considers the first passage times to constant boundaries and the two-sided exit problem for Lévy process with a characteristic exponent in which at least one of the two jumps having rational Laplace transforms. The joint distribution of the first passage times and undershoot/overshoot are obtained. The processes recover many models that have appeared in the literature such as the compound Poisson risk models, the perturbed compound Poisson risk models, and their dual ones. As applications, we obtain the solutions for popular path-dependent options such as lookback and barrier options in terms of Laplace transforms.
Recent advances in machine learning have enabled computers to converse with humans meaningfully. In this study, we propose using this technology to facilitate design conversations in large-scale urban development projects by creating chatbot systems that can automate and streamline information exchange between stakeholders and designers. To this end, we developed and evaluated a proof-of-concept chatbot system that can perform design conversations on a specific construction project and convert those conversations into a list of requirements. Next, in an experiment with 56 participants, we compared the chatbot system to a regular online survey, focusing on user satisfaction and the quality and quantity of collected information. The results revealed that, with regard to user satisfaction, the participants preferred the chatbot experience to a regular survey. However, we found that chatbot conversations produced more data than the survey, with a similar rate of novel ideas but fewer themes. Our findings provide robust evidence that chatbots can be effectively used for design discussions in large-scale design projects and offer a user-friendly experience that can help to engage people in the design process. Based on this evidence, by providing a space for meaningful conversations between stakeholders and expanding the reach of design projects, the use of chatbot systems in interactive design systems can potentially improve design processes and their outcomes.
As the world has become more digitally dependent, questions of data governance, such as ethics, institutional arrangements, and statistical protection measures, have increased in significance. Understanding the economic contribution of investments in data sharing and data governance is highly problematic: outputs and outcomes are often widely dispersed and hard to measure, and the value of those investments is very context-dependent. The “Five Safes” is a popular data governance framework. It is used to design and critique data management strategies across the world and has also been used as a performance framework to measure the effectiveness of data access operations. We report on a novel application of the Five Safes framework to structure the economic evaluation of data governance. The Five Safes was designed to allow structured investigation into data governance. Combining this with more traditional logic models can provide an evaluation methodology that is practical, reproducible, and comparable. We illustrate this by considering the application of the combined logic model-Five Safes framework to data governance for agronomy investments in Ethiopia. We demonstrate how the Five Safes was used to generate the necessary context for a more traditional quantitative study, and consider lessons learned for the wider evaluation of data and data governance investments.
Domain adaptation is important in agriculture because agricultural systems have their own individual characteristics. Applying the same treatment practices (e.g., fertilization) to different systems may not have the desired effect due to those characteristics. Domain adaptation is also an inherent aspect of digital twins. In this work, we examine the potential of transfer learning for domain adaptation in pasture digital twins. We use a synthetic dataset of grassland pasture simulations to pretrain and fine-tune machine learning metamodels for nitrogen response rate prediction. We investigate the outcome in locations with diverse climates, and examine the effect on the results of including more weather and agricultural management practices data during the pretraining phase. We find that transfer learning seems promising to make the models adapt to new conditions. Moreover, our experiments show that adding more weather data on the pretraining phase has a small effect on fine-tuned model performance compared to adding more management practices. This is an interesting finding that is worth further investigation in future studies.
This paper explores and experimentally compares the effectiveness of robot-stopping approaches based on the speed and separation monitoring for improving fluency in collaborative robotics. In the compared approaches, a supervisory controller checks the distance between the bounding volumes enclosing human operator and robot and prevents potential collisions by determining the robot’s stop time and triggering a stop trajectory if necessary. The methods are tested on a Franka Emika robot with 7 degrees of freedom, involving 27 volunteer participants, who are asked to walk along assigned paths to cyclically intrude the robot workspace, while the manipulator is working. The experimental results show that scaling online the dynamic safety zones is beneficial for improving fluency of human-robot collaboration, showing significant statistical differences with respect to alternative approaches.