Given two k-graphs (k-uniform hypergraphs) F and H, a perfect F-tiling (or F-factor) in H is a set of vertex-disjoint copies of F that together cover the vertex set of H. For all complete k-partite k-graphs K, Mycroft proved a minimum codegree condition that guarantees a K-factor in an n-vertex k-graph, which is tight up to an error term o(n). In this paper we improve the error term in Mycroft’s result to a sublinear term that relates to the Turán number of K when the differences of the sizes of the vertex classes of K are co-prime. Furthermore, we find a construction which shows that our improved codegree condition is asymptotically tight in infinitely many cases, thus disproving a conjecture of Mycroft. Finally, we determine exact minimum codegree conditions for tiling K(k)(1, … , 1, 2) and tiling loose cycles, thus generalizing the results of Czygrinow, DeBiasio and Nagle, and of Czygrinow, respectively.

This study explores interactions among language learners with the support of online resources in a collaborative writing task and how online resources assisted collaborating learners in the meaning-making process. The study was conducted in the freshman English course at a national university in Taiwan. Fifty-six students constructed an essay in pairs firstly without the support of online resources, and subsequently constructed another essay with the support of online resources. Each pair’s interactional patterns and dynamics of peer scaffolding across the two settings were examined. The findings show that the availability of online resources fosters a variety of interaction characteristics among learners with varied collaboration orientation. Results also suggest that learners’ collaboration predisposition at the onset plays a critical role in influencing the way they used online resources to support their interaction. This study thus suggests that learners’ collaborative patterns and their use of online resources have mutual impact, which may inform teachers seeking to integrate online resources to enhance their students’ collaborative learning.

Consider any fixed graph whose edges have been randomly and independently oriented, and write {S ⇝} to indicate that there is an oriented path going from a vertex s ∊ S to vertex i. Narayanan (2016) proved that for any set S and any two vertices i and j, {S ⇝ i} and {S ⇝ j} are positively correlated. His proof relies on the Ahlswede–Daykin inequality, a rather advanced tool of probabilistic combinatorics.

In this short note I give an elementary proof of the following, stronger result: writing V for the vertex set of the graph, for any source set S, the events {S ⇝ i}, i ∊ V, are positively associated, meaning that the expectation of the product of increasing functionals of the family {S ⇝ i} for i ∊ V is greater than the product of their expectations.

Galois connections are a foundational tool for structuring abstraction in semantics, and their use lies at the heart of the theory of abstract interpretation. Yet, mechanization of Galois connections using proof assistants remains limited to restricted modes of use, preventing their general application in mechanized metatheory and certified programming. This paper presents constructive Galois connections, a variant of Galois connections that is effective both on paper and in proof assistants; is complete with respect to a large subset of classical Galois connections; and enables more general reasoning principles, including the “calculational” style advocated by Cousot. To design constructive Galois connections, we identify a restricted mode of use of classical ones which is both general and amenable to mechanization in dependently typed functional programming languages. Crucial to our metatheory is the addition of monadic structure to Galois connections to control a “specification effect.” Effectful calculations may reason classically, while pure calculations have extractable computational content. Explicitly moving between the worlds of specification and implementation is enabled by our metatheory. To validate our approach, we provide two case studies in mechanizing existing proofs from the literature: the first uses calculational abstract interpretation to design a static analyzer, and the second forms a semantic basis for gradual typing. Both mechanized proofs closely follow their original paper-and-pencil counterparts, employ reasoning principles not captured by previous mechanization approaches, support the extraction of verified algorithms, and are novel.

We obtain the best possible upper bounds for the moments of a single-order statistic from independent, nonnegative random variables, in terms of the population mean. The main result covers the independent identically distributed case. Furthermore, the case of the sample minimum for merely independent (not necessarily identically distributed) random variables is treated in detail.

Biological fish can create high forward swimming speed due to change of thrust/drag area of pectoral fins between power stroke and recovery stroke in rowing mode. In this paper, we proposed a novel type of folding pectoral fins for the fish robot, which provides a simple approach in generating effective thrust only through one degree of freedom of fin actuator. Its structure consists of two elemental fin panels for each pectoral fin that connects to a hinge base through the flexible joints. The Morison force model is adopted to discover the relationship of the dynamic interaction between fin panels and surrounding fluid. An experimental platform for the robot motion using the pectoral fin with different flexible joints was built to validate the proposed design. The results express that the performance of swimming velocity and turning radius of the robot are enhanced effectively. The forward swimming velocity can reach 0.231 m/s (0.58 BL/s) at the frequency near 0.75 Hz. By comparison, we found an accord between the proposed dynamic model and the experimental behavior of the robot. The attained results can be used to design controllers and optimize performances of the robot propelled by the folding pectoral fins.

In this article, we tell a story about incompleteness in modal logic. The story weaves together an article of van Benthem (1979), “Syntactic aspects of modal incompleteness theorems,” and a longstanding open question: whether every normal modal logic can be characterized by a class of completely additive modal algebras, or as we call them, ${\cal V}$-baos. Using a first-order reformulation of the property of complete additivity, we prove that the modal logic that starred in van Benthem’s article resolves the open question in the negative. In addition, for the case of bimodal logic, we show that there is a naturally occurring logic that is incomplete with respect to ${\cal V}$-baos, namely the provability logic $GLB$ (Japaridze, 1988; Boolos, 1993). We also show that even logics that are unsound with respect to such algebras do not have to be more complex than the classical propositional calculus. On the other hand, we observe that it is undecidable whether a syntactically defined logic is ${\cal V}$-complete. After these results, we generalize the Blok Dichotomy (Blok, 1978) to degrees of ${\cal V}$-incompleteness. In the end, we return to van Benthem’s theme of syntactic aspects of modal incompleteness.

Exoskeleton robots have been widely used in many fields at present. When wearing the exoskeleton to operate, the wearer may be unconscious of the position of exoskeleton or affected by the surrounding environment, causing collision between two arms of exoskeleton or between arms and environment. The collision may result in the exoskeleton destroyed or even the wearer injured. This paper proposes a hierarchical safety control strategy for exoskeleton robots based on maximum correntropy Kalman filter and bounding box to ensure safe operation. Accurate joint angle prediction can be obtained by filtering out non-Gaussian impulsive noise using maximum correntropy criterion as evaluation criterion. Relative position relationship of the arms can be derived based on bounding box to realize hierarchical safe control. Enough experiments have been carried out, and the results validated the feasibility of the proposed method.

Visual homing is a local navigation technique used to direct a robot to a previously seen location by comparing the image of the original location with the current visual image. Prior work has shown that exploiting depth cues such as image scale or stereo-depth in homing leads to improved homing performance. While it is not unusual to use a panoramic field of view (FOV) camera in visual homing, it is unusual to have a panoramic FOV stereo-camera. So, while the availability of stereo-depth information may improve performance, the concomitant-restricted FOV may be a detriment to performance, unless specialized stereo hardware is used. In this paper, we present an investigation of the effect on homing performance of varying the FOV widths in a stereo-vision-based visual homing algorithm using a common stereo-camera. We have collected six stereo-vision homing databases – three indoor and three outdoor. Based on over 350,000 homing trials, we show that while a larger FOV yields performance improvements for larger homing offset angles, the relative improvement falls off with increasing FOVs, and in fact decreases for the widest FOV tested. We conduct additional experiments to identify the cause of this fall-off in performance, which we term the ‘blinder’ effect, and which we predict should affect other correspondence-based visual homing algorithms.

This paper studies the variability of both series and parallel systems comprised of heterogeneous (and dependent) components. Sufficient conditions are established for the star and dispersive orderings between the lifetimes of parallel [series] systems consisting of dependent components having multiple-outlier proportional hazard rates and Archimedean [Archimedean survival] copulas. We also prove that, without any restriction on the scale parameters, the lifetime of a parallel or series system with independent heterogeneous scaled components is larger than that with independent homogeneous scaled components in the sense of the convex transform order. These results generalize some corresponding ones in the literature to the case of dependent scenarios or general settings of components lifetime distributions.

In order to make the end of the three-axis platform follow the control command and achieve stable control of the end attitude, an improved orientation vector spherical linear interpolation (SLERP) method is proposed for the requirements, which specifically handles the position of the gimbal lock, so that the platform can move smoothly around the gimbal lock position. A three-axis platform with a camera at the end is set up for the validity of the proposed algorithm. At first, an adaptive speed measurement method based on incremental encoder is introduced, which can automatically adapt to high and low speed, and estimate the ultra-low speed to realize the speed measurement of large dynamic range, and this is used for the motion control of the three-axis platform. Then, the SLERP method for the quaternion interpolation on the starting and ending attitudes represented in quaternion is introduced in detail, and it is continuously improved in response to its existing problems for the platform. Finally, an orientation vector SLERP method is proposed, which uses viscosity factor and rejection factor to adjust the algorithm near the platform’s gimbal lock position. A tracking experiment was designed using the red ball as the following target detected by the designed target tracking algorithm using the camera, which verified the effectiveness of the attitude tracking control based on the proposed improved orientation vector SLERP.

This study examines the impact of group composition (one-on-one vs. multiple-to-multiple) and task design (student-selected vs. teacher-assigned) on undergraduate foreign language learners’ interactions in a mobile-based intercultural exchange. The participants, 27 Korean students learning English as a foreign language and 27 American students learning Korean as a foreign language, interacted in pairs and groups via mobile phones to complete weekly tasks for eight weeks. This study used mixed methods to analyze the data from mobile chat scripts, questionnaires, and interviews. The results indicated that the one-on-one and multiple-to-multiple groups did not differ significantly regarding contact frequency or number of written chats. However, one-on-one and multiple-to-multiple interactions did differ with regard to the quality of the interactions, reflecting the unique nature of each group composition. A one-on-one relationship promoted a higher level of intimacy and friendship, thus rendering it appropriate for providing linguistic and emotional support in learning foreign languages. In contrast, multiple-to-multiple communications were found to be more beneficial for learning about different perspectives on the target cultures. In terms of task design, teacher-assigned tasks guided students to engage in productive interactions effectively, whereas student-selected tasks elicited their personal investment in the tasks. Supporting social interdependence theory (Johnson & Johnson, 1989, 2009), we argue that the establishment of intimate relationships among group members may be the key to quality interactions in mobile-based intercultural exchanges.

The purpose of our study was to get deeper insights into sprinting with and without running-specific prostheses and to perform a comparison of the two by combining analysis of known motion capture data with mathematical modeling and optimal control problem (OCP) findings. We established rigid multi-body system models with 14 bodies and 16 degrees of freedom in the sagittal plane for one unilateral transtibial amputee and three non-amputee sprinters. The internal joints are powered by torque actuators except for the passive prosthetic ankle joint which is equipped with a linear spring–damper system. For each model, the dynamics of one sprinting trial was reconstructed by solving a multiphase least squares OCP with discontinuities and constraints. We compared the motions of the amputee athlete and the non-amputee reference group by computing characteristic criteria such as the contribution of joint torques, the absolute mechanical work, step frequency and length, among others. By comparing the amputee athlete with the non-amputee athletes, we found reduced activity in the joints of the prosthetic limb, but increased torques and absolute mechanical work in the arms. We also compared the recorded motions to synthesized motions using different optimality criteria and found that the recorded motions are still far from the optimal solutions for both amputee and non-amputee sprinting.

This paper presents PFLP, a library for probabilistic programming in the functional logic programming language Curry. It demonstrates how the concepts of a functional logic programming language support the implementation of a library for probabilistic programming. In fact, the paradigms of functional logic and probabilistic programming are closely connected. That is, language characteristics from one area exist in the other and vice versa. For example, the concepts of non-deterministic choice and call-time choice as known from functional logic programming are related to and coincide with stochastic memoization and probabilistic choice in probabilistic programming, respectively. We will further see that an implementation based on the concepts of functional logic programming can have benefits with respect to performance compared to a standard list-based implementation and can even compete with full-blown probabilistic programming languages, which we illustrate by several benchmarks.

Many students complete PhDs in functional programming each year. As a service to the community, twice per year the Journal of Functional Programming publishes the abstracts from PhD dissertations completed during the previous year.