An (improper) graph colouring has defect d if each monochromatic subgraph has maximum degree at most d, and has clustering c if each monochromatic component has at most c vertices. This paper studies defective and clustered list-colourings for graphs with given maximum average degree. We prove that every graph with maximum average degree less than (2d+2)/(d+2)k is k-choosable with defect d. This improves upon a similar result by Havet and Sereni (J. Graph Theory, 2006). For clustered choosability of graphs with maximum average degree m, no (1-ɛ)m bound on the number of colours was previously known. The above result with d=1 solves this problem. It implies that every graph with maximum average degree m is $\lfloor{\frac{3}{4}m+1}\rfloor$-choosable with clustering 2. This extends a result of Kopreski and Yu (Discrete Math., 2017) to the setting of choosability. We then prove two results about clustered choosability that explore the trade-off between the number of colours and the clustering. In particular, we prove that every graph with maximum average degree m is $\lfloor{\frac{7}{10}m+1}\rfloor$-choosable with clustering 9, and is $\lfloor{\frac{2}{3}m+1}\rfloor$-choosable with clustering O(m). As an example, the later result implies that every biplanar graph is 8-choosable with bounded clustering. This is the best known result for the clustered version of the earth–moon problem. The results extend to the setting where we only consider the maximum average degree of subgraphs with at least some number of vertices. Several applications are presented.

This paper presents an advanced robust active disturbance rejection control (ADRC) for flexible link manipulator (FLM) to track desired trajectories in the joint space and minimize the link’s vibrations. It has been shown that the ADRC technique has a very good disturbance rejection capability. Both the internal dynamics and the external disturbances can be estimated and compensated in real time. The proposed robust ADRC control law is developed to solve the problems existing in the original version of the ADRC related to the disturbance estimation errors and the variation of the parameters. Indeed, these parameters cannot be included in the existing disturbances and then be estimated by the extended state observer. The proposed control law is based on the sliding mode technique, which considers the uncertainties in the control gains and disturbance estimation errors. Lyapunov theory is used to prove the closed-loop stability of the system. The proposed control strategy is simulated and tested experimentally on one FLM. The effect of the observer bandwidth on the system performance is simulated and studied to select the best values of the bandwidth frequency. The simulation and experimental results show that the proposed robust ADRC has better performance than the traditional ADRC.

We analyse the two definitions of generalized quantifiers for logics of dependence and independence that have been proposed by F. Engström, comparing them with a more general, higher order definition of team quantifier. We show that Engström’s definitions (and other quantifiers from the literature) can be identified, by means of appropriate lifts, with special classes of team quantifiers. We point out that the new team quantifiers express a quantitative and a qualitative component, while Engström’s quantifiers only range over the latter. We further argue that Engström’s definitions are just embeddings of the first-order generalized quantifiers into team semantics, and fail to capture an adequate notion of team-theoretical generalized quantifier, save for the special cases in which the quantifiers are applied to flat formulas. We also raise several doubts concerning the meaningfulness of the monotone/nonmonotone distinction in this context. In the appendix we develop some proof theory for Engström’s quantifiers.

This paper addresses the neural network (NN) output feedback formation tracking control of nonholonomic wheeled mobile robots (WMRs) with limited voltage input. A desired formation is achieved based on the leader–follower strategy utilizing hyperbolic tangent saturation functions to reduce the risk of actuator saturation. The controller is developed by incorporating the high-gain observer and radial basis function (RBF) NNs using the inverse dynamics control technique. The high-gain observer is introduced to estimate velocities of the followers. The RBF NN preserves the robustness of the proposed controller against uncertain nonlinearities. The adaptive laws are also combined by a robust control term to estimate the weights of RBF NN, approximation errors, and bounds of unknown time-variant environmental disturbances. A Lyapunov-based stability analysis proves that all signals of the closed-loop system are bounded, and tracking errors are uniformly ultimately bounded. Finally, some simulations are carried out to show the effectiveness of the proposed controller for a number of WMRs.

Position-tracking problems in the structures of rigid formations of nonholonomic mobile robots, such as fixed-wing unmanned aerial vehicle (UAVs), must reconcile tracking precision and flight stability, which usually exclude each other due to nonholonomic motion constraints. Therefore, a position-tracking control that is based on distance and position displacement, defined as inputs of control loops, requires the application of dead zones around target positions, which are the points of instability. For this reason, the control becomes sensitive to any external disturbance causing oscillations of control signals and so it becomes difficult to maintain a zero value of position displacement over a long time horizon. Thus, we propose an approach based on the adaptive mechanism of an asymmetrical local artificial potential field, which is defined by a local frame of reference whose origin is located in the tracked position of a UAV in the formation frame. It couples controls of both airspeed and heading angle into a nonlinear potential function of relative position and orientation with respect to the tracked position and adapts it according to heading rate of the leader. The function splits the area around the tracked position longitudinally into two zones of acceleration and deceleration; therefore, velocity vectors are longer (higher airspeed) only when a UAV is behind the tracked position and shorter (lower airspeed) when it is ahead. The area is laterally symmetrical, and orientations of velocity vectors align asymptotically to the longitudinal direction accordingly with the decrease in the lateral error. Finally, velocity vectors are rotated proportionally to the heading rate of the leader, which improves the tracking precision during turns. If we assumed that a UAV’s tracked position is in motion, it could easily be proven that the position control based on the adaptive asymmetrical potential function becomes asymptotically stable in the tracked position. Numerical simulation verifies this thesis and presents more precise and stable position tracking due to the adaptation mechanism.

This article continues the study of the genus of regular languages that the authors introduced in a 2013 paper (published in 2018). In order to understand further the genus g(L) of a regular language L, we introduce the genus size of |L|gen to be the minimal size of all finite deterministic automata of genus g(L) computing L.We show that the minimal finite deterministic automaton of a regular language can be arbitrarily far away from a finite deterministic automaton realizing the minimal genus and computing the same language, in terms of both the difference of genera and the difference in size. In particular, we show that the genus size |L|gen can grow at least exponentially in size |L|. We conjecture, however, the genus of every regular language to be computable. This conjecture implies in particular that the planarity of a regular language is decidable, a question asked in 1976 by R. V. Book and A. K. Chandra. We prove here the conjecture for a fairly generic class of regular languages having no short cycles. The methods developed for the proof are used to produce new genus-based hierarchies of regular languages and in particular, we show a new family of regular languages on a two-letter alphabet having arbitrary high genus.

In the subject of optimal stopping, the classical secretary problem is concerned with optimally selecting the best of n candidates when their relative ranks are observed sequentially. This problem has been extended to optimally selecting the kth best candidate for k ≥ 2. While the optimal stopping rule for k=1,2 (and all n ≥ 2) is known to be of threshold type (involving one threshold), we solve the case k=3 (and all n ≥ 3) by deriving an explicit optimal stopping rule that involves two thresholds. We also prove several inequalities for p(k, n), the maximum probability of selecting the k-th best of n candidates. It is shown that (i) p(1, n) = p(n, n) > p(k, n) for 1<k<n, (ii) p(k, n) ≥ p(k, n + 1), (iii) p(k, n) ≥ p(k + 1, n + 1) and (iv) p(k, ∞): = lim n→∞p(k, n) is decreasing in k.

Though significant efforts are made to develop mathematical models of the limit cycle walking (LCW), there is still a lack of a general and efficient framework to study the periodic solution and robustness of a complex model like human with knees, ankles and flat feet. In this study, a numerical framework of the LCW based on general multibody system dynamics is proposed, especially the impacts between the feet and the ground are modeled by Hunt–Crossley normal contact force and Coulomb friction force, and the modeling of the knee locking is presented as well. Moreover, event-based operating strategies are presented to deal with controls for the ground clearance and the knee locking. Importantly, a fast and efficient two-step algorithm is proposed to search for stable periodic gaits. Finally, maximum allowable disturbance is adopted as the index for stability analysis. All these features could be readily implemented in the framework. The presented solution is verified on a compass-like passive dynamic walking (PDW) walker with results in the literature. Based on this framework, a fairly complicated level-walking walkers with ankles and knees under control are analyzed and their periodic gaits are obtained, and surprisingly, double stable periodic gaits with, respectively, low speed and high speed are found.

This volume collects together extended and improved versions of papers presented at the twentysecond Workshop on Logic, Language, Information and, Computation (WoLLIC 2015) held at the School of Informatics and Computing, Indiana University, Bloomington, Indiana. WoLLIC is an annual international forum on inter-disciplinary research involving formal logic, computing and programming theory, and natural language and reasoning. Each meeting includes invited talks and tutorials as well as contributed papers. Contributions were invited on all appropriate subjects of Logic, Language, Information, and Computation, with particular interest in cross-disciplinary topics.

Categorical compositional distributional semantics is a model of natural language; it combines the statistical vector space models of words with the compositional models of grammar. We formalise in this model the generalised quantifier theory of natural language, due to Barwise and Cooper. The underlying setting is a compact closed category with bialgebras. We start from a generative grammar formalisation and develop an abstract categorical compositional semantics for it, and then instantiate the abstract setting to sets and relations and to finite-dimensional vector spaces and linear maps. We prove the equivalence of the relational instantiation to the truth theoretic semantics of generalised quantifiers. The vector space instantiation formalises the statistical usages of words and enables us to, for the first time, reason about quantified phrases and sentences compositionally in distributional semantics.

In this paper, a neural network (NN)-based tracking controller is proposed for a general class of type (m,s) wheeled mobile manipulators (WMMs) subjected to model uncertainties with prescribed transient and steady-state performance specifications. First, an input–output model of WMMs is derived by introducing proper output equations. Then, the prescribed performance technique is employed to propose a proportional integral derivative trajectory tracking controller for WMMs to ensure that the tracking errors converge to a smaller, arbitrary ultimate bound with a predefined maximum overshoot/undershoot and convergence speed. The learning capabilities of multilayer NNs are incorporated into the controller to approximate the uncertain nonlinear dynamics of the robot. An adaptive saturation-type controller is utilized to compensate NN estimation errors and external disturbances. A Lyapunov-based stability analysis is used to demonstrate that the tracking errors are uniformly ultimately bounded and converge to a small neighborhood of zero with a guaranteed prescribed performance. Numerical computer simulations are presented to show the effectiveness of the proposed controller.

In this article, we propose an innovative and robust approach to stylometric analysis without annotation and leveraging lexical and sub-lexical information. In particular, we propose to leverage the phonological information of tones and rimes in Mandarin Chinese automatically extracted from unannotated texts. The texts from different authors were represented by tones, tone motifs, and word length motifs as well as rimes and rime motifs. Support vector machines and random forests were used to establish the text classification model for authorship attribution. From the results of the experiments, we conclude that the combination of bigrams of rimes, word-final rimes, and segment-final rimes can discriminate the texts from different authors effectively when using random forests to establish the classification model. This robust approach can in principle be applied to other languages with established phonological inventory of onset and rimes.

Parallel robots are widely used in the fields of manufacturing, medical science, education, scientific research, etc. Many studies have been conducted on the topic already. However, shortcomings still exist, especially in certain situations. To meet the demand of good speed and load performances at the same time, this work presents a novel 2-degree-of-freedom parallel robot. The structural design, static, stiffness, and reachable workspace analysis of the robot are given in the manuscript. Experiment regarding the accuracy and speed performance is conducted, and the results are provided. In the end, potential applications of the proposed robot are suggested.

Humanoid robots (HR) equipped with a sophisticated facial character analysis (FCA) algorithm can able to initiate crucial improvements in human–robot interactions. This paper, for the first time in the literature, proposes a three-stage FCA algorithm for the HR. At the initial stage of this algorithm, the HR detects the face with the Viola–Jones algorithm, and then important facial distance measurements are obtained with the geometric-based facial distance measurement technique. Finally, the measured facial distances are evaluated with the physiognomy science to reveal the characteristic properties of a person. Even though the proposed algorithm can be implemented to all HR, in this paper, it has been specifically applied to NAO HR. The reliability of the developed FCA algorithm is verified by analyzing each terminal decision about the character and its connection with the measured facial distances in the anatomy science.

Using wearable robots is an effective means of rehabilitation for stroke survivors, and effective recognition of human motion intentions is a key premise in controlling wearable robots. In this paper, we propose an inertial measurement unit (IMU)-based gait phase detection system. The system consists of two IMUs that are tied on the thigh and on the shank, respectively, for collecting acceleration and angular velocity. Features were extracted using a sliding window of 150 ms in length, which was then fed into a quadratic discriminant analysis (QDA) classifier for classification. We recruited five stroke survivors to test our system. They walked at their own preferred speed on the level ground. Experimental results show that our proposed system has the ability of recognizing the gait phase of stroke survivors. All recognition accuracy results are above 96.5%, and detections are about 5–15 ms in advance of time. In addition, using only one IMU can also give reliable recognition results. This paper proposes an idea about the further research on human–computer interaction for the control of wearable robots.

In this study, the kinematics and dynamics of a single actuator wave (SAW)-like robot are explored. Comprising a helical spine and links, SAW has the potential for miniaturization. A kinematic model for SAW is firstly established, and the dynamic equation of motion is derived based on Kane’s method. For validation, the motion of SAW is simulated using both MATLAB and ADAMS, and the comparison of results demonstrates the effectiveness of the theoretical models. Then the inverse dynamic analysis is performed to reveal the power consumption. Finally, robot prototypes are developed and tested to confirm the robot velocity predicted by simulations.

Reducing the energy consumed by a car-like mobile robot makes it possible to move at a lower cost, yet it takes more working time. This paper proposes an optimization algorithm for trajectories with optimal times and analyzes the consequences of restricting the energy consumed on the trajectory obtained for a car-like robot. When modeling the dynamic behavior of the vehicle, it is necessary to consider its inertial parameters, the behavior of the motor, and the basic properties of the tire in its interaction with the ground. To obtain collision-free, minimum-time trajectories quadratic sequential optimization techniques are used, where the objective function is the time taken by the robot to move between two given configurations. This is subject to constraints relating to the vehicle and tires as well as the energy consumed, which is the basis for this paper. We work with a real random distribution of consumed energy values following a normal Gaussian distribution in order to analyze its influence on the trajectories obtained by the vehicle. The energy consumed, the time taken, the maximum velocity reached, and the distance traveled are analyzed in order to characterize the properties of the trajectories obtained. The proposed algorithm has been applied to 101 examples, showing that the computational times needed to obtain the solutions are always lower than those required to realize the trajectories. The results obtained allow us to reach conclusions about the energy efficiency of the trajectories.

Supply chains are fundamental to the economy of the world and many supply chains focus on perishable items, such as food, or even clothing that is subject to a limited shelf life due to fashion and seasonable effects. G-networks have not been previously applied to this important area. Thus in this paper, we apply G-networks to supply chain systems and investigate an optimal order allocation problem for a N-node supply chain with perishable products that share the same order source of fresh products. The objective is to find an optimal order allocation strategy to minimize the purchase price per object from the perspective of the customers. An analytical solution based on G-networks with batch removal, together with optimization methods are shown to produce the desired results. The results are illustrated by a numerical example with realistic parameters.