We prove the following 30 year-old conjecture of Győri and Tuza: the edges of every n-vertex graph G can be decomposed into complete graphs C1,. . .,Cℓ of orders two and three such that |C1|+···+|Cℓ| ≤ (1/2+o(1))n2. This result implies the asymptotic version of the old result of Erdős, Goodman and Pósa that asserts the existence of such a decomposition with ℓ ≤ n2/4.

An abelian processor is an automaton whose output is independent of the order of its inputs. Bond and Levine have proved that a network of abelian processors performs the same computation regardless of processing order (subject only to a halting condition). We prove that any finite abelian processor can be emulated by a network of certain very simple abelian processors, which we call gates. The most fundamental gate is a toppler, which absorbs input particles until their number exceeds some given threshold, at which point it topples, emitting one particle and returning to its initial state. With the exception of an adder gate, which simply combines two streams of particles, each of our gates has only one input wire, which sends letters (‘particles’) from a unary alphabet. Our results can be reformulated in terms of the functions computed by processors, and one consequence is that any increasing function from ℕk to ℕℓ that is the sum of a linear function and a periodic function can be expressed in terms of (possibly nested) sums of floors of quotients by integers.

We add Most X are Y to the syllogistic logic of All X are Y and Some X are Y. We prove soundness, completeness, and decidability in polynomial time. Our logic has infinitely many rules, and we prove that this is unavoidable.

The notions of disintegration and Bayesian inversion are fundamental in conditional probability theory. They produce channels, as conditional probabilities, from a joint state, or from an already given channel (in opposite direction). These notions exist in the literature, in concrete situations, but are presented here in abstract graphical formulations. The resulting abstract descriptions are used for proving basic results in conditional probability theory. The existence of disintegration and Bayesian inversion is discussed for discrete probability, and also for measure-theoretic probability – via standard Borel spaces and via likelihoods. Finally, the usefulness of disintegration and Bayesian inversion is illustrated in several examples.

Generalized planning studies the representation, computation and evaluation of solutions that are valid for multiple planning instances. These are topics studied since the early days of AI. However, in recent years, we are experiencing the appearance of novel formalisms to compactly represent generalized planning tasks, the solutions to these tasks (called generalized plans) and efficient algorithms to compute generalized plans. The paper reviews recent advances in generalized planning and relates them to existing planning formalisms, such as planning with domain control knowledge and approaches for planning under uncertainty, that also aim at generality.

In this paper, a novel robust model reference adaptive impedance control (RMRAIC) scheme is presented for an active transtibial ankle prosthesis. The controller makes the closed loop dynamics of the prosthesis similar to a reference impedance model and provides asymptotic tracking of the response trajectory of this impedance model. The interactions between human and prosthesis are taken into account by designing a second-order reference impedance model. The proposed controller is robust against parametric uncertainties in the nonlinear dynamic model of the prosthesis. Also, the controller has robustness against bounded uncertainties due to unavailable ground reaction forces and unmeasurable feedbacks of accelerations at the socket place. Moreover, an appropriate Series Elastic Actuator (SEA) mechanism for the prosthetic ankle is included in this work and its effects are discussed. Tracking performance and stability of the closed-loop system are proven via the Lyapunov stability analysis. Using simulations on an overall amputee prosthetic foot system, the effectiveness of the proposed RMRAIC controller is investigated for the task of level ground walking.

This paper presents a hybrid strategy-based coordinate controller with a novel nonlinear disturbance observer for autonomous underwater vehicle manipulator systems (UVMSs). This method can reduce the influence from external unknown disturbances, inner coupling effects and model uncertainties by using a modified disturbance observer. Considering the natural redundancy property of the UVMS, the redundancy resolution algorithm is often utilized to give desired trajectories in the vehicle–joint space. However, because of the calibration errors, assembling errors and numerical errors, these desired trajectories may not lead the end-effector to the goal point accurately. To realize accurate motion control even when small errors exist in the planning phase, a hybrid strategy is introduced to transform the controller in the joint–vehicle space to the controller in the task space. Numerical simulations based on a UVMS have been carried out to testify the effectiveness of the proposed coordinate controller and the hybrid strategy. During the simulations, unknown disturbances are exerted upon the system. The trajectory tracking and error fixing performances are discussed in comparative analyses. The controller also maintains robust characteristics in comparison with the passivity-based controller and the proposed controller but without the disturbance observer. Experiments are also carried out to test its performance.

When a change request is raised in an engineering project an ad hoc team often forms to manage the request. Prior research shows that practitioners often view engineering changes in a risk-averse manner. As a project progresses the cost of changes increases. Therefore, avoiding changes is reasonable. However, a risk-averse perspective fails to recognize that changes might harbor discoverable and exploitable opportunities. In this research, we investigated how practitioners of ad hoc teams used practices and praxes aimed at discovering and exploiting opportunities in engineering change requests. A single case study design was employed using change request records and practitioner interviews from an engineering project. 87 engineering change requests were analyzed with regards to change triggers, time-to-decision and rejection rate. In total, 25 opportunities were discovered and then 17 exploited. Three practices and six praxes were identified, used by practitioners to discover and exploit opportunities. Our findings emphasize the importance of the informal structure of ad hoc teams, to aid in opportunity discovery. The informal structure enables cross-hierarchal discussions and draws on the proven experience of the team members. Thus, this research guides project managers and presumptive ad hoc teams in turning engineering changes into successful opportunities.

A tree functional is called additive if it satisfies a recursion of the form $F(T) = \sum_{j=1}^k F(B_j) + f(T)$, where B1, …, Bk are the branches of the tree T and f (T) is a toll function. We prove a general central limit theorem for additive functionals of d-ary increasing trees under suitable assumptions on the toll function. The same method also applies to generalized plane-oriented increasing trees (GPORTs). One of our main applications is a log-normal law that we prove for the size of the automorphism group of d-ary increasing trees, but other examples (old and new) are covered as well.

We propose and study a probabilistic logic over an algebraic basis, including equations and domain restrictions. The logic combines aspects from classical logic and equational logic with an exogenous approach to quantitative probabilistic reasoning. We present a sound and weakly complete axiomatization for the logic, parameterized by an equational specification of the algebraic basis coupled with the intended domain restrictions.We show that the satisfiability problem for the logic is decidable, under the assumption that its algebraic basis is given by means of a convergent rewriting system, and, additionally, that the axiomatization of domain restrictions enjoys a suitable subterm property. For this purpose, we provide a polynomial reduction to Satisfiability Modulo Theories. As a consequence, we get that validity in the logic is also decidable. Furthermore, under the assumption that the rewriting system that defines the equational basis underlying the logic is also subterm convergent, we show that the resulting satisfiability problem is NP-complete, and thus the validity problem is coNP-complete.We test the logic with meaningful examples in information security, namely by verifying and estimating the probability of the existence of offline guessing attacks to cryptographic protocols.

During the early stages of any system design, a thorough exploration of the design space can prove to be challenging and computationally expensive. The challenges are further exacerbated when dealing with complex systems, such as an aircraft, due to the high dimensionality of their design space. Arising from the Toyota Product Development System, set-based design allows parallel evaluation of multiple alternative configurations in the early design stages. At the same time, optimisation methods can be employed at later stages to fine-tune the engineering characteristics of design variants. Presented in this paper, is the Augmented set-based Design and OPTimisation (ADOPT) Framework that introduces a novel methodology for integrating the two areas. This allows for a thorough design-space exploration while ensuring the optimality of the selected designs. The framework has been developed using a process-independent and tool-agnostic approach so that it can be applied to the design process of varying kinds of systems. To demonstrate the implementation and potential benefits, the framework has been applied to the design of a generic aircraft fuel system. The results from the case study and the framework itself are discussed, with a number of areas for further development and future work being identified and presented.

Consider a particular bidimensional risk model, in which two insurance companies divide between them in different proportions both the premium income and the aggregate claims. In practice, it can be interpreted as an insurer–reinsurer scenario, where the reinsurer takes over a proportion of the insurer's losses. Under the assumption that the claim sizes and inter-arrival times form a sequence of independent and identically distributed random pairs, with each pair obeying a dependence structure, an asymptotic expression for the ruin probability of this bidimensional risk model with constant interest rates is established.

In this research study, trajectory planning of mobile robot is accomplished using two techniques, namely, a new variant of multi-objective differential evolution (heterogeneous multi-objective differential evolution) and popular elitist non-dominated sorting genetic algorithm (NSGA-II). For this research problem, a wheeled mobile robot with differential drive is considered. A practical, feasible and optimal trajectory between two locations in the presence of obstacles is determined through the proposed algorithms. A safer path is obtained by optimizing certain objectives (travel time and actuators effort) taking into account the limitations of mobile robot’s geometric, kinematic and dynamic parameters. Robot motion is represented by a cubic NURBS trajectory curve. The capability of the proposed optimization techniques is analyzed through numerical simulations. Results ensure that the proposed techniques are more desirable for this problem.

The potential use of onboard vision sensors (e.g., cameras) has long been recognized for the Sense and Avoid (SAA) of unmanned aerial vehicles (UAVs), especially for micro UAVs with limited payload capacity. However, vision-based SAA for UAVs is extremely challenging because vision sensors usually have limitations on accurate distance information measuring. In this paper, we propose a monocular vision-based UAV SAA approach. Within the approach, the host UAV can accurately and efficiently avoid a noncooperative intruder only through angle measurements and perform maneuvers for optimal tradeoff among target motion estimation, intruder avoidance, and trajectory tracking. We realize this feature by explicitly integrating a target tracking filter into a nonlinear model predictive controller. The effectiveness of the proposed approach is verified through extensive simulations.

Trajectory tracking of a mobile manipulator in the Cartesian space based on decentralized control is considered in this paper. The dynamic model is first rearranged to take the form of two interconnected subsystems with constraint flow, namely, a nonholonomic mobile platform subsystem and a holonomic manipulator subsystem. Secondly, using the inverse kinematics, the workspace desired trajectory of the mobile manipulator is transformed to the manipulator joint space as well as the platform desired trajectory. The kinematic control is developed from the desired trajectory of the platform. Then, the desired velocity is derived using the kinematic controller of the mobile platform, after which the velocity is used to obtain the control law of the mobile platform subsystem. Thirdly, the control law of the manipulator subsystem is developed based on the desired and real values of the manipulator, as well as the desired velocity. According to the Lyapunov stability theory, the proposed decentralized control strategy guarantees the global stability of the closed-loop system, and the tracking errors are bounded. Experimental results obtained on a 3-DOF manipulator mounted on a mobile platform are given to demonstrate the feasibility and effectiveness of the proposed approach. This is confirmed by a comparison with the computed torque approach.

Capital allocation is of central importance in portfolio management and risk-based performance measurement. Capital allocations for univariate risk measures have been extensively studied in the finance literature. In contrast to this situation, few papers dealt with capital allocations for multivariate risk measures. In this paper, we propose an axiom system for capital allocation with multivariate risk measures. We first recall the class of the positively homogeneous and subadditive multivariate risk measures, and provide the corresponding representation results. Then it is shown that for a given positively homogeneous and subadditive multivariate risk measure, there exists a capital allocation principle. Furthermore, the uniqueness of the capital allocation principe is characterized. Finally, examples are also given to derive the explicit capital allocation principles for the multivariate risk measures based on mean and standard deviation, including the multivariate mean-standard-deviation risk measures.

Charlotte Angas Scott (1858–1932) was an internationally renowned geometer, the first British woman to earn a doctorate in mathematics, and the chair of the Bryn Mawr mathematics department for forty years. There she helped shape the burgeoning mathematics community in the United States. Scott often motivated her research as providing a “geometric treatment” of results that had previously been derived algebraically. The adjective “geometric” likely entailed many things for Scott, from her careful illustration of diagrams to her choice of references and citations. This article will focus on Scott’s striking and consistent use of geometric to describe a reality of dynamic points, lines, planes, and spaces that could be manipulated analogously to physical objects. By providing geometric interpretations of algebraic derivations, Scott committed to an early-nineteenth-century aesthetic vision of a “whole” analytical geometry that she adapted to modern research areas.

Recently, autonomous field robots have been investigated as a labor-reducing means to scout through commercial strawberry fields for disease detection or fruit harvesting. To achieve accurate over-bed and cross-bed motions, it is preferred to design the motion controller based on a precise dynamic model. Here, a dynamic model is developed for a custom-designed strawberry field robot considering terramechanic wheel–terrain interaction. Different from existing models, a torus geometry is considered for the wheels. In order to obtain a control affine model, the longitudinal force is curve-fitted using a polynomial function of the slip/skid ratio, while the lateral force is curve-fitted using an exponential function of both the slip/skid ratio and slip angle. An extended Kalman filter (EKF) is then developed to estimate the unknown parameters in the approximated model such that the state variables propagated by such a model can match experimental data. The approximated model and the EKF-based parameter estimation method are then validated in a commercial strawberry farm.