Acta Informatica manuscript No. (will be inserted by the editor) A Complete Classification of the Expressiveness of Interval Logics of Allen’s Relations The General and the Dense Cases

Abstract Interval temporal logics take time intervals, instead of time instants, as their primitive temporal entities. One of the most studied interval temporal logics is Halpern and Shoham’s modal logic of time intervals HS, which associates a modal operator with each binary relation between intervals over a linear order (the so-called Allen’s interval relations). In this paper, we compare and classify the expressiveness of all fragments of HS on the class of all linear orders and on the subclass of all dense linear orders. For each of these classes, we identify a complete set of definabilities between HS modalities, valid in that class, thus obtaining a complete classification of the family of all 4096 fragments of HS with respect to their expressiveness. We show that on the class of all linear orders there are exactly 1347 expressively different fragments of HS, while on the class of dense linear orders there are exactly 966 such expressively different fragments

Usefulness of DXA-based bone strain index in postmenopausal women with type 2 diabetes mellitus

Summary : Bone Strain Index (BSI) is a new dual-energy x-ray absorptiometry (DXA)-based index. We retrospectively evaluated data from 153 postmenopausal women with a history of type 2 diabetes mellitus (T2DM). Lumbar spine and femoral Bone Strain Index (BSI) were sensitive to skeletal impairment in postmenopausal women suffering from T2DM. Purpose: Bone Strain Index (BSI) is a new dual-energy X-ray absorptiometry (DXA)-based measurement. We evaluated the performance of BSI in predicting the presence of fragility fractures in type 2 diabetes mellitus (T2DM) postmenopausal women. Methods: We retrospectively evaluated data from a case–control study of 153 postmenopausal women with a history of at least 5 years of T2DM (age from 40 to 90 years). For each subject, we assessed the personal or familiar history of previous fragility fractures and menopause age, and we collected data about bone mineral density (BMD), BSI, and Trabecular Bone Score (TBS) measurements. Statistical analysis was performed having as outcome the history of fragility fractures. Results: Out of a total of 153 subjects, n = 22 (14.4%) presented at least one major fragility fracture. A negative correlation was found between lumbar BSI and lumbar BMD (r = − 0.49, p < 0.001) and between total femur BSI and total femur BMD (r = − 0.49, p < 0.001). A negative correlation was found between femoral neck BSI and femoral neck BMD (r = − 0.22, p < 0.001). Most DXA-based variables were individually able to discriminate between fractured and non-fractured subjects (p < 0.05), and lumbar BSI was the index with the most relative difference between the two populations, followed by femoral BSI. Conclusion: Lumbar spine and femoral BSI are sensitive to skeletal impairment in postmenopausal women suffering from T2DM. The use of BSI in conjunction with BMD and TBS can improve fracture risk assessment

Inverse Kinematics for Industrial Robots using Conformal Geometric Algebra

This paper shows how the recently developed formulation of conformal geometric algebra can be used for analytic inverse kinematics of two six-link industrial manipulators with revolute joints. The paper demonstrates that the solution of the inverse kinematics in this framework relies on the intersection of geometric objects like lines, circles, planes and spheres, which provides the developer with valuable geometric intuition about the problem. It is believed that this will be very useful for new robot geometries and other mechanisms like cranes and topside drilling equipment. The paper extends previous results on inverse kinematics using conformal geometric algebra by providing consistent solutions for the joint angles for the different configurations depending on shoulder left or right, elbow up or down, and wrist flipped or not. Moreover, it is shown how to relate the solution to the Denavit-Hartenberg parameters of the robot. The solutions have been successfully implemented and tested extensively over the whole workspace of the manipulators

Use of Self-Selected Postures to Regulate Multi-Joint Stiffness During Unconstrained Tasks

The human motor system is highly redundant, having more kinematic degrees of freedom than necessary to complete a given task. Understanding how kinematic redundancies are utilized in different tasks remains a fundamental question in motor control. One possibility is that they can be used to tune the mechanical properties of a limb to the specific requirements of a task. For example, many tasks such as tool usage compromise arm stability along specific directions. These tasks only can be completed if the nervous system adapts the mechanical properties of the arm such that the arm, coupled to the tool, remains stable. The purpose of this study was to determine if posture selection is a critical component of endpoint stiffness regulation during unconstrained tasks.Three-dimensional (3D) estimates of endpoint stiffness were used to quantify limb mechanics. Most previous studies examining endpoint stiffness adaptation were completed in 2D using constrained postures to maintain a non-redundant mapping between joint angles and hand location. Our hypothesis was that during unconstrained conditions, subjects would select arm postures that matched endpoint stiffness to the functional requirements of the task. The hypothesis was tested during endpoint tracking tasks in which subjects interacted with unstable haptic environments, simulated using a 3D robotic manipulator. We found that arm posture had a significant effect on endpoint tracking accuracy and that subjects selected postures that improved tracking performance. For environments in which arm posture had a large effect on tracking accuracy, the self-selected postures oriented the direction of maximal endpoint stiffness towards the direction of the unstable haptic environment.These results demonstrate how changes in arm posture can have a dramatic effect on task performance and suggest that postural selection is a fundamental mechanism by which kinematic redundancies can be exploited to regulate arm stiffness in unconstrained tasks

Dynamic and kinematic observers for output coordination control of Euler-Lagrange systems: A comparison and applications

This paper compares a dynamic and a kinematic observer approach for output coordination control of mechanical systems formulated in the Euler-Lagrange framework. The observers are designed to estimate missing velocity and acceleration information based on position/attitude measurements to provide a full state vector to the coordination control algorithm. The kinematic observer approach utilizes a virtual system designed to mimic the kinematic behaviour of the leader in order to estimate unknown states of the state vector with a minimum of information available. The dynamic observer approach is based on utilizing the full dynamic model of the follower system when estimating the missing states. The two observers are compared in terms of estimation principles and practical performance, and applied to two practical examples; leader-follower robot manipulator synchronization control, and underway replenishment operations for surface ships