Towards an Intelligent Tutor for Mathematical Proofs

Computer-supported learning is an increasingly important form of study since it allows for independent learning and individualized instruction. In this paper, we discuss a novel approach to developing an intelligent tutoring system for teaching textbook-style mathematical proofs. We characterize the particularities of the domain and discuss common ITS design models. Our approach is motivated by phenomena found in a corpus of tutorial dialogs that were collected in a Wizard-of-Oz experiment. We show how an intelligent tutor for textbook-style mathematical proofs can be built on top of an adapted assertion-level proof assistant by reusing representations and proof search strategies originally developed for automated and interactive theorem proving. The resulting prototype was successfully evaluated on a corpus of tutorial dialogs and yields good results.Comment: In Proceedings THedu'11, arXiv:1202.453

When does a correct mutual exclusion algorithm guarantee mutual exclusion

Dijkstra introduced mutual exclusion for an N-process system as the requirement “that at any moment only one of these N cyclic processes is in its critical section ” [1]. This requirement, which we call true mutual exclusion, is still the standard definition of mutual exclusion. Mutual exclusion algorithms for shared-memory multiprocessors do not guarantee true mutual exclusion. We give a simple example that shows why a mutual exclusion algorithm can permit two critical sections to be executing at the same time. We prove that a shared-memory mutual exclusion algorithm does provide true mutual exclusion if a processor does not knowin advance what memory operations will follow the critical section. Modern processors can look ahead at operations that followa critical section. If true mutual exclusion is needed, this look-ahead must be inhibited. However, as we will explain, true mutual exclusion is seldom useful in practice. One of the strongest and most common assumptions made about multiprocessor shared memory is sequential consistency. Sequential consistency i

Preclinical Assessment of a Novel Conformable Foam-Based Left Atrial Appendage Closure Device

Background. Left atrial appendage (LAA) occlusion has been established as an alternative to systemic anticoagulation for stroke prevention in patients with atrial fibrillation; however, limitations of current devices have slowed adoption. We present preclinical evaluations of a novel device, the Conformal Left Atrial Appendage Seal (CLAAS). Methods. An in vitro assessment of conformability was conducted to evaluate the two CLAAS devices (regular 27 mm and large 35 mm) and a Watchman 2.5 (27 mm). Devices were placed within silicone tubes and compressed in a vise submerged in a water bath at 37°C. Changes in device diameter and visual seal were noted. Acute (n=1) and chronic 60-day (n=6) canine studies with gross and histologic assessment were performed. Results. Conformability bench tests demonstrated that the regular CLAAS implant was able to seal oval orifices from 20×30 mm to 15×33 mm and the large from 30×35 mm to 20×40 mm. As the CLAAS implant was compressed in the minor diameter, it increased in the major diameter, thereby filling the oval space, whereas the Watchman 2.5 showed gaps and maintained its round configuration when compressed in one direction. Seven devices were successfully implanted in the canine model with complete seal without thrombus. Histologic examination showed complete neointima covering with minimal inflammation at 60 days. Conclusions. Preclinical testing demonstrated the conformability of the CLAAS implant and its ability to seal the LAA. Clinical studies are ongoing to characterize the utility of the CLAAS implant in the treatment of patients with atrial fibrillation