Students´ language in computer-assisted tutoring of mathematical proofs

Truth and proof are central to mathematics. Proving (or disproving) seemingly simple statements often turns out to be one of the hardest mathematical tasks. Yet, doing proofs is rarely taught in the classroom. Studies on cognitive difficulties in learning to do proofs have shown that pupils and students not only often do not understand or cannot apply basic formal reasoning techniques and do not know how to use formal mathematical language, but, at a far more fundamental level, they also do not understand what it means to prove a statement or even do not see the purpose of proof at all. Since insight into the importance of proof and doing proofs as such cannot be learnt other than by practice, learning support through individualised tutoring is in demand. This volume presents a part of an interdisciplinary project, set at the intersection of pedagogical science, artificial intelligence, and (computational) linguistics, which investigated issues involved in provisioning computer-based tutoring of mathematical proofs through dialogue in natural language. The ultimate goal in this context, addressing the above-mentioned need for learning support, is to build intelligent automated tutoring systems for mathematical proofs. The research presented here has been focused on the language that students use while interacting with such a system: its linguistic propeties and computational modelling. Contribution is made at three levels: first, an analysis of language phenomena found in students´ input to a (simulated) proof tutoring system is conducted and the variety of students´ verbalisations is quantitatively assessed, second, a general computational processing strategy for informal mathematical language and methods of modelling prominent language phenomena are proposed, and third, the prospects for natural language as an input modality for proof tutoring systems is evaluated based on collected corpora

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

Evaluation of the possibility of replacing the rapid filtration process with ultrafiltration in surface water treatment systems

The presented study aimed to compare the effectiveness of ultrafiltration and filtration through a sand bed during the water treatment process after the coagulation and sedimentation. The study was conducted in two flow-type water treatment systems: the reference and the test system. Both systems functioned continuously with a throughput of 1 m3/h. The research has shown that both processes ensured a very effective removal of post-coagulation suspensions, however, ultrafiltration was more effective. The filtration process allowed a slightly higher removal of organic substances as compared to ultrafiltration. The effectiveness of the removal of organic substances was determined by the biological activity of sand beds, which is not allowed in the ultrafiltration process. Besides, during the filtration process, aluminum remaining after coagulation was more effectively removed. In turn, the ultrafiltration process ensured an almost 100% effectiveness in reducing the total microorganism cell count, while the effectiveness of the filtration process was approximately half of that. In the end, the possibility of replacing the filtration process with the ultrafiltration process is determined by the costs of both processes

The Effect of Daylight-Saving Time on Percutaneous Coronary Intervention Outcomes in Acute Coronary Syndrome Patients—Data from the Polish National Registry of Percutaneous Coronary Interventions (ORPKI) in the Years 2014–2022

Introduction: Many factors related to the switch to summer/winter time interfere with biological rhythms. Objectives: This study aimed to analyze the impact of time change on clinical outcomes of patients with acute coronary syndromes (ACS) undergoing percutaneous coronary intervention (PCI). Patients and methods: Electronic data of 874,031 patients with ACS who underwent invasive procedures were collected from the Polish National Register of Interventional Cardiology Procedures (ORPKI) between 2014 and 2021. We determined the number of patients undergoing PCI and periprocedural mortality during the day of spring or autumn time change and within the first 3 and 7 days after the time change. Results: We demonstrated the impact of time changes on the periprocedural mortality of ACS patients within 1 day and the period of 3 and 7 days from the time change. We observed that the occurrence of all ACS and NSTEMI on the first day was lower for both time changes and higher in the case of UA and spring time change. The autumn time change significantly reduced the occurrence of all types of ACS. A significant decrease in the number of invasive procedures was found after autumn transition in the period from the first day to 7 days for ACS, NSTEMI, and UA. Conclusions: The occurrence of ACS and the number of invasive procedures were lower for both changes over time. Autumn time change is associated with increased periprocedural mortality in ACS and a less frequent occurrence of UA and NSTEMI within 7 days

Antibodies to periodontogenic bacteria are associated with higher disease activity in lupus patients

OBJECTIVES: Microbial infections and mucosal dysbiosis influence morbidity in patients with systemic lupus erythematosus (SLE). In the oral cavity, periodontal bacteria and subgingival plaque dysbiosis provide persistent inflammatory stimuli at the mucosal surface. This study was undertaken to evaluate whether exposure to periodontal bacteria influences disease parameters in SLE patients. METHODS: Circulating antibodies to specific periodontal bacteria have been used as surrogate markers to determine an ongoing bacterial burden, or as indicators of past exposure to the bacteria. Banked serum samples from SLE patients in the Oklahoma Lupus Cohort were used to measure antibody titres against periodontal pathogens (Aggregatibacter actinomycetemcomitans, Porphyromonas gingivalis, and Treponema denticola) and commensals (Capnocytophaga ochracea, and Streptococcus gordonii) by ELISA. Correlations between anti-bacterial antibodies and different clinicalparameters of SLE including, autoantibodies (anti-dsDNA, anti-SmRNP, anti-SSA/Ro and anti-SSB/La), complement, and disease activity (SLEDAI and BILAG) were studied. RESULTS: SLE patients had varying amounts of antibodies to different oral bacteria. The antibody titres against A. actinomycetemcomitans, P. gingivalis, T. denticola, and C. ochracea were higher in patients positive for anti-dsDNA antibodies, and they showed significant correlations with anti-dsDNA titres and reduced levels of complement. Among the periodontal pathogens, only antibodies to A. actinomycetemcomitans were associated with higher disease activity. CONCLUSIONS: Our results suggest that exposure to specific pathogenic periodontal bacteria influences disease activity in SLE patients. These findings provide a rationale for assessing and improving periodontal health in SLE patients, as an adjunct to lupus therapies

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