scholarly journals Cognitive trajectory of proof by contradiction for transition-to-proof students

2021 ◽  
Vol 62 ◽  
pp. 100849
Author(s):  
Darryl Chamberlain ◽  
Draga Vidakovic
Keyword(s):  
Proof By Contradiction ◽  
Cognitive Trajectory ◽  
Transition To Proof

scholarly journals Cognitive trajectory of patients in the recovery period after ischemic stroke: role of neuroinflammation and structural cerebral factors

2017 ◽  
Vol 98 (4) ◽  
pp. 513-518 ◽  
Author(s):  
Kulesh A.A. ◽  
◽  
Drobakha V.E. ◽  
Kuklina E.M. ◽  
Shestakov V.V. ◽  
...  
Keyword(s):  
Ischemic Stroke ◽  
Recovery Period ◽  
Cognitive Trajectory

scholarly journals Reasoning by contradiction in dynamic geometry

2013 ◽  
Vol 7 (2) ◽  
pp. 63-73
Author(s):  
Anna Baccaglini-Frank ◽  
Samuele Antonini ◽  
Allen Leung ◽  
Maria Alessandra Mariotti
Keyword(s):  
Dynamic Geometry ◽  
Proof By Contradiction ◽  
Dynamic Geometry Systems ◽  
Indirect Argument

This paper addresses contributions that dynamic geometry systems (DGSs) may give in reasoning by contradiction in geometry. We present analyses of three excerpts of students’ work and use the notion of pseudo object, elaborated from previous research, to show some specificities of DGS in constructing proof by contradiction. In particular, we support the claim that a DGS can offer guidance in the solver’s development of an indirect argument thanks to the potential it offers of both constructing certain properties robustly, and of helping the solver perceive pseudo objects.Razonamiento por contradicción en geometría dinámicaEste artículo aborda las contribuciones que los sistemas de geometría dinámica (DGSs) pueden dar al razonamiento por contradicción en geometría. Presentamos un análisis de tres extractos del trabajo de estudiantes y el uso de la noción de pseudo-objeto, elaborado a partir de investigaciones anteriores, para mostrar algunas especificidades del DGS en la construcción de pruebas por contradicción. En particular, afirmamos que un DGS puede orientar en el desarrollo de un argumento indirecto gracias a las posibilidades que ofrece tanto para construir sólidamente algunas propiedades como para ayudar a percibir los pseudoobjetos.Handle: http://hdl.handle.net/10481/22368Nº de citas en WOS (2017): 2 (Citas de 2º orden, 4)Nº de citas en SCOPUS (2017): 1 (Citas de 2º orden, 5)

Be contradictory, because of the infinitude of primes

2020 ◽  
pp. 169-174
Author(s):  
Susan D'Agostino
Keyword(s):  
Infinite Number ◽  
Mathematical Proof ◽  
Prime Numbers ◽  
Mathematics Students ◽  
Proof By Contradiction

“Be contradictory, because of the infinitude of primes” offers encouragement and practice with the “proof-by-contradiction” method of mathematical proof. Any mathematician will tell you that the collection of prime numbers is infinite. However, readers are guided in proving this statement by contradicting it. The activity pushes readers to engage deeply with the reasons supporting the fact that there are an infinite number of primes. Mathematics students and enthusiasts are encouraged to debate with enthusiasm in their mathematical and life pursuits. At the chapter’s end, readers may check their understanding by working on a problem. A solution is provided.

Simulating the Effects of Common Comedications and Genotypes on Alzheimer’s Cognitive Trajectory Using a Quantitative Systems Pharmacology Approach

2020 ◽  
Vol 78 (1) ◽  
pp. 413-424
Author(s):  
Hugo Geerts ◽  
Athan Spiros
Keyword(s):  
Alzheimer’S Disease ◽  
Alzheimer's Disease ◽  
Clinical Trials ◽  
Clinical Practice ◽  
Second Generation ◽  
Standard Of Care ◽  
Systems Pharmacology ◽  
Quantitative Systems Pharmacology ◽  
Pharmacodynamic Interactions ◽  
Cognitive Trajectory

Background: Many Alzheimer’s disease patients in clinical practice are on polypharmacy for treatment of comorbidities. Objective: While pharmacokinetic interactions between drugs have been relatively well established with corresponding treatment guidelines, many medications and common genotype variants also affect central brain circuits involved in cognitive trajectory, leading to complex pharmacodynamic interactions and a large variability in clinical trials. Methods: We applied a mechanism-based and ADAS-Cog calibrated Quantitative Systems Pharmacology biophysical model of neuronal circuits relevant for cognition in Alzheimer’s disease, to standard-of-care cholinergic therapy with COMTVal158Met, 5-HTTLPR rs25531, and APOE genotypes and with benzodiazepines, antidepressants, and antipsychotics, all together 9,585 combinations. Results: The model predicts a variability of up to 14 points on ADAS-Cog at baseline (COMTVV 5-HTTLPRss APOE 4/4 combination is worst) and a four-fold range for the rate of progression. The progression rate is inversely proportional to baseline ADAS-Cog. Antidepressants, benzodiazepines, first-generation more than second generation, and most antipsychotics with the exception of aripiprazole worsen the outcome when added to standard-of-care in mild cases. Low dose second-generation benzodiazepines revert the negative effects of risperidone and olanzapine, but only in mild stages. Non APOE4 carriers with a COMTMM and 5HTTLPRLL are predicted to have the best cognitive performance at baseline but deteriorate somewhat faster over time. However, this effect is significantly modulated by comedications. Conclusion: Once these simulations are validated, the platform can in principle provide optimal treatment guidance in clinical practice at an individual patient level, identify negative pharmacodynamic interactions with novel targets and address protocol amendments in clinical trials.

scholarly journals P1831 Predictors and clinical consequences of silent ischaemic brain lesions following transcatheter aortic valve implantation

2020 ◽  
Vol 21 (Supplement_1) ◽  
Author(s):  
A I Nagy ◽  
A I Bartykowszki ◽  
A I Varga ◽  
F Suhai ◽  
A A Apor ◽  
...  
Keyword(s):  
Aortic Valve ◽  
Transcatheter Aortic Valve Implantation ◽  
Brain Mri ◽  
Brain Lesions ◽  
Transcatheter Aortic Valve ◽  
Cognitive Trajectory ◽  
Ischaemic Brain ◽  
History Of ◽  
Aortic Valve Implantation ◽  
Valve Implantation

Abstract Funding Acknowledgements This study was supported by the János Bolyai Scholarship of the Hungarian Academy of Sciences Background A number of studies aimed to identify the predictors of periprocedural cerebral embolizations related to transcatheter aortic valve implantation (TAVI). Much less investigated is the prevalence and determinants of subacute ischaemic brain lesions that develop following TAVI. Purpose We sought to identify predictors of subacute clinically silent ischaemic brain lesions in patients following TAVI. Methods Patients were included from the Rule out Transcatheter Aortic Valve Thrombosis with Post Implantation Computed Tomography (RETORIC) prospective trial. Echocardiography and brain MRI were performed after TAVI procedure, before hospital discharge. Cardiac CT was performed 6 months later to identify subclinical leaflet thrombosis (HALT), as well as repeat brain MRI, to identify any silent ischaemic lesions that appeared since the intervention. The cognitive trajectory of patients was assessed using the Addenbrookes cognitive test (ACE), performed shortly after TAVI and at 6-month follow-up (FU). All-cause mortality data was retrieved from the National Mortality Database. Results 79 consecutive patients were included in the present analysis. 28% had known history of atrial fibrillation (AF). 33% of the cohort was treated with oral anticoagulant, of these 56% with single and 25% with dual antiplatelet therapy (DAPT). The mean CHA2DS2VASC score was 4. From discharge to the 6-month FU, 20 patients (25%) developed new silent ischaemic brain lesions on MRI. Clinically manifest stroke did not occur. On the 6-month CT, HALT was identified in 6 patients (8%). Clinical and imaging parameters, including age, body mass index, hypertension, dyslipidaemia, diabetes, smoking, statin-, OAC- and DAPT therapy, history of AF, history of stroke, echocardiographic metrics of left ventricular (ejection fraction, stroke volume index) and atrial (left atrial strain) function as well as HALT were analysed for association with ischaemic brain lesions. Of the above, only HALT showed significant association (OR:6,58; p = 0.04) with silent brain embolizations. The cognitive trajectory from discharge till 6-month FU did not differ between patients with or without ischaemic focuses (ΔACEscore: 1.0 vs. 0.1; p = NS). Over a median FU of 553 (IQR 453 – 665) days, 8 patients died; 2 with and 6 without ischaemic lesions. Kaplan-Meyer analysis showed no difference in outcome between the two groups (p = 0.68) Conclusion Subclinical leaflet thrombosis was identified as a significant predictor of subacute silent ischaemic brain lesions after TAVI. These lesions did not affect the overall cognitive performance or outcome of the patients.

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