Touching the transcendentals: tractional motion from the birth of calculus to future perspectives

When the rigorous foundation of calculus was developed, it marked an epochal change in the approach of mathematicians to geometry. Tools from geometry had been one of the foundations of mathematics until the 17th century but today, mainstream conception relegates geometry to be merely a tool of visualization. In this snapshot, however, we consider geometric and constructive components of calculus. We reinterpret \u201ctractional motion\u201d, a late 17th century method to draw transcendental curves, in order to reintroduce \u201cideal machines\u201d in math foundation for a constructive approach to calculus that avoids the concept of infinity

REFLECTING ON THE BASES OF GEOMETRY: CONSTRUCTION WITH THE TRACTRIX

Construction is, historically, the first form of geometry, and from early days the subtleties of how constructions are done have been considered important. In this paper, we examine geometric construction using a straightedge and a device for drawing tractrices. The tractrix was the first curve traced by the mechanical solution of an inverse tangent problem, the geometrical issue at the basis of Leibniz's conception of infinitesimal analysis. This nonalgebraic curve cannot be axiomatized simply, as the circle can. We show that some important constructions can be done based on a weak axiomatization that does not fully specify the curve, and that more may be done using its Cartesian representation

Conics constructions by pins and string: tangential and physical properties

2noopenWe introduce conic sections' construction by pins and string, without rigid linear components. In addition to well-known methods (as gardener’s ellipse), we analyze some recent constructions based on tangent properties and, as an original contribution, extend these constructions to all kinds of conics. In this setting, the physical analysis of the string's tension permits us to smoothly analyze these constructions since the first years of high school. From a didactical perspective, we think that such ideas can be fruitfully adopted in laboratory activities to deepen the tangential properties of conics by a rich interaction between mathematics and physics. Furthermore, the simplicity of the required materials allows the introduction of these manipulative activities in distance learning.openMilici P; Salvi MMilici, P; Salvi,

Local Charge Excesses in Metallic Alloys: a Local Field Coherent Potential Approximation Theory

Electronic structure calculations performed on very large supercells have shown that the local charge excesses in metallic alloys are related through simple linear relations to the local electrostatic field resulting from distribution of charges in the whole crystal. By including local external fields in the single site Coherent Potential Approximation theory, we develop a novel theoretical scheme in which the local charge excesses for random alloys can be obtained as the responses to local external fields. Our model maintains all the computational advantages of a single site theory but allows for full charge relaxation at the impurity sites. Through applications to CuPd and CuZn alloys, we find that, as a general rule, non linear charge rearrangements occur at the impurity site as a consequence of the complex phenomena related with the electronic screening of the external potential. This nothwithstanding, we observe that linear relations hold between charge excesses and external potentials, in quantitative agreement with the mentioned supercell calculations, and well beyond the limits of linearity for any other site property.Comment: 11 pages, 1 table, 7 figure

Kinase inhibitors for the treatment of inflammatory and autoimmune disorders

Drugs targeting inhibition of kinases for the treatment of inflammation and autoimmune disorders have become a major focus in the pharmaceutical and biotech industry. Multiple kinases from different pathways have been the targets of interest in this endeavor. This review describes some of the recent developments in the search for inhibitors of IKK2, Syk, Lck, and JAK3 kinases. It is anticipated that some of these compounds or newer inhibitors of these kinases will be approved for the treatment of rheumatoid arthritis, psoriasis, organ transplantation, and other autoimmune diseases

Age-Specific Epigenetic Drift in Late-Onset Alzheimer's Disease

Despite an enormous research effort, most cases of late-onset Alzheimer's disease (LOAD) still remain unexplained and the current biomedical science is still a long way from the ultimate goal of revealing clear risk factors that can help in the diagnosis, prevention and treatment of the disease. Current theories about the development of LOAD hinge on the premise that Alzheimer's arises mainly from heritable causes. Yet, the complex, non-Mendelian disease etiology suggests that an epigenetic component could be involved. Using MALDI-TOF mass spectrometry in post-mortem brain samples and lymphocytes, we have performed an analysis of DNA methylation across 12 potential Alzheimer's susceptibility loci. In the LOAD brain samples we identified a notably age-specific epigenetic drift, supporting a potential role of epigenetic effects in the development of the disease. Additionally, we found that some genes that participate in amyloid-β processing (PSEN1, APOE) and methylation homeostasis (MTHFR, DNMT1) show a significant interindividual epigenetic variability, which may contribute to LOAD predisposition. The APOE gene was found to be of bimodal structure, with a hypomethylated CpG-poor promoter and a fully methylated 3′-CpG-island, that contains the sequences for the ε4-haplotype, which is the only undisputed genetic risk factor for LOAD. Aberrant epigenetic control in this CpG-island may contribute to LOAD pathology. We propose that epigenetic drift is likely to be a substantial mechanism predisposing individuals to LOAD and contributing to the course of disease

The additional value of patient-reported health status in predicting 1-year mortality after invasive coronary procedures: A report from the Euro Heart Survey on Coronary Revascularisation

Objective: Self-perceived health status may be helpful in identifying patients at high risk for adverse outcomes. The Euro Heart Survey on Coronary Revascularization (EHS-CR) provided an opportunity to explore whether impaired health status was a predictor of 1-year mortality in patients with coronary artery disease (CAD) undergoing angiographic procedures. Methods: Data from the EHS-CR that included 5619 patients from 31 member countries of the European Society of Cardiology were used. Inclusion criteria for the current study were completion of a self-report measure of health status, the EuroQol Questionnaire (EQ-5D) at discharge and information on 1-year follow-up, resulting in a study population of 3786 patients. Results: The 1-year mortality was 3.2% (n = 120). Survivors reported fewer problems on the five dimensions of the EQ-5D as compared with non-survivors. A broad range of potential confounders were adjusted for, which reached a p<0.10 in the unadjusted analyses. In the adjusted analyses, problems with self-care (OR 3.45; 95% CI 2.14 to 5.59) and a low rating (≤ 60) on health status (OR 2.41; 95% CI 1.47 to 3.94) were the most powerful independent predictors of mortality, among the 22 clinical variables included in the analysis. Furthermore, patients who reported no problems on all five dimensions had significantly lower 1-year mortality rates (OR 0.47; 95% CI 0.28 to 0.81). Conclusions: This analysis shows that impaired health status is associated with a 2-3-fold increased risk of all-cause mortality in patients with CAD, independent of other conventional risk factors. These results highlight the importance of including patients' subjective experience of their own health status in the evaluation strategy to optimise risk stratification and management in clinical practice

Un kit laboratoriale per (ri)concepire praticamente l’analisi infinitesimale

Lontano dal concetto di limite, l'intuizione geometrica dietro la concezione di Leibniz dell’analisi infinitesimale si basava sulla risoluzione del problema inverso delle tangenti. In questo articolo si introduce un nuovo strumento meccanico che, guidando la direzione di una curva, puo' essere adottato in classe per introdurre o consolidare alcuni concetti dell’analisi infinitesimale in modo tangibile, dinamico ed interattivo. Tale artefatto favorisce la naturale integrazione di contenuti storici ed epistemologici in attività pratiche e laboratoriali