A note on Pythagorean Triples

Some relations among Pythagorean triples are established. The main tool is a fundamental characterization of the Pythagorean triples through a chatetus which allows to determine relationships with Pythagorean triples having the same chatetus raised to an integer power.Comment: Paper accepted for publication in International Journal of Mathematics and Computer Science, Volume 15, no. 2, 2020, 485_49

Schizophrenia and vitamin D related genes could have been subject to latitude-driven adaptation

<p>Abstract</p> <p>Background</p> <p>Many natural phenomena are directly or indirectly related to latitude. Living at different latitudes, indeed, has its consequences with being exposed to different climates, diets, light/dark cycles, etc. In humans, one of the best known examples of genetic traits following a latitudinal gradient is skin pigmentation. Nevertheless, also several diseases show latitudinal clinals such as hypertension, cancer, dismetabolic conditions, schizophrenia, Parkinson's disease and many more.</p> <p>Results</p> <p>We investigated, for the first time on a wide genomic scale, the latitude-driven adaptation phenomena. In particular, we selected a set of genes showing signs of latitude-dependent population differentiation. The biological characterization of these genes showed enrichment for neural-related processes. In light of this, we investigated whether genes associated to neuropsychiatric diseases were enriched by Latitude-Related Genes (LRGs). We found a strong enrichment of LRGs in the set of genes associated to schizophrenia. In an attempt to try to explain this possible link between latitude and schizophrenia, we investigated their associations with vitamin D. We found in a set of vitamin D related genes a significant enrichment of both LRGs and of genes involved in schizophrenia.</p> <p>Conclusions</p> <p>Our results suggest a latitude-driven adaptation for both schizophrenia and vitamin D related genes. In addition we confirm, at a molecular level, the link between schizophrenia and vitamin D. Finally, we discuss a model in which schizophrenia is, at least partly, a maladaptive by-product of latitude dependent adaptive changes in vitamin D metabolism.</p

Signature of Energy Losses on the Cosmic Ray Electron Spectrum

We show that the fine structure of the electron spectrum in cosmic rays, especially the excess claimed by AMS-02 at energies $\sim$42 GeV, is fully accounted for in terms of inverse Compton losses in the photon background dominated by ultraviolet, infrared and CMB photons, plus the standard synchrotron losses in the Galactic magnetic field. The transition to the Klein-Nishina regime on the ultraviolet background causes the feature. Hence, contrary to previous statements, observations do not require the overlap of different components. We stress that the feature observed by AMS-02 at energies $\sim$42 GeV is not related to the positron excess, which instead requires the existence of positron sources, such as pulsars. Because energy losses are the physical explanation of this feature, we indirectly confirm that the transport of leptons in the Galaxy is loss-dominated down to energies of the order of tens of GeV. This finding imposes strong constraints on the feasibility of alternative theories of cosmic transport in which the grammage is accumulated in cocoons concentrated around sources, requiring that electrons and positrons become loss dominated only at very high energies.Comment: 5 pages, 3 figures, minor updates in the text, fixed a typo in Eq.

A Genotypic-oriented View of CFTR Genetics Highlights Specific Mutational Patterns Underlying Clinical Macro-categories of Cystic Fibrosis.

Cystic Fibrosis (CF) is a monogenic disease caused by mutations of the Cystic Fibrosis Transmembrane conductance Regulator (CFTR) gene. The genotype-phenotype relationship in this disease is still unclear, and diagnostic, prognostic and therapeutic challenges persist. We enrolled 610 patients with different forms of CF and studied them from a clinical, biochemical, microbiological and genetic point of view. Overall, 125 different mutated alleles (11 of which with novel mutations and 10 of which complex) and 225 genotypes were found. A strong correlation between mutational patterns at the genotypic level and phenotypic macro-categories emerged. This specificity appears to be largely dependent on rare and individual mutations, as well as on the varying prevalence of common alleles in different clinical macro-categories. However, 19 genotypes appeared to underlie different clinical forms of the disease. The dissection of the pathway from the CFTR mutated genotype to the clinical phenotype allowed to identify at least two components of the variability usually found in the genotype - phenotype relationship. One component seems to depend on the genetic variation of CFTR, the other component on the cumulative effect of variations in other genes and cellular pathways independent from CFTR. The experimental dissection of the overall biological CFTR pathway appears to be a powerful approach for a better comprehension of the genotype - phenotype relationship. However, a change from an allele-oriented to a genotypic-oriented view of CFTR genetics is mandatory, as well as a better assessment of sources of variability within the CFTR pathway

Local anesthesia for treatment of hernia in elder patients: Levobupicavaine or Bupivacaine?

BACKGROUND: Inguinal hernia is one of the most common diseases in the elderly. Treatment of this pathology is exclusively surgical and relies almost always on the use of local anesthesia. While in the past hernia surgery was carried out mainly by general anesthesia, in recent years there has been growing emphasis on the role of local anesthesia. METHODS: The aim of our study was to compare intra-and postoperative analgesia obtained by the use of levobupivacaine to the same obtained by bupivacaine. Bupivacaine is one of the main local anesthetics used in the intervention of inguinal hernioplasty. Levobupivacaine is an enantiomer of racemic bupivacaine with less cardiotoxicity and neurotoxicity. The study was conducted from March 2011 to March 2013. We collected data of eighty patients, male and female, aged between 65 and 86 years, who underwent inguinal hernioplasty with local anesthesia. RESULTS: Evaluation of intra-operatively pain shows that minimal pain is the same in both groups. Mild pain was more frequent in the group who used levobupivacaine. Moderate pain was slightly more frequent in the group who used bupivacaine. Only one reported intense pain. Two drugs seem to have the same effect at a distance of six, twelve, eighteen and twentyfour hours. Bupivacaine shows a significantly higher number of complications, as already demonstrated by previous studies. Degree of satisfaction expressed by patients has been the same in the two groups. Levobupivacaine group has shown a greater request for paracetamol while patients who experienced bupivacaine have showed a higher request of other analgesics. CONCLUSIONS: Clinical efficacy of levobupivacaine and racemic bupivacaine are actually similar, when used under local intervention of inguinal hernioplasty. In the field of ambulatorial surgery our working group prefers levobupivacaine for its fewer side effects and for its easy handling

Cyst-like periapical lesion healing in an orthodontic patient: A case report with five-year follow-up

Abstract Aim To report the orthodontic movement of two central incisors through the healing site of a maxillary cyst-like lesion of endodontic origin after nonsurgical treatment. Case summary This report shows the treatment of a 18-year old patient, male, with a Class II division 2 malocclusion. He came to our attention seeking for orthodontic treatment. Radiographic examinations revealed a large cyst-like lesion in the maxillary anterior area, extending from the mesial surface of tooth 12 to the distal surface of tooth 21. The two upper incisors were nonresponsive to pulp sensitivity tests. Endodontic treatment was performed first. One week after root canal treatment had been completed with gutta-percha fillings, orthodontic treatment was started while the bone lesion healing was still underway. At the end of the orthodontic treatment, incisor retroclination was corrected, periapical lesion healing was completed and there were no signs of root resorption. The five-year follow-up revealed that occlusal relationship and dental alignment were kept stable and excellent radiographic resolution of the periapical lesion was obtained