Challenges in approximating the Black and Scholes call formula with hyperbolic tangents

In this paper, we introduce the concept of standardized call function and we obtain a new approximating formula for the Black and Scholes call function through the hyperbolic tangent. Differently from other solutions proposed in the literature, this formula is invertible; hence, it is useful for pricing and risk management as well as for extracting the implied volatility from quoted options. The latter is of particular importance since it indicates the risk of the underlying and it is the main component of the option’s price. That is what trading desks focus on. Further we estimate numerically the approximating error of the suggested solution and, by comparing our results in computing the implied volatility with the most common methods available in the literature, we discuss the challenges of this approach

Applied Spectral Analysis

In this chapter, we first explain what we mean by a signal, and then we describe some characteristics such as energy, frequency, phase, power spectrum, etc. We show how to analyse it by the means of spectral analysis and Fourier transform. Moreover, as the Fourier transform does not provide any information about the time at which each frequency appears, we explain how to deal with this problem with the Gabor and wavelet transform

Minor Phytocannabinoids: A Misleading Name but a Promising Opportunity for Biomedical Research

Despite the very large number of phytocannabinoids isolated from Cannabis (Cannabis sativa L.), bioactivity studies have long remained focused on the so called "Big Four" [Δ9-THC (1), CBD (2), CBG (3) and CBC (4)] because of their earlier characterization and relatively easy availability via isolation and/or synthesis. Bioactivity information on the chemical space associated with the remaining part of the cannabinome, a set of ca 150 compounds traditionally referred to as "minor phytocannabinoids", is scarce and patchy, yet promising in terms of pharmacological potential. According to their advancement stage, we sorted the bioactivity data available on these compounds, better referred to as the "dark cannabinome", into categories: discovery (in vitro phenotypical and biochemical assays), preclinical (animal models), and clinical. Strategies to overcome the availability issues associated with minor phytocannabinoids are discussed, as well as the still unmet challenges facing their development as mainstream drugs

Regiodivergent Synthesis of <i>ortho</i>- and <i>para</i>-Cannabinoquinones

Spurred by the remarkable biological profile of cannabinoquinoids, we have systematically investigated the periodinane oxidation of their resorcinolic precursors, discovering that the regiochemistry of oxidation, a critical maneuver for bioactivity, depends not only on the nature of the oxidant (\u3bb3- vs. \u3bb5-iodanes), but also on post-oxidative prototropic- and valence tautomeric equilibria that isomerize ortho-quinones to para-quinones. By complementary selection of the periodinane oxidant and by freezing prototropic equilibration with O-methylation, isomeric ortho- and para-quinones could be obtained from mono- and diphenolic cannabinoids, setting the stage for the exploration of novel areas of the biological space, and establishing a blueprint for the extension of this strategy to other classes of bioactive alkylresorcinols

Taste and Smell: A Unifying Chemosensory Theory

Since antiquity, the sense of smell (olfaction) is considered as a distance sense, just like sight and hear- ing. Conversely, the sense of taste (gustation) is thought to operate by direct contact, similarly to touch. With the progress of natural sciences, information at molecular, anatomical, and neurobiological levels has also contributed to the taste-smell dichotomy, but much evidence inconsistent with a sharp differenti- ation of these two senses has emerged, especially when considering species other than humans. In spite of this, conflicting information has been interpreted so that it could conform to the traditional differentia- tion. As a result, a confirmation bias is currently affecting scientific research on chemosensory systems and is also hindering the development of a satisfactory narrative of the evolution of chemical communi- cation across taxa. From this perspective, the chemosensory dichotomy loses its validity and usefulness. We thus propose the unification of all chemosensory modalities into a single sense, moving toward a synthetic, complex, and interconnected perspective on the gradual processes by which a vast variety of chemicals have become signals that are crucially important to communication among and within cells, organs, and or- ganisms in a wide variety of environmental conditions

Taste and Smell: A Unifying Chemosensory Theory

Since antiquity, the sense of smell (olfaction) is considered as a distance sense, just like sight and hearing. Conversely, the sense of taste (gustation) is thought to operate by direct contact, similarly to touch. With the progress of natural sciences, information at molecular, anatomical, and neurobiological levels has also contributed to the taste-smell dichotomy, but much evidence inconsistent with a sharp differentiation of these two senses has emerged, especially when considering species other than humans. In spite of this, conflicting information has been interpreted so that it could conform to the traditional differentiation. As a result, a confirmation bias is currently affecting scientific research on chemosensory systems and is also hindering the development of a satisfactory narrative of the evolution of chemical communication across taxa. From this perspective, the chemosensory dichotomy loses its validity and usefulness. We thus propose the unification of all chemosensory modalities into a single sense, moving toward a synthetic, complex, and interconnected perspective on the gradual processes by which a vast variety of chemicals have become signals that are crucially important to communication among and within cells, organs, and organisms in a wide variety of environmental condition

Comparative Safety of Originator and Biosimilar Epoetin Alfa Drugs: An Observational Prospective Multicenter Study

Background: Erythropoiesis-stimulating agents (ESAs) are biological molecules approved for the treatment of anemia associated with chronic renal failure. Biosimilars were licensed for use in Europe in 2007. Aim: This study aimed to compare the safety profile of biosimilars with respect to the reference product in a nephrology setting. Methods: A prospective study was conducted in four Italian regions between 1 October 2013 and 30 June 2015. The study population included patients aged 65 18&nbsp;years undergoing hemodialysis and treated with epoetins as per the clinical practice of the participating centers. The two comparison cohorts included patients treated with either an originator or a biosimilar epoetin alfa. Each patient was followed up until occurrence of any safety outcome of interest (grouped into three major categories), switch to a different ESA product, transplant or peritoneal dialysis, death, or end of the study period, whichever came first. Results: Overall, 867 subjects were included in the study (originator: N = 423; biosimilar: N = 444). Biosimilar users were older than originator users (median age of 76 vs 64&nbsp;years, respectively), more frequently affected by arrhythmia (29.3 vs 22.5%), and less frequently candidates for transplantation (3.8 vs 18.2%). Cox-regression analysis showed no increase in risk of safety outcomes in biosimilar users, even after adjusting for confounding factors: 1.0 (95% confidence interval [CI] 0.7\u20131.3) for any outcomes; 1.1 (95% CI 0.7\u20131.8) for problems related to dialysis device; 0.9 (95% CI 0.6\u20131.5) for cardio- and cerebro-vascular conditions; 0.9 (95% CI 0.6\u20131.5) for infections. Conclusion: This study confirms the comparable safety profiles of originator and biosimilar epoetin alfa drugs when used in patients receiving dialysis