An Hilbert space approach for a class of arbitrage free implied volatilities models

We present an Hilbert space formulation for a set of implied volatility models introduced in \cite{BraceGoldys01} in which the authors studied conditions for a family of European call options, varying the maturing time and the strike price $T$ an $K$, to be arbitrage free. The arbitrage free conditions give a system of stochastic PDEs for the evolution of the implied volatility surface ${\hat\sigma}_t(T,K)$. We will focus on the family obtained fixing a strike $K$ and varying $T$. In order to give conditions to prove an existence-and-uniqueness result for the solution of the system it is here expressed in terms of the square root of the forward implied volatility and rewritten in an Hilbert space setting. The existence and the uniqueness for the (arbitrage free) evolution of the forward implied volatility, and then of the the implied volatility, among a class of models, are proved. Specific examples are also given.Implied volatility; Option pricing; Stochastic SPDE; Hilbert space

Computational modeling of human sinoatrial node: what simulations tell us about pacemaking

The Sinoatrial node (SAN) is the primary pacemaker in physiological conditions. SAN tissue is characterized by auto-ryhthmicity, i.e. it does not need external stimuli to initiate its electrical activity. The auto-rhythmic behavior is due to the spontaneous slow depolarization during the diastolic phase. Understanding the biophysical mechanisms at the base of diastolic depolarization is crucial to modulate the heart rate (HR). In turn, HR modulation is fundamental to treat cardiac arrhythmias, so that atria and ventricles can fill and pump the blood properly. The overall aim of the thesis is the investigation of the underlying mechanisms responsible for the pacemaking in human. To this end, a human computational model of the action potential (AP) of the SAN was developed. Pacemaking modulation at single cell level, effects of ion channel mutations on the beating rate and propagation of the electrical trigger from SAN to atrial tissue are the faced topics The human single cell SAN model was developed starting from the rabbit SAN by Severi et al.; the parent model was updated with experimental data and automatic optimization to match the AP features reported in literature. A sensitivity analysis was performed to identify the most influencing parameters. The investigation of pacemaking modulation was carried out through the simulation of current blockade and mimicking the stimulation of the autonomic nervous system. The model was validated comparing the simulated electrophysiological effects due to ion channel mutations on beating rate with clinical data of symptomatic subjects carriers of the mutation. More insights on pacemaking mechanisms were obtained thanks to the inclusion of calcium-activated potassium currents, which link changes in the intracellular calcium to the membrane. Finally, the propagation of the AP from the SAN to the atrial tissue and the source-sink interplay was investigated employing a mono-dimensional strand composed by SAN and atrial models

Reproducibility study of the Fabbri et al. 2017 model of the human sinus node action potential

The sinoatrial node (SAN) is the natural pacemaker of the mammalian heart. It has been the subject of several mathematical studies, aimed at reproducing its electrical response under normal sinus rhythms, as well as under various conditions. Such studies were traditionally done using data from rabbit SAN cells. More recently, human SAN cell data have become available, resulting in the publication of a human SAN cell model (Fabbri et al., 2017), along with its CellML version. Here, we used the CellML file provided by the model authors, together with some SED-ML files and Python scripts that we created to reproduce the main results of the aforementioned modeling study. EDITOR'S NOTE (v2): this article and its OMEX archive are republished with technical changes made to the corresponding Python scripts to remove a run-time error message displayed when executing each simulation

Inter-species differences in the response of sinus node cellular pacemaking to changes of extracellular calcium

Changes of serum and extracellular ion concentrations occur regularly in patients with chronic kidney disease (CKD). Recently, hypocalcemia, i.e. a decrease of the extracellular calcium concentration $[Ca^{2+}]_o$, has been suggested as potential pathomechanism contributing to the unexplained high rate of sudden cardiac death (SCD) in CKD patients. In particular, there is a hypothesis that hypocalcaemia could slow down natural pacemaking in the human sinus node to fatal degrees. Here, we address the question whether there are inter-species differences in the response of cellular sinus node pacemaking to changes of $[Ca^{2+}]_o$. Towards this end, we employ computational models of mouse, rabbit and human sinus node cells. The Fabbri et al. human model was updated to consider changes of intracellular ion concentrations. We identified crucial inter-species differences in the response of cellular pacemaking in the sinus node to changes of $[Ca^{2+}]_o$ with little changes of cycle length in mouse and rabbit models (1000 ms). Our results suggest that experiments with human sinus node cells are required to investigate the potential mechanism of hypocalcaemia-induced bradycardic SCD in CKD patients and small animal models are not well suited

A nonlinear and time-dependent leak current in the presence of calcium fluoride patch-clamp seal enhancer [version 1; peer review: 2 approved with reservations]

Automated patch-clamp platforms are widely used and vital tools in both academia and industry to enable high-throughput studies such as drug screening. A leak current to ground occurs whenever the seal between a pipette and cell (or internal solution and cell in high-throughput machines) is not perfectly insulated from the bath (extracellular) solution. Over 1 GΩ seal resistance between pipette and bath solutions is commonly used as a quality standard for manual patch work. With automated platforms it can be difficult to obtain such a high seal resistance between the intra- and extra-cellular solutions. One suggested method to alleviate this problem is using an F− containing internal solution together with a Ca2+ containing external solution — so that a CaF2 crystal forms when the two solutions meet which ‘plugs the holes’ to enhance the seal resistance. However, we observed an unexpected nonlinear-in-voltage and time-dependent current using these solutions on an automated patch-clamp platform. We performed manual patch-clamp experiments with the automated patch-clamp solutions, but no biological cell, and observed the same nonlinear time-dependent leak current. The current could be completely removed by washing out F− ions to leave a conventional leak current that was linear and not time-dependent. We therefore conclude fluoride ions interacting with the CaF2 crystal are the origin of the nonlinear time-dependent leak current. The consequences of such a nonlinear and time-dependent leak current polluting measurements should be considered carefully if it cannot be isolated and subtracted

A systematic review and meta-analysis of Anakinra, Sarilumab, Siltuximab and Tocilizumab for Covid-19

Background There is accumulating evidence for an overly activated immune response in severe Covid-19, with several studies exploring the therapeutic role of immunomodulation. Through systematic review and meta-analysis, we assess the effectiveness of specific interleukin inhibitors for the treatment of Covid-19.Methods Electronic databases were searched on 7th January 2021 to identify studies of immunomodulatory agents (anakinra, sarilumab, siltuximab and tocilizumab) for the treatment of Covid-19. The primary outcomes were severity on an ordinal scale measured at day 15 from intervention and days to hospital discharge. Key secondary endpoints included overall mortality.Results 71 studies totalling 22,058 patients were included, six were randomised trials. Most explored outcomes in patients who received tocilizumab (59/71). In prospective studies, tocilizumab was associated with improved unadjusted survival (RR 0.83 95%CI 0.72;0.96 I2 = 0.0%), but conclusive benefit was not demonstrated for other outcomes. In retrospective studies, tocilizumab was associated with less severe outcomes on an ordinal scale (Generalised odds ratio 1.34 95%CI 1.10;1.64, I2=98%) and adjusted mortality risk (HR 0.52 95%CI 0.41;0.66, I2 =76.6%). The mean difference in duration of hospitalisation was 0.36 days (95%CI -0.07;0.80, I2 =93.8%). There was substantial heterogeneity in retrospective studies, and estimates should be interpreted cautiously. Other immunomodulatory agents showed similar effects to tocilizumab, but insufficient data precluded meta-analysis by agent.Conclusion Tocilizumab was associated with a lower relative risk of mortality in prospective studies, but effects were inconclusive for other outcomes. Current evidence for the efficacy of anakinra, siltuximab or sarilumab in Covid-19 is insufficient, with further studies urgently needed for conclusive findings

A nonlinear and time-dependent leak current in the presence of calcium fluoride patch-clamp seal enhancer

Automated patch-clamp platforms are widely used and vital tools in both academia and industry to enable high-throughput studies such as drug screening. A leak current to ground occurs whenever the seal between a pipette and cell (or internal solution and cell in high-throughput machines) is not perfectly insulated from the bath (extracellular) solution. Over 1 G seal resistance between pipette and bath solutions is commonly used as a quality standard for manual patch work. With automated platforms it can be difficult to obtain such a high seal resistance between the intra- and extra-cellular solutions. One suggested method to alleviate this problem is using an F containing internal solution together with a Ca 2+ containing external solution so that a CaF 2 crystal forms when the two solutions meet which plugs the holes' to enhance the seal resistance. However, we observed an unexpected nonlinear-in-voltage and time-dependent current using these solutions on an automated patch-clamp platform. We performed manual patch-clamp experiments with the automated patch-clamp solutions, but no biological cell, and observed the same nonlinear time-dependent leak current. The current could be completely removed by washing out F ions to leave a conventional leak current that was linear and not time-dependent. We therefore conclude fluoride ions interacting with the CaF 2 crystal are the origin of the nonlinear time-dependent leak current. The consequences of such a nonlinear and time-dependent leak current polluting measurements should be considered carefully if it cannot be isolated and subtracted

Management of Interests & External Interactions: A SPECTRUM Policy Document

The SPECTRUM Management of Interests and External Interactions document aims to make clear the official position of the Consortium with respect to engagement with external partners particularly where they may constitute, or give rise to, a conflict of interest or present a reputational or other risk to the Consortium. Additionally, it: - clarifies what interests and interactions are covered by the policy, - explains what is meant by conflict of interest, - provides guidance to members on the processes for proactively identifying risks and conflicts in order to prevent them, and how to mitigate and manage them if and when they do arise

Widespread exploitation of the honeybee by early Neolithic farmers.

This is the author's version of an article subsequently published in Nature. The definitive version is available from the publisher via: doi: 10.1038/nature15757.Copyright © 2015, Rights Managed by Nature Publishing GroupThe pressures on honeybee (Apis mellifera) populations, resulting from threats by modern pesticides, parasites, predators and diseases, have raised awareness of the economic importance and critical role this insect plays in agricultural societies across the globe. However, the association of humans with A. mellifera predates post-industrial-revolution agriculture, as evidenced by the widespread presence of ancient Egyptian bee iconography dating to the Old Kingdom (approximately 2400 BC). There are also indications of Stone Age people harvesting bee products; for example, honey hunting is interpreted from rock art in a prehistoric Holocene context and a beeswax find in a pre-agriculturalist site. However, when and where the regular association of A. mellifera with agriculturalists emerged is unknown. One of the major products of A. mellifera is beeswax, which is composed of a complex suite of lipids including n-alkanes, n-alkanoic acids and fatty acyl wax esters. The composition is highly constant as it is determined genetically through the insect's biochemistry. Thus, the chemical 'fingerprint' of beeswax provides a reliable basis for detecting this commodity in organic residues preserved at archaeological sites, which we now use to trace the exploitation by humans of A. mellifera temporally and spatially. Here we present secure identifications of beeswax in lipid residues preserved in pottery vessels of Neolithic Old World farmers. The geographical range of bee product exploitation is traced in Neolithic Europe, the Near East and North Africa, providing the palaeoecological range of honeybees during prehistory. Temporally, we demonstrate that bee products were exploited continuously, and probably extensively in some regions, at least from the seventh millennium cal BC, likely fulfilling a variety of technological and cultural functions. The close association of A. mellifera with Neolithic farming communities dates to the early onset of agriculture and may provide evidence for the beginnings of a domestication process.Natural Environment Research Council (NERC)English HeritageEuropean Research Council (ERC)Leverhulme TrustMinistère de la Culture et de la CommunicationMinistère de l’Enseignement Supérieur et de la RechercheRoyal SocietyWellcome Trus