Model-Independent Pricing of Asian Options via Optimal Martingale Transport

In this article we discuss the problem of calculating optimal model-independent (robust) bounds for the price of Asian options with discrete and continuous averaging. We will give geometric characterisations of the maximising and the minimising pricing model for certain types of Asian options in discrete and continuous time. In discrete time the problem is reduced to finding the optimal martingale transport for the cost function $|x+y|$. In the continuous time case we consider the cases with one and two given marginals. We describe the maximising models in both of these cases as well as the minimising model in the one-marginal case and relate the two-marginals case to the discrete time problem with two marginals

Environmental stimuli shape adaptive immunity by enhancing T helper cell differentiation and the germinal centre response

Immune cells have evolved to respond to external danger signals and to incorporate information about environmental cues to adapt their differentiation and effector function. Because of this, it is important that immune cells are studied in the context of their surroundings. In this thesis, I investigated the roles of environmental endoplasmic reticulum (ER) stress, the gut microbiome and ageing on adaptive immunity. Immune cells have been shown to integrate inflammatory signalling with the ER stress response pathway. This response is triggered by a variety of environmental stresses such as low nutrient availability, hypoxia and mechanical stress. I found that the ER stress response acts as a potent driver of T helper 17 (Th17) cell differentiation resulting in Th17 cells with a pathogenic gene expression signature. This suggests a link between ER stress-inducing conditions such as low nutrient availability, and the pathology of Th17 cell-mediated autoimmune diseases. Another physiological scenario in which the immune microenvironment changes is during ageing. Ageing-related changes of the gut microbiome have recently been linked to increased frailty and systemic inflammation. This change in microbial composition with age occurs in parallel with a decline in function of the gut immune system, however it is not clear if there is a causal link between the two. Here, I establish that the defective germinal centre (GC) reaction in Peyer’s patches in the small intestine of aged mice can be rescued by co-housing of adult and aged mice, and via faecal transfers from adult into aged mice. This demonstrates that the poor GC reaction in aged animals is not irreversible, and that it is possible to improve immune responses in older individuals by replenishing the gut microbiome. To determine whether GC responses can also be improved in peripheral lymph nodes, we investigated the role of defective helper T cell priming in aged mice. We observed that the age-associated defect in the GC reaction is partly due to impaired T cell priming by dendritic cells (DCs). By boosting type I interferon signalling in DCs at the time of immunisation, I was able to improve T cell priming and GC formation in aged mice. This demonstrates that not only the gut microbiome, but also DCs are exciting targets to improve GC responses in ageing and highlights the importance of environmental stimuli in shaping adaptive immunity.PhD funding was provided by the EU-funded Horizon 2020 ENLIGHT-TEN project No. 675395 and additional consumables funding was provided by Marc Veldhoen and Michelle Linterman

Linear Constraints in Optimal Transport

This thesis studies the problem of optimal mass transportation with linear constraints -- supermartingale and martingale transport in discrete and continuous time. Appropriate versions of corresponding dual problems are introduced and shown to satisfy fundamental properties: weak duality, absence of a duality gap, and the existence of a dual optimal element. We show how the existence of a dual optimizer implies that primal optimizers can be characterized geometrically through their support -- an infinite dimensional analogue of complementary slackness. In discrete time martingale and supermartingale transport problems, we utilize this result to establish the existence of canonical transport plans, that is joint optimizers for large families of reward functions. To this end, we show that the optimal support coincides for these families. We additionally characterize these transport plans through order-theoretic minimality properties, with respect to second stochastic order and convex order, respectively, in the supermartingale and the martingale case. This characterization further shows that the canonical transport plan is unique

Heterotrophic growth of the cyanobacterium Anabaena (Nostoc) sp. strain PCC7120 and its dependence on a functional cox1 locus encoding cytochrome c oxidase

Cyanobakterien sind Prokaryoten, welche oxygene Photosynthese betreiben. Dennoch können alle Cyanobakterien im Dunkeln atmen. Im Gegensatz zu photosynthetischen Eukaryoten (Algen, höhere Pflanzen), wo Photosynthese und Atmung in Chloroplasten und Mitochondrien räumlich voneinander getrennt stattfinden, laufen diese beiden Prozesse in Cyanobakterien in ein und demselben Kompartiment ab und einige Komponenten werden von beiden Elektronentransportketten verwendet. Die respiratorischen terminalen Oxidasen (RTOs) sind Schlüsselenzyme, da sie nicht direkt an der Photosynthese beteiligt sind, sondern die Elektronen zum terminalen Akzeptor O2 leiten. Respiratorische Oxidasen in Cyanobakterien gehören verschiedenen Klassen an. Wichtige Klassen sind die Häm Kupfer Oxidasen, welche homolog zur Cytochrom c Oxidase in Mitochondrien ist, die Chinon Oxidase, welche homolog zu Cytochrom bd in E. coli ist, sowie die Klasse jener RTOs, die homolog zu Plastid terminalen Oxidasen (Ptox) in Chloroplasten ist. Fast alle Cyanobakterien besitzen zumindest eine Cytochrom c oxidase vom Cytochrom aa3 type. Drei verschiedene Unterklassen von Cytochrom aa3 Typ RTOs sind identifiziert worden: a) echte Cytochrom c Oxidasen, welche die charakteristischen Motive enthalten; b) eine 2. Unterklasse, welche alternative respiratorische terminale Oxidase (ARTO) genannt wird; c) eine Oxidase vom cbb3 Typ (zuerst in Purpurbakterien charakterisiert). Anabaena PCC7120 gehört zu den unverzweigten filamentösen Cyanobakterien, welche zur Zelldifferenzierung befähigt sind. Bei einem Mangel an gebundenem Stickstoff (Nitrat, Nitrit, Ammoniak) können einige vegetative Zellen zu Heterocysten differenzieren (in nicht zufälliger Verteilung innerhalb eines Filaments). PCC7120 hat 5 verschiedene respiratorische terminale Oxidasen: 1 echte Cytochrom c Oxidase (Cox), 2 ARTOs, eine Chinon Oxidase (Qox) und 1 Plastid terminale Oxidase (Ptox). Da die Expression der beiden ARTOs auf die Heterocysten beschränkt zu sein scheint, verbleiben in den vegetativen Zellen 1 Cox, 1 Qox und 1 Ptox. Wenn der cox Locus durch eine Antibiotikumkassette ausgeschaltet wird, verliert der neue Mutantenstamm jegliche Cytochrom c oxidase Aktivität, wie Versuche mit isolierten Membranen aus dem Mutantenstamm und aus Pferdeherz isoliertem Cytochrom c550 bewiesen. Außerdem scheint Cox essentiell für das chemoheterotrophe Wachstum von PCC7120 im Dunkeln zu sein. Trotz bisheriger Untersuchungen, welche diesen Stamm als streng photolithoautotroph klassifizierten, zeigten neue Versuche, dass PCC7120 heterotroph wachsen kann, vorrausgesetzt hohe Mengen an Fruktose wurden dem Medium hinzugesetzt. Offenbar hat PCC7120 eine gewisse Kapazität für heterotrophes Wachstum und Fruktosemetabolismus im Inneren der Zelle. Sehr hohe Konzentrationen im Nährmedium reichen aus, dass Fructose über die Zellwand und die Membranen ins Innere gelangt. Experimente haben gezeigt, dass umso mehr Fruktose eindringt, je höher die Konzentration im äußeren Medium ist. Das Einschleusen des Glukose carrier Gens gtr aus PCC6803 führt zu einem transgenen Stamm, der im Gegensatz zum Wildtyp bereits bei geringeren Fruktosekonzentrationen photoorganoheterotroph wachsen kann. Glukose ist jedoch toxisch für PCC7120gtr+, während der Wildtyp dieser gegenüber tolerant ist. Der Mutantenstamm, in welchem cox ausgeschaltet worden ist, kann nicht mehr chemoheterotroph wachsen. Ähnliche Ergebnisse gibt es auch von Synechocystis PCC6803 und Anabaena variabilis ATCC29413, in welchen Cox ebenfalls notwendig für das chemoheterotrophe Wachstum ist.Cyanobacteria are prokaryotes that perform oxygenic photosynthesis. However, all cyanobacteria respire at dark periods. In eukaryotic phototrophs like algae and higher plants photosynthesis and respiration are separated to the different organells chloroplasts and mitochondria, while in cyanobacteria these two processes occur in the same compartment and many components are shared. The respiratory terminal oxidases (RTOs) are key enzymes because they are not involved directly in photosynthesis but transfer electrons to terminal acceptor O2. Cyanobacterial oxidases belong to different classes. There are the heme copper oxidases homologous to mitochondrial cytochrome c oxidase, the quinol oxidases homologous to cytochrome bd in Escherichia coli and homologues to the plastid terminal oxidases that are insensitive to cyanide. Nearly all cyanobacteria contain at least one heme copper oxidase of the cytochrome aa3 type. There are three different subclasses identified: a) The genuine cytochrome c oxidases, containing the characteristic motives. b) A second class, called alternative respiratory terminal oxidase (ARTO). c) An oxidase of type cbb3 (first characterized in purple bacteria). Anabaena sp. PCC7120 belongs to the unbranched filamentous cyanobacteria that can undergo cell differentiation. If bound nitrogen (nitrate, nitrite, ammonia) is absent some vegetative cells will differentiate into heterocysts with a non random distribution. PCC 7120 has five different respiratory terminal oxidases: one genuine cytochrome c oxidase (Cox), two ARTOs, one quinol oxidase (Qox) and one plastid terminal oxidase (Ptox). As the two ARTOs seem to be restricted to heterocysts, only 1 Cox, 1 Qox and 1 Ptox remain in vegetative cells. When cox is knocked out by an antibiotic resistance cassette the strain loses any cytochrome c oxidase activity as an assay clearly demonstrated with isolated membranes and cytochrome c550 isolated from horse heart. Moreover the Cox seems to be essential for chemoheterotrophic growth in the dark. Despite previous reports, which classify PCC7120 as strictly photolithoautotrophs, experiments revealed that this strain can grow heterotrophically when high amounts of fructose were added to the medium. Evidently PCC7120 has the capacity for heterotrophic growth and fructose metabolism inside its cells, however, heterotrophic growth can only be observed at very high fructose concentrations (at least 50mM) in the medium. Experiments have shown that fructose enters the cells the faster the higher the outside concentration is. Introduction of glucose carrier gene gtr from Synechocystis PCC6803 by conjugation results in a transgenic strain that can grow photoorganoheterotrophically on lower concentrations of fructose than the wild type (WT). However, glucose is toxic for PCC7120gtr+ while the WT is tolerant towards it. The mutant from which cox has been deleted fails to grow chemoheterotrophically. This is analogous to experiments in Synechocystis PCC6803 and Anabaena variabilis ATCC29413, where also the genuine cytochrome c oxidase is essential for chemoheterotrophic growth

Safety and efficacy of amlitelimab, a fully human nondepleting, noncytotoxic anti-OX40 ligand monoclonal antibody, in atopic dermatitis: results of a phase IIa randomized placebo-controlled trial

Background Atopic dermatitis (AD) is an inflammatory skin disease with significant unmet need. Blockade of the OX40–OX40 ligand (OX40L) costimulation pathway by targeting OX40L on antigen-presenting cells (APCs) with a fully human noncytotoxic, nondepleting anti-OX40L monoclonal antibody (amlitelimab; SAR445229; KY1005) is a novel way to modulate persistent inflammation. Objectives To assess the safety and efficacy of amlitelimab over 16 weeks in adults with AD in a phase IIa double-blind placebo-controlled study. Methods The study was conducted at 19 hospitals in Germany, Poland, Spain and the UK. Eligible patients with moderate-to-severe AD were randomized (1 : 1 : 1) to low-dose intravenous (IV) amlitelimab (200 mg), high-dose IV amlitelimab (500 mg) or placebo, followed by three maintenance doses (50% of loading dose) at 4, 8 and 12 weeks, with safety follow-up to week 36. The co-primary endpoints were the incidence of treatment-emergent adverse events (all patients who received ≥ 1 dose of the study drug) and mean percentage change in Eczema Area and Severity Index (EASI) to week 16 (full analysis set). Results Between 13 December 2018 and 12 May 2020, 89 patients were randomly assigned to low- (n = 29) or high-dose amlitelimab (n = 30) or placebo (n = 29), of whom 88 proceeded to treatment [37 women (42%), 51 (58%) men; mean (SD) age 33.6 (11.9) years]. Amlitelimab was generally well tolerated with an unremarkable safety profile; no hypersensitivity events were reported. For the primary endpoint, the least square mean percentage change in EASI from baseline to week 16 was –80.12% [95% confidence interval (CI) –95.55 to –64.68; P = 0.009 vs. placebo] and –69.97% (95% CI –85.04 to –54.60; P = 0.07 vs. placebo) for the low- (n = 27) and high-dose (n = 27) amlitelimab groups, respectively, vs. –49.37% (95% CI –66.02 to –32.72) for placebo (n = 24). Numerically greater reductions in EASI were observed for amlitelimab vs. placebo from weeks 2 to 16. Conclusions Novel targeting of OX40L-expressing APCs with amlitelimab was well tolerated and resulted in clinically meaningful improvements in AD

Regulation of the Germinal Center Response

The germinal center (GC) is a specialized microstructure that forms in secondary lymphoid tissues, producing long-lived antibody secreting plasma cells and memory B cells, which can provide protection against reinfection. Within the GC, B cells undergo somatic mutation of the genes encoding their B cell receptors which, following successful selection, can lead to the emergence of B cell clones that bind antigen with high affinity. However, this mutation process can also be dangerous, as it can create autoreactive clones that can cause autoimmunity. Because of this, regulation of GC reactions is critical to ensure high affinity antibody production and to enforce self-tolerance by avoiding emergence of autoreactive B cell clones. A productive GC response requires the collaboration of multiple cell types. The stromal cell network orchestrates GC cell dynamics by controlling antigen delivery and cell trafficking. T follicular helper (Tfh) cells provide specialized help to GC B cells through cognate T-B cell interactions while Foxp3+ T follicular regulatory (Tfr) cells are key mediators of GC regulation. However, regulation of GC responses is not a simple outcome of Tfh/Tfr balance, but also involves the contribution of other cell types to modulate the GC microenvironment and to avoid autoimmunity. Thus, the regulation of the GC is complex, and occurs at multiple levels. In this review we outline recent developments in the biology of cell subsets involved in the regulation of GC reactions, in both secondary lymphoid tissues, and Peyer's patches (PPs). We discuss the mechanisms which enable the generation of potent protective humoral immunity whilst GC-derived autoimmunity is avoided

Rejuvenating conventional dendritic cells and T follicular helper cell formation after vaccination.

Germinal centres (GCs) are T follicular helper cell (Tfh)-dependent structures that form in response to vaccination, producing long-lived antibody secreting plasma cells and memory B cells that protect against subsequent infection. With advancing age the GC and Tfh cell response declines, resulting in impaired humoral immunity. We sought to discover what underpins the poor Tfh cell response in ageing and whether it is possible to correct it. Here, we demonstrate that older people and aged mice have impaired Tfh cell differentiation upon vaccination. This deficit is preceded by poor activation of conventional dendritic cells type 2 (cDC2) due to reduced type 1 interferon signalling. Importantly, the Tfh and cDC2 cell response can be boosted in aged mice by treatment with a TLR7 agonist. This demonstrates that age-associated defects in the cDC2 and Tfh cell response are not irreversible and can be enhanced to improve vaccine responses in older individuals