We address the challenge of estimating rare events associated with stochastic differential equations using importance sampling. The importance sampling zero variance measure in these settings can be inferred from a solution to the Hamilton-Jacobi-Bellman partial differential equation (HJB-PDE) associated with a value function for the underlying process. Guided by this equation, we use a neural network to learn the zero variance change of measure. To improve performance of our estimation, we pursue two new ideas. First, we adopt a loss function that combines three objectives which collectively contribute to improving the performance of our estimator. Second, we embed our rare event problem into a sequence of problems with increasing rarity. We find that a well chosen schedule of rarity increase substantially speeds up rare event simulation. Our approach is illustrated on Brownian motion, Orstein-Uhlenbeck (OU) process, Cox–Ingersoll–Ross (CIR) process as well as Langevin double-well diffusion.

In this article, an iterative deterministic policy gradient method for finding optimal strategies in the presence of market impact is introduced. The derivation of the policy gradient sheds light on a proper way of handling the market impact of trades in the context of reinforcement learning. Similar to many machine learning methods, the proposed deterministic policy gradient method is based on mini-batch stochastic gradient descent optimization. The method is demonstrated to consistently perform well for several different objectives and market dynamics when applied to the financial applications of order execution and option hedging.

The Kingman coalescent is a fundamental process in population genetics modelling the ancestry of a sample of individuals backwards in time. In this paper, in a largesample -size regime, we study asymptotic properties of the coalescent under neutrality and a general finite -alleles mutation scheme, i.e. including both parent independent and parent dependent mutation. In particular, we consider a sequence of Markov chains that is related to the coalescent and consists of block -counting and mutationcounting components. We show that these components, suitably scaled, converge weakly to deterministic components and Poisson processes with varying intensities, respectively. Along the way, we develop a novel approach, based on a change of measure, to generalise the convergence result from the parent independent to the parent dependent mutation setting, in which several crucial quantities are not known explicitly.

In this work, a generative model based on recurrent neural networks for the complete dynamics of a limit order book is developed. The model captures the dynamics of the limit order book by decomposing the probability of each transition into a product of conditional probabilities of order type, price level, order size and time delay. Each such conditional probability is modelled by a recurrent neural network. Several evaluation metrics for generative models related to trading execution are introduced. Using these metrics, it is demonstrated that the generative model can be successfully trained to fit both synthetic and real data from the Nasdaq Stockholm exchange.

Endothelial dysfunction and impaired vasodilation are linked with adverse cardiovascular events. T lymphocytes expressing choline acetyltransferase (ChAT), the enzyme catalyzing biosynthesis of the vasorelaxant acetylcholine (ACh), regulate vasodilation and are integral to the cholinergic antiinflammatory pathway in an inflammatory reflex in mice. Here, we found that human T cell ChAT mRNA expression was induced by T cell activation involving the PI3K signaling cascade. Mechanistically, we identified that ChAT mRNA expression was induced following the attenuation of RE-1 Silencing Transcription factor REST-mediated methylation of the ChAT promoter, and that ChAT mRNA expression levels were up-regulated by GATA3 in human T cells. In functional experiments, T cell-derived ACh increased endothelial nitric oxide-synthase activity, promoted vasorelaxation, and reduced vascular endothelial activation and promoted barrier integrity by a cholinergic mechanism. Further, we observed that survival in a cohort of patients with severe circulatory failure correlated with their relative frequency of ChAT+CD4+ T cells in blood. These findings on ChAT+ human T cells provide a mechanism for cholinergic immune regulation of vascular endothelial function in human inflammation.

The results in this paper provide new information on asymptotic properties of classical models: the neutral Kingman coalescent under a general finite-alleles, parent-dependent mutation mechanism, and its generalisation, the ancestral selection graph. Several relevant quantities related to these fundamental models are not explicitly known when mutations are parent dependent. Examples include the probability that a sample taken from a population has a certain type configuration, and the transition probabilities of their block counting jump chains. In this paper, asymptotic results are derived for these quantities, as the sample size goes to infinity. It is shown that the sampling probabilities decay polynomially in the sample size with multiplying constant depending on the stationary density of the Wright-Fisher diffusion and that the transition probabilities converge to the limit of frequencies of types in the sample.

This article considers importance sampling for estimation of rare-event probabilities in a specific collection of Markovian jump processes used for, e.g., modeling of credit risk. Previous attempts at designing importance sampling algorithms have resulted in poor performance and the main contribution of the article is the design of efficient importance sampling algorithms using subsolutions. The dynamics of the jump processes cause the corresponding Hamilton-Jacobi equations to have an intricate state-dependence, which makes the design of efficient algorithms difficult. We provide theoretical results that quantify the performance of importance sampling algorithms in general and construct asymptotically optimal algorithms for some examples. The computational gain compared to standard Monte Carlo is illustrated by numerical examples.

We study two of the most popular performance metrics in medical image segmentation, Accuracy and Dice, when the target labels are noisy. For both metrics,several statements related to characterization and volume properties of the set ofoptimal segmentations are proved, and associated experiments are provided. Ourmain insights are: (i) the volume of the solutions to both metrics may deviatesignificantly from the expected volume of the target, (ii) the volume of a solutionto Accuracy is always less than or equal to the volume of a solution to Dice and(iii) the optimal solutions to both of these metrics coincide when the set of feasiblesegmentations is constrained to the set of segmentations with the volume equal tothe expected volume of the target.

We study two of the most popular performance metrics in medical image segmentation, Accuracy and Dice, when the target labels are noisy. For both metrics, several statements related to characterization and volume properties of the set of optimal segmentations are proved, and associated experiments are provided. Our main insights are: (i) the volume of the solutions to both metrics may deviate significantly from the expected volume of the target, (ii) the volume of a solution to Accuracy is always less than or equal to the volume of a solution to Dice and (iii) the optimal solutions to both of these metrics coincide when the set of feasible segmentations is constrained to the set of segmentations with the volume equal to the expected volume of the target.

Nonresolving inflammation underlies a range of chronic inflammatory diseases, and therapeutic acceleration of resolution of inflammation may improve outcomes. Neural reflexes regulate the intensity of inflammation (for example, through signals in the vagus nerve), but whether activation of the vagus nerve promotes the resolution of inflammation in vivo has been unknown. To investigate this, mice were subjected to electrical vagus nerve stimulation (VNS) or sham surgery at the cervical level followed by zymosan-induced peritonitis. The duration of inflammation resolution was significantly reduced and efferocytosis was significantly increased in mice treated with VNS as compared with sham. Lipid mediator (LM) metabololipidomics revealed that mice treated with VNS had higher levels of specialized proresolving mediators (SPMs), particularly from the omega-3 docosahexaenoic (DHA) and docosapentaenoic (n-3 DPA) metabolomes, in peritoneal exudates. VNS also shifted the ratio between proinflammatory and proresolving LMs toward a proresolving profile, but this effect by VNS was inverted in mice deficient in 12/15-lipoxgenase (Alox15), a key enzyme in this SPM biosynthesis. The significant VNS-mediated reduction of neutrophil numbers in peritoneal exudates was absent in mice deficient in the cholinergic α7-nicotinic acetylcholine receptor subunit (α7nAChR), an essential component of the inflammatory reflex. Thus, VNS increased local levels of SPM and accelerated resolution of inflammation in zymosan-induced peritonitis by a mechanism that involves Alox15 and requires the α7nAChR.