Deep learning of value at risk through generative neural network models: The case of the Variational auto encoder.

We present in this paper a method to compute, using generative neural networks, an estimator of the "Value at Risk" for a financial asset. The method uses a Variational Auto Encoder with an 'energy' (a.k.a. Radon-Sobolev) kernel. The result behaves according to intuition and is in line with more classical methods.•Estimation of the Value at Risk with generative neural networks•No a priori assumptions on the distribution of the returns•Good practical behavior.

COVID-19 Adaptive Humoral Immunity Models: Weakly Neutralizing Versus Antibody-Disease Enhancement Scenarios.

The interplay between the virus, infected cells and immune responses to SARS-CoV-2 is still under debate. By extending the basic model of viral dynamics, we propose here a formal approach to describe neutralisation versus weak (or non-)neutralisation scenarios and compare them with the possible effects of antibody-dependent enhancement (ADE). The theoretical model is consistent with the data available in the literature; we show that both weakly neutralising antibodies and ADE can result in final viral clearance or disease progression, but that the immunodynamics are different in each case. As a significant proportion of the world's population is already naturally immune or vaccinated, we also discuss the implications for secondary infections after vaccination or in the presence of immune system dysfunctions.

Radon-Sobolev Variational Auto-Encoders.

The quality of generative models (such as Generative adversarial networks and Variational Auto-Encoders) depends heavily on the choice of a good probability distance. However some popular metrics like the Wasserstein or the Sliced Wasserstein distances, the Jensen-Shannon divergence, the Kullback-Leibler divergence, lack convenient properties such as (geodesic) convexity, fast evaluation and so on. To address these shortcomings, we introduce a class of distances that have built-in convexity. We investigate the relationship with some known paradigms (sliced distances - a synonym for Radon distances - reproducing kernel Hilbert spaces, energy distances). The distances are shown to possess fast implementations and are included in an adapted Variational Auto-Encoder termed Radon-Sobolev Variational Auto-Encoder (RS-VAE) which produces high quality results on standard generative datasets.

Immunity after COVID-19: Protection or sensitization?

Motivated by historical and present clinical observations, we discuss the possible unfavorable evolution of the immunity (similar to documented antibody-dependent enhancement scenarios) after a first infection with COVID-19. More precisely we ask the question of how the epidemic outcomes are affected if the initial infection does not provide immunity but rather sensitization to future challenges. We first provide background comparison with the 2003 SARS epidemic. Then we use a compartmental epidemic model structured by immunity level that we fit to available data; using several scenarios of the fragilization dynamics, we derive quantitative insights into the additional expected numbers of severe cases and deaths.

A New Transmission Route for the Propagation of the SARS-CoV-2 Coronavirus.

BACKGROUND: Starting late 2019, a novel coronavirus spread from the capital of the Hubei province in China to the rest of the country, then to most of the world. To anticipate future trends in the development of the pandemic, we explore here, based on public records of infected persons, how variation in the virus tropism could end up in different patterns, warranting a specific strategy to handle the epidemic. METHODS: We use a compartmental model to describe the evolution of an individual through several possible states: susceptible, infected, alternative infection, detected, and removed. We fit the parameters of the model to the existing data, taking into account significant quarantine changes where necessary. RESULTS: The model indicates that Wuhan quarantine measures were effective, but that alternative virus forms and a second propagation route are compatible with available data. For the Hong Kong, Singapore, and Shenzhen regions, the secondary route does not seem to be active. CONCLUSIONS: Hypotheses of an alternative infection tropism (the gut tropism) and a secondary propagation route are discussed using a model fitted by the available data. Corresponding prevention measures that take into account both routes should be implemented to the benefit of epidemic control.

[Biochemical and statistical lessons from the evolution of the SARS-CoV-2 virus: paths for novel antiviral warfare]. / Leçons biochimiques et statistiques de l'évolution du virus SARS-CoV-2 : nouveaux chemins pour combattre les virus.

In the fight against the spread of COVID-19 the emphasis is on vaccination or on reactivating existing drugs used for other purposes. The tight links that necessarily exist between the virus as it multiplies and the metabolism of its host are systematically ignored. Here we show that the metabolism of all cells is coordinated by the availability of a core building block of the cell's genome, cytidine triphosphate (CTP). This metabolite is also the key to the synthesis of the viral envelope and to the translation of its genome into proteins. This unique role explains why evolution has led to the early emergence in animals of an antiviral immunity enzyme, viperin, that synthesizes a toxic analogue of CTP. The constraints arising from this dependency guide the evolution of the virus. With this in mind, we explored the real-time experiment taking place before our eyes using probabilistic modelling approaches to the molecular evolution of the virus. We have thus followed, almost on a daily basis, the evolution of the composition of the viral genome to link it to the progeny produced over time, particularly in the form of blooms that sparked a firework of viral mutations. Some of those certainly increase the propagation of the virus. This led us to make out the critical role in this evolution of several proteins of the virus, such as its nucleocapsid N, and more generally to begin to understand how the virus ties up the host metabolism to its own benefit. A way for the virus to escape CTP-dependent control in cells would be to infect cells that are not expected to grow, such as neurons. This may account for unexpected body sites of viral development in the present epidemic.

Dans la lutte contre la propagation de la COVID-19 l'accent est mis sur la vaccination, d'une part, et sur le redéploiement de traitements utilisés pour d'autres usages, d'autre part. Les liens qui existent nécessairement entre la multiplication du virus et le métabolisme de l'hôte sont systématiquement ignorés. Ici nous montrons que le métabolisme de toutes les cellules est coordonné par l'accessibilité d'un composant central du génome cellulaire, le triphosphate de cytidine (CTP). Ce métabolite est aussi la clé de la synthèse de l'enveloppe virale et de la traduction de son génome en protéines. Ce rôle unique explique pourquoi l'évolution a fait apparaître très tôt chez les animaux une activité enzymatique de l'immunité antivirale, la vipérine, destinée à synthétiser un analogue toxique du CTP. Les contraintes nées de cette dépendance orientent l'évolution du virus. Avec cette servitude à l'esprit, nous avons exploré l'expérience en vraie grandeur qui se déroule sous nos yeux au moyen d'approches de modélisation probabiliste de l'évolution moléculaire du virus. Nous avons ainsi suivi, presque au jour le jour, le devenir de la composition du génome viral pour la relier à la descendance produite au cours du temps, en particulier sous la forme d'efflorescences où apparaît un véritable feu d'artifice de mutations virales. Certaines d'entre elles augmentent certainement la propagation du virus. Cela nous conduit à proposer un rôle important dans cette évolution à certaines protéines du virus, comme celle de la nucléocapside N et plus généralement de commencer à comprendre comment le virus asservit à son bénéfice le métabolisme de l'hôte. L'un des moyens possibles pour le virus d'échapper au contrôle par le CTP serait d'infecter des cellules qui ne se multiplient pas, comme les neurones. Cela pourrait expliquer les sites de développement viral inattendus qu'on observe dans l'épidémie actuelle.

Optimal individual strategies for influenza vaccines with imperfect efficacy and durability of protection.

We analyze a model of agent based vaccination campaign against influenza with imperfect vaccine efficacy and durability of protection. We prove the existence of a Nash equilibrium by Kakutani's fixed point theorem in the context of non-persistent immunity. Subsequently, we propose and test a novel numerical method to find the equilibrium. Various issues of the model are then discussed, such as the dependence of the optimal policy with respect to the imperfections of the vaccine, as well as the best vaccination timing. The numerical results show that, under specific circumstances, some counter-intuitive behaviors are optimal, such as, for example, an increase of the fraction of vaccinated individuals when the efficacy of the vaccine is decreasing up to a threshold. The possibility of finding optimal strategies at the individual level can help public health decision makers in designing efficient vaccination campaigns and policies.

Individual Vaccination as Nash Equilibrium in a SIR Model with Application to the 2009-2010 Influenza A (H1N1) Epidemic in France.

The vaccination against ongoing epidemics is seldom compulsory but remains one of the most classical means to fight epidemic propagation. However, recent debates concerning the innocuity of vaccines and their risk with respect to the risk of the epidemic itself lead to severe vaccination campaign failures, and new mass behaviors appeared driven by individual self-interest. Prompted by this context, we analyze, in a Susceptible-Infected-Recovered model, whether egocentric individuals can reach an equilibrium with the rest of the society. Using techniques from the "Mean Field Games" theory, we extend previous results and show that an equilibrium exists and characterizes completely the individual best vaccination strategy (with or without discounting). We also compare with a strategy based only on overall societal optimization and exhibit a situation with nonnegative price of anarchy. Finally, we apply the theory to the 2009-2010 Influenza A (H1N1) vaccination campaign in France and hint that a group of individuals stopped vaccinating at levels that indicated a pessimistic perception of the risk of the vaccine.

Global optimal vaccination in the SIR model: properties of the value function and application to cost-effectiveness analysis.

This work focuses on optimal vaccination policies for an Susceptible-Infected-Recovered (SIR) model; the impact of the disease is minimized with respect to the vaccination strategy. The problem is formulated as an optimal control problem and we show that the value function is the unique viscosity solution of an Hamilton-Jacobi-Bellman (HJB) equation. This allows to find the best vaccination policy. At odds with existing literature, it is seen that the value function is not always smooth (sometimes only Lipschitz) and the optimal vaccination policies are not unique. Moreover we rigorously analyze the situation when vaccination can be modeled as instantaneous (with respect to the time evolution of the epidemic) and identify the global optimum solutions. Numerical applications illustrate the theoretical results. In addition the pertussis vaccination in adults is considered from two perspectives: first the maximization of DALY averted in presence of vaccine side-effects; then the impact of the herd immunity on the cost-effectiveness analysis is discussed on a concrete example.

A smoothing monotonic convergent optimal control algorithm for nuclear magnetic resonance pulse sequence design.

The past decade has demonstrated increasing interests in using optimal control based methods within coherent quantum controllable systems. The versatility of such methods has been demonstrated with particular elegance within nuclear magnetic resonance (NMR) where natural separation between coherent and dissipative spin dynamics processes has enabled coherent quantum control over long periods of time to shape the experiment to almost ideal adoption to the spin system and external manipulations. This has led to new design principles as well as powerful new experimental methods within magnetic resonance imaging, liquid-state and solid-state NMR spectroscopy. For this development to continue and expand, it is crucially important to constantly improve the underlying numerical algorithms to provide numerical solutions which are optimally compatible with implementation on current instrumentation and at same time are numerically stable and offer fast monotonic convergence toward the target. Addressing such aims, we here present a smoothing monotonically convergent algorithm for pulse sequence design in magnetic resonance which with improved optimization stability lead to smooth pulse sequence easier to implement experimentally and potentially understand within the analytical framework of modern NMR spectroscopy.

A parasite vector-host epidemic model for TSE propagation.

BACKGROUND: Transmissible spongiform encephalopathies (TSEs) are a family of diseases that infect mammals. They are explained by cross-contamination through an unknown route or from infection of food contaminated with prion proteins (PrPs), natural proteins that take an infectious form contributing to the slow destruction of the animal brain. While the extreme resistance of PrPs to denaturation and proteolysis accounts for a route from the mouth to the brain, the possible role of another route of contamination is explored here. Many diseases are spread by vectors, as seen in plague, typhus, malaria, or dengue. The situation where PrPs would be transmitted by a vector and, from the characteristics of outbreaks, proposed hypotheses about the biological nature of such vectors are explored. MATERIAL/METHODS: The nontrivial situation where contamination by the vector prevents infection by making the host immune to further vector contamination was analyzed. To investigate the nature of a possible vector, the spread of a disease in a closed population of hosts and vectors where the number of hosts is constant and the vectors multiply in the host was modeled mathematically. In this model, the disease is caused by an infective agent and is spread by a vector, while direct host-to-host spread is not permitted. RESULTS: Concrete values of the parameters of the model were computed from simulation of the BSE outbreak in the UK as a possible example of the process. CONCLUSIONS: Microbial vector-borne diseases might play an unexpected role in the spread of epidemics, warranting further exploration.

A closed-loop identification protocol for nonlinear dynamical systems.

A previous work introduced an optimal identification (OI) technique for reliably extracting model parameters of biochemical reaction systems from tailored laboratory experiments. The notion of optimality enters through seeking an external control in the laboratory producing data that leads to minimum uncertainties in the identified parameter distributions. A number of algorithmic and operational improvements are introduced in this paper to OI, aiming to build a more practical and efficient closed-loop identification protocol/procedure (CLIP) for nonlinear dynamical systems. The improvements in CLIP include (a) inversion cost function modification to preferably search for the upper and lower boundaries of the parameter distributions consistent with the observed data, (b) dynamic search range updating of the unknown parameters to better exploit the information from the prior iterative experiments, (c) replacing the control genetic algorithm by the simplex method to enable better balance between operational cost and inversion quality, and (d) utilizing virtual sensitivity optimization techniques to further reduce the laboratory costs. The workings of CLIP utilizing these new algorithms are illustrated in indentifying a simulated tRNA proofreading model, and the results demonstrate enhanced performance of CLIP in terms of algorithmic reliability and efficiency.

On the relationship between the local tracking procedures and monotonic schemes in quantum optimal control.

Numerical simulations of (bilinear) quantum control often rely on either monotonically convergent algorithms or tracking schemes. However, despite their mathematical simplicity, very limited intuitive understanding exists at this time to explain the former type of algorithms. Departing from the usual mathematical formalization, we present in this paper an interpretation of the monotonic algorithms as finite horizon, local in time, tracking schemes. Our purpose is not to present a new class of procedures but rather to introduce the necessary rigorous framework that supports this interpretation. As a by-product we show that at each instant, estimates of the future quality of the current control field are available and used in the optimization. When the target is expressed as reaching a prescribed final state, we also present an intuitive geometrical interpretation as the minimization of the distance between two correlated trajectories: one starting from the given initial state and the other backward in time from the target state. As an illustration, a stochastic monotonic algorithm is introduced. Numerical discretizations of the two procedures are also presented.

Optimal molecular alignment and orientation through rotational ladder climbing.

We study the control by electromagnetic fields of molecular alignment and orientation in a linear, rigid-rotor model. With the help of a monotonically convergent algorithm, we find that the optimal field is in the microwave part of the spectrum and acts by resonantly exciting the rotation of the molecule progressively from the ground state, i.e., by rotational ladder climbing. This mechanism is present not only when maximizing orientation or alignment, but also when using prescribed target states that simultaneously optimize the efficiency of orientation/alignment and its duration. The extension of the optimization method to consider a finite rotational temperature is also presented.

Reference trajectory tracking for locally designed coherent quantum controls.

Local time control methods are used in the simulation of quantum control phenomena because they conveniently ensure an increase of a predefined performance index and also avoid singularities associated with tracking procedures. However, the drawback of the existing implementations is that they only take into account one-photon, direct transitions and may stop at nonoptimal values of the index. We propose in this paper a modification of the currently used algorithms that addresses this issue and explain how the convergence is improved. Furthermore, when iterations are required, we show that this approach can be inserted into a monotonically convergent algorithm.

High-order averaging schemes with error bounds for thermodynamical properties calculations by molecular dynamics simulations.

We introduce high-order formulas for the computation of statistical averages based on the long-time simulation of molecular dynamics trajectories. In some cases, this allows us to significantly improve the convergence rate of time averages toward ensemble averages. We provide some numerical examples that show the efficiency of our scheme. When trajectories are approximated using symplectic integration schemes (such as velocity Verlet), we give some error bounds that allow one to fix the parameters of the computation in order to reach a given desired accuracy in the most efficient manner.

Efficient algorithms for the laboratory discovery of optimal quantum controls.

The laboratory closed-loop optimal control of quantum phenomena, expressed as minimizing a suitable cost functional, is currently implemented through an optimization algorithm coupled to the experimental apparatus. In practice, the most commonly used search algorithms are variants of genetic algorithms. As an alternative choice, a direct search deterministic algorithm is proposed in this paper. For the simple simulations studied here, it outperforms the existing approaches. An additional algorithm is introduced in order to reveal some properties of the cost functional landscape.

Generalized monotonically convergent algorithms for solving quantum optimal control problems.

A wide range of cost functionals that describe the criteria for designing optimal pulses can be reduced to two basic functionals by the introduction of product spaces. We extend previous monotonically convergent algorithms to solve the generalized pulse design equations derived from those basic functionals. The new algorithms are proved to exhibit monotonic convergence. Numerical tests are implemented in four-level model systems employing stationary and/or nonstationary targets in the absence and/or presence of relaxation. Trajectory plots that conveniently present the global nature of the convergence behavior show that slow convergence may often be attributed to "trapping" and that relaxation processes may remove such unfavorable behavior.

A double epidemic model for the SARS propagation.

BACKGROUND: An epidemic of a Severe Acute Respiratory Syndrome (SARS) caused by a new coronavirus has spread from the Guangdong province to the rest of China and to the world, with a puzzling contagion behavior. It is important both for predicting the future of the present outbreak and for implementing effective prophylactic measures, to identify the causes of this behavior. RESULTS: In this report, we show first that the standard Susceptible-Infected-Removed (SIR) model cannot account for the patterns observed in various regions where the disease spread. We develop a model involving two superimposed epidemics to study the recent spread of the SARS in Hong Kong and in the region. We explore the situation where these epidemics may be caused either by a virus and one or several mutants that changed its tropism, or by two unrelated viruses. This has important consequences for the future: the innocuous epidemic might still be there and generate, from time to time, variants that would have properties similar to those of SARS. CONCLUSION: We find that, in order to reconcile the existing data and the spread of the disease, it is convenient to suggest that a first milder outbreak protected against the SARS. Regions that had not seen the first epidemic, or that were affected simultaneously with the SARS suffered much more, with a very high percentage of persons affected. We also find regions where the data appear to be inconsistent, suggesting that they are incomplete or do not reflect an appropriate identification of SARS patients. Finally, we could, within the framework of the model, fix limits to the future development of the epidemic, allowing us to identify landmarks that may be useful to set up a monitoring system to follow the evolution of the epidemic. The model also suggests that there might exist a SARS precursor in a large reservoir, prompting for implementation of precautionary measures when the weather cools down.