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In this doctoral thesis, I present my research within the field of Mathematical Finance, focused on topics arising within the financial ‘xVA’ framework, in which classical asset pricing theory is augmented to accommodate additional frictions and risks inherent in modern risk management. The first two main chapters of our work revolve around the collateral choice option, a financial option that emerges when there is the possibility to select the collateral between various currencies or assets. We phrase this problem in terms of underlying collateral spreads, for which we develop a stochastic model leading to the representation of the option price as a non-linear functional of a stochastic process which is obtained by taking the maximum of the stochastic processes used to depict the collateral spreads. The lack of tractability of this model is resolved by imposing a specific ‘common factor’ structure onto the marginal distributions of the collateral spreads, from which we obtain an estimator for the option value. This is further refined through enhancements to account for the dynamics of the process. We analyse the numerical complexity of the obtained approximators and their behaviour within the parameter space. We further apply this model towards sensitivity calculations of an asset imbued with the collateral choice option. We further consider the hedging problem posed by such an asset and develop a variance-minimising hedging strategy based on the assumption of stochastic collateral spreads.In the third main chapter, we consider the efficient calculation of expected exposure sensitivities. The objective here is to improve the numerical complexity of Monte Carlo simulations involving many portfolio valuations. We replace costly exact valuation functions with an interpolation scheme, in which the interpolation points are determined by the probability distribution of the random variables underlying the assets in the portfolio. We utilise this approach to efficiently co, Dans cette thèse de doctorat, je présente mes recherches dans le domaine de la Finance Mathématique, centrées sur des sujets émergeant dans le cadre financier du « xVA », où la théorie classique de tarification des actifs est augmentée pour accommoder des frictions et des risques supplémentaires inhérents à la gestion moderne des risques. Les deux premiers chapitres principaux de notre travail tournent autour de l'option de choix de collatéral, une option financière qui émerge lorsqu'il y a la possibilité de sélectionner le collatéral entre différentes devises ou actifs. Nous formulons ce problème en termes de spreads de collatéral sous-jacents, pour lesquels nous développons un modèle stochastique menant à la représentation du prix de l'option comme une fonctionnelle non linéaire d'un processus stochastique qui est obtenu en prenant le maximum des processus stochastiques utilisés pour modéliser les spreads de collatéral. L'absence de solution explicite de ce modèle est résolue en imposant une structure de « facteur commun » spécifique sur les distributions marginales des spreads de collatéral, à partir de laquelle nous obtenons un estimateur pour la valeur de l'option. Ceci est encore affiné par des améliorations pour tenir compte de la dynamique du processus. Nous analysons la complexité numérique des approximations obtenues et leur comportement dans l'espace paramétrique. Nous appliquons en outre ce modèle aux calculs de sensibilité d'un actif doté de l'option de choix de collatéral. Nous considérons également le problème de couverture posé par un tel actif et développons une stratégie de couverture minimisant la variance basée sur l'hypothèse de spreads de collatéral stochastiques.Dans le troisième chapitre principal, nous considérons le calcul efficace des sensibilités de l’ « expected exposure ». L'objectif ici est d'améliorer la complexité numérique des simulations de Monte Carlo impliquant de nombreuses évaluations de portefeuille. Nous remplaçons les foncti, Doctorat en Sciences, info:eu-repo/semantics/nonPublished

Dominance relations and diagnostic tools based on Lorenz and Concentration curves in order to compare competing estimators of the regression function have recently been proposed. This approach turns out to be equivalent to forecast dominance when the estimators under consideration are auto-calibrated. A new characterization of auto-calibration is established, based on the graphs of Lorenz and Concentration curves. This result is exploited to propose an effective testing procedure for auto-calibration. A simulation study is conducted to evaluate its performances and its relevance for practice is demonstrated on an insurance data set., SCOPUS: ar.j, info:eu-repo/semantics/published

Green infrastructure (GI) is increasingly linked to urban water management and can contribute to achieving water security in communities. This research uses a variation-finding comparative approach to recognize how far GI solutions are currently used to address water security in the urban developments of Monterrey City, Mexico, and Brussels-Capital Region, Belgium. A comparative content analysis of seven related urban development/sectoral plans is conducted using ATLAS.ti 9 software. The results depict the overall distribution of GI implementations, their typologies and spatial scales, water-security aspects that are addressed by GI, and the related definitions in the plans. In general, our analysis does not present a promising situation for the Monterrey case, although it reveals that policymakers have started to use GI in urban plans to address water security. Considering Brussels’ conditions, although GI solutions are much more frequent and advanced than in Monterrey plans, the region cannot be considered a frontrunner of GI policies. Comparing these two remarkably diverse areas is beneficial to illuminate universal aspects of planning, as the method provides an opportunity to gain insight from a multi-city perspective, whether developed or developing, showing the potential areas to advance urban policies., SCOPUS: re.j, info:eu-repo/semantics/published

We consider the propagation of a stochastic SIR-type epidemic in two connected populations: a relatively small local population of interest which is surrounded by a much larger external population. External infectives can temporarily enter the small population and contribute to the spread of the infection inside this population. The rules for entry of infectives into the small population as well as their length of stay are modeled by a general Markov queueing system. Our main objective is to determine the distribution of the total number of infections within both populations. To do this, the approach we propose consists of deriving a family of martingales for the joint epidemic processes and applying classical stopping time or convergence theorems. The study then focuses on several particular cases where the external infection is described by a linear branching process and the entry of external infectives obeys certain specific rules. Some of the results obtained are illustrated by numerical examples., SCOPUS: ar.j, info:eu-repo/semantics/published

Summary: SIMSApiper is a Nextflow pipeline that creates reliable, structure-informed MSAs of thousands of protein sequences faster than standard structure-based alignment methods. Structural information can be provided by the user or collected by the pipeline from online resources. Parallelization with sequence identity-based subsets can be activated to significantly speed up the alignment process. Finally, the number of gaps in the final alignment can be reduced by leveraging the position of conserved secondary structure elements., SCOPUS: ar.j, info:eu-repo/semantics/published

Motivation: Whole exome sequencing (WES) has emerged as a powerful tool for genetic research, enabling the collection of a tremendous amount of data about human genetic variation. However, properly identifying which variants are causative of a genetic disease remains an important challenge, often due to the number of variants that need to be screened. Expanding the screening to combinations of variants in two or more genes, as would be required under the oligogenic inheritance model, simply blows this problem out of proportion. Results: We present here the High-throughput oligogenic prioritizer (Hop), a novel prioritization method that uses direct oligogenic information at the variant, gene and gene pair level to detect digenic variant combinations in WES data. This method leverages information from a knowledge graph, together with specialized pathogenicity predictions in order to effectively rank variant combinations based on how likely they are to explain the patient’s phenotype. The performance of Hop is evaluated in cross-validation on 36 120 synthetic exomes for training and 14 280 additional synthetic exomes for independent testing. Whereas the known pathogenic variant combinations are found in the top 20 in approximately 60% of the cross-validation exomes, 71% are found in the same ranking range when considering the independent set. These results provide a significant improvement over alternative approaches that depend simply on a monogenic assessment of pathogenicity, including early attempts for digenic ranking using monogenic pathogenicity scores., SCOPUS: ar.j, info:eu-repo/semantics/published

Stein's method is used to study discrete representations of multidimensional distributions that arise as approximations of states of quantum harmonic oscillators. These representations model how quantum effects result from the interaction of finitely many classical 'worlds', with the role of sample size played by the number of worlds. Each approximation arises as the ground state of a Hamiltonian involving a particular interworld potential function. Our approach, framed in terms of spherical coordinates, provides the rate of convergence of the discrete approximation to the ground state in terms of Wasserstein distance. Applying a novel Stein's method technique to the radial component of the ground state solution, the fastest rate of convergence to the ground state is found to occur in three dimensions., SCOPUS: ar.j, info:eu-repo/semantics/published

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Stein’s method compares probability distributions through the study of a class of linear operators called Stein operators.While mainly studied in probability and used to underpin theoretical statistics, Stein’s method has led to significant advances in computational statistics in recent years. The goal of this survey is to bring together some of these recent developments, and in doing so, to stimulate further research into the successful field of Stein’s method and statistics. The topics we discuss include tools to benchmark and compare sampling methods such as approximate Markov chain Monte Carlo, deterministic alternatives to sampling methods, control variate techniques, parameter estimation and goodness-of-fit testing, SCOPUS: ar.j, info:eu-repo/semantics/published

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Power laws and power laws with exponential cut-off are two distinct families of distributions on the positive real half-line. In the present paper, we propose a unified treatment of both families by building a family of distributions that interpolates between them, which we call Interpolating Family (IF) of distributions. Our original construction, which relies on techniques from statistical physics, provides a connection for hitherto unrelated distributions like the Pareto and Weibull distributions, and sheds new light on them. The IF also contains several distributions that are neither of power law nor of power law with exponential cut-off type. We calculate quantile-based properties, moments and modes for the IF. This allows us to review known properties of famous distributions on (Formula presented.) and to provide in a single sweep these characteristics for various less known (and new) special cases of our Interpolating Family., SCOPUS: ar.j, info:eu-repo/semantics/published

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This paper provides a general framework for Stein’s density method for multivariate continuous distributions. The approach associates to any probability density function a canonical operator and Stein class, as well as an infinite collection of operators and classes which we call standardizations. These in turn spawn an entire family of Stein identities and characterizations for any continuous distribution on Rd, among which we highlight those based on the score function and the Stein kernel. A feature of these operators is that they do not depend on normalizing constants. A new definition of Stein kernel is introduced and examined; integral formulas are obtained through a connection with mass transport, as well as ready-to-use explicit formulas for elliptical distributions. The flexibility of the kernels is used to compare in Stein discrepancy (and therefore 2-Wasserstein distance) between two normal distributions, Student and normal distributions, as well as two normal-gamma distributions. Upper and lower bounds on the 1-Wasserstein distance between continuous distributions are provided, and computed for a variety of examples: comparison between different normal distributions (improving on existing bounds in some regimes), posterior distributions with different priors in a Bayesian setting (including logistic regression), centred Azzalini–Dalla Valle distributions. Finally the notion of weak Stein equation and weak Stein factors is introduced. Bounds for solutions of the weak Stein equation are obtained for Lipschitz test functions if the distribution admits a Poincaré constant. We use these bounds to compare different copulas on the unit square in 1-Wasserstein distance., SCOPUS: ar.j, info:eu-repo/semantics/published

Contaminated water and poor sanitation are associated with disease transmission. Absent, inadequate, or improperly managed water resources and sanitation systems expose individuals to preventable health risks. Billions of people lack access to these basic services today and will remain in this condition for decades to come. As we are usually thinking and talking about water, sanitation and hygiene services have changed. Looking back at the history of water, sanitation, and hygiene can help us understand the challenges and opportunities of these issues and draw lessons to achieve sustainable development in the future. Throughout history, civilizations have successfully experimented with treating water and using it for drinking, sanitation, and agriculture. For example, the Minoan civilizations originally focused on water treatment and cleaning to improve the aesthetic properties of drinking water. During prehistoric times, Minoan and Indus Valley civilizations, dating back to about 2000 BC, were the first to focus on the treatment of water supplies. From the early Minoan period, they relied on rainwater collection. During historic times, Hippocrates was the first to invent and used a water filter in the form of a cloth bag, at about 400 BC, known today as the Hippocrates Sleeve. The Romans perfected existing water technologies on a larger scale and initiated their spread throughout the Empire. Hygiene in ancient Rome was promoted by the famous public baths and toilets, which were supplied with water through widely branched aqueducts that had a high standard of cleanliness for the time and were regularly maintained., SCOPUS: re.j, info:eu-repo/semantics/published

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Extending rank-based inference to a multivariate setting such as multiple-output regression or MANOVA with unspecified d-dimensional error density has remained an open problem for more than half a century. None of the many solutions proposed so far is enjoying the combination of distribution-freeness and efficiency that makes rank-based inference a successful tool in the univariate setting. A concept of center-outward multivariate ranks and signs based on measure transportation ideas has been introduced recently. Center-outward ranks and signs are not only distribution-free but achieve in dimension d > 1 the (essential) maximal ancillarity property of traditional univariate ranks. In the present case, we show that fully distribution-free testing procedures based on center-outward ranks can achieve parametric efficiency. We establish the Hájek representation and asymptotic normality results required in the construction of such tests in multiple-output regression and MANOVA models. Simulations and an empirical study demonstrate the excellent performance of the proposed procedures., SCOPUS: ar.j, info:eu-repo/semantics/published

Many marine and terrestrial species live in groups, whose sizes and dynamics can vary depending on the type and strength of their social interactions. Typical examples of such groups in vertebrates are schools of fish or flocks of bird. Natural habitats can encompass a wide range of spatial heterogeneities, which can also shape the structure of animal groups, depending on the interplay between the attraction/repulsion of environmental cues and social interactions. A key issue in modern applied ecology and conservation is the need to understand the relationship between these ethological and ecological scales in order to account for the social behaviour of animals in their natural environments. Here, we introduce a modeling approach which studies animal groups within heterogeneous habitats constituted by a set of aggregative sites. The model properties are investigated considering the case study of tropical tuna schools and their associative behavior with floating objects, a question of global concern, given the thousands of floating objects deployed by industrial tropical tuna fisheries worldwide. The effects of increasing numbers of aggregative sites (floating objects) on tuna schools are studied. This study offers a general modeling framework to study social species in their habitats, accounting for both ethological and ecological drivers of animal group dynamics., SCOPUS: ar.j, info:eu-repo/semantics/published

We use a minimalistic mathematical model with a limited number of parameters to evaluate the impact of interindividual differences in the collective decision-making of a group. As it turns out, in most cases, heterogeneous groups are more efficient in their decision-making than homogenous ones, especially when considering small group sizes. In reality, being different disfavours the emergence of an hysteresis and a collective threshold which are characteristics of such cooperative species while keeping inter-attractions the same between individuals. Finally, when the cooperativity becomes very large, we observe an explosion of accessible stable states., SCOPUS: ar.j, info:eu-repo/semantics/published

Consider a linear elliptic partial differential equation in divergence form with a random coefficient field. The solution-operator displays fluctuations around its expectation. The recently-developed pathwise theory of fluctuations in stochastic homogenization reduces the characterization of these fluctuations to those of the so-called standard homogenization commutator. In this contribution, we investigate the scaling limit of this key quantity: starting from a Gaussian-like coefficient field with possibly strong correlations, we establish the convergence of the rescaled commutator to a fractional Gaussian field, depending on the decay of correlations of the coefficient field, and we investigate the (non)degeneracy of the limit. This extends to general dimension d ≥ 1 previous results so far limited to dimension d = 1, and to the continuum setting with strong correlations recent results in the discrete i.i.d. case., SCOPUS: ar.j, info:eu-repo/semantics/published

This work is concerned with the mathematical analysis of the bulk rheology of random suspensions of rigid particles settling under gravity in viscous fluids. Each particle generates a fluid flow that in turn acts on other particles and hinders their settling. In an equilibrium perspective, for a given ensemble of particle positions, we analyze both the associated mean settling speed and the velocity fluctuations of individual particles. In the 1970s, Batchelor gave a proper definition of the mean settling speed, a 60-year-old open problem in physics, based on the appropriate renormalization of long-range particle contributions. In the 1980s, a celebrated formal calculation by Caflisch and Luke suggested that velocity fluctuations in dimension d= 3 should diverge with the size of the sedimentation tank, contradicting both intuition and experimental observations. The role of long-range self-organization of suspended particles in form of hyperuniformity was later put forward to explain additional screening of this divergence in steady-state observations. In the present contribution, we develop the first rigorous theory that allows to justify all these formal calculations of the physics literature., SCOPUS: ar.j, info:eu-repo/semantics/published

This work is devoted to the asymptotic behavior of eigenvalues of an elliptic operator with rapidly oscillating random coefficients on a bounded domain with Dirichlet boundary conditions. A sharp convergence rate is obtained for eigenvalues towards those of the homogenized problem, as well as a quantitative two-scale expansion result for eigenfunctions. Next, a quantitative central limit theorem is established for fluctuations of isolated eigenvalues; more precisely, a pathwise characterization of eigenvalue fluctuations is obtained in terms of the so-called homogenization commutator, in parallel with the recent fluctuation theory for the solution operator., SCOPUS: ar.j, info:eu-repo/semantics/published

Thanks to its outstanding performances, boosting has rapidly gained wide acceptance among actuaries. To speed up calculations, boosting is often applied to gradients of the loss function, not to responses (hence the name gradient boosting). When the model is trained by minimizing Poisson deviance, this amounts to apply the least-squares principle to raw residuals. This exposes gradient boosting to the same problems that lead to replace least-squares with Poisson Generalized Linear Models (GLM) to analyze low counts (typically, the number of reported claims at policy level in personal lines). This paper shows that boosting can be conducted directly on the response under Tweedie loss function and log-link, by adapting the weights at each step. Numerical illustrations demonstrate similar or better performances compared to gradient boosting when trees are used as weak learners, with a higher level of transparency since responses are used instead of gradients., SCOPUS: ar.j, info:eu-repo/semantics/published

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In the present paper, we show that several classical nonparametric tests for multivariate location in the Euclidean case can be adapted to nonparametric tests for the location problem on hyperspheres. The tests we consider are spatial signed-rank tests for location on hyperspheres. We compute the asymptotic powers of the latter tests in the classical rotationally symmetric case. In particular, we show that the spatial signed-rank test uniformly dominates the spatial sign test and has performances that are extremely close to the asymptotically optimal test in the well-known von Mises–Fisher case. Monte-Carlo simulations confirm our asymptotic results., SCOPUS: ar.j, info:eu-repo/semantics/published

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In this note, we derive upper bounds on Kendall’s tau and Spearman’s rho for multivariate zero-inflated continuous variables often encountered in insurance. A lower bound for Spearman’s rho is also established in the bivariate case. These bounds are easy to compute and can be estimated from a data set of zero-inflated random vectors as illustrated in this note with a motor insurance portfolio., SCOPUS: ar.j, info:eu-repo/semantics/published

Waterborne pathogens are heterogeneously distributed across various spatiotemporal scales in water resources, and representative sampling is therefore crucial for accurate risk assess-ment. Since regulatory monitoring of microbiological water quality is usually conducted at fixed time intervals, it can miss short-term fecal contamination episodes and underestimate underlying microbial risks. In the present paper, we developed a new automated sampling methodology based on near real-time measurement of a biochemical indicator of fecal pollution. Online monitoring of β-D-glucuronidase (GLUC) activity was used to trigger an automated sampler during fecal contamination events in a drinking water supply and at an urban beach. Significant increases in protozoan parasites, microbial source tracking markers and E. coli were measured during short-term (<24 h) fecal pollution episodes, emphasizing the intermittent nature of their occurrence in water. Synchro-nous triggering of the automated sampler with online GLUC activity measurements further re-vealed a tight association between the biochemical indicator and culturable E. coli. The proposed event sampling methodology is versatile and in addition to the two triggering modes validated here, others can be designed based on specific needs and local settings. In support to regulatory monitoring schemes, it should ultimately help gathering crucial data on waterborne pathogens more efficiently during episodic fecal pollution events., SCOPUS: ar.j, info:eu-repo/semantics/published

Using coupling techniques based on Stein’s method for probability approximation, we revisit classical variance bounding inequalities of Chernoff, Cacoullos, Chen and Klaassen. Our bounds are immediate in any context wherein a Stein identity is available. After providing illustrative examples for a Gaussian and a Gumbel target distribution, our main contributions are new variance bounds in settings where the underlying density function is unknown or intractable. Applications include bounds for analysis of the posterior in Bayesian statistics, bounds for asymptotically Gaussian random variables using zero-biased couplings, and bounds for random variables which are New Better (Worse) than Used in Expectation, SCOPUS: ar.j, info:eu-repo/semantics/published

Unlike the real line, the real space Rd, for d ≥ 2, is not canonically ordered. As a consequence, such fundamental univariate concepts as quantile and distribution functions and their empirical counterparts, involving ranks and signs, do not canonically extend to the multivariate context. Palliating that lack of a canonical ordering has been an open problem for more than half a century, generating an abundant literature and motivating, among others, the development of statistical depth and copula-based methods. We show that, unlike the many definitions proposed in the literature, the measure transportation-based ranks and signs introduced in Chernozhukov, Galichon, Hallin and Henry (Ann. Statist. 45 (2017) 223-256) enjoy all the properties that make univariate ranks a successful tool for semiparametric inference. Related with those ranks, we propose a new center-outward definition of multivariate distribution and quantile functions, along with their empirical counterparts, for which we establish a Glivenko-Cantelli result. Our approach is based on McCann (Duke Math. J. 80 (1995) 309-323) and our results do not require any moment assumptions. The resulting ranks and signs are shown to be strictly distribution-free and essentially maximal ancillary in the sense of Basu (Sankhyā 21 (1959) 247-256) which, in semiparametric models involving noise with unspecified density, can be interpreted as a finite-sample form of semiparametric efficiency. Although constituting a sufficient summary of the sample, empirical center-outward distribution functions are defined at observed values only. A continuous extension to the entire d-dimensional space, yielding smooth empirical quantile contours and sign curves while preserving the essential monotonicity and Glivenko-Cantelli features of the concept, is provided. A numerical study of the resulting empirical quantile contours is conducted., SCOPUS: ar.j, info:eu-repo/semantics/published

Based on a General Dynamic Factor Model with infinite-dimensional factor space and MGARCH volatility models, we develop new estimation and forecasting procedures for conditional covariance matrices in high-dimensional time series. The finite-sample performance of our approach is evaluated via Monte Carlo experiments and outperforms the most alternative methods. This new approach is also used to construct minimum one-step-ahead variance portfolios for a high-dimensional panel of assets. The results are shown to match the results of recent proposals by Engle, Ledoit, and Wolf and achieve better out-of-sample portfolio performance than alternative procedures proposed in the literature., SCOPUS: ar.j, info:eu-repo/semantics/published

Although the assumption of elliptical symmetry is quite common in multivariate analysis and widespread in a number of applications, the problem of testing the null hypothesis of ellipticity so far has not been addressed in a fully satisfactory way. Most papers in the literature indeed are dealing with the null hypothesis of elliptical symmetry with specified location and actually address location rather than non-elliptical alternatives. In this paper, we are proposing new classes of testing procedures, both for specified and unspecified location. The backbone of our construction is Le Cam’s asymptotic theory of statistical experiments, and optimality is to be understood locally and asymptotically within the family of generalized skew-elliptical distributions. The tests we are proposing are enjoying all the desirable properties of a “good” test of elliptical symmetry: they have simple asymptotic distributions under the entire null hypothesis of elliptical symmetry with unspecified radial density and shape parameter; they are affine-invariant, computationally fast, intuitively understandable, and not too demanding in terms of moments. While achieving optimality against generalized skew-elliptical alternatives, they remain quite powerful under a much broader class of non-elliptical distributions and significantly outperform the available competitors., SCOPUS: ar.j, info:eu-repo/semantics/published

Motivated by the long-time transport properties of quantum waves in weakly disordered media, the present work puts random Schrödinger operators into a new spectral perspective. Based on a stationary random version of a Floquet type fibration, we reduce the description of the quantum dynamics to a fibered family of abstract spectral perturbation problems on the underlying probability space. We state a natural resonance conjecture for these fibered operators: in contrast with periodic and quasiperiodic settings, this would entail that Bloch waves do not exist as extended states but rather as resonant modes, and this would justify the expected exponential decay of time correlations. Although this resonance conjecture remains open, we develop new tools for spectral analysis on the probability space, and in particular, we show how ideas from Malliavin calculus lead to rigorous Mourre type results: we obtain an approximate dynamical resonance result and the first spectral proof of the decay of time correlations on the kinetic timescale. This spectral approach suggests a whole new way of circumventing perturbative expansions and renormalization techniques., SCOPUS: ar.j, info:eu-repo/semantics/published

This note is concerned with the global well-posedness of nonlinear Schrödinger equations in the continuum with spatially homogeneous random initial data., SCOPUS: ar.j, info:eu-repo/semantics/published

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A variety of paradigms have been proposed to speed up Markov chain mixing, ranging from non-backtracking random walks to simulated annealing and lifted Metropolis–Hastings. We provide a general characterization of the limits and opportunities of different approaches for designing fast mixing dynamics on graphs using the framework of “lifted Markov chains”. This common framework allows to prove lower and upper bounds on the mixing behavior of these approaches, depending on a limited set of assumptions on the dynamics. We find that some approaches can speed up the mixing time to diameter time, or a time inversely proportional to the graph conductance, while others allow for no speedup at all., SCOPUS: ar.j, DecretOANoAutActif, info:eu-repo/semantics/published

Consider a setting in which a policy maker assigns subjects to treatments, observing each outcome before the next subject arrives. Initially, it is unknown which treatment is best, but the sequential nature of the problem permits learning about the effectiveness of the treatments. While the multi-armed-bandit literature has shed much light on the situation when the policy maker compares the effectiveness of the treatments through their mean, much less is known about other targets. This is restrictive, because a cautious decision maker may prefer to target a robust location measure such as a quantile or a trimmed mean. Furthermore, socio-economic decision making often requires targeting purpose specific characteristics of the outcome distribution, such as its inherent degree of inequality, welfare or poverty. In the present article, we introduce and study sequential learning algorithms when the distributional characteristic of interest is a general functional of the outcome distribution. Minimax expected regret optimality results are obtained within the subclass of explore-then-commit policies, and for the unrestricted class of all policies. Supplementary materials for this article are available online., SCOPUS: ar.j, DecretOANoAutActif, info:eu-repo/semantics/published

The local equilibrium approach previously developed by the authors (J Mabillard and P Gaspard 2020 J. Stat. Mech. 103203) for matter with broken symmetries is applied to crystalline solids. The macroscopic hydrodynamics of crystals and their local thermodynamic and transport properties are deduced from the microscopic Hamiltonian dynamics. In particular, the Green-Kubo formulas are obtained for all the transport coefficients. The eight hydrodynamic modes and their dispersion relation are studied for general and cubic crystals. In the same twenty crystallographic classes as those compatible with piezoelectricity, cross effects coupling transport between linear momentum and heat or crystalline order are shown to split the degeneracy of damping rates for modes propagating in opposite generic directions., SCOPUS: ar.j, info:eu-repo/semantics/published

This paper answers a long-standing open question concerning the 1∕e-strategy for the problem of best choice. N candidates for a job arrive at times independently uniformly distributed in [0,1]. The interviewer knows how each candidate ranks relative to all others seen so far, and must immediately appoint or reject each candidate as they arrive. The aim is to choose the best overall. The 1∕e strategy is to follow the rule: ‘Do nothing until time 1∕e, then appoint the first candidate thereafter who is best so far (if any).’ The question, first discussed with Larry Shepp in 1983, was to know whether the 1∕e-strategy is optimal if one has ‘no information about the total number of options’. Quite what this might mean is open to various interpretations, but we shall take the proportional-increment process formulation of Bruss and Yor (2012). Such processes are shown to have a very rigid structure, being time-changed pure birth processes, and this allows some precise distributional calculations, from which we deduce that the 1∕e-strategy is in fact not optimal., SCOPUS: ar.j, info:eu-repo/semantics/published

This article is a survey of results concerning an inequality, which may be seen as a versatile tool to solve problems in the domain of Applied Probability. The inequality, which we call BRS-inequality, gives a convenient upper bound for the expected maximum number of non-negative random variables one can sum up without exceeding a given upper bound s > 0. One valuable property of the BRS-inequality is that it is valid without any hypothesis about independence of the random variables. Another welcome feature is that, once one sees that one can use it in a given problem, its application is often straightforward or not very involved. This survey is focussed, and we hope that it is pleasant and inspiring to read. Focus is easy to achieve, given that the BRS-inequality and its most useful versions can be displayed in five Theorems and their proofs. We try to present these in an appealing way. The objective to be inspiring is harder, and the best we can think of is offering a variety of applications. Our examples include comparisons between sums of i.i.d. versus non-identically distributed and/or dependent random variables, problems of condensing point processes, awkward processes, monotone subsequence problems, knapsack problems, online algorithms, tiling policies, Borel-Cantelli type problems, up to applications in the theory of resource dependent branching processes. Apart from our wish to present the inequality in an organised way, the motivation for this survey is the hope that interested readers may see potential of the inequality for their own problems., SCOPUS: ar.j, info:eu-repo/semantics/published

Circadian clocks allow living organisms to anticipate and adapt to the daily variations of the environment. The interlocked feedback loops of the transcription factors network in the plant clock generate oscillations with expression peaks at specific times of the day. In this work, we explore the effect of molecular noise on the behavior of the plant circadian clock through numerical simulations. The influence of system size, photoperiod, and mutations of clock genes on the robustness of the oscillations are discussed. Our simulations show that the oscillations remain robust when the mRNA and protein levels are in the range of a few hundreds molecules. Entrainment by light–dark cycles enhances the robustness compared to constant conditions. Multiple light inputs and inter-cellular coupling also contribute to the robustness of the oscillations. The comparison between deterministic and stochastic simulations of single and double mutants shows that stochasticity does not qualitatively affect the behaviour of mutants but that they do not have the same robustness to noise. Finally, the model shows that noise can induce transitions between two limit cycles in a birhythmic clock mutant., SCOPUS: ar.j, info:eu-repo/semantics/published

Exposure to contaminated water during aquatic recreational activities can lead to gastroin-testinal diseases. In order to decrease the exposure risk, the fecal indicator bacteria Escherichia coli is routinely monitored, which is time-consuming, labor-intensive, and costly. To assist the stakeholders in the daily management of bathing sites, models have been developed to predict the microbiological quality. However, model performances are highly dependent on the quality of the input data which are usually scarce. In our study, we proposed a conceptual framework for optimizing the selection of the most adapted model, and to enrich the training dataset. This frameword was successfully applied to the prediction of Escherichia coli concentrations in the Marne River (Paris Area, France). We compared the performance of six machine learning (ML)-based models: K-nearest neighbors, Decision Tree, Support Vector Machines, Bagging, Random Forest, and Adaptive boosting. Based on several statistical metrics, the Random Forest model presented the best accuracy compared to the other models. However, 53.2 ± 3.5% of the predicted E. coli densities were inaccurately estimated according to the mean absolute percentage error (MAPE). Four parameters (temperature, conductiv-ity, 24 h cumulative rainfall of the previous day the sampling, and the river flow) were identified as key variables to be monitored for optimization of the ML model. The set of values to be optimized will feed an alert system for monitoring the microbiological quality of the water through combined strategy of in situ manual sampling and the deployment of a network of sensors. Based on these results, we propose a guideline for ML model selection and sampling optimization., SCOPUS: ar.j, info:eu-repo/semantics/published

Motivation: Long-read sequencing technologies can be employed to detect and map DNA modifications at the nucleotide resolution on a genome-wide scale. However, published software packages neglect the integration of genomic annotation and comprehensive filtering when analyzing patterns of modified bases detected using Pacific Biosciences (PacBio) or Oxford Nanopore Technologies (ONT) data. Here, we present DNA Modification Annotation (DNAModAnnot), a R package designed for the global analysis of DNA modification patterns using adapted filtering and visualization tools. Results: We tested our package using PacBio sequencing data to analyze patterns of the 6-methyladenine (6mA) in the ciliate Paramecium tetraurelia, in which high 6mA amounts were previously reported. We found P. tetraurelia 6mA genome-wide distribution to be similar to other ciliates. We also performed 5-methylcytosine (5mC) analysis in human lymphoblastoid cells using ONT data and confirmed previously known patterns of 5mC. DNAModAnnot provides a toolbox for the genome-wide analysis of different DNA modifications using PacBio and ONT long-read sequencing data., SCOPUS: ar.j, info:eu-repo/semantics/published

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