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1. Antibacterial size effect of ZnO nanoparticles and their role as additives in emulsion waterborne paint

Author

El-Habib, Imroi, Maatouk, Hassan, Lemarchand, Alex, Roynette, Anne, Dine, Sarah, Mielcarek, Christine, Traore, Mamadou, and Azouani, Rabah

Subjects
Condensed Matter - Materials Science
Abstract

Nosocomial infections (NIs) are prevalent in intensive care units due to antibiotic overuse. Metal oxide nanoparticles (NPs), like ZnO, offer potential solutions, yet understanding how NPs size impacts their antibacterial efficacy are lacking. This study focuses on the effect of nanoparticle size on kinetics of bacterial strains growth. NPs were synthesized using a sol-gel process with monoethanolamine (MEA) and water, characterized using X-ray diffraction (XRD), transmission electron microscopy (TEM), and Raman spectroscopy, confirming crystallization and size variations. ZnO NPs with mean size of 22, 35 and 66 nm were used against the most common nosocomial bacteria strains Escherichia coli (Gram-negative), Pseudomonas aeruginosa (Gram-negative), and Staphylococcus aureus (Gram-positive). The evaluation of NPs minimal inhibitory concentration (MIC) and bactericidal concentration (MBC) revealed superior antibacterial activity in smaller NPs. The bacterial population was monitored via optical absorbance, showing reduced specific growth rate, prolonged latency period, and increased inhibition percentage with smaller NPs, indicating a substantial deceleration in the growth of microorganisms. Pseudomonas aeruginosa exhibited the smallest sensitivity to ZnO NPs, attributed to its environmental stress resistance. Furthermore, the antibacterial efficacy of paint containing 1 wt% of 22 nm ZnO NPs was assessed and displayed activity against E. coli and S. aureus.

Published
2024

5. Finite-dimensional approximation of Gaussian processes with inequality constraints

Author

Maatouk, Hassan

Subjects
Statistics - Methodology, Mathematics - Probability
Abstract

Due to their flexibility, Gaussian processes (GPs) have been widely used in nonparametric function estimation. A prior information about the underlying function is often available. For instance, the physical system (computer model output) may be known to satisfy inequality constraints with respect to some or all inputs. We develop a finite-dimensional approximation of GPs capable of incorporating inequality constraints and noisy observations for computer model emulators. It is based on a linear combination between Gaussian random coefficients and deterministic basis functions. By this methodology , the inequality constraints are respected in the entire domain. The mean and the maximum of the posterior distribution are well defined. A simulation study to show the efficiency and the performance of the proposed model in term of predictive accuracy and uncertainty quantification is included., Comment: arXiv admin note: text overlap with arXiv:1606.01265

Published
2017

6. Gaussian process emulators for computer experiments with inequality constraints

Author

Maatouk, Hassan and Bay, Xavier

Subjects
Mathematics - Probability, Statistics - Methodology
Abstract

Physical phenomena are observed in many fields (sciences and engineering) and are often studied by time-consuming computer codes. These codes are analyzed with statistical models, often called emulators. In many situations, the physical system (computer model output) may be known to satisfy inequality constraints with respect to some or all input variables. Our aim is to build a model capable of incorporating both data interpolation and inequality constraints into a Gaussian process emulator. By using a functional decomposition, we propose to approximate the original Gaussian process by a finite-dimensional Gaussian process such that all conditional simulations satisfy the inequality constraints in the whole domain. The mean, mode (maximum a posteriori) and prediction intervals (uncertainty quantification) of the conditional Gaussian process are calculated. To investigate the performance of the proposed model, some conditional simulations with inequality constraints such as boundary, monotonicity or convexity conditions are given. 1. Introduction. In the engineering activity, runs of a computer code can be expensive and time-consuming. One solution is to use a statistical surrogate for conditioning computer model outputs at some input locations (design points). Gaussian process (GP) emulator is one of the most popular choices [23]. The reason comes from the property of the GP that uncertainty quantification can be calculated. Furthermore, it has several nice properties. For example, the conditional GP at observation data (linear equality constraints) is still a GP [5]. Additionally, some inequality constraints (such as monotonicity and convexity) of output computer responses are related to partial derivatives. In such cases, the partial derivatives of the GP are also GPs. Incorporating an infinite number of linear inequality constraints into a GP emulator, the problem becomes more difficult. The reason is that the resulting conditional process is not a GP. In the literature of interpolation with inequality constraints, we find two types of meth-ods. The first one is deterministic and based on splines, which have the advantage that the inequality constraints are satisfied in the whole input domain (see e.g. [16], [24] and [25]). The second one is based on the simulation of the conditional GP by using the subdivision of the input set (see e.g. [1], [6] and [11]). In that case, the inequality constraints are satisfied in a finite number of input locations. Notice that the advantage of such method is that un-certainty quantification can be calculated. In previous work, some methodologies have been based on the knowledge of the derivatives of the GP at some input locations ([11], [21] and [26]). For monotonicity constraints with noisy data, a Bayesian approach was developed in [21]. In [11] the problem is to build a GP emulator by using the prior monotonicity

Published
2016

7. Kriging of financial term-structures

Author

Cousin, Areski, Maatouk, Hassan, and Rullière, Didier

Subjects
Quantitative Finance - Computational Finance, Mathematics - Probability
Abstract

Due to the lack of reliable market information, building financial term-structures may be associated with a significant degree of uncertainty. In this paper, we propose a new term-structure interpolation method that extends classical spline techniques by additionally allowing for quantification of uncertainty. The proposed method is based on a generalization of kriging models with linear equality constraints (market-fit conditions) and shape-preserving conditions such as monotonicity or positivity (no-arbitrage conditions). We define the most likely curve and show how to build confidence bands. The Gaussian process covariance hyper-parameters under the construction constraints are estimated using cross-validation techniques. Based on observed market quotes at different dates, we demonstrate the efficiency of the method by building curves together with confidence intervals for term-structures of OIS discount rates, of zero-coupon swaps rates and of CDS implied default probabilities. We also show how to construct interest-rate surfaces or default probability surfaces by considering time (quotation dates) as an additional dimension.

Published
2016

8. Generalization of the Kimeldorf-Wahba correspondence for constrained interpolation

Author

Bay, Xavier, Grammont, Laurence, and Maatouk, Hassan

Subjects
Mathematics - Probability
Abstract

In this paper, we extend the correspondence between Bayes' estimation and optimal interpolation in a Reproducing Kernel Hilbert Space (RKHS) to the case of linear inequality constraints such as boundedness, monotonicity or convexity. In the unconstrained interpolation case, the mean of the posterior distribution of a Gaussian Process (GP) given data interpolation is known to be the optimal interpolation function minimizing the norm in the RKHS associated to the GP. In the constrained case, we prove that the Maximum A Posteriori (MAP) or Mode of the posterior distribution is the optimal constrained interpolation function in the RKHS. So, the general correspondence is achieved with the MAP estimator and not the mean of the posterior distribution. A numerical example is given to illustrate this last result.

Published
2016

11. Bayesian analysis of constrained Gaussian processes

Author

Maatouk, Hassan, Rullière, Didier, Bay, Xavier, Analyse, Géométrie et Modélisation (AGM - UMR 8088), Centre National de la Recherche Scientifique (CNRS)-CY Cergy Paris Université (CY), Laboratoire d'Informatique, de Modélisation et d'Optimisation des Systèmes (LIMOS), Ecole Nationale Supérieure des Mines de St Etienne (ENSM ST-ETIENNE)-Centre National de la Recherche Scientifique (CNRS)-Université Clermont Auvergne (UCA)-Institut national polytechnique Clermont Auvergne (INP Clermont Auvergne), Université Clermont Auvergne (UCA)-Université Clermont Auvergne (UCA), and Maatouk, Hassan

Subjects
[STAT]Statistics [stat], MAP estimate, multiple constraints, flat region, convex and non-convex constraints, Gaussian processes, HMC sampler, [STAT] Statistics [stat]
Abstract

Due to their flexibility Gaussian processes are a well-known Bayesian framework for nonparametric function estimation. Integrating inequality constraints, such as monotonicity, convexity, and boundedness, into Gaussian process models significantly improves prediction accuracy and yields more realistic credible intervals in various real-world data applications. The Gaussian process approximation, originally proposed in [22] is considered. It satisfies interpolation conditions and handles a wide range of inequality constraints everywhere. Our contribution in this paper is threefold. First, we extend this approach to handle noisy observations and multiple, more general convex and non-convex constraints. Second, we propose new basis functions in order to extend the smoothness of sample paths to differentiability of class C^p , for any p ≥ 1. Third, we examine its behavior in specific scenarios such as monotonicity with flat regions and boundedness near lower and/or upper bounds. In that case, we show that, unlike the Maximum a posteriori (MAP) estimate, the mean a posteriori (mAP) estimate fails to capture flat regions. To address this issue, we propose incorporating multiple constraints, such as monotonicity with bounded slope constraints. According to the theoretical convergence and based on a variety of numerical experiments, the MAP estimate behaves well and outperforms the mAP estimate in terms of prediction accuracy. The performance of the proposed approach is confirmed through real-world data studies.

Published
2023

13. Large scale Gaussian processes with Matheron's update rule and Karhunen-Loève expansion

Author

Maatouk, Hassan, Rullière, Didier, Bay, Xavier, Maatouk, Hassan, Analyse, Géométrie et Modélisation (AGM - UMR 8088), Centre National de la Recherche Scientifique (CNRS)-CY Cergy Paris Université (CY), École des Mines de Saint-Étienne (Mines Saint-Étienne MSE), Institut Mines-Télécom [Paris] (IMT), Laboratoire d'Informatique, de Modélisation et d'Optimisation des Systèmes (LIMOS), Ecole Nationale Supérieure des Mines de St Etienne-Centre National de la Recherche Scientifique (CNRS)-Université Clermont Auvergne (UCA)-Institut national polytechnique Clermont Auvergne (INP Clermont Auvergne), Université Clermont Auvergne (UCA)-Université Clermont Auvergne (UCA), Institut Henri Fayol (FAYOL-ENSMSE), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT), Département Génie mathématique et industriel (FAYOL-ENSMSE), Ecole Nationale Supérieure des Mines de St Etienne-Institut Henri Fayol, Ecole Nationale Supérieure des Mines de St Etienne (ENSM ST-ETIENNE)-Centre National de la Recherche Scientifique (CNRS)-Université Clermont Auvergne (UCA)-Institut national polytechnique Clermont Auvergne (INP Clermont Auvergne), and Ecole Nationale Supérieure des Mines de St Etienne (ENSM ST-ETIENNE)-Institut Henri Fayol

Subjects
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR], [MATH.MATH-PR] Mathematics [math]/Probability [math.PR], [MATH.MATH-GM]Mathematics [math]/General Mathematics [math.GM], [STAT.ME] Statistics [stat]/Methodology [stat.ME], [MATH.MATH-GM] Mathematics [math]/General Mathematics [math.GM], [STAT.ME]Statistics [stat]/Methodology [stat.ME]
Abstract

International audience; Gaussian processes have become essential for non-parametric function estimation and widely used in many fields like machine learning. In this paper, large scale Gaussian process regression (GPR) is investigated. This problem is related to the simulation of high dimensional Gaussian vectors truncated on the intersection of a set of hyperplanes. The main idea is to combine both Matheron's update rule (MUR) and Karhunen-Lovève expansion (KLE). First, by the MUR we show how simulating from the posterior distribution is possible without computing the posterior covariance matrix and its decomposition. Second, by splitting the input domain in smallest nonoverlapping subdomains, the KLE coefficients are conditioned in order to guarantee the correlation structure in the entire domain. The parallelization of this technique is developed and the advantages are highlighted. By this, the computational complexity is drastically reduced. The mean-square block error is computed. It provides accurate results when using a family of covariance functions with compact support. Some numerical examples to study the performance of the proposed approach are included.

Published
2023

14. Gaussian processes for computer experiments

Author

Bachoc François, Contal Emile, Maatouk Hassan, and Rullière Didier

Subjects
Applied mathematics. Quantitative methods, T57-57.97, Mathematics, QA1-939
Abstract

This paper collects the contributions which were presented during the session devoted to Gaussian processes at the Journées MAS 2016. First, an introduction to Gaussian processes is provided, and some current research questions are discussed. Then, an application of Gaussian process modeling under linear inequality constraints to financial data is presented. Also, an original procedure for handling large data sets is described. Finally, the case of Gaussian process based iterative optimization is discussed.

Published
2017
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15. Equivalent between constrained optimal smoothing and Bayesian estimation

Author

Grammont, Laurence, Maatouk, Hassan, Bay, Xavier, Institut Camille Jordan (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS), Modélisation mathématique, calcul scientifique (MMCS), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Analyse, Géométrie et Modélisation (AGM - UMR 8088), Centre National de la Recherche Scientifique (CNRS)-CY Cergy Paris Université (CY), Laboratoire d'Informatique, de Modélisation et d'Optimisation des Systèmes (LIMOS), Ecole Nationale Supérieure des Mines de St Etienne (ENSM ST-ETIENNE)-Université Clermont Auvergne [2017-2020] (UCA [2017-2020])-Centre National de la Recherche Scientifique (CNRS), École des Mines de Saint-Étienne (Mines Saint-Étienne MSE), Institut Mines-Télécom [Paris] (IMT), Institut Henri Fayol (FAYOL-ENSMSE), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT), Département Génie mathématique et industriel (FAYOL-ENSMSE), and Ecole Nationale Supérieure des Mines de St Etienne (ENSM ST-ETIENNE)-Institut Henri Fayol

Subjects
[STAT]Statistics [stat], smoothing, inequality constraints, Reproducing Kernel Hilbert Space, Bayesian estimation, [INFO.INFO-NA]Computer Science [cs]/Numerical Analysis [cs.NA], correspondence
Abstract

In this paper, we extend the correspondence between Bayesian estima- tion and optimal smoothing in a Reproducing Kernel Hilbert Space (RKHS) by adding convex constraints to the problem. Through a sequence of approxi- mating Hilbertian subspaces and a discretized model, we prove that the Max- imum a posteriori (MAP) of the posterior distribution is exactly the optimal constrained smoothing function in the RKHS. This paper can be read as a generalization of the paper [15], where it is proved that the optimal smooth- ing solution is the mean of the posterior distribution. Synthetic and real data studies confirm the correspondence established in this paper.

Published
2023

20. Optimal Smoothing and Gaussian Processes with noisy data under constraints

Author

Grammont, Laurence, Bay, Xavier, Maatouk, Hassan, Maatouk, Hassan, Institut Camille Jordan (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS), Modélisation mathématique, calcul scientifique (MMCS), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), École des Mines de Saint-Étienne (Mines Saint-Étienne MSE), Institut Mines-Télécom [Paris] (IMT), Laboratoire d'Informatique, de Modélisation et d'Optimisation des Systèmes (LIMOS), Ecole Nationale Supérieure des Mines de St Etienne (ENSM ST-ETIENNE)-Centre National de la Recherche Scientifique (CNRS)-Université Clermont Auvergne (UCA)-Institut national polytechnique Clermont Auvergne (INP Clermont Auvergne), Université Clermont Auvergne (UCA)-Université Clermont Auvergne (UCA), Institut Henri Fayol (FAYOL-ENSMSE), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT), Département Génie mathématique et industriel (FAYOL-ENSMSE), Ecole Nationale Supérieure des Mines de St Etienne (ENSM ST-ETIENNE)-Institut Henri Fayol, Analyse, Géométrie et Modélisation (AGM - UMR 8088), and Centre National de la Recherche Scientifique (CNRS)-CY Cergy Paris Université (CY)

Subjects
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR], [MATH.MATH-PR] Mathematics [math]/Probability [math.PR], [MATH.MATH-GM]Mathematics [math]/General Mathematics [math.GM], [STAT.ME] Statistics [stat]/Methodology [stat.ME], ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION, [MATH.MATH-GM] Mathematics [math]/General Mathematics [math.GM], [MATH] Mathematics [math], [MATH]Mathematics [math], [STAT.ME]Statistics [stat]/Methodology [stat.ME]
Abstract

In this paper, we extend the correspondence between Bayesian estimation and optimal smoothing in a Reproducing Kernel Hilbert Space (RKHS) adding a convex constraint on the solution. Through a sequence of approximating Hilbertian spaces and a discretized model, we prove that the Maximum A Posteriori (MAP) of the posterior distribution is exactly the optimal constrained smoothing function in the RKHS. This paper can be read as a generalization of the paper [11] of Kimeldorf-Wahba where it is proved that the optimal smoothing solution is the mean of the posterior distribution. This is also a generalization of the paper [4] where the case of constrained optimal interpolation is treated. Here we relax the interpolation by introducing noise effect in the data. A numerical example is given to illustrate the theoretical result of this paper.

Published
2022

21. Sampling large hyperplane-truncated multivariate normal distributions

Author

Maatouk, Hassan, Rullière, Didier, Bay, Xavier, Maatouk, Hassan, CY Cergy Paris Université (CY), Analyse, Géométrie et Modélisation (AGM - UMR 8088), Centre National de la Recherche Scientifique (CNRS)-CY Cergy Paris Université (CY), École des Mines de Saint-Étienne (Mines Saint-Étienne MSE), Institut Mines-Télécom [Paris] (IMT), Laboratoire d'Informatique, de Modélisation et d'Optimisation des Systèmes (LIMOS), Ecole Nationale Supérieure des Mines de St Etienne (ENSM ST-ETIENNE)-Centre National de la Recherche Scientifique (CNRS)-Université Clermont Auvergne (UCA)-Institut national polytechnique Clermont Auvergne (INP Clermont Auvergne), Université Clermont Auvergne (UCA)-Université Clermont Auvergne (UCA), Institut Henri Fayol (FAYOL-ENSMSE), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT), Département Génie mathématique et industriel (FAYOL-ENSMSE), and Ecole Nationale Supérieure des Mines de St Etienne (ENSM ST-ETIENNE)-Institut Henri Fayol

Subjects
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR], [MATH.MATH-PR] Mathematics [math]/Probability [math.PR], [MATH.MATH-GM]Mathematics [math]/General Mathematics [math.GM], [STAT.ME] Statistics [stat]/Methodology [stat.ME], [MATH.MATH-GM] Mathematics [math]/General Mathematics [math.GM], [STAT.ME]Statistics [stat]/Methodology [stat.ME]
Abstract

Generating multivariate normal distributions is widely used in many fields (such as engineering). In this paper, simulating large multivariate normal distributions truncated on the intersection of a set of hyperplanes is investigated. The proposed methodology focuses on Gaussian vectors extracted from a Gaussian process (GP) in one dimension. It is based on combining both Karhunen-Loève expansions (KLE) and Matheron's update rules (MUR). The KLE requires the computation of the decomposition of the covariance matrix of the random variables. This step becomes expensive when the random vector is too large. To deal with this issue, the input domain is split in smallest subdomains where the eigendecomposition can be computed. By this strategy, the computational complexity is drastically reduced. The mean-square truncation and block errors have been calculated. Some numerical experiments are presented in order to study the efficiency of the proposed approach. Keywords Large scale random fields • hyperplane-truncated • Karhunen-Loève expansion • Matheron's update rule.

Published
2022

22. Constrained Optimal Smoothing and Bayesian Estimation

Author

Grammont, Laurence, Maatouk, Hassan, Bay, Xavier, Institut Camille Jordan (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS), Analyse, Géométrie et Modélisation (AGM - UMR 8088), Centre National de la Recherche Scientifique (CNRS)-CY Cergy Paris Université (CY), Laboratoire d'Informatique, de Modélisation et d'Optimisation des Systèmes (LIMOS), Ecole Nationale Supérieure des Mines de St Etienne-Université Clermont Auvergne [2017-2020] (UCA [2017-2020])-Centre National de la Recherche Scientifique (CNRS), École des Mines de Saint-Étienne (Mines Saint-Étienne MSE), Institut Mines-Télécom [Paris] (IMT), Institut Henri Fayol (FAYOL-ENSMSE), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT), Département Génie mathématique et industriel (FAYOL-ENSMSE), Ecole Nationale Supérieure des Mines de St Etienne-Institut Henri Fayol, Ecole Nationale Supérieure des Mines de St Etienne-Centre National de la Recherche Scientifique (CNRS)-Université Clermont Auvergne (UCA)-Institut national polytechnique Clermont Auvergne (INP Clermont Auvergne), Université Clermont Auvergne (UCA)-Université Clermont Auvergne (UCA), Institut Camille Jordan [Villeurbanne] (ICJ), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), and Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)

Subjects
[STAT]Statistics [stat], FOS: Mathematics, smoothing, inequality constraints, Numerical Analysis (math.NA), Mathematics - Numerical Analysis, Reproducing Kernel Hilbert Space, Bayesian estimation, [INFO.INFO-NA]Computer Science [cs]/Numerical Analysis [cs.NA], correspondence, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

In this paper, we extend the correspondence between Bayesian estima- tion and optimal smoothing in a Reproducing Kernel Hilbert Space (RKHS) by adding convex constraints to the problem. Through a sequence of approxi- mating Hilbertian subspaces and a discretized model, we prove that the Max- imum a posteriori (MAP) of the posterior distribution is exactly the optimal constrained smoothing function in the RKHS. This paper can be read as a generalization of the paper [15], where it is proved that the optimal smooth- ing solution is the mean of the posterior distribution. Synthetic and real data studies confirm the correspondence established in this paper.

Published
2021

24. Estimation de la courbe d'actualisation par krigeage sous contraintes

Author

Cousin, Areski, Maatouk, Hassan, Rullière, Didier, Laboratoire de Sciences Actuarielle et Financière (SAF), Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon, École des Mines de Saint-Étienne (Mines Saint-Étienne MSE), Institut Mines-Télécom [Paris] (IMT), Méthodes d'Analyse Stochastique des Codes et Traitements Numériques (GdR MASCOT-NUM), Centre National de la Recherche Scientifique (CNRS), and Maatouk, Hassan

Subjects
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR], [STAT]Statistics [stat], [MATH.MATH-PR] Mathematics [math]/Probability [math.PR], [QFIN]Quantitative Finance [q-fin], [QFIN] Quantitative Finance [q-fin], [STAT] Statistics [stat]
Abstract

La construction de structures par terme est au coeur de l'´ evaluationfinancì ere et de la gestion du risque voir e.g. [1], [2], [3], [4] et [5]. Une structure par terme est une courbe qui d'´ ecrit l'´ evolution d'une grandeuréconomiquegrandeuréconomique oufinancì ere comme une fonction de la maturité ou horizon de temps. Des exemples typiques sont la structure par terme des taux d'intérêt sans risque, la structure par terme d'obligations, la structure par terme de probabilités de défaut et la structure par terme de volatilités implicites de rendements d'actifs financiers. En pratique, les cotations des marchés des produits financiers sous-jacents sont utilisées et fournissent une information partielle sur les structures par terme considérées. De plus, cette information est plus au moins fiable en fonction de la liquidité de la maturité des marchés en question. Leprobì eme est d'obtenir une courbe continue en la maturitématuritéà partir de ces informations.

Published
2016

25. Finite-dimensional approximation of Gaussian processes with inequality constraints and errors measurements

Author

Maatouk , Hassan, Institut National de Recherche en Informatique et en Automatique ( Inria ), Méthodes d'Analyse Stochastique des Codes et Traitements Numériques ( GdR MASCOT-NUM ), Centre National de la Recherche Scientifique ( CNRS ), Institut de Recherche Mathématique de Rennes ( IRMAR ), Université de Rennes 1 ( UR1 ), Université de Rennes ( UNIV-RENNES ) -Université de Rennes ( UNIV-RENNES ) -AGROCAMPUS OUEST-École normale supérieure - Rennes ( ENS Rennes ) -Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut National des Sciences Appliquées ( INSA ) -Université de Rennes 2 ( UR2 ), Université de Rennes ( UNIV-RENNES ) -Centre National de la Recherche Scientifique ( CNRS ), Méthodes d'Analyse Stochastique des Codes et Traitements Numériques (GdR MASCOT-NUM), Centre National de la Recherche Scientifique (CNRS), Institut de Recherche Mathématique de Rennes (IRMAR), AGROCAMPUS OUEST, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Université de Rennes 2 (UR2), Université de Rennes (UNIV-RENNES)-École normale supérieure - Rennes (ENS Rennes)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA), Applications of interacting particle systems to statistics (ASPI), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-AGROCAMPUS OUEST, Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Inria Rennes – Bretagne Atlantique, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2), Université de Rennes (UNIV-RENNES)-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-AGROCAMPUS OUEST, Université de Rennes (UNIV-RENNES)-AGROCAMPUS OUEST-Institut National des Sciences Appliquées - Rennes (INSA Rennes), and Université de Rennes (UNIV-RENNES)-AGROCAMPUS OUEST-Inria Rennes – Bretagne Atlantique

Subjects
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Shape constraint, Truncated Gaussian vector, [ STAT.ME ] Statistics [stat]/Methodology [stat.ME], uncertainty quantification, Gaussian processes, Noisy data, inequality constraints, Finite-dimensional approximation, [STAT.ME]Statistics [stat]/Methodology [stat.ME], [ MATH.MATH-PR ] Mathematics [math]/Probability [math.PR], Gaussian processe
Abstract

Due to their flexibility, Gaussian processes (GPs) have been widely used in nonparametric function estimation. A prior information about the underlying function is often available. For instance, the physical system (computer model output) may be known to satisfy inequality constraints with respect to some or all inputs. We develop a finite-dimensional approximation of GPs capable of incorporating inequality constraints and noisy observations for computer model emulators. It is based on a linear combination between Gaussian random coefficients and deterministic basis functions. By this methodology , the inequality constraints are respected in the entire domain. The mean and the maximum of the posterior distribution are well defined. A simulation study to show the efficiency and the performance of the proposed model in term of predictive accuracy and uncertainty quantification is included.

Published
2017

26. Patients' knowledge and attitudes about myocardial infarction.

Author

Noureddine, Samar, Dumit, Nuhad Y., and Maatouk, Hassan

Subjects
STATISTICAL correlation, PROPRIETARY hospitals, INTERVIEWING, RESEARCH methodology, MYOCARDIAL infarction, STATISTICAL sampling, STATISTICS, DATA analysis, HEALTH literacy, DATA analysis software, PATIENTS' attitudes, DESCRIPTIVE statistics, MANN Whitney U Test, ONE-way analysis of variance
Abstract

Delay in seeking emergency care contributes significantly to the mortality associated with myocardial infarction. The aims of this descriptive study were to determine Lebanese patients' knowledge, attitudes, and beliefs about heart disease following their hospitalization for acute myocardial infarction, the factors associated, and to investigate the education they receive about heart disease. The study targeted 50 participants diagnosed with myocardial infarction who were interviewed about their knowledge, attitudes, and perceived control related to heart disease in their home 1 month after being discharged from hospital using the Acute Coronary Syndrome Response Index and the Control Attitude Scale–Revised. The findings showed inadequate knowledge, with only 26% scoring over 70%. Moreover, only 16% reported having received education about heart disease. The participants reported confidence in recognizing symptoms and getting assistance during a myocardial infarction. However, their beliefs regarding the importance of prompt seeking of emergency care for myocardial infarction and control over their disease were inconsistent. Patient education and counseling about recognizing and responding adequately to symptoms of myocardial infarction must be improved in both acute and primary healthcare settings. [ABSTRACT FROM AUTHOR]

Published
2020
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27. Correspondence between Gaussian processes with inequality constraints and constrained splines

Author

Maatouk, Hassan, Laboratoire d'Informatique, de Modélisation et d'optimisation des Systèmes (LIMOS), SIGMA Clermont (SIGMA Clermont)-Université d'Auvergne - Clermont-Ferrand I (UdA)-Ecole Nationale Supérieure des Mines de St Etienne-Centre National de la Recherche Scientifique (CNRS)-Université Blaise Pascal - Clermont-Ferrand 2 (UBP), Département Décision en Entreprise : Modélisation, Optimisation (DEMO-ENSMSE), École des Mines de Saint-Étienne (Mines Saint-Étienne MSE), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Institut Henri Fayol, Université Blaise Pascal - Clermont-Ferrand 2 (UBP)-Université d'Auvergne - Clermont-Ferrand I (UdA)-SIGMA Clermont (SIGMA Clermont)-Ecole Nationale Supérieure des Mines de St Etienne (ENSM ST-ETIENNE)-Centre National de la Recherche Scientifique (CNRS), and Breuil, Florent

Subjects
[INFO.INFO-MO] Computer Science [cs]/Modeling and Simulation, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, ComputingMilieux_MISCELLANEOUS
Abstract

National audience

Published
2015

28. Correspondence between Gaussian process regression and interpolation splines under linear inequality constraints. Theory and applications

Author

Maatouk, Hassan, STAR, ABES, Département Décision en Entreprise : Modélisation, Optimisation (DEMO-ENSMSE), École des Mines de Saint-Étienne (Mines Saint-Étienne MSE), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Institut Henri Fayol, Ecole Nationale Supérieure des Mines de Saint-Etienne, Olivier Roustant, and Laurence Grammont

Subjects
[SPI.OTHER]Engineering Sciences [physics]/Other, Splines, Bayesian Estimation, [SPI.OTHER] Engineering Sciences [physics]/Other, Inequality Constraints, Interpolation, Kriging, Estimation Bayésienne, RKHS, Régression par Processus Gaussien, Uncertainty Quantification, Gaussien Process Regression, Quantification d'Incertitude, Krigeage, Contraintes Inégalité
Abstract

This thesis is dedicated to interpolation problems when the numerical function is known to satisfy some properties such as positivity, monotonicity or convexity. Two methods of interpolation are studied. The first one is deterministic and is based on convex optimization in a Reproducing Kernel Hilbert Space (RKHS). The second one is a Bayesian approach based on Gaussian Process Regression (GPR) or Kriging. By using a finite linear functional decomposition, we propose to approximate the original Gaussian process by a finite-dimensional Gaussian process such that conditional simulations satisfy all the inequality constraints. As a consequence, GPR is equivalent to the simulation of a truncated Gaussian vector to a convex set. The mode or Maximum A Posteriori is defined as a Bayesian estimator and prediction intervals are quantified by simulation. Convergence of the method is proved and the correspondence between the two methods is done. This can be seen as an extension of the correspondence established by [Kimeldorf and Wahba, 1971] between Bayesian estimation on stochastic process and smoothing by splines. Finally, a real application in insurance and finance is given to estimate a term-structure curve and default probabilities., On s'intéresse au problème d'interpolation d'une fonction numérique d'une ou plusieurs variables réelles lorsque qu'elle est connue pour satisfaire certaines propriétés comme, par exemple, la positivité, monotonie ou convexité. Deux méthodes d'interpolation sont étudiées. D'une part, une approche déterministe conduit à un problème d'interpolation optimale sous contraintes linéaires inégalité dans un Espace de Hilbert à Noyau Reproduisant (RKHS). D'autre part, une approche probabiliste considère le même problème comme un problème d'estimation d'une fonction dans un cadre bayésien. Plus précisément, on considère la Régression par Processus Gaussien ou Krigeage pour estimer la fonction à interpoler sous les contraintes linéaires de type inégalité en question. Cette deuxième approche permet également de construire des intervalles de confiance autour de la fonction estimée. Pour cela, on propose une méthode d'approximation qui consiste à approcher un processus gaussien quelconque par un processus gaussien fini-dimensionnel. Le problème de krigeage se ramène ainsi à la simulation d'un vecteur gaussien tronqué à un espace convexe. L'analyse asymptotique permet d'établir la convergence de la méthode et la correspondance entre les deux approches déterministeet probabiliste, c'est le résultat théorique de la thèse. Ce dernier est vu comme unegénéralisation de la correspondance établie par [Kimeldorf and Wahba, 1971] entre estimateur bayésien et spline d'interpolation. Enfin, une application réelle dans le domainede l'assurance (actuariat) pour estimer une courbe d'actualisation et des probabilités dedéfaut a été développée.

Published
2015

29. Gaussian processes for computer experiments with monotonicity information

Author

Maatouk, Hassan, Département Décision en Entreprise : Modélisation, Optimisation (DEMO-ENSMSE), École des Mines de Saint-Étienne (Mines Saint-Étienne MSE), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Institut Henri Fayol, Laboratoire d'Informatique, de Modélisation et d'optimisation des Systèmes (LIMOS), SIGMA Clermont (SIGMA Clermont)-Université d'Auvergne - Clermont-Ferrand I (UdA)-Ecole Nationale Supérieure des Mines de St Etienne-Centre National de la Recherche Scientifique (CNRS)-Université Blaise Pascal - Clermont-Ferrand 2 (UBP), Université Blaise Pascal - Clermont-Ferrand 2 (UBP)-Université d'Auvergne - Clermont-Ferrand I (UdA)-SIGMA Clermont (SIGMA Clermont)-Ecole Nationale Supérieure des Mines de St Etienne (ENSM ST-ETIENNE)-Centre National de la Recherche Scientifique (CNRS), and Breuil, Florent

Subjects
[INFO.INFO-MO] Computer Science [cs]/Modeling and Simulation, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation
Abstract

PhDStudentsDay, PhDAbstracts, https://www1.ethz.ch/ibk/su/mascotnum2014/PhDStudentsDay/PhDAbstracts/MN14_-_Maatouk.pdf; International audience; Recently, statistical researchers have shown increased interest in Gaussian process modeling with mono- tonicity constraints (see [2], [4] and [5]). In computer experiments, the true function (scalar output) may be known to be monotone with respect to some or all input variables. We propose a new methodology based on the Bayesian Gaussian process metamodeling to sample from posterior distribution including monotonicity information in the monovariate case. Let y = f (x) be a monotonic increasing function where the input x is assumed to be scalar and in the domain [0, 1]. We consider a set of computer experiments {(xi , yi ) | i = 1, * * * , n} of size n and assume that yi = f (xi ), 1 ≤ i ≤ n. (1) Also suppose that M is the space of increasing functions and (Yx )x∈[0,1] is a zero-mean Gaussian process (GP) with kernel k(x, xt) given by a priori knowledge about the relationship between the input x and the output y. The following experimental results (see figures below) are obtained with the classical Gaussian kernel. We are interested in the simulation of the conditional (or posterior) distribution of the GP Y given data and monotonicity information...

Published
2014

30. A new rejection sampling method for truncated multivariate Gaussian random variables

Author

Maatouk, Hassan, Bay, Xavier, Laboratoire d'Informatique, de Modélisation et d'optimisation des Systèmes (LIMOS), SIGMA Clermont (SIGMA Clermont)-Université d'Auvergne - Clermont-Ferrand I (UdA)-Ecole Nationale Supérieure des Mines de St Etienne-Centre National de la Recherche Scientifique (CNRS)-Université Blaise Pascal - Clermont-Ferrand 2 (UBP), Département Décision en Entreprise : Modélisation, Optimisation (DEMO-ENSMSE), École des Mines de Saint-Étienne (Mines Saint-Étienne MSE), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Institut Henri Fayol, Université Blaise Pascal - Clermont-Ferrand 2 (UBP)-Université d'Auvergne - Clermont-Ferrand I (UdA)-SIGMA Clermont (SIGMA Clermont)-Ecole Nationale Supérieure des Mines de St Etienne (ENSM ST-ETIENNE)-Centre National de la Recherche Scientifique (CNRS), and Breuil, Florent

Subjects
[INFO.INFO-MO] Computer Science [cs]/Modeling and Simulation, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation
Abstract

International audience; Statistical researchers have shown increased interest in generating of truncatedmultivariate normal distributions. In this paper, we assume that the acceptanceregion is convex and our focus is on the rejection sampling. We propose a newalgorithm that outperforms crude rejection method for the simulation of truncatedmultivariate normal distribution. Our algorithm is based on a generalization ofVon Neumann’s rejection technique which requires the determination of the modeof the truncated multivariate density function. We provide a theoretical upperbound for the ratio of the target probability density function that the proposeddensity function is defined from the mode. This algorithm is used in the case wherethe maximum likelihood lies outside the acceptance region and the dimension ofthe multivariate density is high. The simulation results show that using rejectionsampling from the mode is more efficient than the usual rejection sampling. Inorder to support the theoretical aspect of our work, we have used an illustrativeexample.

Published
2014

32. Simulation of Gaussian processes with interpolation and inequality constraints - A correspondence with optimal smoothing splines

Author

Maatouk, Hassan, Bay, Xavier, Grammont, L., Breuil, Florent, Laboratoire d'Informatique, de Modélisation et d'optimisation des Systèmes (LIMOS), Université Blaise Pascal - Clermont-Ferrand 2 (UBP)-Université d'Auvergne - Clermont-Ferrand I (UdA)-SIGMA Clermont (SIGMA Clermont)-Ecole Nationale Supérieure des Mines de St Etienne (ENSM ST-ETIENNE)-Centre National de la Recherche Scientifique (CNRS), Département Décision en Entreprise : Modélisation, Optimisation (DEMO-ENSMSE), École des Mines de Saint-Étienne (Mines Saint-Étienne MSE), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Institut Henri Fayol, and SIGMA Clermont (SIGMA Clermont)-Université d'Auvergne - Clermont-Ferrand I (UdA)-Ecole Nationale Supérieure des Mines de St Etienne-Centre National de la Recherche Scientifique (CNRS)-Université Blaise Pascal - Clermont-Ferrand 2 (UBP)

Subjects
[INFO.INFO-MO] Computer Science [cs]/Modeling and Simulation, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation
Abstract

International audience; Complex physical phenomena are observed in many fields (sciences and engineering) and are often studied by time - consuming computer codes.These codes are analyzed with faster statistical models, often called emulators. The Gaussian process (GP) emulator is one of the most popular choice (Sacks et al., 1989) . In many situations, the physical system (computer model output) may be known to satisfy some inequality constraints with respect to some or all input variables. Incorporating inequality constraints into a GP emulator, the problem becomes more challenging since the resulting conditional process is not a GP. To this end, we suggest to approximate the original GP by a finite dimensional Gaussian processY N such that all conditional simulations satisfy the inequality constraints in the whole domain. In the second part of the talk, we investigate the convergence of the proposed approach and the relationship with thin plate splines (Duchon, 1976) . We show that the mode of the conditional GPYN (maximum a posteriori ) converges uniformly to the interpolation thin plate splines with in equality constraints. This extends to the case of inequality constraints the correspondence established by Kimeldorf and Wahba (1970) between Bayesian estimation on stochastic process and smoothing by splines.

Published
2014

34. Antibacterial Size Effect of ZnO Nanoparticles and Their Role as Additives in Emulsion Waterborne Paint.

Author

El-Habib I, Maatouk H, Lemarchand A, Dine S, Roynette A, Mielcarek C, Traoré M, and Azouani R

Abstract

Nosocomial infections, a prevalent issue in intensive care units due to antibiotic overuse, could potentially be addressed by metal oxide nanoparticles (NPs). However, there is still no comprehensive understanding of the impact of NPs' size on their antibacterial efficacy. Therefore, this study provides a novel investigation into the impact of ZnO NPs' size on bacterial growth kinetics. NPs were synthesized using a sol-gel process with monoethanolamine (MEA) and water. X-ray diffraction (XRD), transmission electron microscopy (TEM), and Raman spectroscopy confirmed their crystallization and size variations. ZnO NPs of 22, 35, and 66 nm were tested against the most common nosocomial bacteria: Escherichia coli , Pseudomonas aeruginosa (Gram-negative), and Staphylococcus aureus (Gram-positive). Evaluation of minimum inhibitory and bactericidal concentrations (MIC and MBC) revealed superior antibacterial activity in small NPs. Bacterial growth kinetics were monitored using optical absorbance, showing a reduced specific growth rate, a prolonged latency period, and an increased inhibition percentage with small NPs, indicating a slowdown in bacterial growth. Pseudomonas aeruginosa showed the lowest sensitivity to ZnO NPs, attributed to its resistance to environmental stress. Moreover, the antibacterial efficacy of paint containing 1 wt% of 22 nm ZnO NPs was evaluated, and showed activity against E. coli and S. aureus .

Published
2024
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