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1. Streptococcus thermophilus: A Source of Postbiotics Displaying Anti-Inflammatory Effects in THP 1 Macrophages

Author: Rania Allouche, Zeeshan Hafeez, Annie Dary-Mourot, Magali Genay, and Laurent Miclo
Subjects: S. thermophilus, postbiotics, intracellular proteins, pancreatic proteases, anti-inflammatory, THP-1 macrophages, Organic chemistry, QD241-441
Abstract: In addition to traditional use in fermented dairy products, S. thermophilus also exhibits anti-inflammatory properties both in live and heat-inactivated form. Recent studies have highlighted that some hydrolysates from surface proteins of S. thermophilus could be responsible partially for overall anti-inflammatory activity of this bacterium. It was hypothesized that anti-inflammatory activity could also be attributed to peptides resulting from the digestion of intracellular proteins of S. thermophilus. Therefore, total intracellular proteins (TIP) from two phenotypically different strains, LMD-9 and CNRZ-21N, were recovered by sonication followed by ammonium sulphate precipitation. The molecular masses of the TIP of both strains were very close to each other as observed by SDS-PAGE. The TIP were fractionated by size exclusion fast protein liquid chromatography to obtain a 3–10 kDa intracellular protein (IP) fraction, which was then hydrolysed with pancreatic enzyme preparation, Corolase PP. The hydrolysed IP fraction from each strain exhibited anti-inflammatory activity by modulating pro-inflammatory mediators, particularly IL-1β in LPS-stimulated THP-1 macrophages. However, a decrease in IL-8 secretion was only observed with hydrolysed IP fraction from CNRZ-21N, indicating that strain could be an important parameter in obtaining active hydrolysates. Results showed that peptides from the 3–10 kDa IP fraction of S. thermophilus could therefore be considered as postbiotics with potential beneficial effects on human health. Thus, it can be used as a promising bioactive ingredient for the development of functional foods to prevent low-grade inflammation.
Published: 2024
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2. In Vitro Anti-Inflammatory Activity of Peptides Obtained by Tryptic Shaving of Surface Proteins of Streptococcus thermophilus LMD-9

Author: Rania Allouche, Zeeshan Hafeez, Florent Papier, Annie Dary-Mourot, Magali Genay, and Laurent Miclo
Subjects: Streptococcus thermophilus, cell surface proteins, tryptic hydrolysis, anti-inflammatory, Chemical technology, TP1-1185
Abstract: Streptococcus thermophilus, a lactic acid bacterium widely used in the dairy industry, is consumed regularly by a significant proportion of the population. Some strains show in vitro anti-inflammatory activity which is not fully understood. We hypothesized that peptides released from the surface proteins of this bacterium during digestion could be implied in this activity. Consequently, we prepared a peptide hydrolysate by shaving and hydrolysis of surface proteins using trypsin, and the origin of peptides was checked by liquid chromatography–tandem mass spectrometry (LC-MS/MS) analysis. Most of the identified peptides originated from bacterial cell surface proteins. The anti-inflammatory activity of peptide hydrolysate was investigated under inflammatory conditions in two cell models. Peptide hydrolysate significantly decreased secretion of pro-inflammatory cytokine IL-8 in lipopolysaccharide (LPS)-stimulated human colon epithelial HT-29 cells. It also reduced the production of pro-inflammatory cytokines IL-8, IL-1β and the protein expression levels of Pro-IL-1β and COX-2 in LPS-stimulated THP-1 macrophages. The results showed that peptides released from bacterial surface proteins by a pancreatic protease could therefore participate in an anti-inflammatory activity of S. thermophilus LMD-9 and could prevent low-grade inflammation.
Published: 2022
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3. Role of the Sortase A in the Release of Cell-Wall Proteinase PrtS in the Growth Medium of Streptococcus thermophilus 4F44

Author: Ahoefa Ablavi Awussi, Emeline Roux, Catherine Humeau, Zeeshan Hafeez, Bernard Maigret, Oun Ki Chang, Xavier Lecomte, Gérard Humbert, Laurent Miclo, Magali Genay, Clarisse Perrin, and Annie Dary-Mourot
Subjects: Streptococcus thermophilus, sortase A, cell envelope proteinase, LPNTG motif, cell wall-anchoring, Biology (General), QH301-705.5
Abstract: Growth of the lactic acid bacterium Streptococcus thermophilus in milk depends on its capacity to hydrolyze proteins of this medium through its surface proteolytic activity. Thus, strains exhibiting the cell envelope proteinase (CEP) PrtS are able to grow in milk at high cellular density. Due to its LPNTG motif, which is possibly the substrate of the sortase A (SrtA), PrtS is anchored to the cell wall in most S. thermophilus strains. Conversely, a soluble extracellular PrtS activity has been reported in the strain 4F44. It corresponds, in fact, to a certain proportion of PrtS that is not anchored to the cell wall but rather is released in the growth medium. The main difference between PrtS of strain 4F44 (PrtS4F44) and other PrtS concerns the absence of a 32-residue imperfect duplication in the prodomain of the CEP, postulated as being required for the maturation and correct subsequent anchoring of PrtS. In fact, both mature (without the prodomain at the N-terminal extremity) and immature (with the prodomain) forms are found in the soluble PrtS4F44 form along with an intact LPNTG at their C-terminal extremity. Investigations we present in this work show that (i) the imperfect duplication is not implied in PrtS maturation; (ii) the maturase PrtM is irrelevant in PrtS maturation which is probably automaturated; and (iii) SrtA allows for the PrtS anchoring in S. thermophilus but the SrtA of strain 4F44 (SrtA4F44) displays an altered activity.
Published: 2021
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4. Mapping in mice the brain regions involved in the anxiolytic-like properties of α-casozepine, a tryptic peptide derived from bovine αs1-casein

Author: Simon Benoit, Catherine Chaumontet, Jessica Schwarz, Céline Cakir-Kiefer, Daniel Tomé, and Laurent Miclo
Subjects: α-Casozepine, Anxiety, Bioactive peptide, c-Fos, Neuronal activity modulation, Nutrition. Foods and food supply, TX341-641
Abstract: α-Casozepine, a bioactive peptide from milk casein, displays an anxiolytic-like activity in many species. Since its mode of action is still not elucidated, a study was conducted in Swiss mice to investigate c-Fos expression, a marker of neuronal activity, in different brain areas. After an intraperitoneal injection of α-casozepine (1 mg/kg), animals were placed either in a non-stressful or in an anxiety-inducing situation triggered with a light/dark box. No effect of α-casozepine on c-Fos expression was observed in the non-stressful situation. In the stressful situation, modulation of neuronal activity by α-casozepine was observed in different brain regions compared to that of vehicle. However, while diazepam, a benzodiazepine, modulated neuronal activity the same way in hippocampus, accumbens nucleus and hypothalamus, differences were observed in c-Fos expression in amygdala and prefrontal cortex compared to α-casozepine. These results strengthen the assumption that the anxiolytic mechanisms of α-casozepine differ partly of those of diazepam.
Published: 2017
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5. Swarm gradient dynamics for global optimization: the mean-field limit case.

Author: Jérôme Bolte, Laurent Miclo, and Stéphane Villeneuve
Published: 2024
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6. Quantum walks, the discrete wave equation and Chebyshev polynomials.

Author: Simon Apers and Laurent Miclo
Published: 2024
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7. On the forward algorithm for stopping problems on continuous-time Markov chains.

Author: Laurent Miclo and Stéphane Villeneuve
Published: 2021
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8. Les nouvelles graines, des superaliments ?

Author: Laurent Miclo
Subjects: Nutrition and Dietetics
Published: 2023
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9. Intérêts des polyols et limites à leur utilisation

Author: Laurent Miclo
Subjects: Nutrition and Dietetics
Published: 2022
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10. Monotonicity of the extremal functions for one-dimensional inequalities of logarithmic Sobolev type

Author: Laurent, Miclo, Donati-Martin, Catherine, editor, Émery, Michel, editor, Rouault, Alain, editor, and Stricker, Christophe, editor
Published: 2009
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11. Cell Proteins Obtained by Peptic Shaving of Two Phenotypically Different Strains of

Author: Rania, Allouche, Magali, Genay, Annie, Dary-Mourot, Zeeshan, Hafeez, and Laurent, Miclo
Subjects: Lipopolysaccharides, Bacterial Proteins, Interleukin-8, Endopeptidases, Anti-Inflammatory Agents, Streptococcus thermophilus, Peptides, Peptide Hydrolases
Published: 2022

12. The Anxiolytic-like Properties of a Tryptic Hydrolysate of Bovine αs1 Casein Containing α-Casozepine Rely on GABAA Receptor Benzodiazepine Binding Sites but Not the Vagus Nerve

Author: Simon Benoit, Catherine Chaumontet, Nicolas Violle, Audrey Boulier, Zeeshan Hafeez, Céline Cakir-Kiefer, Daniel Tomé, Jessica Schwarz, and Laurent Miclo
Subjects: Nutrition and Dietetics, α-casozepine, anxiolysis, casein tryptic hydrolysate, GABAA, vagotomy, Food Science
Abstract: (1) Background: A tryptic hydrolysate of bovine αs1-casein (CH) exerts anxiolytic-like properties in many species, including humans. This is mainly related to the presence of α-casozepine (α-CZP), which yields these properties in rodents. This study evaluates, in a rat model, the roles of the vagus nerve and the benzodiazepine binding site of GABAA receptors in the mode of action of CH. (2) Methods: The conditioned defensive burying test was used to evaluate anxiety. (3) Results: Participation of the vagus nerve in the mode of action of CH was excluded, as the global anxiety score in vagotomised rats was not significantly different from that of non-vagotomised animals. The blocking of the binding sites of benzodiazepines with flumazenil antagonised CH anxiolytic-like properties. (4) Conclusions: The vagus nerve does not play a role in the anxiolytic-like properties of CH. On the other hand, this anxiolytic-like activity relies on the benzodiazepine binding site of the GABAA receptors. This result is consistent with previous in vitro studies and, more specifically with the discovery of α-CZP, the peptide responsible for the anxiolytic-like properties of CH.
Published: 2022
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13. On the cut-off phenomenon for the transitivity of randomly generated subgroups.

Author: André Galligo and Laurent Miclo
Published: 2012
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14. On Barycentric Subdivision.

Author: Persi Diaconis and Laurent Miclo
Published: 2011
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15. Food protein-derived anxiolytic peptides: their potential role in anxiety management

Author: Laurent Miclo, Céline Cakir-Kiefer, Simon Benoit, Zeeshan Hafeez, and Annie Dary
Subjects: Fish Proteins, 0301 basic medicine, Protein Hydrolysates, medicine.drug_class, Ribulose-Bisphosphate Carboxylase, Peptide, Anxiety, Pharmacology, Anxiolytic, 03 medical and health sciences, 0302 clinical medicine, In vivo, medicine, Animals, Humans, chemistry.chemical_classification, Food protein, business.industry, Caseins, General Medicine, Milk Proteins, Anxiety Disorders, Peptide Fragments, In vitro, Bioavailability, 030104 developmental biology, Anti-Anxiety Agents, chemistry, Soybean Proteins, Dietary Proteins, medicine.symptom, business, Oligopeptides, 030217 neurology & neurosurgery, Food Science
Abstract: About one in three people are affected by anxiety disorders during their lifetime. Anxiety episodes can be brief due to a stressful event, but anxiety disorders can last at least 6 months. A wide variety of therapeutic drugs are available for the treatment of anxiety disorders, but due to the associated side effects of these anxiolytics, it is interesting to find alternatives. Some food protein hydrolysates or active peptide fragments present in such hydrolysates provide a natural and promising mean for preventing certain forms of anxiety. To date, only a small number of hydrolysates or peptides from food proteins with anxiolytic-like activity have been characterized. Most of these hydrolysates or peptides have displayed potent anxiolytic profiles in animal or clinical studies. The results suggest that these molecules may exert their effects at different levels. This paper reviews the data of the structure/activity relationship, physiological effects displayed in in vitro and in vivo assays, bioavailability, and safety profiles of anxiolytic peptides.
Published: 2021
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16. On Intertwining Relations Between Ehrenfest, Yule and Ornstein-Uhlenbeck Processes

Author: Laurent Miclo and Pierre Patie
Published: 2022
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17. Optimal epidemic suppression under an ICU constraint: an analytical solution

Author: Laurent Miclo, Daniel Spiro, Jörgen Weibull, Institut de Mathématiques de Toulouse UMR5219 (IMT), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Toulouse School of Economics (TSE-R), Université de Toulouse (UT)-Université de Toulouse (UT)-École des hautes études en sciences sociales (EHESS)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Uppsala University, Département d'Économie de l'École Polytechnique (X-DEP-ECO), École polytechnique (X), Department of Economics, Stockholm School of Economics (SSE/ECON), and Stockholm School of Economics (SSE)
Subjects: Hälso- och sjukvårdsorganisation, hälsopolitik och hälsoekonomi, Economics and Econometrics, Suppression, Applied Mathematics, Epidemic, Health Care Service and Management, Health Policy and Services and Health Economy, JEL: D - Microeconomics/D.D6 - Welfare Economics, [SHS.ECO]Humanities and Social Sciences/Economics and Finance, Optimal control, JEL: I - Health, Education, and Welfare/I.I1 - Health/I.I1.I18 - Government Policy • Regulation • Public Health, JEL: C - Mathematical and Quantitative Methods/C.C6 - Mathematical Methods • Programming Models • Mathematical and Simulation Modeling/C.C6.C61 - Optimization Techniques • Programming Models • Dynamic Analysis, Health, Corona, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Infection
Abstract: How much and when should we limit economic and social activity to ensure that the healthcare system is not overwhelmed during an epidemic? We study a setting where ICU resources are constrained and suppression is costly. Providing a fully analytical solution we show that the common wisdom of "flattening the curve", where suppression measures are continuously taken to hold down the spread throughout the epidemic, is suboptimal. Instead, the optimal suppression is discontinuous. The epidemic should be left unregulated in a first phase and when the ICU constraint is approaching society should quickly lock down (a discontinuity). After the lockdown, regulation should gradually be lifted, holding the rate of infected constant, thus respecting the ICU resources while not unnecessarily limiting economic activity. In a final phase, regulation is lifted. We call this strategy "filling the box". The cost under the optimal strategy is obtained in closed form as an explicit function of economic and medical fundamentals. We show that the policy is optimal also when there, in addition, is a small cost associated with the number of infected. The tighter the ICU constraint, the wider is the range of such cost for which the policy is still optimal. This suggests the primary focus of poor countries (with few ICU resources) should be to protect the health-care system, while richer countries (with extensive ICU resources) may strive to reduce the number of infected even more. (c) 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
Published: 2022
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18. Discrete self-similar and ergodic Markov chains

Author: Laurent Miclo, Pierre Patie, and Rohan Sarkar
Subjects: Mathematics - Functional Analysis, Mathematics - Spectral Theory, Statistics and Probability, Probability (math.PR), 41A60, 47G20, 33C45, 47D07, 37A30, 60J27, 60J60, FOS: Mathematics, Statistics, Probability and Uncertainty, Spectral Theory (math.SP), Mathematics - Probability, Functional Analysis (math.FA)
Abstract: The first aim of this paper is to introduce a class of Markov chains on $\mathbb{Z}_+$ which are discrete self-similar in the sense that their semigroups satisfy an invariance property expressed in terms of a discrete random dilation operator. After showing that this latter property requires the chains to be upward skip-free, we first establish a gateway relation, a concept introduced in [26], between the semigroup of such chains and the one of spectrally negative self-similar Markov processes on $\mathbb{R}_+$. As a by-product, we prove that each of these Markov chains, after an appropriate scaling, converge in the Skorohod metric, to the associated self-similar Markov process. By a linear perturbation of the generator of these Markov chains, we obtain a class of ergodic Markov chains, which are non-reversible. By means of intertwining and interweaving relations, where the latter was recently introduced in [27], we derive several deep analytical properties of such ergodic chains including the description of the spectrum, the spectral expansion of their semigroups, the study of their convergence to equilibrium in the $\Phi$-entropy sense as well as their hypercontractivity property., Comment: 50 pages
Published: 2022
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19. Role of the Sortase A in the Release of Cell-Wall Proteinase PrtS in the Growth Medium of Streptococcus thermophilus 4F44

Author: Magali Genay, Emeline Roux, Catherine Humeau, Zeeshan Hafeez, Laurent Miclo, Oun Ki Chang, Gérard Humbert, Bernard Maigret, Annie Dary-Mourot, Ahoefa Ablavi Awussi, Xavier Lecomte, Clarisse Perrin, Composés Alimentaires : Biofonctionnalités et risques Neurotoxiques (CALBINOTOX), Université de Lorraine (UL), Laboratoire Réactions et Génie des Procédés (LRGP), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Computational Algorithms for Protein Structures and Interactions (CAPSID), Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Department of Complex Systems, Artificial Intelligence & Robotics (LORIA - AIS), Laboratoire Lorrain de Recherche en Informatique et ses Applications (LORIA), Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire Lorrain de Recherche en Informatique et ses Applications (LORIA), Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Gwangju Regional Office of Food and Drug Safety, Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL), and Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)
Subjects: Microbiology (medical), Streptococcus thermophilus, QH301-705.5, Microbiology, Article, Cell wall, 03 medical and health sciences, chemistry.chemical_compound, sortase A, Virology, cell envelope proteinase, Extracellular, cell wall-anchoring, LPNTG motif, [SDV.BBM]Life Sciences [q-bio]/Biochemistry, Molecular Biology, Biology (General), 030304 developmental biology, cell wallanchoring, 0303 health sciences, Growth medium, Strain (chemistry), biology, 030306 microbiology, Chemistry, biology.organism_classification, [SDV.BIBS]Life Sciences [q-bio]/Quantitative Methods [q-bio.QM], [SDV.MP.BAC]Life Sciences [q-bio]/Microbiology and Parasitology/Bacteriology, Cell biology, Lactic acid bacterium, Sortase A, Cell envelope, [INFO.INFO-BI]Computer Science [cs]/Bioinformatics [q-bio.QM], [SDV.AEN]Life Sciences [q-bio]/Food and Nutrition
Abstract: Growth of the lactic acid bacterium Streptococcus thermophilus in milk depends on its capacity to hydrolyze proteins of this medium through its surface proteolytic activity. Thus, strains exhibiting the cell envelope proteinase (CEP) PrtS are able to grow in milk at high cellular density. Due to its LPNTG motif, which is possibly the substrate of the sortase A (SrtA), PrtS is anchored to the cell wall in most S. thermophilus strains. Conversely, a soluble extracellular PrtS activity has been reported in the strain 4F44. It corresponds, in fact, to a certain proportion of PrtS that is not anchored to the cell wall but rather is released in the growth medium. The main difference between PrtS of strain 4F44 (PrtS4F44) and other PrtS concerns the absence of a 32-residue imperfect duplication in the prodomain of the CEP, postulated as being required for the maturation and correct subsequent anchoring of PrtS. In fact, both mature (without the prodomain at the N-terminal extremity) and immature (with the prodomain) forms are found in the soluble PrtS4F44 form along with an intact LPNTG at their C-terminal extremity. Investigations we present in this work show that (i) the imperfect duplication is not implied in PrtS maturation, (ii) the maturase PrtM is irrelevant in PrtS maturation which is probably automaturated, and (iii) SrtA allows for the PrtS anchoring in S. thermophilus but the SrtA of strain 4F44 (SrtA4F44) displays an altered activity.
Published: 2021
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20. Induced idleness leads to deterministic heavy traffic limits for queue-based random-access algorithms

Author: Florian Simatos, Laurent Miclo, Sem Borst, Eyal Castiel, Philip Whiting, Stochastic Operations Research, Centre National de la Recherche Scientifique - CNRS (FRANCE), Ecole des Hautes Etudes en Sciences Sociales - EHESS (FRANCE), Institut national de recherche pour l'agriculture, l'alimentation et l'environnement - INRAE (FRANCE), Institut Supérieur de l'Aéronautique et de l'Espace - ISAE-SUPAERO (FRANCE), Macquarie University (AUSTRALIA), Université Toulouse 1 Capitole - UT1 (FRANCE), Eindhoven University of Technology - TU/e (NETHERLANDS), Institut Supérieur de l'Aéronautique et de l'Espace (ISAE-SUPAERO), Department of mathematics and computing science [Eindhoven], Eindhoven University of Technology [Eindhoven] (TU/e), Institut de Mathématiques de Toulouse UMR5219 (IMT), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Macquarie University, Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Département d'Ingénierie des Systèmes Complexes (DISC), Toulouse School of Economics (TSE), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-École des hautes études en sciences sociales (EHESS)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), and ANR-17-EURE-0010,CHESS,Toulouse Graduate School défis en économie et sciences sociales quantitatives(2017)
Subjects: [SPI.OTHER]Engineering Sciences [physics]/Other, Statistics and Probability, Interference graph, 0211 other engineering and technologies, 02 engineering and technology, Heavy traffic, 01 natural sciences, State space collapse, 010104 statistics & probability, CSMA algorithms, Autre, FOS: Mathematics, Limit (mathematics), 0101 mathematics, B- ECONOMIE ET FINANCE, Stochastic averaging principle, Queue, Scaling, Central limit theorem, Mathematics, 021103 operations research, 60K25 (primary), 60K35 (secondary), Probability (math.PR), 16. Peace & justice, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Fully coupled, Statistics, Probability and Uncertainty, Algorithm, Mathematics - Probability, Random access
Abstract: We examine a queue-based random-access algorithm where activation and deactivation rates are adapted as functions of queue lengths. We establish its heavy traffic behavior on a complete interference graph, which turns out to be highly nonstandard in two respects: (1) the scaling depends on some parameter of the algorithm and is not the $N/N^2$ scaling usually found in functional central limit theorems; (2) the heavy traffic limit is deterministic. We discuss how this nonstandard behavior arises from the idleness induced by the distributed nature of the algorithm. In order to prove our main result, we developed a new method for obtaining a fully coupled stochastic averaging principle., Comment: 40 pages
Published: 2021
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21. On interweaving relations

Author: Laurent Miclo, Pierre Patie, Toulouse School of Economics (TSE), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-École des hautes études en sciences sociales (EHESS)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Centre National de la Recherche Scientifique (CNRS), and ANR-17-EURE-0010,CHESS,Toulouse Graduate School défis en économie et sciences sociales quantitatives(2017)
Subjects: Hyperboundedness, Pure mathematics, Semigroup, Interweaving relations, 010102 general mathematics, Degenerate energy levels, [SHS.ECO]Humanities and Social Sciences/Economics and Finance, 01 natural sciences, Mathematics - Analysis of PDEs, Laguerre processes, Mixing (mathematics), Hypoelliptic operator, Entropic convergence to equilibrium, 0103 physical sciences, Convergence (routing), Laguerre polynomials, Ergodic theory, 010307 mathematical physics, 0101 mathematics, Variety (universal algebra), Analysis, Mathematics - Probability, Hypoelliptic diffusions, Mathematics
Abstract: National audience; Interweaving relations are introduced and studied here in a general Markovian setting as a strengthening of usual intertwining relations between semigroups, obtained by adding a randomized delay feature. They provide a new classification scheme of the set of Markovian semigroups which enables to transfer from a reference semigroup and up to an independent warm-up time, some ergodic, analytical and mixing properties including the φ-entropy convergence to equilibrium, the hyperboundedness and, when the warm-up time is deterministic, the cut-off phenomena. We also present several useful transformations that preserve interweaving relations. We provide a variety of examples of interweaving relations ranging from classical, discrete, and non-local Laguerre and Jacobi semigroups to degenerate hypoelliptic Ornstein-Uhlenbeck semigroups and some non-colliding particle systems.
Published: 2021
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22. On A Family of Isospectral Pure-Birth Processes

Author: Laurent Miclo, Chi Zhang, Toulouse School of Economics (TSE), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-École des hautes études en sciences sociales (EHESS)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Institut de Mathématiques de Toulouse UMR5219 (IMT), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS), Université Fédérale Toulouse Midi-Pyrénées, Toulouse School of Economics (TSE-R), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-École des hautes études en sciences sociales (EHESS)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Université de Toulouse (UT), Ocean University of China (OUC), and ANR-17-EURE-0010,CHESS,Toulouse Graduate School défis en économie et sciences sociales quantitatives(2017)
Subjects: Statistics and Probability, Pure mathematics, Pure-birth processes, Isospectral, Spectra of Markov processes, Intertwining relations, [SHS.ECO]Humanities and Social Sciences/Economics and Finance, Mixing rates, Mathematics
Abstract: National audience; It is shown that every spectrum of a finite irreducible Markov generator whose eigen-values are real and of geometric multiplicity 1 can be obtained as the spectrum of an irreducible pure-birth Markov process with jumps from the right-most boundary to all the other points. A whole isospectral family of such processes is exhibited and their mixing rates are compared.
Published: 2021
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23. Strong stationary times for finite Heisenberg walks

Author: Laurent Miclo, Institut de Mathématiques de Toulouse UMR5219 (IMT), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Toulouse School of Economics (TSE), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-École des hautes études en sciences sociales (EHESS)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), ANR-17-EURE-0010,CHESS,Toulouse Graduate School défis en économie et sciences sociales quantitatives(2017), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Toulouse School of Economics (TSE-R), and Université de Toulouse (UT)-Université de Toulouse (UT)-École des hautes études en sciences sociales (EHESS)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)
Subjects: Statistics and Probability, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Absorbing Markov chains, Finite Heisenberg random walks, Strong stationary times, Random mappings
Abstract: The random mapping construction of strong stationary times is applied here to finite Heisenberg random walks over ℤM, for odd M ⩾ 3. When they correspond to 3 × 3 matrices, the strong stationary times are of order M6, estimate which can be improved to M4 if we are only interested in the convergence to equilibrium of the last column. Simulations by Chhaibi suggest that the proposed strong stationary time is of the right M2 order. These results are extended to N × N matrices, with N ⩾ 3. All the obtained bounds are thought to be non-optimal, nevertheless this original approach is promising, as it relates the investigation of the previously elusive strong stationary times of such random walks to new absorbing Markov chains with a statistical physics flavor and whose quantitative study is to be pushed further. In addition, for N = 3, a strong equilibrium time is proposed in the same spirit for the non-Markovian coordinate in the upper right corner. This result would extend to separation discrepancy the corresponding fast convergence for this coordinate in total variation and open a new method for the investigation of this phenomenon in higher dimension.
Published: 2020

24. Higher order Cheeger inequalities for Steklov eigenvalues

Author: Laurent Miclo, Asma Hassannezhad, Institut Mittag-Leffler, Institut de Mathématiques de Toulouse UMR5219 (IMT), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), ANR-12-BS01-0019,STAB,Stabilité du comportement asymptotique d'EDP, de processus stochastiques et de leurs discrétisations.(2012), Laboratoire de Mathématiques et Physique Théorique (LMPT), Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), and Centre National de la Recherche Scientifique (CNRS)-Université de Tours
Subjects: Mathematics - Differential Geometry, Dirichlet–to–Neumann operator, Spectral theory, General Mathematics, 01 natural sciences, Upper and lower bounds, Laplace-Beltrami operator, higher order Cheeger inequalities, Combinatorics, Mathematics - Spectral Theory, 0103 physical sciences, FOS: Mathematics, Order (group theory), 0101 mathematics, Spectral Theory (math.SP), B- ECONOMIE ET FINANCE, Dirichlet--to--Neumann operator, 35P15, 58J50, 58J65, 60J25, 60J27, Mathematics, MSC2010: 15A18, 35P15, 58J50, 58J65, 60J25, 60J27, 60J60, 60J75, Dirichlet-to-Neumann operator, Probability (math.PR), 010102 general mathematics, Spectrum (functional analysis), eigenvalues, higher or-der Cheeger inequalities, Mathematics::Spectral Theory, jump Markov processes, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Steklov problems, Differential Geometry (math.DG), Differential geometry, Laplace–Beltrami operator, Bounded function, Steklov problem, Brownian motion on Riemannian manifolds, 010307 mathematical physics, isoperimetric ratios, finite Markov processes, Isoperimetric inequality, Mathematics - Probability, [MATH.MATH-SP]Mathematics [math]/Spectral Theory [math.SP]
Abstract: We prove a lower bound for the $k$-th Steklov eigenvalues in terms of an isoperimetric constant called the $k$-th Cheeger-Steklov constant in three different situations: finite spaces, measurable spaces, and Riemannian manifolds. These lower bounds can be considered as higher order Cheeger type inequalities for the Steklov eigenvalues. In particular it extends the Cheeger type inequality for the first nonzero Steklov eigenvalue previously studied by Escobar in 1997 and by Jammes in 2015 to higher order Steklov eigenvalues. The technique we develop to get this lower bound is based on considering a family of accelerated Markov operators in the finite and mesurable situations and of mass concentration deformations of the Laplace-Beltrami operator in the manifold setting which converges uniformly to the Steklov operator. As an intermediary step in the proof of the higher order Cheeger type inequality, we define the Dirichlet-Steklov connectivity spectrum and show that the Dirichlet connectivity spectra of this family of operators converges to (or bounded by) the Dirichlet-Steklov spectrum uniformly. Moreover, we obtain bounds for the Steklov eigenvalues in terms of its Dirichlet-Steklov connectivity spectrum which is interesting in its own right and is more robust than the higher order Cheeger type inequalities. The Dirichlet-Steklov spectrum is closely related to the Cheeger-Steklov constants., Correcting few typos and doing some changes on pages 41 and 45
Published: 2020
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25. On the construction of measure-valued dual processes

Author: Laurent Miclo
Subjects: Statistics and Probability, coalescing stochastic flows, set-valued dual processes, random mappings, 01 natural sciences, Measure (mathematics), one-dimensional diffusions, Diaconis-Fill couplings, 010104 statistics & probability, 60J05, Mathematics::Probability, measure-valued dual processes, 60J25, Convergence (routing), Pitman’s theorem, 60J65, 0101 mathematics, Brownian motion, Mathematics, 60J60, 37A25, Markov chain, Stochastic process, 010102 general mathematics, Probabilistic logic, Coupling (probability), Algebra, Discrete time and continuous time, 60G17, 60J10, Statistics, Probability and Uncertainty, Markov intertwining relations
Abstract: Markov intertwining is an important tool in stochastic processes: it enables to prove equalities in law, to assess convergence to equilibrium in a probabilistic way, to relate apparently distinct random models or to make links with wave equations, see Carmona, Petit and Yor [8], Aldous and Diaconis [2], Borodin and Olshanski [7] and Pal and Shkolnikov [23] for examples of applications in these domains. Unfortunately the basic construction of Diaconis and Fill [10] is not easy to manipulate. An alternative approach, where the underlying coupling is first constructed, is proposed here as an attempt to remedy to this drawback, via random mappings for measure-valued dual processes, first in a discrete time and finite state space setting. This construction is related to the evolving sets of Morris and Peres [22] and to the coupling-from-the-past algorithm of Propp and Wilson [27]. Extensions to continuous frameworks enable to recover, via a coalescing stochastic flow due to Le Jan and Raimond [16], the explicit coupling underlying the intertwining relation between the Brownian motion and the Bessel-3 process due to Pitman [25]. To generalize such a coupling to more general one-dimensional diffusions, new coalescing stochastic flows would be needed and the paper ends with challenging conjectures in this direction.
Published: 2020

26. Anxiolytic Activity and Brain Modulation Pattern of the α-Casozepine-Derived Pentapeptide YLGYL in Mice

Author: Catherine Chaumontet, Daniel Tomé, Audrey Boulier, Jessica Schwarz, Laurent Miclo, Simon Benoit, Céline Cakir-Kiefer, Physiologie de la Nutrition et du Comportement Alimentaire (PNCA (UMR 0914)), AgroParisTech-Université Paris-Saclay-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Unité de Recherches Animal et Fonctionnalités des Produits Animaux (URAFPA), Université de Lorraine (UL)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Université Paris-Saclay, INGREDIA, Composés Alimentaires : Biofonctionnalités et risques Neurotoxiques (CALBINOTOX), Université de Lorraine (UL), Miclo, Laurent [0000-0002-6010-611X], and Apollo - University of Cambridge Repository
Subjects: Male, 0301 basic medicine, medicine.drug_class, [SDV.NEU.NB]Life Sciences [q-bio]/Neurons and Cognition [q-bio.NC]/Neurobiology, α-Casozepine, lcsh:TX341-641, Pharmacology, Pentapeptide repeat, Anxiolytic, Amygdala, Article, proteolytic fragments, Benzodiazepines, Mice, 03 medical and health sciences, 0302 clinical medicine, medicine, Animals, Nucleus raphe magnus, Benzodiazepine, c-Fos, Diazepam, Nutrition and Dietetics, Chemistry, Brain, Caseins, milk bioactive peptide, anxiety, Peptide Fragments, 3. Good health, 030104 developmental biology, medicine.anatomical_structure, Anti-Anxiety Agents, neuronal activity modulation, [SDV.SP.PHARMA]Life Sciences [q-bio]/Pharmaceutical sciences/Pharmacology, Cattle, Raphe nuclei, lcsh:Nutrition. Foods and food supply, Proto-Oncogene Proteins c-fos, Nucleus, 030217 neurology & neurosurgery, Food Science, medicine.drug
Abstract: &alpha, Casozepine (&alpha, CZP) is an anxiolytic-like bioactive decapeptide derived from bovine &alpha, s1‑casein. The N-terminal peptide YLGYL was previously identified after proteolysis of the original peptide in an in vitro digestion model. Its putative anxiolytic-like properties were evaluated in a Swiss mice model using a light/dark box (LDB) after an intraperitoneal injection (0.5 mg/kg). The effect of YLGYL on c-Fos expression in brain regions linked to anxiety regulation was afterwards evaluated via immunofluorescence and compared to those of &alpha, CZP and diazepam, a reference anxiolytic benzodiazepine. YLGYL elicited some anxiolytic-like properties in the LDB, similar to &alpha, ‑CZP and diazepam. The two peptides displayed some strong differences compared with diazepam in terms of c-Fos expression modulation in the prefontal cortex, the amygdala, the nucleus of the tractus solitarius, the periaqueductal grey, and the raphe magnus nucleus, implying a potentially different mode of action. Additionally, YLGYL modulated c-Fos expression in the amygdala and in one of the raphe nuclei, displaying a somewhat similar pattern of activation as &alpha, &shy, ‑CZP. Nevertheless, some differences were also spotted between the two peptides, making it possible to formulate the hypothesis that these peptides could act differently on anxiety regulation. Taken together, these results showed that YLGYL could contribute to the in vivo overall action of &alpha, ‑CZP.
Published: 2020
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27. On the fastest finite Markov processes

Author: Vivek S. Borkar and Laurent Miclo
Subjects: Discrete mathematics, Uniform distribution (continuous), Markov chain, Applied Mathematics, 010102 general mathematics, Markov process, Permutation matrix, 01 natural sciences, Hamiltonian path, 010101 applied mathematics, symbols.namesake, Discrete time and continuous time, symbols, 0101 mathematics, Invariant (mathematics), B- ECONOMIE ET FINANCE, Analysis, Hamiltonian (control theory), Mathematics
Abstract: Consider a finite state irreducible Markov process with transition graph G and invariant probability distribution π. Its inverse communication speed is defined as the expectation of the time to go from x to y when are sampled independently according to π. We study this in the context of both discrete and continuous time. One of our goals is to show (under a suitable normalization condition on the transition rates for the continuous time case) that the shortest inverse communication speed among all Markov processes compatible with G and π is attained on those whose successive positions follow a Hamiltonian cycle, assuming one exists, and that π is close enough to the uniform distribution υ. This result is no longer true when π is sufficiently different from υ. Another purpose of the paper is to prove that when the invariance with respect to π is dropped and the inverse communication speed is replaced by the unweighted sum of the hitting times, then the Hamiltonian cycles, when they exist, are still the minimizers over all processes compatible with the prescribed directed graph G of permitted transitions, not only Markov processes, thus extending some previous results.
Published: 2020

28. On the Markov commutator

Author: Laurent Miclo, Toulouse School of Economics (TSE), École des hautes études en sciences sociales (EHESS)-Institut National de la Recherche Agronomique (INRA)-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées, Institut de Mathématiques de Toulouse UMR5219 ( IMT ), Université Toulouse 1 Capitole ( UT1 ) -Université Toulouse - Jean Jaurès ( UT2J ) -Université Toulouse III - Paul Sabatier ( UPS ), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-PRES Université de Toulouse-Institut National des Sciences Appliquées - Toulouse ( INSA Toulouse ), Institut National des Sciences Appliquées ( INSA ) -Institut National des Sciences Appliquées ( INSA ) -Centre National de la Recherche Scientifique ( CNRS ), ANR-12-BS01-0019,STAB,Stabilité du comportement asymptotique d'EDP, de processus stochastiques et de leurs discrétisations. ( 2012 ), DSR-SCD-UT1C, Service Publications, Institut de Mathématiques de Toulouse UMR5219 (IMT), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), ANR-12-BS01-0019,STAB,Stabilité du comportement asymptotique d'EDP, de processus stochastiques et de leurs discrétisations.(2012), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), and Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)
Subjects: Pure mathematics, Markov kernel, General Mathematics, Duality (optimization), Markov process, Hypergroup property, Markov commutator, 01 natural sciences, law.invention, symbols.namesake, law, FOS: Mathematics, 0101 mathematics, [SHS.ECO] Humanities and Social Sciences/Economics and Finance, B- ECONOMIE ET FINANCE, Mathematics, Birth and death chains, Metropolis algorithms, Markov chain, Symmetry group of a Markov kernel, Semigroup, 010102 general mathematics, Probability (math.PR), One-dimensional discrete wave equations, Commutator (electric), finite Markov kernels, [SHS.ECO]Humanities and Social Sciences/Economics and Finance, Birth–death process, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], {MSC2010:} primary: 60J10, secondary: 15A27, 20N20, 52C99, 39A12, Monotone polygon, Achour-Trimèche theorem, symbols, [ MATH.MATH-PR ] Mathematics [math]/Probability [math.PR], Mathematics - Probability, Duality by intertwining
Abstract: International audience; The Markov commutator associated to a finite Markov kernel P is the convex semigroup consisting of all Markov kernels commuting with P. Its interest comes from its relation with the hypergroup property and with the notion of Markovian duality by intertwining. In particular, it is shown that the discrete analogue of the Achour-Trimèche's theorem, asserting the preservation of non-negativity by the wave equations associated to certain Metropolis birth and death transition kernels, cannot be extended to all convex potentials. But it remains true for symmetric and monotone convex potentials. Keywords: finite Markov kernels, Markov commutator, symmetry group of a Markov kernel, hypergroup property, duality by intertwining, Achour-Trimèche theorem, birth and death chains, Metropolis algorithms, one-dimensional discrete wave equations.
Published: 2019

29. The X-prolyl dipeptidyl-peptidase PepX of Streptococcus thermophilus initially described as intracellular is also responsible for peptidase extracellular activity

Author: Zeeshan Hafeez, Xavier Lecomte, Céline Cakir-Kiefer, Annie Dary-Mourot, Laurent Miclo, Composés Alimentaires : Biofonctionnalités et risques Neurotoxiques (CALBINOTOX), and Université de Lorraine (UL)
Subjects: Streptococcus thermophilus, Proteolysis, [SDV]Life Sciences [q-bio], Mutant, Dipeptidyl peptidase, 03 medical and health sciences, Genetics, medicine, Extracellular, Animals, Dipeptidyl-Peptidases and Tripeptidyl-Peptidases, Chromatography, High Pressure Liquid, ComputingMilieux_MISCELLANEOUS, 030304 developmental biology, chemistry.chemical_classification, Chromatography, Reverse-Phase, 0303 health sciences, biology, medicine.diagnostic_test, Hydrolysis, 0402 animal and dairy science, Wild type, food and beverages, 04 agricultural and veterinary sciences, biology.organism_classification, 040201 dairy & animal science, Peptide Fragments, Milk, Enzyme, Biochemistry, chemistry, Animal Science and Zoology, Endorphins, Peptides, Intracellular, Peptide Hydrolases, Food Science
Abstract: This study addresses the hypothesis that the extracellular cell-associated X-prolyl dipeptidyl-peptidase activity initially described in Streptococcus thermophilus could be attributable to the intracellular X-prolyl dipeptidyl-peptidase PepX. For this purpose, a PepX-negative mutant of S. thermophilus LMD-9 was constructed by interrupting the pepX gene and named LMD-9-ΔpepX. When cultivated, the S. thermophilus LMD-9 wild type strain grew more rapidly than its ΔpepX mutant counterpart. Thus, the growth rate of the LMD-9-ΔpepX strain was reduced by a factor of 1.5 and 1.6 in milk and LM17 medium (M17 medium supplemented with 2% lactose), respectively. The negative effect of the PepX inactivation on the hydrolysis of β-casomorphin-7 was also observed. Indeed, when incubated with this peptide, the LMD-9-ΔpepX mutant cells were unable to hydrolyze it, whereas this peptide was completely degraded by the S. thermophilus LMD-9 wild type cells. This hydrolysis was not due to leakage of intracellular PepX, as no peptide hydrolysis was highlighted in cell-free filtrate of wild type strain. Therefore, based on these results, it can be presumed that though lacking an export signal, the intracellular PepX might have accessed the β-casomorphin-7 externally, perhaps via its galactose-binding domain-like fold, this domain being known to help enzymes bind to several proteins and substrates. Therefore, the identification of novel distinctive features of the proteolytic system of S. thermophilus will further enhance its credibility as a starter in milk fermentation.
Published: 2019
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30. Isoperimetric stability of boundary barycenters in the plane

Author: Laurent Miclo, Institut de Mathématiques de Toulouse UMR5219 (IMT), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1)-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Toulouse School of Economics (TSE), École des hautes études en sciences sociales (EHESS)-Institut National de la Recherche Agronomique (INRA)-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse 1 Capitole (UT1), ANR-05-PADD-0012,PRODDIG,Promotion du Développement Durable par les Indications Géographiques(2005), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées, Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Toulouse School of Economics (TSE-R), and Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National de la Recherche Agronomique (INRA)-École des hautes études en sciences sociales (EHESS)-Centre National de la Recherche Scientifique (CNRS)
Subjects: Boundary (topology), 02 engineering and technology, [MATH.MATH-CA]Mathematics [math]/Classical Analysis and ODEs [math.CA], Isoperimetric dimension, isoperimetric stability, 01 natural sciences, boundary barycenter, Mathematics::Group Theory, Dimension (vector space), Mathematics::Metric Geometry, 0101 mathematics, B- ECONOMIE ET FINANCE, Mathematics, convex domains, MSC2010: primary: 51M04, secondary: 51M25, 51M16, 52A20, 52A40, 41A25, Algebra and Number Theory, Plane (geometry), Euclidean space, Applied Mathematics, 010102 general mathematics, Mathematical analysis, Regular polygon, isoperimetric deficit, 021001 nanoscience & nanotechnology, Isoperimetric inequality on the plane, Mathematics::Differential Geometry, Geometry and Topology, Isoperimetric inequality, 0210 nano-technology, Constant (mathematics), Analysis
Abstract: International audience; Consider an open domain D on the plane, whose isoperimetric deficit is smaller than 1. This note shows that the difference between the barycenter of D and the barycenter of its boundary is bounded above by a constant times the isoperimetric deficit to the power 1/4. This power can be improved to 1/2, when D is furthermore assumed to be a convex domain, in any Euclidean space of dimension larger than 2. Keywords: Isoperimetric inequality on the plane, isoperimetric deficit, boundary barycenter, convex domains, isoperimetric stability.
Published: 2019

31. Some drawbacks of finite modified logarithmic Sobolev inequalilities

Author: Laurent Miclo, Institut de Mathématiques de Toulouse UMR5219 (IMT), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), ANR-12-BS01-0019,STAB,Stabilité du comportement asymptotique d'EDP, de processus stochastiques et de leurs discrétisations.(2012), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Université Toulouse 1 Capitole (UT1)-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UPS), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-PRES Université de Toulouse-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Institut de Mathématiques de Toulouse UMR5219 ( IMT ), Université Toulouse 1 Capitole ( UT1 ) -Université Toulouse - Jean Jaurès ( UT2J ) -Université Toulouse III - Paul Sabatier ( UPS ), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-PRES Université de Toulouse-Institut National des Sciences Appliquées - Toulouse ( INSA Toulouse ), Institut National des Sciences Appliquées ( INSA ) -Institut National des Sciences Appliquées ( INSA ) -Centre National de la Recherche Scientifique ( CNRS ), and ANR-12-BS01-0019,STAB,Stabilité du comportement asymptotique d'EDP, de processus stochastiques et de leurs discrétisations. ( 2012 )
Subjects: Logarithm, intersection method, General Mathematics, [ MATH.MATH-FA ] Mathematics [math]/Functional Analysis [math.FA], [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA], 01 natural sciences, Poincaré's inequality, Sobolev inequality, 010104 statistics & probability, Intersection, 0101 mathematics, ComputingMilieux_MISCELLANEOUS, finite irreducible Markov generator, Mathematics, AMS MSC2010: primary: 46E39, secondary: 60J27, 94A17, 60E15, 15A18, symmetrization, Markov chain, 010102 general mathematics, Mathematical analysis, umbrella sampling, Sobolev space, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Symmetrization, Spectral gap, Invariant measure, [ MATH.MATH-PR ] Mathematics [math]/Probability [math.PR], modified logarithmic Sobolev inequality
Abstract: Classically, finite modified logarithmic Sobolev inequalities are used to deduce a differential inequality for the evolution of the relative entropy with respect to the invariant measure. We will check that these inequalities are ill-behaved with respect, on one hand, to the symmetrization procedure, and on the other hand, to the umbrella sampling procedure for Poincaré inequalities. A short spectral proof of the latter method is given to estimate the spectral gap of a finite reversible Markov generator $L$ in terms of the spectral gap of the restrictions of $L$ on two subsets whose union is the whole state space and whose intersection is not empty.
Published: 2018
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32. On a gateway between continuous and discrete Bessel and Laguerre processes

Author: Pierre Patie, Laurent Miclo, Institut de Mathématiques de Toulouse UMR5219 (IMT), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Toulouse School of Economics (TSE), École des hautes études en sciences sociales (EHESS)-Institut National de la Recherche Agronomique (INRA)-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées, Cornell University [New York], Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Toulouse School of Economics (TSE-R), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National de la Recherche Agronomique (INRA)-École des hautes études en sciences sociales (EHESS)-Centre National de la Recherche Scientifique (CNRS), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1)-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), and Cornell University
Subjects: linear birth-death processes, Pure mathematics, Squared Bessel processes, Property (philosophy), Computer science, Connection (vector bundle), [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA], 01 natural sciences, Identity (music), 010104 statistics & probability, symbols.namesake, Mathematics - Analysis of PDEs, FOS: Mathematics, Ergodic theory, 0101 mathematics, continuous and discrete scaling, 010102 general mathematics, Probability (math.PR), Gateway (computer program), [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], spectral decomposition, Path (graph theory), symbols, Laguerre polynomials, intertwining, Bessel function, Mathematics - Probability, Analysis of PDEs (math.AP)
Abstract: By providing instances of approximation of linear diffusions by birth-death processes, Feller [13], has offered an original path from the discrete world to the continuous one. In this paper, by identifying an intertwining relationship between squared Bessel processes and some linear birth-death processes, we show that this connection is in fact more intimate and goes in the two directions. As by-products, we identify some properties enjoyed by the birth-death family that are inherited from squared Bessel processes. For instance, these include a discrete self-similarity property and a discrete analogue of the beta-gamma algebra. We proceed by explaining that the same gateway identity also holds for the corresponding ergodic Laguerre semi-groups. It follows again that the continuous and discrete versions are more closely related than thought before, and this enables to pass information from one semi-group to the other one., Comment: 47 pages
Published: 2018

33. Séminaire de probabilités XLIX

Author: P Petit, Jean Brossard, Patrick Cattiaux, Antoine Lejay, Mireille Capitaine, Peter Kratz, Benedikt Wilbertz, Emmanuel Boissard, Rajeev Bhaskaran, Denis Villemonais, Florian Bouguet, Paul McGill, Laurent Miclo, Arnaud Guillin, Henri Elad Altman, Koléhé Abdoulaye Coulibaly-Pasquier, Gilles Pagès, Hiroshi Tsukada, Etienne Pardoux, Laurent Serlet, Nicolas Champagnat, Christophe Leuridan, Institut de Mathématiques de Toulouse UMR5219 (IMT), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques Blaise Pascal (LMBP), Université Clermont Auvergne [2017-2020] (UCA [2017-2020])-Centre National de la Recherche Scientifique (CNRS), Université de Lorraine (UL), Biology, genetics and statistics (BIGS), Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Institut Fourier (IF ), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), TO Simulate and CAlibrate stochastic models (TOSCA), Inria Sophia Antipolis - Méditerranée (CRISAM), Laboratoire de Probabilités, Statistique et Modélisation (LPSM (UMR_8001)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Aix-Marseille Université - Faculté des Sciences (AMU SCI), Aix Marseille Université (AMU), Université Claude Bernard Lyon 1 (UCBL), Université de Lyon, Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Indian Statistical Institute [Bangalore] (ISI), Graduate School of Engineering Science [Toyonaka, Osaka], Osaka University, Donati-Martin, Catherine, Lejay, Antoine, Rouault, Alain, Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Sorbonne Université - Faculté de Médecine (SU FM), Sorbonne Université (SU), Laboratoire de Probabilités, Statistiques et Modélisations (LPSM (UMR_8001)), Graduate School of Engineering Science [Osaka], Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1)-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques Blaise Pascal - Clermont Auvergne (LMBP), Université Clermont Auvergne (UCA)-Centre National de la Recherche Scientifique (CNRS), Institut Fourier (IF), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA), Graduate School of Engineering Science, and Osaka University [Osaka]
Subjects: Quasi-stationary Distribution, Stochastic process, 010102 general mathematics, Martingale Theory, 01 natural sciences, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], 010104 statistics & probability, Large deviations, Stochastic processes, Large deviations theory, Statistical physics, 0101 mathematics, Random matrix, Diffusion processes, Martingale theory, ComputingMilieux_MISCELLANEOUS, Random Matrices, Mathematics
Abstract: International audience
Published: 2018
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34. Préface

Author: Laurent Miclo
Subjects: General Medicine
Published: 2016
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35. Ornstein-Uhlenbeck Pinball and the Poincaré Inequality in a Punctured Domain

Author: Laurent Miclo, Patrick Cattiaux, Arnaud Guillin, Emmanuel Boissard, Institut de Mathématiques de Toulouse UMR5219 (IMT), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques Blaise Pascal (LMBP), Université Clermont Auvergne [2017-2020] (UCA [2017-2020])-Centre National de la Recherche Scientifique (CNRS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), and Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)
Subjects: 010102 general mathematics, Open set, Poincaré inequality, Ornstein–Uhlenbeck process, Gaussian measure, 01 natural sciences, Domain (mathematical analysis), Combinatorics, 010104 statistics & probability, symbols.namesake, Disjoint union (topology), Mathematics::Probability, Bounded function, symbols, Hypercube, [MATH]Mathematics [math], 0101 mathematics, ComputingMilieux_MISCELLANEOUS, Mathematics
Abstract: In this paper we study the Poincare constant for the Gaussian measure restricted to $D={\mathbb R}^d - \mathbb {B}$ where $\mathbb {B}$ is the disjoint union of bounded open sets. We will mainly look at the case where the obstacles are Euclidean balls B(xi, ri) with radii ri, or hypercubes with vertices of length 2ri, and d ≥ 2. This will explain the asymptotic behavior of a d-dimensional Ornstein-Uhlenbeck process in the presence of obstacles with elastic normal reflections (the Ornstein-Uhlenbeck pinball).
Published: 2018
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36. On the Markovian Similarity

Author: Laurent Miclo, Institut de Mathématiques de Toulouse UMR5219 (IMT), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), ANR-12-BS01-0019,STAB,Stabilité du comportement asymptotique d'EDP, de processus stochastiques et de leurs discrétisations.(2012), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), and Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)
Subjects: similarity relation, Discrete mathematics, Markov chain mixing time, Markov kernel, ϕ-entropies, Markov chain, Variable-order Markov model, 010102 general mathematics, Markov process, isospectrality, convergence to equilibrium, 01 natural sciences, con-vergence to equilibrium, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], symbols.namesake, Markov generators, Balance equation, symbols, {MSC2010:} primary: 60J27, secondary: 60J35, 60J25, 05C50, 37A30, 58J53, Equivalence relation, Markov intertwinings, Markov property, 0101 mathematics, Mathematics
Abstract: International audience; Two finite Markov generators $L$ and $\widetilde L$ are said to be intertwined if there exists a Markov kernel $\Lambda$ such that$L\Lambda=\Lambda\widetilde L$.The goal of this paper is to investigate the equivalence relation between finite Markov generators obtained by imposing mutualintertwinings through invertible Markov kernels, in particular its links with the traditional similarity relation.Some consequences on the comparison of speeds of convergence to equilibrium for finite irreducible Markov processes are deduced.The situation of infinite state spaces is also quickly mentioned, by showing that the Laplacians of isospectral compact Riemannian manifolds are weakly Markov-similar.
Published: 2018
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37. Complex intertwinings and quantification of discrete free motions

Author: Laurent Miclo, Institut de Mathématiques de Toulouse UMR5219 ( IMT ), Université Toulouse 1 Capitole ( UT1 ) -Université Toulouse - Jean Jaurès ( UT2J ) -Université Toulouse III - Paul Sabatier ( UPS ), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-PRES Université de Toulouse-Institut National des Sciences Appliquées - Toulouse ( INSA Toulouse ), Institut National des Sciences Appliquées ( INSA ) -Institut National des Sciences Appliquées ( INSA ) -Centre National de la Recherche Scientifique ( CNRS ), ANR-12-BS01-0019,STAB,Stabilité du comportement asymptotique d'EDP, de processus stochastiques et de leurs discrétisations. ( 2012 ), Institut de Mathématiques de Toulouse UMR5219 (IMT), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), ANR-12-BS01-0019,STAB,Stabilité du comportement asymptotique d'EDP, de processus stochastiques et de leurs discrétisations.(2012), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), and Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)
Subjects: Statistics and Probability, Pure mathematics, Markov process, 01 natural sciences, Interpretation (model theory), symbols.namesake, Quantification, Euclidean geometry, Doob transform, 0101 mathematics, Abelian group, Eigenvalues and eigenvectors, Mathematics, Markov chain, Computer Science::Information Retrieval, MSC2010: primary: 81Q35, secondary: 47D08, 35K08, 39A12, 60J27, 010102 general mathematics, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], 010101 applied mathematics, symbols, intertwining, free motion, Complex number, Laplace operator, [ MATH.MATH-PR ] Mathematics [math]/Probability [math.PR]
Abstract: The traditional quantification of free motions on Euclidean spaces into the Laplacian is revisited as a complex intertwining obtained through Doob transforms with respect to complex eigenvectors. This approach can be applied to free motions on finitely generated discrete Abelian groups: ℤm, with m ∈ ℕ, finite tori and their products. It leads to a proposition of Markov quantification. It is a first attempt to give a probability-oriented interpretation of exp(ξL), when L is a (finite) Markov generator and ξ is a complex number of modulus 1.
Published: 2017
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38. Duality and hypoellipticity: one-dimensional case studies

Author: Laurent Miclo, Institut de Mathématiques de Toulouse UMR5219 ( IMT ), Université Toulouse 1 Capitole ( UT1 ) -Université Toulouse - Jean Jaurès ( UT2J ) -Université Toulouse III - Paul Sabatier ( UPS ), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-PRES Université de Toulouse-Institut National des Sciences Appliquées - Toulouse ( INSA Toulouse ), Institut National des Sciences Appliquées ( INSA ) -Institut National des Sciences Appliquées ( INSA ) -Centre National de la Recherche Scientifique ( CNRS ), ANR-12-BS01-0019,STAB,Stabilité du comportement asymptotique d'EDP, de processus stochastiques et de leurs discrétisations. ( 2012 ), Institut de Mathématiques de Toulouse UMR5219 (IMT), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), ANR-12-BS01-0019,STAB,Stabilité du comportement asymptotique d'EDP, de processus stochastiques et de leurs discrétisations.(2012), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), and Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)
Subjects: Statistics and Probability, Pure mathematics, Bessel 3 process, Duality (mathematics), Markov process, Type (model theory), 01 natural sciences, Measure (mathematics), strong stationary times, 010104 statistics & probability, symbols.namesake, duality by intertwining, Simple (abstract algebra), Quantification, 60F05, Hörmander’s density theorem, Doob transform, 0101 mathematics, Randomness, Mathematics, 60J60, 37A25, MSC2010: primary: 60J60, secondary: 60J35, 60H30, 35K65, 60F05, 37A25, 010102 general mathematics, Degenerate energy levels, hypoellipticity, 35K65, 16. Peace & justice, Dual (category theory), [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], symbols, 60J35, intertwining, One-dimensional diffusions, free motion, Statistics, Probability and Uncertainty, 60H30, Hörmander's density theorem, [ MATH.MATH-PR ] Mathematics [math]/Probability [math.PR]
Abstract: International audience; To visualize how the randomness of a Markov process X is spreading, one can consider subset-valued dual processes I constructed by intertwining. In the framework of one-dimensional diffu-sions, we investigate the behavior of such dual processes I in the presence of hypoellipticity for X. The Pitman type property asserting that the measure of I is a time-changed Bessel 3 process is preserved, the effect of hypoellipticity is only found at the level of the time change. It enables to recover the density theorem of Hörmander in this simple degenerate setting, as well as to construct strong stationary times by introducing different dual processes.
Published: 2017
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39. On the hypergroup property

Author: Laurent Miclo, Institut de Mathématiques de Toulouse UMR5219 (IMT), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), ANR-12-BS01-0019,STAB,Stabilité du comportement asymptotique d'EDP, de processus stochastiques et de leurs discrétisations.(2012), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), and Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)
Subjects: Pure mathematics, Markov chain, Dirichlet (minor) eigenvalues, Generalization, hypergroup property, 010102 general mathematics, biaised Ehrenfest model, Boundary (topology), Context (language use), finite birth and death processes, General Medicine, Neumann eigenvectors, Characterization (mathematics), Random walk, finite reversible Markov processes, 01 natural sciences, Convolution, AMS MSC2010: primary: 20N20, secondary: 60J05, 60J10, 15A18, 15A42, 60J80, 65F15, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], 010104 statistics & probability, Ehrenfest model, 0101 mathematics, Mathematics
Abstract: International audience; The hypergroup property satisfied by certain reversible Markov chains can be seen as a generalization of the convolution related features of class random walks on groups.Carlen, Geronimo and Loss~\cite{MR2764893} developed a method for checking this property in the context of Jacobi eigen-polynomials.A probabilistic extension of their approach is proposed here, enabling to recover the discrete example of the biased Ehrenfest model due to Eagleson \cite{MR0328162}.Next a spectral characterization is provided for finite birth and death chains enjoying the hypergroup property with respect to one of the boundary points.
Published: 2017

40. Poincaré Inequality for Dirichlet Distributions and Infinite-Dimensional Generalizations

Author: Shui Feng, Laurent Miclo, Feng-Yu Wang, Department of Mathematics and Statistics, McMaster University, Institut de Mathématiques de Toulouse UMR5219 (IMT), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Center for Applied Mathematics, Tianjin University, Department of Mathematics and Statistics [Hamilton], McMaster University [Hamilton, Ontario], Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), and Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)
Subjects: Statistics and Probability, Pure mathematics, Inequality, media_common.quotation_subject, 010102 general mathematics, 01 natural sciences, Dirichlet distribution, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], 010104 statistics & probability, symbols.namesake, symbols, 0101 mathematics, Mathematics, media_common
Abstract: International audience; For any N ≥ 2 and α = (α 1 , · · · , α N +1) ∈ (0, ∞) N +1 , let µ(N) α be the corresponding Dirichlet distribution on ∆(N) :=x = (xi)1≤i≤N ∈ [0,1]N : |x|1 := P1≤i≤N xi ≤1. We prove the Poincar´e inequality µ(N) α (f2) ≤ 1 αN+1 Z∆(N)n1−|x|1 N X n=1 xn(∂nf)2oµ(N) α (dx) + µ(N) α (f)2, for f ∈ C1(∆(N)), and show that the constant 1 αN+1 is sharp. Consequently, the associated diﬀusion process on ∆(N) converges to µ(N) α in L2(µ(N) α ) at the exponentially rate αN+1. The whole spectrum of the generator is also characterized. Moreover, the sharp Poincar´e inequality is extended to the inﬁnite-dimensional setting, and the spectral gap of the corresponding discrete model is derived.
Published: 2017

41. Spectral decompositions and $\mathbb{L}^2$-operator norms of toy hypocoercive semi-groups

Author: Laurent Miclo, Sébastien Gadat, Institut de Mathématiques de Toulouse UMR5219 (IMT), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), and Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)
Subjects: Physics, Numerical Analysis, kinetic evolution equations, hypocoercive Markovian semi-groups, 010102 general mathematics, Scalar (mathematics), Kinetic energy, convergence to equilibrium, 01 natural sciences, spectral decompositions, $\LL^2$-operator norms, Matrix decomposition, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Combinatorics, 010104 statistics & probability, Modeling and Simulation, 35K65, 35H10, 47A10, 15A18, 15A60, 37A30, 60J60, Ornstein-Ulhenbeck generator, Invariant measure, 0101 mathematics, Arithmetic, Eigenvalues and eigenvectors
Abstract: 56 pages; International audience; For any $a>0$, consider the hypocoercive generators $y\partial_x+a\partial_y^2-y\partial_y$ and $y\partial_x-ax\partial_y+\partial_y^2-y\partial_y$, respectively for $(x,y)\in\RR/(2\pi\ZZ)\times\RR$ and $(x,y)\in\RR\times\RR$. The goal of the paper is to obtain exactly the $\LL^2(\mu_a)$-operator norms of the corresponding Markov semi-group at any time, where $\mu_a$ is the associated invariant measure. The computations are based on the spectral decomposition of the generator and especially on the scalar products of the eigenvectors. The motivation comes from an attempt to find an alternative approach to classical ones developed to obtain hypocoercive bounds for kinetic models.
Published: 2013
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42. A stochastic algorithm finding $p$-means on the circle

Author: Laurent Miclo, Marc Arnaudon, Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Institut de Mathématiques de Toulouse UMR5219 (IMT), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1)-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Institut de Mathématiques de Bordeaux ( IMB ), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux ( UB ) -Institut Polytechnique de Bordeaux ( Bordeaux INP ) -Centre National de la Recherche Scientifique ( CNRS ), Institut de Mathématiques de Toulouse UMR5219 ( IMT ), Université Toulouse 1 Capitole ( UT1 ) -Université Toulouse - Jean Jaurès ( UT2J ) -Université Toulouse III - Paul Sabatier ( UPS ), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-PRES Université de Toulouse-Institut National des Sciences Appliquées - Toulouse ( INSA Toulouse ), Institut National des Sciences Appliquées ( INSA ) -Institut National des Sciences Appliquées ( INSA ) -Centre National de la Recherche Scientifique ( CNRS ), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), and Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)
Subjects: Statistics and Probability, spectral gap at small temperature, homogenization, first: 60D05, secondary: 58C35, 60J75, 37A30, 47G20, 53C21, 60J65, 010103 numerical & computational mathematics, 01 natural sciences, Homogenization (chemistry), 010104 statistics & probability, Stochastic algorithms, FOS: Mathematics, 0101 mathematics, intrinsic p-means, Brownian motion, ComputingMilieux_MISCELLANEOUS, Gibbs measures, Probability measure, Mathematics, Probability (math.PR), probability measures on compact Riemannian manifolds, Riemannian manifold, intrinsic $p$-means, instantaneous invariant measures, probability mea-sures on compact Riemannian manifolds, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Simulated annealing, Spectral gap, simulated annealing, Algorithm, Random variable, [ MATH.MATH-PR ] Mathematics [math]/Probability [math.PR], Mathematics - Probability
Abstract: A stochastic algorithm is proposed, finding some elements from the set of intrinsic $p$-mean(s) associated to a probability measure $\nu$ on a compact Riemannian manifold and to $p\in[1,\infty)$. It is fed sequentially with independent random variables $(Y_n)_{n\in \mathbb{N}}$ distributed according to $\nu$, which is often the only available knowledge of $\nu$. Furthermore, the algorithm is easy to implement, because it evolves like a Brownian motion between the random times when it jumps in direction of one of the $Y_n$, $n\in\mathbb{N}$. Its principle is based on simulated annealing and homogenization, so that temperature and approximations schemes must be tuned up (plus a regularizing scheme if $\nu$ does not admit a H\"{o}lderian density). The analysis of the convergence is restricted to the case where the state space is a circle. In its principle, the proof relies on the investigation of the evolution of a time-inhomogeneous $\mathbb{L}^2$ functional and on the corresponding spectral gap estimates due to Holley, Kusuoka and Stroock. But it requires new estimates on the discrepancies between the unknown instantaneous invariant measures and some convenient Gibbs measures., Comment: Published at http://dx.doi.org/10.3150/15-BEJ728 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)
Published: 2016
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43. On nodal domains and higher-order Cheeger inequalities of finite reversible Markov processes

Author: Laurent Miclo, Ramin Javadi, and Amir Daneshgar
Subjects: Discrete mathematics, Statistics and Probability, Physical constant, Applied Mathematics, Spectrum (functional analysis), Markov process, Eigenfunction, Mathematics::Spectral Theory, Cheeger’s inequality, Reversible Markovian generator, Optimal partitions of state space, Cheeger constant (graph theory), Dirichlet distribution, symbols.namesake, Principal Dirichlet eigenvalues, Dirichlet connectivity spectra, Nodal domains of eigenfunctions, Modeling and Simulation, Modelling and Simulation, symbols, State space, Spectral decomposition, Finite set, Markov processes on discrete cycles, Mathematics
Abstract: Let L be a reversible Markovian generator on a finite set V . Relations between the spectral decomposition of L and subpartitions of the state space V into a given number of components which are optimal with respect to min–max or max–min Dirichlet connectivity criteria are investigated. Links are made with higher-order Cheeger inequalities and with a generic characterization of subpartitions given by the nodal domains of an eigenfunction. These considerations are applied to generators whose positive rates are supported by the edges of a discrete cycle Z N , to obtain a full description of their spectra and of the shapes of their eigenfunctions, as well as an interpretation of the spectrum through a double-covering construction. Also, we prove that for these generators, higher Cheeger inequalities hold, with a universal constant factor 48.
Published: 2012
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44. Variability of Hydrolysis of β-, αs1-, and αs2-Caseins by 10 Strains of Streptococcus thermophilus and Resulting Bioactive Peptides

Author: Emilie Brusseaux, Clarisse Perrin, Chantal Poirson, Nawara Jameh, Emeline Roux, Magali Genay, Laurent Miclo, Annie Dary, Unité de Recherches Animal et Fonctionnalités des Produits Animaux (URAFPA), Institut National de la Recherche Agronomique (INRA)-Université de Lorraine (UL), Université de Lorraine (UL), and Université de Lorraine (UL)-Institut National de la Recherche Agronomique (INRA)
Subjects: Streptococcus thermophilus, animal structures, medicine.medical_treatment, Molecular Sequence Data, Angiotensin-Converting Enzyme Inhibitors, Peptide, Microbiology, 03 medical and health sciences, Hydrolysis, chemistry.chemical_compound, 0404 agricultural biotechnology, Bacterial Proteins, Casein, cell envelope proteinase, [SDV.IDA]Life Sciences [q-bio]/Food engineering, medicine, Animals, Amino Acid Sequence, casein hydrolysis, 030304 developmental biology, chemistry.chemical_classification, 0303 health sciences, Protease, biology, Serine Endopeptidases, Caseins, 04 agricultural and veterinary sciences, General Chemistry, biology.organism_classification, 040401 food science, Lactic acid, chemistry, Biochemistry, bioactive peptide, protéinase, Cattle, Cell envelope, Peptides, General Agricultural and Biological Sciences, Bacteria
Abstract: International audience; Milk proteins contain numerous potential bioactive peptides, which may be released by digestive proteases or by the proteolytic system of lactic acid bacteria during food processing. The capacity of Streptococcus thermophilus to generate peptides, especially bioactive peptides, from bovine caseins was investigated. Strains expressing various levels of the cell envelope proteinase, PrtS, were incubated with alpha(s1)-, alpha(s2)-, or beta-casein. Analysis of the supernatants by LC-ESI-MS/MS showed that the beta-casein was preferentially hydrolyzed, followed by alpha(s2)-casein and then alpha(s1)-casein. Numbers and types of peptides released were strain-dependent. Hydrolysis appeared to be linked with the accessibility of different casein regions by protease. Analysis of bonds hydrolyzed in the region 1-23 of alpha(s1)-casein suggests that PrtS is at least in part responsible for the peptide production. Finally, among the generated peptides, 13 peptides from beta-casein, 5 from alpha(s2)-casein, and 2 from alpha(s1)-casein have been reported as bioactive, 15 of them being angiotensin-converting enzyme inhibitors.
Published: 2012
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45. Isolation and identification of antioxidative peptides from bovine α-lactalbumin

Author: Marie-Andrée N’Negue, Jean-Michel Girardet, Leïla Sadat, Laurent Miclo, Jean-Luc Gaillard, and Céline Cakir-Kiefer
Subjects: Lactalbumin, chemistry.chemical_classification, Whey protein, Antioxidant, ABTS, Chromatography, medicine.medical_treatment, Peptide, Applied Microbiology and Biotechnology, chemistry.chemical_compound, chemistry, Biochemistry, Thermolysin, medicine, Trolox, Gallic acid, Food Science
Abstract: The second main bovine whey protein, α-lactalbumin, was hydrolyzed by thermolysin at 70 °C, i.e., in a molten-globule conformational state susceptible to enzyme attack, for production of small peptides with potential antioxidative properties. The main thermolytic fragments were then purified by reversed-phase liquid chromatography and identified by mass spectrometry. Antioxidant activities of the protein, its thermolytic hydrolyzate, and pure peptides were evaluated using 2,2′-azinobis[3-ethylbenzothiazoline-6-sulfonate] (ABTS+) radical-scavenging activity. The whole protein and its hydrolyzate exhibited antioxidant activities comparable with that of Trolox, a vitamin E analog. Among the thermolytic fragments, five peptides, all containing at least one Tyr or Trp residue located at one of the extremities of the sequence, displayed the most efficient antioxidant activities. In particular, Ile101-Asn-Tyr-Trp104 and Leu115-Asp-Gln-Trp118 possessed remarkable radical-scavenging capacity, 5-fold and 10-fold higher, respectively, than those of gallic acid and Trolox tested under the same experimental conditions.
Published: 2011
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46. In Vitro Digestibility of α-Casozepine, a Benzodiazepine-like Peptide from Bovine Casein, and Biological Activity of Its Main Proteolytic Fragment

Author: Marie Trabalon, Jean-Luc Gaillard, François Laurent, Laurent Miclo, Annie Dary, Yves Le Roux, Céline Cakir-Kiefer, and Frédérique Balandras
Subjects: Male, animal structures, medicine.drug_class, Proteolysis, Peptide, Models, Biological, Anxiolytic, Hydrolysate, Casein, medicine, Animals, Chymotrypsin, Humans, Trypsin, Rats, Wistar, chemistry.chemical_classification, medicine.diagnostic_test, Chemistry, Hydrolysis, Caseins, Biological activity, General Chemistry, Peptide Fragments, In vitro, Rats, Biochemistry, Cattle, Digestion, General Agricultural and Biological Sciences
Abstract: α-Casozepine is a peptide, corresponding to the sequence 91-100 of the bovine α(s1)-casein, displaying anxiolytic activity in the rat. The α(s1)-casein tryptic hydrolysate containing this peptide decreases stress effects after oral administration in various species including man. Therefore, the stability of this peptide toward gastric and pancreatic proteases has been assessed by using pepsin, chymotrypsin/trypsin, Corolase PP, pepsin followed by chymotrypsin/trypsin or pepsin followed by Corolase PP. α-Casozepine was slowly degraded by chymotrypsin, much more sensitive to pepsin and Corolase PP but not completely destroyed after 4 h kinetics. The bonds in the region 91 to 95 of the α-casozepine were totally resistant to hydrolysis by all studied proteases. Surprisingly, a fragment, corresponding to the sequence 91-97 and found in all the hydrolysis media in significant amount, possessed an anxiolytic activity in three behavioral tests measuring this parameter. This peptide could participate in the in vivo activity of α-casozepine.
Published: 2011
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47. Identification of phosphorylation sites of equineβ-casein isoforms

Author: Jean-Luc Gaillard, Catherine Corbier, Laurent Miclo, Jean-Michel Girardet, Daniel Mollé, and Aurélie Matéos
Subjects: Gene isoform, Chromatography, Electrospray ionization, Organic Chemistry, Phosphate, Tandem mass spectrometry, Trypsin, Analytical Chemistry, chemistry.chemical_compound, Affinity chromatography, chemistry, Biochemistry, medicine, Phosphorylation, Peptide sequence, Spectroscopy, medicine.drug
Abstract: Equine beta-casein is phosphorylated at variable degrees and isoforms carrying 3 to 7 phosphate groups (3P-7P) have been found in milk, but the phosphorylated amino acid residues of each isoform are not yet identified. In the present work, the different phosphorylation variants were first isolated by ion-exchange chromatography and then hydrolysed by trypsin to generate caseinophosphopeptides (CPPs), each containing all the potential phosphorylation sites. The equine CPPs were prepared by metal oxide affinity chromatography, a method based on the affinity of phosphate groups towards titanium dioxide immobilized onto a micro-column. This method turned out to be an efficient tool to separate the CPPs Arg(1)-Lys(34) and Glu(4)-Lys(34) from non-phosphorylated peptides. Purification was achieved by reversed-phase high-performance liquid chromatography (RP-HPLC) and each CPP was hydrolyzed by endoproteinase Glu-C. Finally, the digests were analyzed by RP-HPLC/electrospray ionization mass spectrometry (RP-HPLC/ESI-MS) and identified by nano-electrospray ionization tandem mass spectrometry (nESI-MS/MS) to locate the phosphorylated sites of the beta-casein isoforms 4P-7P with accuracy. Thus, the isoform 4P was found to be phosphorylated on residues Ser(9), Ser(23), Ser(24), and Ser(25). Addition of phosphate groups on Ser(18), Thr(12), and Ser(10) led to the formation of the isoforms 5P-7P, respectively. The results indicated that the in vivo phosphorylation of the equine beta-casein follows a sequential way and is not randomly performed.
Published: 2010
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48. On Times to Quasi-stationarity for Birth and Death Processes

Author: Laurent Miclo and Persi Diaconis
Subjects: Statistics and Probability, General Mathematics, Mathematical analysis, Probabilistic logic, State (functional analysis), Birth–death process, Exponential function, Dirichlet eigenvalue, State space, Applied mathematics, Statistics, Probability and Uncertainty, Eigenvalues and eigenvectors, Mathematics, Generator (mathematics)
Abstract: The purpose of this paper is to present a probabilistic proof of the well-known result stating that the time needed by a continuous-time finite birth and death process for going from the left end to the right end of its state space is a sum of independent exponential variables whose parameters are the negatives of the eigenvalues of the underlying generator when the right end is treated as an absorbing state. The exponential variables appear as fastest strong quasi-stationary times for successive dual processes associated to the original absorbed process. As an aftermath, we get an interesting probabilistic representation of the time marginal laws of the process in terms of “local equilibria.”
Published: 2009
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49. On eigenfunctions of Markov processes on trees

Author: Laurent Miclo, Laboratoire d'Analyse, Topologie, Probabilités (LATP), Université Paul Cézanne - Aix-Marseille 3-Université de Provence - Aix-Marseille 1-Centre National de la Recherche Scientifique (CNRS), and Miclo, Laurent
Subjects: Statistics and Probability, [MATH.MATH-PR] Mathematics [math]/Probability [math.PR], Pure mathematics, Markov process, isospectral partition, 60J80, 15A18, 49R50, 26A48, Markov processes on trees, 01 natural sciences, Dirichlet distribution, Cheeger inequalities, Combinatorics, 010104 statistics & probability, symbols.namesake, nodal domains, Probability theory, spectral gap, 0101 mathematics, Eigenvalues and eigenvectors, Mathematics, 010102 general mathematics, eigendecomposition of generators, birth and death processes, Eigenfunction, Minimax, Birth–death process, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], symbols, Spectral gap, Statistics, Probability and Uncertainty, Dirichlet eigenproblems, Analysis
Abstract: International audience; We begin by studying the eigenvectors associated to irreducible finite birth and death processes, showing that the $i^{\mathrm{th}}$ nontrivial eigenvector $\varphi_i$ admits a succession of $i$ decreasing or increasing stages, each of them crossing zero. Imbedding naturally the finite state space into a continuous segment, one can unequivocally define the zeros of $\varphi_i$, which are interlaced with those of $\varphi_{i+1}$. These kind of results are deduced from a general investigation of minimax multi-sets Dirichlet eigenproblems, which leads to a direct construction of the eigenvectors associated to birth and death processes. This approach can be generically extended to eigenvectors of Markov processes living on trees. This enables to reinterpret the eigenvalues and the eigenvectors in terms of the previous Dirichlet eigenproblems and a more general conjecture is presented about related higher order Cheeger inequalities. Finally, we carefully study the geometric structure of the eigenspace associated to the spectral gap on trees.
Published: 2007
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50. Modulations de l’activité cérébrale par l’α-casozépine, un peptide laitier aux propriétés anxiolytiques

Author: Catherine Chaumontet, Daniel Tomé, Simon Benoit, Laurent Miclo, Céline Cakir-Kiefer, Physiologie de la Nutrition et du Comportement Alimentaire (PNCA), Institut National de la Recherche Agronomique (INRA)-AgroParisTech, Unité de Recherches Animal et Fonctionnalités des Produits Animaux (URAFPA), Université de Lorraine (UL)-Institut National de la Recherche Agronomique (INRA), AgroParisTech-Institut National de la Recherche Agronomique (INRA), and Institut National de la Recherche Agronomique (INRA)-Université de Lorraine (UL)
Subjects: 0303 health sciences, 03 medical and health sciences, 0302 clinical medicine, Nutrition and Dietetics, 030309 nutrition & dietetics, Endocrinology, Diabetes and Metabolism, [SDV]Life Sciences [q-bio], Internal Medicine, 030209 endocrinology & metabolism, ComputingMilieux_MISCELLANEOUS, 3. Good health
Abstract: Introduction et but de l’etude L’hydrolysat trypsique de la caseine α s1 de lait bovin possede des proprietes anxiolytiques reconnues chez differentes especes animales ainsi que chez l’homme. En outre, contrairement aux benzodiazepines, classe de medicaments la plus prescrite en tant qu’anxiolytiques, l’ hydrolysat trypsique de caseine ne presente pas d’accoutumance, de dependance, de sedation et de toxicite. L’hydrolysat est commercialise sous la forme de complement alimentaire utilise en medecine humaine et veterinaire (allegations obtenues par l’Afssa et la DGCCRF). La recherche d’une molecule porteuse du mecanisme d’action a abouti a l’α-casozepine, un decapeptide dont les proprietes anxiolytiques ont pu etre retrouvees chez le rongeur. Son affinite pour le recepteur Gaba A a permis de rapprocher l’α-casozepine des molecules de la famille des benzodiazepines, malgre une affinite plus faible que le diazepam, une benzodiazepine de reference. Bien qu’une action centrale reste l’hypothese principale du mecanisme d’action de l’α-casozepine, aucune regulation de l’activite de zones cerebrales n’a ete montree auparavant. Ainsi, cette etude s’interesse a caracteriser chez la souris par un marquage de l’activite neuronale, les zones cerebrales impliquees dans la diminution de l’anxiete suite a une administration d’α-casozepine. Materiel et methodes Des souris Swiss sont habitues a un regime substituant les proteines laitieres de l’alimentation par des proteines de soja, afin d’empecher la formation de peptides laitiers endogenes. Les animaux sont places dans une situation anxiogene (boite claire–obscure) a la suite d’une injection intraperitoneale d’α-casozepine (1 mg/kg), de diazepam (1 mg/kg) ou du vehicule ayant servi a solubiliser ces molecules et perfuses au formol 1 h 30 apres ce stimulus. Les profils de l’expression cerebrale de c-Fos (un marqueur de l’activite neuronale) sont reveles par immunofluorescence sur des coupes sagittales de cerveaux congeles. Resultats Les effets anxiolytiques de l’α-casozepine chez la souris ont ete confirmes au moyen du dispositif de la boite claire–obscure. Concernant les etudes d’immunofluorescence, une diminution de l’expression de c-Fos au niveau du cortex prefrontal, de l’hippocampe, du noyau accumbens et de l’hypothalamus a ete constatee apres administration de l’α-casozepine en comparaison avec le vehicule. Ces profils sont identiques a ceux suite a une injection de diazepam. Une augmentation de l’expression de c-Fos au niveau de l’amygdale, observee uniquement apres administration d’α-casozepine indique un mecanisme d’action different de celui du diazepam. Conclusion L’administration d’α-casozepine par voie intraperitoneale permet une modulation de l’activite neuronale dans differentes regions impliquees dans la regulation de l’anxiete, ce qui permet en partie d’expliquer l’activite anxiolytique du peptide. Une liaison specifique de l’α-casozepine sur un sous-type de recepteur Gaba A (α 2 β 3 γ 2 ), dont la repartition coincide avec les zones regulees par l’α-casozepine et qui est le mediateur des effets anxiolytiques des benzodiazepines, pourrait etre envisagee. Un mecanisme d’action different de celui du diazepam pourrait etre a l’origine de l’absence d’effet secondaire associee a l’hydrolysat trypsique de caseine : l’activation d’une population de neurones gabaergiques dans cette region pourrait aussi etre a l’origine de l’anxiolyse declenchee par le peptide.
Published: 2015
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