Institut de Mathématiques de Bordeaux

Providing therapies tailored to each patient is the vision of precision medicine, enabled by the increasing ability to capture extensive data about individual patients. In this position paper, we argue that the second enabling pillar towards this vision is the increasing power of computers and algorithms to learn, reason, and build the 'digital twin' of a patient. Computational models are boosting the capacity to draw diagnosis and prognosis, and future treatments will be tailored not only to current health status and data, but also to an accurate projection of the pathways to restore health by model predictions. The early steps of the digital twin in the area of cardiovascular medicine are reviewed in this article, together with a discussion of the challenges and opportunities ahead. We emphasize the synergies between mechanistic and statistical models in accelerating cardiovascular research and enabling the vision of precision medicine.

Abstract Ethylphenols are important aromatic compounds of red wines. These compounds are formed in wines by some yeast species belonging to the genus Brettanomyces/Dekkera in the presence of hydroxycinnamic acids. These volatile phenols are responsible for the ‘phenolic’, ‘animal’ and ‘stable’ off‐odours found in certain red wines. The results presented show that the synthesis of the high quantities of ethylphenols found in the ‘phenolic’ red wines can occur during the ageing of wines having normally completed their alcoholic and malo‐lactic fermentations. This olfactory fault caused by Brettanomyces/Dekkera is found more frequently than the classical ‘mousy‐taint’ attributed to this yeast genus. In addition, the study of the mechanisms of biosynthesis of ethylphenols by Brettanomyces/Dekkera has shown the sequential activities of two enzymes. The first, is a cinnamate decarboxylase (CD), which assures the transformation of certain cinnamic acids into the correspondent vinylphenols; the second is a vinylphenol reductase, which catalyses the reduction of vinylphenols into ethylphenols. The CD activity of Brettanomyces/Dekkera is not inhibited by the polyphenolic compounds of red wines (procyanidins and catechins) while these compounds do inhibit the CD activity of Saccharomyces cerevisiae. On the other hand, the substrate specificities of the CD activities of Brettanomyces/Dekkera and Saccharomyces are different.

Despite internal complexity, tumor growth kinetics follow relatively simple laws that can be expressed as mathematical models. To explore this further, quantitative analysis of the most classical of these were performed. The models were assessed against data from two in vivo experimental systems: an ectopic syngeneic tumor (Lewis lung carcinoma) and an orthotopically xenografted human breast carcinoma. The goals were threefold: 1) to determine a statistical model for description of the measurement error, 2) to establish the descriptive power of each model, using several goodness-of-fit metrics and a study of parametric identifiability, and 3) to assess the models' ability to forecast future tumor growth. The models included in the study comprised the exponential, exponential-linear, power law, Gompertz, logistic, generalized logistic, von Bertalanffy and a model with dynamic carrying capacity. For the breast data, the dynamics were best captured by the Gompertz and exponential-linear models. The latter also exhibited the highest predictive power, with excellent prediction scores (≥80%) extending out as far as 12 days in the future. For the lung data, the Gompertz and power law models provided the most parsimonious and parametrically identifiable description. However, not one of the models was able to achieve a substantial prediction rate (≥70%) beyond the next day data point. In this context, adjunction of a priori information on the parameter distribution led to considerable improvement. For instance, forecast success rates went from 14.9% to 62.7% when using the power law model to predict the full future tumor growth curves, using just three data points. These results not only have important implications for biological theories of tumor growth and the use of mathematical modeling in preclinical anti-cancer drug investigations, but also may assist in defining how mathematical models could serve as potential prognostic tools in the clinic.

We present a new Lagrangian cell-centered scheme for two-dimensional compressible flows. The primary variables in this new scheme are cell-centered, i.e., density, momentum, and total energy are defined by their mean values in the cells. The vertex velocities and the numerical fluxes through the cell interfaces are not computed independently, contrary to standard approaches, but are evaluated in a consistent manner due to an original solver located at the nodes. The main new feature of the algorithm is the introduction of four pressures on each edge, two for each node on each side of the edge. This extra degree of freedom allows us to construct a nodal solver which fulfills two properties. First, the conservation of momentum and total energy is ensured. Second, a semidiscrete entropy inequality is provided. In the case of a one-dimensional flow, the solver reduces to the classical Godunov acoustic solver: it can be considered as its two-dimensional generalization. Many numerical tests are presented. They are representative test cases for compressible flows and demonstrate the robustness and the accuracy of this new solver.

Speckle noise is an inherent problem in coherent imaging systems such as synthetic aperture radar. It creates strong intensity fluctuations and hampers the analysis of images and the estimation of local radiometric, polarimetric, or interferometric properties. Synthetic aperture radar (SAR) processing chains thus often include a multilooking (i.e., averaging) filter for speckle reduction, at the expense of a strong resolution loss. Preservation of point-like and fine structures and textures requires to adapt locally the estimation. Nonlocal (NL)-means successfully adapt smoothing by deriving data-driven weights from the similarity between small image patches. The generalization of nonlocal approaches offers a flexible framework for resolution-preserving speckle reduction. We describe a general method, i.e., NL-SAR, that builds extended nonlocal neighborhoods for denoising amplitude, polarimetric, and/or interferometric SAR images. These neighborhoods are defined on the basis of pixel similarity as evaluated by multichannel comparison of patches. Several nonlocal estimations are performed, and the best one is locally selected to form a single restored image with good preservation of radar structures and discontinuities. The proposed method is fully automatic and handles single and multilook images, with or without interferometric or polarimetric channels. Efficient speckle reduction with very good resolution preservation is demonstrated both on numerical experiments using simulated data, airborne, and spaceborne radar images. The source code of a parallel implementation of NL-SAR is released with this paper.

Quantum magnetism originates from the exchange coupling between quantum mechanical spins. Here, we report on the observation of nearest-neighbor magnetic correlations emerging in the many-body state of a thermalized Fermi gas in an optical lattice. The key to obtaining short-range magnetic order is a local redistribution of entropy, which allows temperatures below the exchange energy for a subset of lattice bonds. When loading a repulsively interacting gas into either dimerized or anisotropic simple cubic configurations of a tunable-geometry lattice, we observe an excess of singlets as compared with triplets consisting of two opposite spins. For the anisotropic lattice, the transverse spin correlator reveals antiferromagnetic correlations along one spatial axis. Our work facilitates addressing open problems in quantum magnetism through the use of quantum simulation.

The allocation of surgeries to operating rooms (ORs) is a challenging combinatorial optimization problem. There is also significant uncertainty in the duration of surgical procedures, which further complicates assignment decisions. In this paper, we present stochastic optimization models for the assignment of surgeries to ORs on a given day of surgery. The objective includes a fixed cost of opening ORs and a variable cost of overtime relative to a fixed length-of-day. We describe two types of models. The first is a two-stage stochastic linear program with binary decisions in the first stage and simple recourse in the second stage. The second is its robust counterpart, in which the objective is to minimize the maximum cost associated with an uncertainty set for surgery durations. We describe the mathematical models, bounds on the optimal solution, and solution methodologies, including an easy-to-implement heuristic. Numerical experiments based on real data from a large health-care provider are used to contrast the results for the two models and illustrate the potential for impact in practice. Based on our numerical experimentation, we find that a fast and easy-to-implement heuristic works fairly well, on average, across many instances. We also find that the robust method performs approximately as well as the heuristic, is much faster than solving the stochastic recourse model, and has the benefit of limiting the worst-case outcome of the recourse problem.

1. Introduced predators account for a large part of the extinction of endemic insular species, which constitutes a major component of the loss of biodiversity among vertebrates. Eradication of alien predators from these ecosystems is often considered the best solution. 2. In some ecosystems, however, it can generate a greater threat for endemic prey through what is called the ‘mesopredator release’. This process predicts that, once superpredators are suppressed, a burst of mesopredators may follow which leads their shared prey to extinction. 3. This process is studied through a mathematical model describing a three species system (prey–mesopredator–superpredator). Analysis of the model, with and without control of meso‐ and superpredators, shows that this process does indeed exist and can drive shared prey to rapid extinction. 4. This work emphasizes that, although counter‐intuitive, eradication of introduced superpredators, such as feral domestic cats, is not always the best solution to protect endemic prey when introduced mesopredators, such as rats, are also present.

A hyperbolic two-phase flow model involving five partial differential equations is constructed for liquid–gas interface modelling. The model is able to deal with interfaces of simple contact where normal velocity and pressure are continuous as well as transition fronts where heat and mass transfer occur, involving pressure and velocity jumps. These fronts correspond to extra waves in the system. The model involves two temperatures and entropies but a single pressure and a single velocity. The closure is achieved by two equations of state that reproduce the phase diagram when equilibrium is reached. Relaxation toward equilibrium is achieved by temperature and chemical potential relaxation terms whose kinetics is considered infinitely fast at specific locations only, typically at evaporation fronts. Thus, metastable states are involved for locations far from these fronts. Computational results are compared to the experimental ones. Computed and measured front speeds are of the same order of magnitude and the same tendency of increasing front speed with initial temperature is reported. Moreover, the limit case of evaporation fronts propagating in highly metastable liquids with the Chapman–Jouguet speed is recovered as an expansion wave of the present model in the limit of stiff thermal and chemical relaxation.

This monograph provides a comprehensive and self-contained study on the theory of water waves equations, a research area that has been very active in recent years. The vast literature devoted to the study of water waves offers numerous asymptotic models. Which model provides the best description of waves such as tsunamis or tidal waves? How can water waves equations be transformed into simpler asymptotic models for applications in, for example, coastal oceanography? This book proposes a simple and robust framework for studying these questions.The book should be of interest to graduate students and researchers looking for an introduction to water waves equations or for simple asymptotic models to describe the propagation of waves. Researchers working on the mathematical analysis of nonlinear dispersive equations may also find inspiration in the many (and sometimes new) models derived here, as well as precise information on their physical relevance.

This article proposes a surprisingly simple framework for the random generation of combinatorial configurations based on what we call Boltzmann models . The idea is to perform random generation of possibly complex structured objects by placing an appropriate measure spread over the whole of a combinatorial class – an object receives a probability essentially proportional to an exponential of its size. As demonstrated here, the resulting algorithms based on real-arithmetic operations often operate in linear time. They can be implemented easily, be analysed mathematically with great precision, and, when suitably tuned, tend to be very efficient in practice.

Abstract p ‐Hydroxymercuribenzoic acid (pHMB), reacts reversibly with thiols. Using this principle, an extraction method of the thiols present in wines has been established. Injecting the extracts from Vitis vinifera L. var. Sauvignon wines on to a gas‐chromatographic column using the purge and trap technique and a flame photometric detector enabled us to discover some sulphur compounds present in wines from this cultivar. On several capillary columns of different polarities, one of the peaks possesses the same retention time as the potent odourant, 4‐mercapto‐4‐methylpentan‐2‐one, which evokes odours of box tree and cat urine. The identification of this compound in Sauvignon wines was confirmed by mass spectrometry. These results confirm previous work obtained by coupling gas chromatography and olfactometry, and show that this thiol is present in Sauvignon wines. The perception threshold of this compound in water and in wine is very low (close to 0.1 ng/1 and 3 ng/1s respectively) and despite its low concentration in Sauvignon wines, 4‐mercapto‐4‐methylpentan‐2‐one seems to play a major role in the varietal aroma of the wines from this cultivar.

Abstract Enthesopathies—that is, “musculo‐skeletal stress markers”—are frequently used to reconstruct past lifestyles and activity patterns. Relatively little attention has been paid in physical anthropology to methodological gaps implicit in this approach: almost all methods previously employed neglect current medical insights into enthesopathies and the distinction between healthy and pathological aspects has been arbitrary. This study presents a new visual method of studying fibrocartilaginous enthesopathies of the upper limb (modified from Villotte: Bull Mém Soc Anthropol Paris n.s. 18 (2006) 65–85), and application of this method to 367 males who died between the 18th and 20th centuries, from four European identified skeletal collections: the Christ Church Spitalfields Collection, the identified skeletal collection of the anthropological museum of the University of Coimbra, and the Sassari and Bologna collections of the museum of Anthropology, University of Bologna. The analysis, using generalized estimating equations to model repeated binary outcome variables, has established a strong link between enthesopathies and physical activity: men with occupations involving heavy manual tasks have significantly ( P ‐value < 0.001) more lesions of the upper limbs than nonmanual and light manual workers. Probability of the presence of an enthesopathy also increases with age and is higher for the right side compared with the left. Our study failed to distinguish significant differences between the collections when adjusted for the other effects. It appears that enthesopathies can be used to reconstruct past lifestyles of populations if physical anthropologists: 1) pay attention to the choice of entheses in their studies and 2) use appropriate methods. Am J Phys Anthropol, 2010. © 2009 Wiley‐Liss, Inc.

Dantzig-Wolfe decomposition as applied to an integer program is a specific form of problem reformulation that aims at providing a tighter linear programming relaxation bound. The reformulation gives rise to an integer master problem, whose typically large number of variables is dealt with implicitly by using an integer programming column generation procedure, also known as branch-and-price algorithm. There is a large class of integer programs that are well suited for this solution technique. In this paper, we propose to base the Dantzig-Wolfe decomposition of an integer program on the discretization of the integer polyhedron associated with a subsystem of constraints (as opposed to its convexification). This allows us to formulate the integrality restriction directly on the master variables and sets a theoretical framework for dealing with specific issues such as branching or the introduction of cutting planes in the master. We discuss specific branching schemes and their effect on the structure of the column generation subproblem. We give theoretical bounds on the complexity of the separation process and the extent of the modifications to the column generation subproblem. Our computational tests on the cutting stock problem and a generalisation—the cutting strip problem—show that, in practice, all fractional solutions can be eliminated using branching rules that preserve the tractability of the subproblem, but there is a trade-off between branching efficiency and subproblem tractability.

This study investigates a fictitious domain model for the numerical solution of various incompressible viscous flows. It is based on the so-called Navier–Stokes/Brinkman and energy equations with discontinuous coefficients all over an auxiliary embedding domain. The solid obstacles or walls are taken into account by a penalty technique. Some volumic control terms are directly introduced in the governing equations in order to prescribe immersed boundary conditions. The implicit numerical scheme, which uses an upwind finite volume method on staggered Cartesian grids, is of second-order accuracy in time and space. A multigrid local mesh refinement is also implemented, using the multi-level Zoom Flux Interface Correction (FIC) method, in order to increase the precision where it is needed in the domain. At each time step, some iterations of the augmented Lagrangian method combined with a preconditioned Krylov algorithm allow the divergence-free velocity and pressure fields be solved for. The tested cases concern external steady or unsteady flows around a circular cylinder, heated or not, and the channel flow behind a backward-facing step. The numerical results are shown in good agreement with other published numerical or experimental data. Copyright © 2000 John Wiley & Sons, Ltd.

Clustering of variables is as a way to arrange variables into homogeneous clusters, i.e., groups of variables which are strongly related to each other and thus bring the same information. These approaches can then be useful for dimension reduction and variable selection. Several specific methods have been developed for the clustering of numerical variables. However concerning qualitative variables or mixtures of quantitative and qualitative variables, far fewer methods have been proposed. The R package <b>ClustOfVar</b> was specifically developed for this purpose. The homogeneity criterion of a cluster is defined as the sum of correlation ratios (for qualitative variables) and squared correlations (for quantitative variables) to a synthetic quantitative variable, summarizing ``as good as possible'' the variables in the cluster. This synthetic variable is the first principal component obtained with the PCAMIX method. Two clustering algorithms are proposed to optimize the homogeneity criterion: iterative relocation algorithm and ascendant hierarchical clustering. We also propose a bootstrap approach in order to determine suitable numbers of clusters. We illustrate the methodologies and the associated package on small datasets.

Abstract Vinylphenols (4‐vinylphenol and 4‐vinylguaiacol) are natural constituents of wine and can play a role in wine aroma. However, only white wines contain important quantities of these volatile substances which, beyond a certain concentration (limit threshold = 725 μg litre −1 of 4‐vinylguaiacol+4‐vinylphenol (1:1)), can be responsible for a depreciating ‘phenolic’ or ‘pharmaceutic’ characteristic, Saccharomyces cerevisiae possesses a type‐(E) enzymic activity, substituted cinnamate carboxy‐lyase (SCD), which is capable of transforming, by non‐oxidative decarboxylation, the phenolic acids in the must, (E) p ‐coumaric and (E) ferulic acids, into corresponding vinylphenols. This endocellular activity is constitutive, it is only expressed during alcoholic fermentation and with a variable intensity depending on the yeast strain. Furthermore, the enzyme is rapidly inhibited by catechic tannins, which explains why, in comparison with white wines, red and rosé wines contain low levels of vinylphenols despite having more precursors. A yeast strain with a weak SCD activity has been selected and its use in vinification should eliminate the appearance of the phenolic taint in white wines coming from grapes rich in decarboxylable hydroxycinnamic acids.

The current best asymptotic lower bound on the minimum distance of quantum LDPC codes with a fixed non-zero rate is logarithmic in the blocklength. We propose a construction of quantum LDPC codes with fixed non-zero rate and prove that the minimum distance grows proportionally to the square root of the blocklength.

At the beginning of a COVID-19 infection, there is a period of time known as the exposed or latency period, before an infected person is capable of transmitting the infection to another person. We develop two differential equations models to account for this period. The first is a model that incorporates infected persons in the exposed class, before transmission is possible. The second is a model that incorporates a time delay in infected persons, before transmission is possible. We apply both models to the COVID-19 epidemic in China. We estimate the epidemiological parameters in the models, such as the transmission rate and the basic reproductive number, using data of reported cases. We thus evaluate the role of the exposed or latency period in the dynamics of a COVID-19 epidemic.

We present a numerical method for computing transitional flows as described by the BGK equation of gas kinetic theory. Using the minimum entropy principle to define a discrete equilibrium function, a discrete velocity model of this equation is proposed. This model, like the continuous one, ensures positivity of solutions, conservation of moments, and dissipation of entropy. The discrete velocity model is then discretized in space and time by an explicit finite volume scheme which is proved to satisfy the previous properties. A linearized implicit scheme is then derived to efficiently compute steady-states; this method is then verified with several test cases.