Short relaxation times but long transient times in both simple and complex reaction networks

When relaxation towards an equilibrium or steady state is exponential at large times, one usually considers that the associated relaxation time $\tau$, i.e., the inverse of that decay rate, is the longest characteristic time in the system. However that need not be true, and in particular other times such as the lifetime of an infinitesimal perturbation can be much longer. In the present work we demonstrate that this paradoxical property can arise even in quite simple systems such as a chain of reactions obeying mass action kinetics. By mathematical analysis of simple reaction networks, we pin-point the reason why the standard relaxation time does not provide relevant information on the potentially long transient times of typical infinitesimal perturbations. Overall, we consider four characteristic times and study their behavior in both simple chains and in more complex reaction networks taken from the publicly available database "Biomodels." In all these systems involving mass action rates, Michaelis-Menten reversible kinetics, or phenomenological laws for reaction rates, we find that the characteristic times corresponding to lifetimes of tracers and of concentration perturbations can be much longer than $\tau$

Short time growth of a KPZ interface with flat initial conditions

The short time behavior of the 1+1 dimensional KPZ growth equation with a flat initial condition is obtained from the exact expressions of the moments of the partition function of a directed polymer with one endpoint free and the other fixed. From these expressions, the short time expansions of the lowest cumulants of the KPZ height field are exactly derived. The results for these two classes of cumulants are checked in high precision lattice numerical simulations. The short time limit considered here is relevant for the study of the interface growth in the large diffusivity/weak noise limit, and describes the universal crossover between the Edwards-Wilkinson and KPZ universality classes for an initially flat interface.Comment: 9 pages, 7 figure

Modélisation cinétique du métabolisme: construction du modèle, analyse et applications biotechnologiques

This thesis shows how to build a kinetic model the central carbon metabolism of the Escherichia coli bacterium to test a bioengineering strategy where the gene expression machinery (GEM) is controllable. The idea is to reorient the machinery from growth to the production of industrially interesting com- pounds. Because this controlled bacterium will no longer maximize growth, flux balance frameworks are inadequate and instead a kinetic modelling approach is necessary. Given the large number of re- actions included in the network, a pipeline has been built to automatically generate kinetic laws from reaction stoichiometries. In this context a precise description of the reactional mechanism is impossible and I use the convenience kinetic framework for reversible reaction or Michaelis-Menten for irreversible ones; both are derived assuming independent reactants. The parameter fitting searches for the model that matches best the steady state conditions of concentration and flux, prior distributions for parameters built from literature data, and time course data for tracers. The thesis highlights the importance of including these time courses and of understanding the different characteristic times in such systems, the standard relaxation time not always being the longest characteristic time. Lastly, the optimised model is used to show that the yield of a target metabolite is increased by down regulating the GEM.Cette thèse décrit une méthode pour développer un modèle du métabolisme carboné central chez la bactérie Escherichia coli afin de tester une stratégie de bio-ingénierie sur une souche pour laquelle la machinerie d’expression génique(GEM) est contrôlable. L’idée est de réorienter la machine cellulaire depuis sa croissance vers la production d’un composé industriellement intéressant. La bactérie ainsi contrôlée ne va plus maximiser sa croissance, ce qui rend le cadre de la “Flux balance analysis” inapproprié pour la modélisation; un modèle cinétique lui est préféré. Étant donné le nombre important de réactions présentes dans le réseau, un pipeline a été mis en place pour produire automatiquement les lois cinétiques à partir des stœchiométries de réaction. Dans ce contexte, une description précise des mécanismes de réaction est impossible ce qui m’a poussé à choisir des modélisations de type "convenience kinetic" pour les réactions réversibles ou "Michaelis-Menten" pour les irréversibles; dans les deux cas les réactants sont supposés indépendants. L’ajustement des paramètres cherche à s’accorder au mieux avec des valeurs à l’état stationnaire de flux et concentrations, des distributions a priori de paramètres construites à partir de la littérature ainsi que des données de dynamique pour des traceurs. La thèse met en avant l’importance d’intégrer ces dernières et décrit les différents temps qui caractérisent un tel système, notamment le temps de relaxation n’est pas toujours celui le plus lent. Pour finir, le modèle optimisé est utilisé pour montrer qu'inhiber le GEM permet d'augmenter le rendement pour la production d'un métabolite cible

Linear-in-Complexity Computational Strategies for Modeling and Dosimetry at TeraHertz

This work presents a fast direct solver strategy allowing full-wave modeling and dosimetry at terahertz (THz) frequencies. The novel scheme leverages a preconditioned combined field integral equation together with a regularizer for its elliptic spectrum to enable its compression into a non-hierarchical skeleton, invertible in quasi-linear complexity. Numerical results will show the effectiveness of the new scheme in a realistic skin modeling scenario

Linear-in-Complexity Computational Strategies for Modeling and Dosimetry at TeraHertz

This work presents a fast direct solver strategy allowing full-wave modeling and dosimetry at terahertz (THz) frequencies. The novel scheme leverages a preconditioned combined field integral equation together with a regularizer for its elliptic spectrum to enable its compression into a non-hierarchical skeleton, invertible in quasi-linear complexity. Numerical results will show the effectiveness of the new scheme in a realistic skin modeling scenario

Local Coordination Environments and Vibrational Dynamics of Protons in Hexagonal and Cubic Sc-Doped BaTiO3 Proton-Conducting Oxides

The proton local coordination environments and vibrational dynamics associated with the two order of magnitude change in proton conductivity in hydrated forms of hexagonal and cubic structured BaTi1-xScxO3Hx (0.16 < x < 0.7) were investigated using optical spectroscopy, neutron spectroscopy, and first-principles calculations. Whereas the cubic structure compositions display a single proton site, we show that protons occupy three distinct sites in compositions exhibiting the hexagonal structure. The principal site is characterized by interoctahedral hydrogen bonds, while two additional low occupancy sites are similar to those in the cubic structure, with classic intraoctahedral geometry. Furthermore, the proton hydrogen bond strength increases with decreasing scandium doping level. We infer from this that the stronger, more energetic hydrogen bonds in the hexagonal structure, resulting from proton sites with lower symmetry (lower multiplicity), are predominantly responsible for the significant reduction in macroscopic conductivity between cubic and hexagonal BaTi1-xScxO3Hx materials, rather than simply the absolute number of protons. Our findings are highly relevant to the field, clarifying the advantages of high-symmetry structures with high-multiplicity proton sites to favorable properties in ceramic proton-conducting oxides

On the Fast Direct Solution of a Preconditioned Electromagnetic Integral Equation

This work presents a fast direct solver strategy for electromagnetic integral equations in the high-frequency regime. The new scheme relies on a suitably preconditioned combined field formulation and results in a single skeleton form plus identity equation. This is obtained after a regularization of the elliptic spectrum through the extraction of a suitably chosen equivalent circulant problem. The inverse of the system matrix is then obtained by leveraging the Woodbury matrix identity, the low-rank representation of the extracted part of the operator, and fast circulant algebra yielding a scheme with a favorable complexity and suitable for the solution of multiple right-hand sides. Theoretical considerations are accompanied by numerical results both of which are confirming and showing the practical relevance of the newly developed scheme

Quantum Feature Maps for Graph Machine Learning on a Neutral Atom Quantum Processor

Using a quantum processor to embed and process classical data enables the generation of correlations between variables that are inefficient to represent through classical computation. A fundamental question is whether these correlations could be harnessed to enhance learning performances on real datasets. Here, we report the use of a neutral atom quantum processor comprising up to $32$ qubits to implement machine learning tasks on graph-structured data. To that end, we introduce a quantum feature map to encode the information about graphs in the parameters of a tunable Hamiltonian acting on an array of qubits. Using this tool, we first show that interactions in the quantum system can be used to distinguish non-isomorphic graphs that are locally equivalent. We then realize a toxicity screening experiment, consisting of a binary classification protocol on a biochemistry dataset comprising $286$ molecules of sizes ranging from $2$ to $32$ nodes, and obtain results which are comparable to those using the best classical kernels. Using techniques to compare the geometry of the feature spaces associated with kernel methods, we then show evidence that the quantum feature map perceives data in an original way, which is hard to replicate using classical kernels