Institut de Mathématiques de Bourgogne

The human pathogenic fungus Candida albicans can cause systemic infections by invading epithelial barriers to gain access to the bloodstream. One of the main reservoirs of C. albicans is the gastrointestinal tract and systemic infections predominantly originate from this niche. In this study, we used scanning electron and fluorescence microscopy, adhesion, invasion and damage assays, fungal mutants and a set of fungal and host cell inhibitors to investigate the interactions of C. albicans with oral epithelial cells and enterocytes. Our data demonstrate that adhesion, invasion and damage by C. albicans depend not only on fungal morphology and activity, but also on the epithelial cell type and the differentiation stage of the epithelial cells, indicating that epithelial cells differ in their susceptibility to the fungus. C. albicans can invade epithelial cells by induced endocytosis and/or active penetration. However, depending on the host cell faced by the fungus, these routes are exploited to a different extent. While invasion into oral cells occurs via both routes, invasion into intestinal cells occurs only via active penetration.

Financial theory, access to deal flow, selection, and monitoring skills are used to explain syndication in venture capital firms in six European countries. In contrast with U.S. findings, portfolio management motives are more important for syndication than individual deal management motives. Risk sharing, portfolio diversification, and access to larger deals are more important than selection and monitoring of deals. This holds for later stage and for early stage investors. Value adding is a stronger motive for syndication for early stage investors than for later stage investors, however. Nonlead investors join syndicates for the selection and value–adding skills of the syndicate partners.

We show that, for every compact n-dimensional manifold, n 1, there is a residual subset of Diff 1 (M ) of diffeomorphisms for which the homoclinic class of any periodic saddle of f verifies one of the following two possibilities: Either it is contained in the closure of an infinite set of sinks or sources (Newhouse phenomenon), or it presents some weak form of hyperbolicity called dominated splitting (this is a generalization of a bidimensional result of Ma [Ma3]). In particular, we show that any C 1 -robustly transitive diffeomorphism admits a dominated splitting.

We apply the techniques of control theory and of sub-Riemannian geometry to laser-induced population transfer in two- and three-level quantum systems. The aim is to induce complete population transfer by one or two laser pulses minimizing the pulse fluences. Sub-Riemannian geometry and singular-Riemannian geometry provide a natural framework for this minimization, where the optimal control is expressed in terms of geodesics. We first show that in two-level systems the well-known technique of “π-pulse transfer” in the rotating wave approximation emerges naturally from this minimization. In three-level systems driven by two resonant fields, we also find the counterpart of the “π-pulse transfer.” This geometrical picture also allows one to analyze the population transfer by adiabatic passage.

In a coherent, exhaustive and progressive way, this book presents the tools for studying local bifurcations of limit cycles in families of planar vector fields. A systematic introduction is given to s

We study the stability of quasinormal modes (QNM) in asymptotically flat black hole spacetimes by means of a pseudospectrum analysis. The construction of the Schwarzschild QNM pseudospectrum reveals the following: (i) the stability of the slowest-decaying QNM under perturbations respecting the asymptotic structure, reassessing the instability of the fundamental QNM discussed by Nollert [H. P. Nollert, About the Significance of Quasinormal Modes of Black Holes, Phys. Rev. D 53, 4397 (1996)] as an "infrared" effect; (ii) the instability of all overtones under small-scale ("ultraviolet") perturbations of sufficiently high frequency, which migrate towards universal QNM branches along pseudospectra boundaries, shedding light on Nollert's pioneer work and Nollert and Price's analysis [H. P. Nollert and R. H. Price, Quantifying Excitations of Quasinormal Mode Systems, J. Math. Phys. (N.Y.) 40, 980 (1999)]. Methodologically, a compactified hyperboloidal approach to QNMs is adopted to cast QNMs in terms of the spectral problem of a non-self-adjoint operator. In this setting, spectral (in)stability is naturally addressed through the pseudospectrum notion that we construct numerically via Chebyshev spectral methods and foster in gravitational physics. After illustrating the approach with the Pschl-Teller potential, we address the Schwarzschild black hole case, where QNM (in)stabilities are physically relevant in the context of black hole spectroscopy in gravitational-wave physics and, conceivably, as probes into fundamental highfrequency spacetime fluctuations at the Planck scale.

We give a derivation of quantum spectral curve (QSC) — a finite set of Riemann-Hilbert equations for exact spectrum of planar $$ \mathcal{N}=4 $$ SYM theory proposed in our recent paper Phys. Rev. Lett. 112 (2014). We also generalize this construction to all local single trace operators of the theory, in contrast to the TBA-like approaches worked out only for a limited class of states. We reveal a rich algebraic and analytic structure of the QSC in terms of a so called Q-system — a finite set of Baxter-like Q-functions. This new point of view on the finite size spectral problem is shown to be completely compatible, though in a far from trivial way, with already known exact equations (analytic Y-system/TBA, or FiNLIE). We use the knowledge of this underlying Q-system to demonstrate how the classical finite gap solutions and the asymptotic Bethe ansatz emerge from our formalism in appropriate limits.

Lipid transfer proteins (LTPs) and elicitins are both able to load and transfer lipidic molecules and share some structural and functional properties. While elicitins are known as elicitors of plant defence mechanisms, the biological function of LTP is still an enigma. We show that a wheat LTP1 binds with high affinity sites. Binding and in vivo competition experiments point out that these binding sites are common to LTP1 and elicitins and confirm that they are the biological receptors of elicitins. A mathematical analysis suggests that these receptors could be represented by an allosteric model corresponding to an oligomeric structure with four identical subunits.

Latex file. 40 pages with 2 figures.

In this paper, we investigate the topology of a class of non-Kähler compact complex manifolds generalizing that of Hopf and Calabi-Eckmann manifolds. These manifolds are diffeomorphic to special systems of real quadrics Cn which are invariant with respect to the natural action of the real torus (S1)n onto Cn. The quotient space is a simple convex polytope. The problem reduces thus to the study of the topology of certain real algebraic sets and can be handled using combinatorial results on convex polytopes. We prove that the homology groups of these compact complex manifolds can have arbitrary amount of torsion so that their topology is extremely rich. We also resolve an associated wall-crossing problem by introducing holomorphic equivariant elementary surgeries related to some transformations of the simple convex polytope. Finally, as a nice consequence, we obtain that affine non-Kähler compact complex manifolds can have arbitrary amount of torsion in their homology groups, contrasting with the Kähler situation.

Nous étudions une classe de processus de Markov déterministes par morceaux, sur espace d’états $\mathbb{R}^{d}\times E$ où $E$ est un ensemble fini. La composante continue du processus évolue suivant le flot d’un champ de vecteur, qui change lorsque la composante discrète saute. Les taux de saut peuvent dépendre des deux composantes. Sous l’hypothèse que le processus reste dans un ensemble compact, nous détaillons une construction possible et caractérisons son support en termes de solution d’une inclusion différentielle. Nous étudions ensuite le comportement en temps long, en faisant apparaître un certain ensemble de points accessibles, qui se trouve être fortement lié au support des mesures invariantes. Sous des conditions de type Hörmander sur les crochets de Lie entre les champs de vecteurs, nous montrons qu’il existe une unique mesure invariante vers laquelle le processus converge en variation totale. Nous donnons enfin des exemples où la condition d’unicité n’est pas vérifiée, et où le nombre de mesures invariantes dépend des taux de saut entre les flots.

Our discovery of multi-rogue wave (MRW) solutions in 2010 completely changed the viewpoint on the links between the theory of rogue waves and integrable systems, and helped explain many phenomena which were never understood before. It is enough to mention the famous Three Sister waves observed in oceans, the creation of a regular approach to studying higher Peregrine breathers, and the new understanding of 2 + 1 dimensional rogue waves via the NLS-KP correspondence. This article continues the study of the MRW solutions of the NLS equation and their links with the KP-I equation started in a previous series of articles (Dubard et al 2010 Eur. Phys. J. 185 247–58, Dubard and Matveev 2011 Natural Hazards Earth Syst. Sci. 11 667–72, Matveev and Dubard 2010 Proc. Int. Conf. FNP-2010 (Novgorod, St Petersburg) pp 100–101, Dubard 2010 PhD Thesis). In particular, it contains a discussion of the large parametric asymptotics of these solutions, which has never been studied before.

Determination of the membrane lipid composition of Saccharomyces cerevisiae revealed an increase in the unsaturation index, qualitative and quantitative changes in sterol content and an alteration of the activity of the plasma membrane ATPase when cells were pre-adapted to ethanol. All these changes may constitute different adaptation mechanisms which allow the cell to cope with ethanol stress. The importance of the lipid environment on the plasma membrane ATPase activity is also discussed.

The present work addresses the aggregation/dispersion properties of two commercial titanias for application as photocatalysts in concrete technology. A microsized m ‐TiO 2 (average particle size 153.7 ± 48.1 nm) and a nanosized n ‐TiO 2 (average particle size 18.4 ± 5.0 nm) have been tested in different ionic media (Na + , K + , Ca 2+ , Cl − , SO 4 2− , synthetic cement pore solution) at different pHs and in real cement paste specimens. Results highlighted that ion–ion correlations play a fundamental role in TiO 2 particles aggregation in the cement environment. A particle aggregation model derived from TiO 2 surface chemistry is proposed here and used to justify such aggregation phenomena in real cement paste. Scanning electron microscopy–energy‐dispersive X‐ray spectroscopic investigations on hardened cement specimens completely confirmed the qualitative model based on titania surface chemistry. Experimental results also show how size and nature of TiO 2 aggregates dramatically influence the overall photocatalytic activity of cementitious materials containing TiO 2 .

We prove by explicit construction that graph braid groups and most surface groups can be embedded in a natural way in right-angled Artin groups, and we point out some consequences of these embedding results.We also show that every right-angled Artin group can be embedded in a pure surface braid group.On the other hand, by generalising to rightangled Artin groups a result of Lyndon for free groups, we show that the Euler characteristic -1 surface group (given by the relation x 2 y 2 = z 2 ) never embeds in a right-angled Artin group.

Black hole (BH) spectroscopy has emerged as a powerful approach to extracting spacetime information from gravitational wave (GW) observed signals. Yet, quasinormal mode (QNM) spectral instability under small scale perturbations has been recently shown to be a common classical general relativistic phenomenon [J. L. Jaramillo et al., Phys. Rev. X 11, 031003 (2021)PRXHAE2160-330810.1103/PhysRevX.11.031003]. This requires assessing its impact on the BH QNM spectrum, in particular on BH QNM overtone frequencies. We conclude (i) perturbed BH QNM overtones are indeed potentially observable in the GW waveform, providing information on small-scale environment BH physics, and (ii) their detection poses a challenging data analysis problem of singular interest for LISA astrophysics. We adopt a twofold approach, combining theoretical results from scattering theory with a fine-tuned data analysis on a highly accurate numerical GW ringdown signal. The former introduces a set of effective parameters (partially relying on a BH Weyl law) to characterize QNM instability physics. The latter provides a proof of principle demonstrating that the QNM spectral instability is indeed accessible in the time-domain GW waveform, though certainly requiring large signal-to-noise ratios. Particular attention is devoted to discussing the patterns of isospectrality loss under QNM instability, since the disentanglement between axial and polar GW parities may already occur within the near-future detection range.

Using a Fourier spectral method, we provide a detailed numerical investigation of dispersive Schrödinger-type equations involving a fractional Laplacian in an one-dimensional case. By an appropriate choice of the dispersive exponent, both mass and energy sub- and supercritical regimes can be identified. This allows us to study the possibility of finite time blow-up versus global existence, the nature of the blow-up, the stability and instability of nonlinear ground states and the long-time dynamics of solutions. The latter is also studied in a semiclassical setting. Moreover, we numerically construct ground state solutions of the fractional nonlinear Schrödinger equation.

In a Hilbert space $\mathcal H$, assuming $(\alpha_k)$ a general sequence of nonnegative numbers, we analyze the convergence properties of the inertial forward-backward algorithm $(IFB)\{\begin{array}{l} y_k=x_k+\alpha_k(x_k-x_{k-1}), x_{k+1}={\rm prox}_{s\Psi}(y_k-s\nabla \Phi(y_k)) \end{array},$ where $\Psi: \mathcal H \to \mathbb R \cup \lbrace + \infty \rbrace $ is a proper lower-semicontinuous convex function, and $\Phi: \mathcal H \to \mathbb R$ is a differentiable convex function, whose gradient is Lipschitz continuous. Various options for the sequence $(\alpha_k)$ are considered in the literature. Among them, the Nesterov choice leads to the FISTA algorithm and accelerates convergence from $\mathcal{O}(1/k)$ to $\mathcal{O}(1/k^2)$ for the values. Several variants are used to guarantee the convergence of the iterates or to improve the rate of convergence for the values. For the design of fast optimization methods, the tuning of the sequence $(\alpha_k)$ is a subtle issue, which we deal with in this paper in general. We show that the convergence rate of the algorithm can be obtained simply by analyzing the sequence of positive real numbers $(\alpha_k)$. In addition to the case $\alpha_k= 1 -\frac{\alpha}{k} $ with $\alpha\geq 3$, our results apply equally well to $\alpha_k = 1- \frac{\alpha}{k^r}$, with an exponent $0<r<1$, and to Polyak's heavy ball method. Thus, we unify most of the existing results based on the accelerated gradient method of Nesterov. In the process, we improve some of them and discover new ones.

Abstract A Riemannian metric is adapted to a hyperbolic set of a diffeomorphism if, in this metric, the expansion/contraction of the unstable/stable directions is seen after only one iteration. A dominated splitting is a notion of weak hyperbolicity where the tangent bundle of the manifold splits in invariant subbundles such that the vector expansion on one bundle is uniformly smaller than that on the next bundle. The existence of an adapted metric for a dominated splitting has been considered by Hirsch, Pugh and Shub (M. Hisch, C. Pugh and M. Shub. Invariant Manifolds (Lecture Notes in Mathematics, 583) . Springer, Berlin, 1977). This paper gives a complete answer to this problem, building adapted metrics for dominated splittings and partially hyperbolic splittings in arbitrarily many subbundles of arbitrary dimensions. These results stand for diffeomorphisms and for flows.