arXiv subjects

François David

Publications and source records attributed to François David.

13 recordsLinked to original sources

arXiv2026

Classifying absence seizure generation mechanisms: A critical transitions framework

Understanding how the brain switches from normal activity to an epileptic seizure is essential for improving seizure therapy, yet the underlying seizure generation mechanisms remain largely unknown. In particular, while seizure onset has been described as a critical transition (CT), there is no consensus on whether (i) bifurcation-induced, (ii) noise-induced, or (iii) bifurcation/noise-induced CTs are responsible. To clarify this, we develop a versatile CT-classification framework that can be applied to seizures in both animals and humans. First, we identify a canonical mathematical model which displays CTs that closely resemble voltage recordings of real seizures and can be of the three types mentioned above. We then identify distinctive properties of each CT-type in the model's output and use them to train a machine learning CT-type classifier. Finally, we apply the model-trained classifier to voltage recordings from epileptic rodents which consist of thousands of real absence seizures. We find that the largest proportion of analysed seizures are classified as noise-induced CTs. In other words, our results on absence seizures in rodents are in contrast to the conventional view that seizures are predominantly bifurcation-induced, and indicate that different CT mechanisms may dominate different seizure types.

math.DS↗

arXiv2026

Detecting seizure onset and offset times using human intelligence: A critical-transitions-based approach

Most existing seizure detection algorithms require extensive pre-processing of the data and rely on heuristic or currently unexplainable machine learning approaches. These approaches often struggle with balancing detection sensitivity and specificity in the presence of variable seizure morphologies, interictal epileptiform discharges, and artefacts. Here, we consider an alternative approach: our seizure detection algorithm, which is based on the concept of critical transitions and overcomes the aforementioned limitations. Specifically, we perform a receiver-operating-characteristic analysis to quantify the performance of our algorithm in terms of its agreement with expert annotations of seizure onset and offset times in the voltage recordings of seizure activity in epileptic rodents with different seizure morphologies. We demonstrate how performance depends on algorithm parameters and varies across different rodent recording sessions. We determine the optimal set of algorithm parameters for each recording session, with near expert-level performance achieved in most cases. Finally, we derive a single general set of algorithm parameters applicable across all recording sessions. The algorithm maintains its high performance in this general setting, demonstrating its versatility, robustness across varying seizure morphologies, and potential to complement machine learning algorithms.

math.DS↗

arXiv2026

Quantum walk on a random comb

We study continuous time quantum walk on a random comb graph with infinite teeth. Due to localization effects along the spine, the walk cannot go to infinity in the spine direction, while it can escape to infinity along the teeth of the comb. Starting from an initial vertex, the walk has a nonzero probability to stay trapped in a finite region. These results are obtained by studying the spectrum and eigenstates of the random Hamiltonian for the graphand analysing its properties. We use both analytic and numerical methods, many of which come from the theory of Anderson localization in one dimension.

quant-ph↗

arXiv2025

Forecasting Excessive Anesthesia Depth Using EEG α-Spindle Dynamics and Machine Learning

Objectives. Accurately predicting transitions to anesthetic drugs overdosage is a critical challenge in general anesthesia as it requires the identification of EEG indicators relevant for anticipating the evolution of the depth of anesthesia. Methods. In this study, we introduce a real-time, data-driven framework based on alpha spindle dynamics extracted from frontal EEG recordings. Using Empirical Mode Decomposition, we segment transient alpha spindle events and extract statistical features such as amplitude, duration, frequency, and suppression intervals. We apply these features to train a Light Gradient Boosting Machine, LGBM, classifier on a clinical EEG dataset spanning induction, maintenance, and emergence phases of general anesthesia. Results. Our model accurately classifies anesthesia phases with over 80 percent accuracy and anticipates the onset of isoelectric suppression, a marker of anesthetic drugs overdosage, with 96 percent accuracy up to 90 seconds in advance. Conclusion. The spindle-based metrics provides a non-invasive, interpretable, and predictive approach. This real-time method can be used to forecast unintentional anesthetic drugs overdosage, enabling proactive anesthesia management based solely on EEG signals. Significance. This new method is the first to provide a way to prevent too deep anesthesia and its consequence for the well-being of patients after the recovery from anesthesia.

q-bio.NC↗

arXiv2025

Can Text-to-Image Generative Models Accurately Depict Age? A Comparative Study on Synthetic Portrait Generation and Age Estimation

Text-to-image generative models have shown remarkable progress in producing diverse and photorealistic outputs. In this paper, we present a comprehensive analysis of their effectiveness in creating synthetic portraits that accurately represent various demographic attributes, with a special focus on age, nationality, and gender. Our evaluation employs prompts specifying detailed profiles (e.g., Photorealistic selfie photo of a 32-year-old Canadian male), covering a broad spectrum of 212 nationalities, 30 distinct ages from 10 to 78, and balanced gender representation. We compare the generated images against ground truth age estimates from two established age estimation models to assess how faithfully age is depicted. Our findings reveal that although text-to-image models can consistently generate faces reflecting different identities, the accuracy with which they capture specific ages and do so across diverse demographic backgrounds remains highly variable. These results suggest that current synthetic data may be insufficiently reliable for high-stakes age-related tasks requiring robust precision, unless practitioners are prepared to invest in significant filtering and curation. Nevertheless, they may still be useful in less sensitive or exploratory applications, where absolute age precision is not critical.

cs.CV↗

arXiv2025

JAM: A Comprehensive Model for Age Estimation, Verification, and Comparability

This paper introduces a comprehensive model for age estimation, verification, and comparability, offering a comprehensive solution for a wide range of applications. It employs advanced learning techniques to understand age distribution and uses confidence scores to create probabilistic age ranges, enhancing its ability to handle ambiguous cases. The model has been tested on both proprietary and public datasets and compared against one of the top-performing models in the field. Additionally, it has recently been evaluated by NIST as part of the FATE challenge, achieving top places in many categories.

cs.CV↗

arXiv2018

Local properties of the random Delaunay triangulation model and topological 2D gravity

Delaunay triangulations provide a bijection between a set of $N+3$ points in the complex plane, and the set of triangulations with given circumcircle intersection angles. The uniform Lebesgue measure on these angles translates into a Kähler measure for Delaunay triangulations, or equivalently on the moduli space $\mathcal M_{0,N+3}$ of genus zero Riemann surfaces with $N+3$ marked points. We study the properties of this measure. First we relate it to the topological Weil-Petersson symplectic form on the moduli space $\mathcal M_{0,N+3}$. Then we show that this measure, properly extended to the space of all triangulations on the plane, has maximality properties for Delaunay triangulations. Finally we show, using new local inequalities on the measures, that the volume $\mathcal{V}_N$ on triangulations with $N+3$ points is monotonically increasing when a point is added, $N\to N+1$. We expect that this can be a step towards seeing that the large $N$ limit of random triangulations can tend to the Liouville conformal field theory.

math-ph↗

arXiv2017

Large Strebel graphs and $(3,2)$ Liouville CFT

2D quantum gravity is the idea that a set of discretized surfaces (called map, a graph on a surface), equipped with a graph measure, converges in the large size limit (large number of faces) to a conformal field theory (CFT), and in the simplest case to the simplest CFT known as pure gravity, also known as the gravity dressed (3,2) minimal model. Here we consider the set of planar Strebel graphs (planar trivalent metric graphs) with fixed perimeter faces, with the measure product of Lebesgue measure of all edge lengths, submitted to the perimeter constraints. We prove that expectation values of a large class of observables indeed converge towards the CFT amplitudes of the (3,2) minimal model.

math-ph↗

arXiv2015

Liouville Quantum Gravity on the Riemann sphere

In this paper, we rigorously construct $2d$ Liouville Quantum Field Theory on the Riemann sphere introduced in the 1981 seminal work by Polyakov "Quantum Geometry of bosonic strings". We also establish some of its fundamental properties like conformal covariance under PSL$_2(\mathbb{C})$-action, Seiberg bounds, KPZ scaling laws, KPZ formula and the Weyl anomaly (Polyakov-Ray-Singer) formula for Liouville Quantum Gravity.

math.PR↗

arXiv2015

Renormalizability of Liouville Quantum Gravity at the Seiberg bound

Liouville Quantum Field Theory can be seen as a probabilistic theory of 2d Riemannian metrics $e^{ϕ(z)}dz^2$, conjecturally describing scaling limits of discrete $2d$-random surfaces. The law of the random field $ϕ$ in LQFT depends on weights $α\in \mathbb{R}$ that in classical Riemannian geometry parametrize power law singularities in the metric. A rigorous construction of LQFT has been carried out in \cite{DKRV} in the case when the weights are below the so called Seiberg bound: $α<Q$ where $Q$ parametrizes the random surface model in question. These correspond to conical singularities in the classical setup. In this paper, we construct LQFT in the case when the Seiberg bound is saturated which can be seen as the probabilistic version of Riemann surfaces with cusp singularities. Their construction involves methods from Gaussian Multiplicative Chaos theory at criticality.

math.PR↗

arXiv2015

Liouville Quantum Gravity on the complex tori

In this paper, we construct Liouville Quantum Field Theory (LQFT) on the toroidal topology in the spirit of the 1981 seminal work by Polyakov. Our approach follows the construction carried out by the authors together with A. Kupiainen in the case of the Riemann sphere. The difference is here that the moduli space for complex tori is non trivial. Modular properties of LQFT are thus investigated. This allows us to sum up the LQFT on complex tori over the moduli space, to compute the law of the random Liouville modulus, therefore recovering (and extending) formulae obtained by physicists, and make conjectures about the relationship with random planar maps of genus one, eventually weighted by a conformal field theory and conformally embedded onto the torus.

math.PR↗

arXiv2007

Mass distribution exponents for growing trees

We investigate the statistics of trees grown from some initial tree by attaching links to preexisting vertices, with attachment probabilities depending only on the valence of these vertices. We consider the asymptotic mass distribution that measures the repartition of the mass of large trees between their different subtrees. This distribution is shown to be a broad distribution and we derive explicit expressions for scaling exponents that characterize its behavior when one subtree is much smaller than the others. We show in particular the existence of various regimes with different values of these mass distribution exponents. Our results are corroborated by a number of exact solutions for particular solvable cases, as well as by numerical simulations.

cond-mat.stat-mech↗

arXiv2005

Instanton calculus for the self-avoiding manifold model

We compute the normalisation factor for the large order asymptotics of perturbation theory for the self-avoiding manifold (SAM) model describing flexible tethered (D-dimensional) membranes in d-dimensional space, and the epsilon-expansion for this problem. For that purpose, we develop the methods inspired from instanton calculus, that we introduced in a previous publication (Nucl. Phys. B 534 (1998) 555), and we compute the functional determinant of the fluctuations around the instanton configuration. This determinant has UV divergences and we show that the renormalized action used to make perturbation theory finite also renders the contribution of the instanton UV-finite. To compute this determinant, we develop a systematic large-d expansion. For the renormalized theory, we point out problems in the interplay between the limits epsilon->0 and d->infinity, as well as IR divergences when epsilon= 0. We show that many cancellations between IR divergences occur, and argue that the remaining IR-singular term is associated to amenable non-analytic contributions in the large-d limit when epsilon= 0. The consistency with the standard instanton-calculus results for the self-avoiding walk is checked for D = 1.

cond-mat.stat-mech↗