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Bringing GRAPPA to non-Cartesian MRI through SPARKLING: An application to MPRAGE anatomical MRI
No full textInternational audienceMotivationWell established clinically used parallel imaging techniques like GRAPPA and CAIPIRINHA are mostly limited to Cartesian sampling, and their extension to non-Cartesian sampling is not direct.GoalsWe propose to extend the SPARKLING framework to ensure GRAPPA accelerated Cartesian sampling in k-space center, while allowing non-Cartesian sampling in the periphery.ApproachThrough affine constraints, we can enforce Cartesian acceleration in the center of k-space, while allowing non-Cartesian sampling in the periphery.ResultsUsing 2x2 GRAPPA with SPARKLING trajectories for anatomical MRI with MPRAGE sequences enables 10x acceleration, achieving 1mm isotropic whole-brain scans in 1 minute.ImpactThis novel technique will help bring conventional multi-coil acceleration to non-Cartesian imaging, which can be used independently to massively accelerate MR scans, enabling faster and higher resolution imaging, which will be beneficial for varied clinical applications
Tail Modulo Cons, OCaml, and Relational Separation Logic
No full textInternational audienceCommon functional languages incentivize tail-recursive functions, as opposed to general recursive functions that consume stack space and may not scale to large inputs. This distinction occasionally requires writing functions in a tail-recursive style that may be more complex and slower than the natural, non-tail-recursive definition. This work describes our implementation of the tail modulo constructor (TMC) transformation in the OCaml compiler, an optimization that provides stack-efficiency for a larger class of functions --- tail-recursive modulo constructors --- which includes in particular the natural definition of 'List.map' and many similar recursive data-constructing functions. We prove the correctness of this program transformation in a simplified setting --- a small untyped calculus --- that captures the salient aspects of the OCaml implementation. Our proof is mechanized in the Coq proof assistant, using the Iris base logic. An independent contribution of our work is an extension of the Simuliris approach to define simulation relations that support different calling conventions. To our knowledge, this is the first use of Simuliris to prove the correctness of a compiler transformation
A Floyd-Warshall Approach to Value Computation in Markov Decision Processes
No full textValue and policy iteration are classical algorithms to maximize the average discounted reward of an MDP. They rely on a breadth-first exploration strategy in the future of each state to update its value and possibly change the action policy at this state. This paper revisits this paradigm and examines a depth-first search strategy. It reformulates the average reward computation as an integral over (future) paths that is better expressed in the formalism of weighted automata. Policy evaluation can then be solved by a Floyd-Warshall algorithm, which gathers at once the rewards along possibly infinite runs. This reformulation opens the way to new approximation schemes for the value function. The same formalism also gives access to other quantities of interest, as the gradient of the average reward with respect to model or policy parameters, or the variance of the reward. The behaviors and performances of this value estimation scheme are illustrated on several benchmarks.</div
Theoretical / numerical study of modulated traveling waves in inhibition stabilized networks
No full textWe prove a principle of linearized stability for traveling wave solutions to neural field equations posed on the real line. Additionally, we provide the existence of a finite dimensional invariant center manifold close to a traveling wave, this allows to study bifurcations of traveling waves. Finally, the spectral properties of the modulated traveling waves are investigated. Numerical schemes for the computation of modulated traveling waves are provided. We then apply these results and methods to study a neural field model in a inhibitory stabilized regime. We showcase Fold, Hopf and Bodgdanov-Takens bifurcations of traveling pulses. Additionally, we continue the modulated traveling pulses as function of the time scale ratio of the two neural populations and show numerical evidences for snaking of modulated traveling pulses
Environmental and bioclimatic data for epidemiological analysis over French Mediterranean areas
No full textInternational audienceRisk-based surveillance is now a well-established paradigm in epidemiology, involving the distribution of sampling efforts differentially in time, space, and within populations, based on multiple risk factors. To assess and map the risk of the presence of the bacterium Xylella fastidiosa, we have compiled a dataset that includes factors influencing plant development and thus the spread of such harmful organism. To this end, we have collected, preprocessed, and gathered information and data related to land types, soil compositions, and climatic conditions to predict and assess the probability of risk associated with X. fastidiosa in relation to environmental features. This resource can be of interest to researchers conducting analyses on X. fastidiosa and, more generally, to researchers working on geospatial modeling of risk related to plant infectious diseases
Gaussian entropic optimal transport: Schr\"odinger bridges and the Sinkhorn algorithm
No full text68 pagesEntropic optimal transport problems are regularized versions of optimal transport problems. These models play an increasingly important role in machine learning and generative modelling. For finite spaces, these problems are commonly solved using Sinkhorn algorithm (a.k.a. iterative proportional fitting procedure). However, in more general settings the Sinkhorn iterations are based on nonlinear conditional/conjugate transformations and exact finite-dimensional solutions cannot be computed. This article presents a finite-dimensional recursive formulation of the iterative proportional fitting procedure for general Gaussian multivariate models. As expected, this recursive formulation is closely related to the celebrated Kalman filter and related Riccati matrix difference equations, and it yields algorithms that can be implemented in practical settings without further approximations. We extend this filtering methodology to develop a refined and self-contained convergence analysis of Gaussian Sinkhorn algorithms, including closed form expressions of entropic transport maps and Schr\"odinger bridges
Absorbing Markov decision processes and their occupation measures
No full textInternational audienceWe consider an absorbing Markov decision process with Borel state and action spaces. We study conditions under which the MDP is uniformly absorbing and the set of occupation measures of the MDP is compact in the usual weak topology. These include suitable continuity requirements on the transition kernel and conditions on the dynamics of the system at the boundary of the absorbing set. We generalize previously known results and give an answer to some conjectures that have been mentioned in the related literature
Mapping potential environmental impacts of alien species in the face of climate change
No full textInternational audienceRisk maps are a useful tool to prioritise sites for management and allocate resources where they are most needed as they can show us where impacts of biological invasions are most likely to happen or expected to be largest. Given the pace of global changes, we need to understand not only the risks under current conditions, but future risks taking these changes into account. In this study, we use Australian acacias alien to South Africa as a case study to model their potential distribution under future climate change to map their potential impacts at the middle and end of the century and the uncertainty related to three socio-economic pathways and five climatic models. The resulting risk maps across South Africa are a pioneering attempt to combine impacts of alien species with potential future distributions. We found that although climatic suitability and therefore the risk is predicted to decrease under climate change in 51,4% of the country’s area, the opposite is predicted for 26% of the area and the highly vulnerable fynbos biome remains an area with high projected impacts. Such risk maps can help us prioritise management actions and aid the development of suitable plans to protect biodiversity under current and future climate conditions. However, they have to be interpreted with caution and we highlight some shortcomings around species distribution models in general, vulnerability of ecosystems to the potential impacts, data gaps on impacts, as well as currently benign or unknown invaders, which are not included in the projections
The Multiplex Deep Latent Position Model for the Clustering of nodes in Multiview Networks
No full textInternational audienceMultiplex networks capture multiple types of interactions among the same set of nodes, creating a complex, multi-relational framework. A typical example is a social network where nodes (actors) are connected by various types of ties, such as professional, familial, or social relationships. Clustering nodes in these networks is a key challenge in unsupervised learning, given the increasing prevalence of multiview data across domains. While previous research has focused on extending statistical models to handle such networks, these adaptations often struggle to fully capture complex network structures and rely on computationally intensive Markov chain Monte Carlo (MCMC) for inference, rendering them less feasible for effective network analysis. To overcome these limitations, we propose the multiplex deep latent position model (MDLPM), which generalizes and extends latent position models to multiplex networks. MDLPM combines deep learning with variational inference to effectively tackle both the modelling and computational challenges raised by multiplex networks. Unlike most existing deep learning models for graphs that require external clustering algorithms (e.g., k-means) to group nodes based on their latent embeddings, MDLPM integrates clustering directly into the learning process, enabling a fully unsupervised, end-to-endapproach. This integration improves the ability to uncover and interpret clusters in multiplex networks without relying on external procedures. Numerical experiments across various synthetic data sets and two real-world networks demonstrate the performance of MDLPM compared to state-of-the-art methods, highlighting its applicability and effectiveness for multiplex network analysis
Computing isogenies from modular equations in genus two
No full textInternational audienceWe present an algorithm solving the following problem: given two genus 2 curves over a field k with isogenous Jacobians, compute such an isogeny explicitly. This isogeny can be either an l-isogeny or, in the real multiplication case, an isogeny with cyclic kernel; we require that k have large enough characteristic and that the curves be sufficiently generic. Our algorithm uses modular equations for these isogeny types, and makes essential use of an explicit Kodaira--Spencer isomorphism in genus 2