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Non triviality of the percolation threshold and Gumbel fluctuations for Branching Interlacements
No full textWe consider the model of Branching Interlacements, introduced by Zhu, which is a natural analogue of Sznitman's Random Interlacements model, where the random walk trajectories are replaced by ranges of some suitable tree-indexed random walks. We first prove a basic decorrelation inequality for events depending on the state of the field on distinct boxes. We then show that in all relevant dimensions, the vacant set undergoes a nontrivial phase transition regarding the existence of an infinite connected component. Finally we obtain the Gumbel fluctuations for the cover level of finite sets, which is analogous to Belius' result in the setting of Random Interlacements
Heat flow in a periodically forced, unpinned thermostatted chain
No full textInternational audienceWe prove the hydrodynamic limit for a one-dimensional harmonic chain of interacting atoms with a random flip of the momentum sign. The systemis open: at the left boundary it is attached to a heat bath at temperature T_,while at the right endpoint it is subject to an action of a force which reads as, where F ⩾ 0 and F̃(t) is a periodic function. Here n is the size of the microscopic system. Under a diffusive scaling of space-time, we prove that the empirical profiles of the two locally conserved quantities – the volume stretch and the energy – converge, as n → +∞, to the solution of a non-linear diffusive system of conservative partial differential equations with a Dirichlet type and Neumann boundary conditions on the left and the right endpoints, respectively
On the geometry of isomonodromic deformations on the torus and the elliptic Calogero-Moser system
No full textWe consider isomonodromic deformations of connections with a simple pole on the torus, motivated by the elliptic version of the sixth Painlevé equation. We establish an extended symmetry, complementing known results. The Calogero-Moser system in its elliptic version is shown to fit nicely in the geometric framework, the extended symplectic two-form is introduced and shown to be closed
Termination of Injective DPO Graph Rewriting Systems using Subgraph Counting with anti-patterns
No full textA machine-checkable sufficient condition for relative termination of double-pushout graph rewriting systems with injective rules on edge-labeled multigraphs is presented. It defines a graph's weight as the sum of weights of occurrences of a set of graphs within that graph. It resolves termination cases that prior interpretation-based methods cannot. An implementation 1 is also provided.</div
Normal forms of Hopf–Bogdanov–Takens bifurcation for retarded differential equations
No full textInternational audienceThis article explores the process of computing normal forms related to a codimension-three Hopf–Bogdanov–Takens (H–B–T) bifurcation in the framework of retarded functional differential equations. The focus is on the behavior of dynamic systems defined by such equations, which exhibit a pair of purely imaginary roots along with a double zero root, referred to as the H–B–T eigenvalue. By employing center manifold reduction alongside the normal form technique, explicit formulas are derived to facilitate the computation of the normal forms for these systems, integrating three parameters for unfolding. To demonstrate the relevance of our results, we apply the analysis to a particular type of bidirectional associative memory network composed of three neurons, where we explore and illustrate the system’s dynamic behavior through an illustrative example and associated numerical simulations
Mechanism of Heteroepitaxial Growth of Boron Carbide on the Si-Face of 4H-SiC
No full textInternational audienceHeteroepitaxial boron carbide (BxC) can be grown on Si face 4H-SiC(0001) using a two-step process involving substrate boridation at 1200°C under BCl3 + H2 followed by a chemical vapor deposition (CVD) growth step at 1600°C by adding C3H8 precursor. However, in-depth investigation of the early growth stages revealed that complex reactions occur before starting the CVD at high temperature. Indeed, after boridation, the 35 nm BxC buffer layer is covered by an amorphous B-containing layer which evolves and reacts during the temperature ramp up between 1200 to 1600°C. Despite the formation of new phases (Si, SiB6), which could be explained by significant solid-state diffusion of Si, C and B elements through the thin BxC layer, the CVD epitaxial re-growth upon reaching 1600°C does not seems to be affected by these phases. The resulting single crystalline BxC layers display the epitaxial relationships [1010]BxC(0001)‖[1010]4H-SiC(0001). The layers exhibit a B4C composition, e.g. the highest possible C content for the BxC solid solution
Using Sinkhorn in the JKO scheme adds linear diffusion
No full textThe JKO scheme is a time-discrete scheme of implicit Euler type that allows to construct weak solutions of evolution PDEs which have a Wasserstein gradient structure. The purpose of this work is to study the effect of replacing the classical quadratic optimal transport problem by the Schr\"odinger problem (\emph{a.k.a.}\ the entropic regularization of optimal transport, efficiently computed by the Sinkhorn algorithm) at each step of this scheme. We find that if is the regularization parameter of the Schr\"odinger problem, and is the time step parameter, considering the limit with results in adding the term on the right-hand side of the limiting PDE. In the case we improve a previous result by Carlier, Duval, Peyré and Schmitzer (2017)
Multi-attribute based self-stabilizing algorithm for leader election in distributed systems
No full textInternational audienc
Unsupervised meta-learning for few-shot medical image classification based on metric learning
No full textInternational audienceDue to the high costs associated with establishing large-scale medical image datasets, few-shot learning (FSL) has demonstrated remarkable potential in the field of medical image analysis. However, current FSL methods still have high labeling requirements for datasets, and FSL techniques suitable for medical scenarios need further development. Meta-learning has provided an alternative framework to address the challenging FSL setting. In this paper, we propose an Unsupervised Meta-Learning (UML) framework based on metric learning for medical image classification. We propose Mini-Batch Sampling (MBS), which optimizes the sampling strategy of UML by conducting multiple non-repeating samples of individual tasks during each training epoch. By combining a semi-normalized similarity calculation method with residual network, we obtain a stable deep learning paradigm. We extracted and reconstructed three small-sample image datasets, namely BLOOD, PATHOLOGY, and CHEST, from three publicly available medical image datasets of different types. Our proposed method outperforms current small-sample image classification methods on these three datasets, enabling the training of high-performance image classification models using small amounts of unlabeled data