Related papers: Slow-fast normal forms arising from piecewise smoo…
This article is devoted to the analysis of semilinear, parabolic, Stochastic Partial Differential Equations, with slow and fast time scales. Asymptotically, an averaging principle holds: the slow component converges to the solution of…
We establish strong uniqueness for a class of degenerate SDEs of weak H{\"o}rmander type under suitable H{\"o}lder regularity conditions for the associated drift term. Our approach relies on the Zvonkin transform which requires to exhibit…
Phase diagram of microcanonical ensembles of self-attracting particles is studied for two types of short-range potential regularizations: self-gravitating fermions and classical particles interacting via attractive soft…
We consider a class of linear programs on graphs with total variation regularization and a budgetary constraint. For these programs, we give a characterization of basic solutions in terms of rooted spanning forests with orientation on the…
We study generic constrained differential equations (CDEs) with three parameters, thereby extending Takens's classification of singularities of such equations. In this approach, the singularities analyzed are the Swallowtail, the…
Graph convolutional neural networks (GCNNs) have been widely used in graph learning. It has been observed that the smoothness functional on graphs can be defined in terms of the graph Laplacian. This fact points out in the direction of…
The normal form theory for polynomial vector fields is extended to those for $C^\infty$ vector fields vanishing at the origin. Explicit formulas for the $C^\infty$ normal form and the near identity transformation which brings a vector field…
Regularization is a core component of modern inverse problems, as it helps establish the well-posedness of the solution of interest. Popular regularization approaches include variational regularization and iterative regularization. The…
In this paper we investigate regularity properties of weak solutions to a PDE system that arises in the study of biological transport networks. The system consists of a possibly singular elliptic equation for the scalar pressure of the…
Slender-body approximations have been successfully used to explain many phenomena in low-Reynolds number fluid mechanics. These approximations typically use a line of singularity solutions to represent the flow. These singularities can be…
We consider a slow-fast differential system (SF) in dimension two which appears in the study of some linear model (LM) with periodic coefficients in population dynamics. We show existence of "canard solutions" of (SF) along semi-stable slow…
Our object of study is non smooth vector fields on $\R^2$. We apply the techniques of geometric singular perturbations in non smooth vector fields after regularization and a blow$-$up. In this way we are able to bring out some results that…
Solving inverse problems involving measurement noise and modeling errors requires regularization in order to avoid data overfit. Geophysical inverse problems, in which the Earth's highly heterogeneous structure is unknown, present a…
A weak wild arithmetic quotient singularity arises from the quotient of a smooth arithmetic surface by a finite group action, where the inertia group of a point on a closed characteristic p fiber is a p-group acting with smallest possible…
We propose a novel framework for learning stabilizable nonlinear dynamical systems for continuous control tasks in robotics. The key contribution is a control-theoretic regularizer for dynamics fitting rooted in the notion of…
The folded node is a singularity associated with loss of normal hyperbolicity in systems where mixtures of slow and fast timescales arise due to singular perturbations. Canards are special solutions that reveal a counteractive feature of…
We reveal the critical properties of the phase transition towards superfluid order that has been proposed to occur in large spin fermionic systems. For this purpose, we consider the bosonic field theory for fluctuations of the complex…
In this paper, we determine a condition of applicability of a very simple formalism for the calculation of a fast process taking place in a non-equilibrium medium, in which the particle distribution functions are frozen in time. Indeed, a…
We formulate and study analytically and computationally two families of piecewise linear degree one circle maps. These families offer the rare advantage of being non-trivial but essentially solvable models for the phenomenon of mode-locking…
We give necessary and sufficient criteria for a distribution to be smooth or uniformly H\"{o}lder continuous in terms of approximation sequences by smooth functions; in particular, in terms of those arising as regularizations…