Related papers: Recent progress in smoothing estimates for evoluti…
We propose a new statistical observation scheme of diffusion processes named convolutional observation, where it is possible to deal with smoother observation than ordinary diffusion processes by considering convolution of diffusion…
In this paper we consider the semi-discretization in space of a first order scalar transport equation. For the space discretization we use standard continuous finite elements. To obtain stability we add a penalty on the jump of the gradient…
Non-parametric estimation of a multivariate density estimation is tackled via a method which combines traditional local smoothing with a form of global smoothing but without imposing a rigid structure. Simulation work delivers encouraging…
The smoothing distribution is the conditional distribution of the diffusion process in the space of trajectories given noisy observations made continuously in time. It is generally difficult to sample from this distribution. We use the…
In this paper we prove optimal error estimates for {solutions with natural regularity} of the equations describing the unsteady motion of incompressible shear-thinning fluids. We consider a full space-time semi-implicit scheme for the…
For certain non linear evolution equations, existence of global in time flows for large data is a fundamental and difficult question. In general, for dispersive and wave equations high regularity of the data does not automatically guarantee…
In this overview paper, we show existence of smooth solitary-wave solutions to the nonlinear, dispersive evolution equations of the form \begin{equation*} \partial_t u + \partial_x(\Lambda^s u + u\Lambda^r u^2) = 0, \end{equation*} where…
In this paper, we introduce a new class of convolution-type inequalities in variable exponent Lebesgue spaces and derive several related estimates, including the \(L^{r(\cdot)}\)--\(L^{p(\cdot)}\) smoothing estimate for the fractional heat…
We present new gradient estimates and Harnack inequalities for positive solutions to nonlinear slow diffusion equations. The framework is that of a smooth metric measure space $(\mathscr M,g,d\mu)$ with invariant weighted measure…
We consider evolutionary systems, i.e. systems of linear partial differential equations arising from the mathematical physics. For these systems there exists a general solution theory in exponentially weighted spaces which can be exploited…
In this work, we consider the numerical solution of an initial boundary value problem for the distributed order time fractional diffusion equation. The model arises in the mathematical modeling of ultra-slow diffusion processes observed in…
In this paper, we consider the estimation of a change-point for possibly high-dimensional data in a Gaussian model, using a k-means method. We prove that, up to a logarithmic term, this change-point estimator has a minimax rate of…
We show some new local smoothing estimates of the fractional Schr\"odinger equations with initial data in $\alpha$-modulation spaces via decoupling inequalities. Furthermore, our necessary conditions show that the local smoothing estimates…
We study the classical optimization problem $\min_{x \in \mathbb{R}^d} f(x)$ and analyze the gradient descent (GD) method in both nonconvex and convex settings. It is well-known that, under the $L$-smoothness assumption ($\|\nabla^2 f(x)\|…
In this paper we consider a nonlocal evolution problem and obtain by a scaling method the first term in the asymptotic behavior of the solutions. The method employed treats in different way the smooth and the rough part of the solution.
In this paper is proposed a new heuristic approach belonging to the field of evolutionary Estimation of Distribution Algorithms (EDAs). EDAs builds a probability model and a set of solutions is sampled from the model which characterizes the…
This paper considers the distributed smooth optimization problem in which the objective is to minimize a global cost function formed by a sum of local smooth cost functions, by using local information exchange. The standard assumption for…
First order optimization algorithms play a major role in large scale machine learning. A new class of methods, called adaptive algorithms, were recently introduced to adjust iteratively the learning rate for each coordinate. Despite great…
We establish new, optimal gradient continuity estimates for solutions to a class of 2nd order partial differential equations, $\mathscr{L}(X, \nabla u, D^2 u) = f$, whose diffusion properties (ellipticity) degenerate along the \textit{a…
In this paper, we would like to study the linear Cauchy problems for semi-linear $\sigma$-evolution models with mixing a parabolic like damping term corresponding to $\sigma_1 \in [0,\sigma/2)$ and a $\sigma$-evolution like damping…