15 citations · 35 across the 12 of their papers we have counts for
12 papers
Dimension Independent Data Sets Approximation and Applications to Classification
Patrick Guidotti
We revisit the classical kernel method of approximation/interpolation theory in a very specific context motivated by the desire to obtain a robust procedure to approximate discrete…
On Wiener's Violent Oscillations, Popov's curves and Hopf's Supercritical Bifurcation for a Scalar Heat Equation
Patrick Guidotti, Sandro Merino
A parameter dependent perturbation of the spectrum of the scalar Laplacian is studied for a class of nonlocal and non-self-adjoint rank one perturbations. A detailed description of…
On the Maximal Parameter Range of Global Stability for a Nonlocal Thermostat Model
Patrick Guidotti, Sandro Merino
The global asymptotic stability of the unique steady state of a nonlinear scalar parabolic equation with a nonlocal boundary condition is studied. The equation describes the evolut…
The Smooth Selection Embedding Method with Chebyshev Polynomials
Daniel Agress, Patrick Guidotti, Dong Yan
We propose an implementation of the Smooth Selection Embedding Method (SSEM) in the setting of Chebyshev polynomials. The SSEM is a hybrid fictitious domain / collocation method wh…
A Novel Optimization Approach to Fictitious Domain Methods
Daniel Agress, Patrick Guidotti
A new approach to the solution of boundary value problems within the so-called fictitious domain methods philosophy is proposed which avoids well known shortcomings of other fictit…
Improving LBP and its variants using anisotropic diffusion
Mariane B. Neiva, Patrick Guidotti, Odemir M. Bruno
The main purpose of this paper is to propose a new preprocessing step in order to improve local feature descriptors and texture classification. Preprocessing is implemented by usin…
Domain Variations for Moving Boundary Problems
Patrick Guidotti
In the past few decades maximal regularity theory has successfully been applied to moving boundary problems. The basic idea is to reduce the system with varying domains to one in a…
Wellposedness of a nonlocal nonlinear diffusion equation of image processing
Patrick Guidotti, Yuanzhen Shao
Existence and uniqueness are established for a degenerate regularization of the well-known Perona-Malik equation proposed by the first author for non-smooth initial data. The resul…
A Class Of Elliptic Equations with Interior Degeneration
Patrick Guidotti
A class of linear degenerate elliptic equations inspired by nonlinear diffusions of image processing is considered. It is characterized by an interior degeneration of the diffusion…
Using an Encompassing Periodic Box to Perform Numerical Calculations on General Domains
Patrick Guidotti
This paper shows how numerical methods on a regular grid in a box can be used to generate numerical schemes for problems in general smooth domains contained in the box with no need…
A New Well-posed Nonlocal Perona-Malik Type Equation
Patrick Guidotti
A modification of the Perona-Malik equation is proposed for which the local nonlinear diffusion term is replaced by a nonlocal term of slightly reduced ``strength''. The new equati…
A Class of Free Boundary Problems with Onset of a new Phase
Patrick Guidotti
A class of diffusion driven Free Boundary Problems is considered which is characterized by the initial onset of a phase and by an explicit kinematic condition for the evolution of…