Publications related to Sur quelques équations aux dérivées partielles en lien avec le lemme de Poincaré

Splines Are Universal Solutions of Linear Inverse Problems with Generalized TV Regularization

Michaël Unser, Julien René Pierre Fageot, John Paul Ward

Splines come in a variety of flavors that can be characterized in terms of some differential operator L. The simplest piecewise-constant model corresponds to the derivative operator. Likewise, one can extend the traditional notion of total variation by con ...

2017

The microfluidic nebulator: production of submicrometer sized airborne drops

Esther Amstad

Many powders employed in the food and pharmaceutical industries are produced through spray drying because it is a cost efficient process that offers control over the particle size. However, most commercially available spray-driers cannot produce drops with ...

Royal Soc Chemistry2017

Characterization of the Solution of Linear Inverse Problems with Generalized TV Regularization

Michaël Unser

Ill-posed inverse problems are often constrained by imposing a bound on the total variation of the solution. Here, we consider a generalized version of total-variation regularization that is tied to some differential operator L. We then show that the gener ...

OSA2016

Multi-index stochastic collocation convergence rates for random PDEs with parametric regularity

Fabio Nobile, Lorenzo Tamellini

We analyze the recent Multi-index Stochastic Collocation (MISC) method for computing statistics of the solution of a partial differential equation (PDE) with random data, where the random coefficient is parametrized by means of a countable sequence of term ...

2016

Can Dissipative Properties of Single Molecules Be Extracted from a Force Spectroscopy Experiment?

Giovanni Dietler, Andrzej Kulik, Fabrizio Benedetti, Dmitry Klinov

We performed dynamic force spectroscopy of single dextran and titin 127 molecules using small-amplitude and low-frequency (40-240 Hz) dithering of an atomic force microscope tip excited by a sine wave voltage fed onto the tip-carrying piezo. We show that f ...

Elsevier2016

Bifurcation points of a singular boundary-value problem on (0,1)

Charles Stuart

Following earlier work on some special cases [17,11] and on the analogous problem in higher dimensions [10,20], we make a more thorough investigation of the bifurcation points for a nonlinear boundary value problem of the form -{A(x)u' (x)}'.= f (lambda, x ...

Academic Press Inc Elsevier Science2016

A block algorithm for computing antitriangular factorizations of symmetric matrices

Daniel Kressner, Zvonimir Bujanovic

Any symmetric matrix can be reduced to antitriangular form in finitely many steps by orthogonal similarity transformations. This form reveals the inertia of the matrix and has found applications in, e.g., model predictive control and constraint preconditio ...

Springer2016

Representer Theorems for Sparsity-Promoting $ ℓ _{ 1 } $ Regularization

Michaël Unser, Julien René Pierre Fageot, Harshit Gupta

We present a theoretical analysis and comparison of the effect of

ℓ _{ 1 }

versus

ℓ _{ 2 }

regularization for the resolution of ill-posed linear inverse and/or compressed sensing problems. Our formulation covers the most general setting where the s ...

IEEE2016

MATHICSE Technical Report : Spectral methods for multiscale stochastic differential equations

Assyr Abdulle, Grigorios A. Pavliotis

This paper presents a new method for the solution of multiscale stochastic differential equations at the diffusive time scale. In contrast to averaging-based methods, e.g., the heterogeneous multiscale method (HMM) or the equation-free method, which rely o ...

MATHICSE2016

Existence and Uniqueness Theorems for the Two-Dimensional Ericksen-Leslie System

Tudor Ratiu

In this paper we study the two dimensional Ericksen-Leslie equations for the nematodynamics of liquid crystals if the moment of inertia of the molecules does not vanish. We prove short time existence and uniqueness of strong solutions for the initial value ...

Springer Verlag2016

Sur quelques équations aux dérivées partielles en lien avec le lemme de Poincaré

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Splines Are Universal Solutions of Linear Inverse Problems with Generalized TV Regularization

The microfluidic nebulator: production of submicrometer sized airborne drops

Characterization of the Solution of Linear Inverse Problems with Generalized TV Regularization

Multi-index stochastic collocation convergence rates for random PDEs with parametric regularity

Can Dissipative Properties of Single Molecules Be Extracted from a Force Spectroscopy Experiment?

Bifurcation points of a singular boundary-value problem on (0,1)

A block algorithm for computing antitriangular factorizations of symmetric matrices

Representer Theorems for Sparsity-Promoting $ ℓ _{ 1 } $ Regularization

MATHICSE Technical Report : Spectral methods for multiscale stochastic differential equations

Existence and Uniqueness Theorems for the Two-Dimensional Ericksen-Leslie System

Multi-index stochastic collocation convergence rates for random PDEs with parametric regularity

The microfluidic nebulator: production of submicrometer sized airborne drops

Characterization of the Solution of Linear Inverse Problems with Generalized TV Regularization

Splines Are Universal Solutions of Linear Inverse Problems with Generalized TV Regularization

A block algorithm for computing antitriangular factorizations of symmetric matrices

Can Dissipative Properties of Single Molecules Be Extracted from a Force Spectroscopy Experiment?

Bifurcation points of a singular boundary-value problem on (0,1)

MATHICSE Technical Report : Spectral methods for multiscale stochastic differential equations

Representer Theorems for Sparsity-Promoting $ ℓ _{ 1 } $ Regularization

Existence and Uniqueness Theorems for the Two-Dimensional Ericksen-Leslie System