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Microcanonical gradient descent is a sampling procedure for energy-based models allowing for efficient sampling of distributions in high dimension. It works by transporting samples from a high-entropy distribution, such as Gaussian white…
Although an intimate relation between entropy and diffusion has been advocated for many years and even seems to have been verified in theory and experiments, a quantitatively reliable study, and any derivation of an algebraic relation…
A distributional route to Gaussianity, associated with the concept of Conservative Mixing Transformations in ensembles of random vector-valued variables, is proposed. This route is completely different from the additive mechanism…
A fundamental characteristic of excitable systems is their ability to exhibit distinct subthreshold and suprathreshold behaviors. Precisely quantifying this distinction requires a proper definition of the threshold, which has remained…
The effect of introducing a mass dependent diffusion rate ~ m^{-alpha} in a model of coagulation with single-particle break up is studied both analytically and numerically. The model with alpha=0 is known to undergo a nonequilibrium phase…
We develop a gradient-flow theory for time-dependent functionals defined in abstract metric spaces. Global well-posedness and asymptotic behavior of solutions are provided. Conditions on functionals and metric spaces allow to consider the…
The electron density, its gradient, and the Kohn-Sham orbital kinetic energy density are the local ingredients of a meta-generalized gradient approximation (meta-GGA). We construct a meta-GGA density functional for the exchange-correlation…
Inducing-point-based sparse variational Gaussian processes have become the standard workhorse for scaling up GP models. Recent advances show that these methods can be improved by introducing a diagonal scaling matrix to the conditional…
Systems evolving according to the standard concept of biological or technological evolution are often described by catalytic evolution equations. We study the structure of these equations and find a deep relationship to classical…
We study the gradient flow of the potential energy on the infinite-dimensional Riemannian manifold of spatial curves parametrized by the arc length, which models overdamped motion of a falling inextensible string. We prove existence of…
In this work, we investigate links between the formulation of the flow of marginals of reversible diffusion processes as gradient flows in the space of probability measures and path wise large deviation principles for sequences of such…
Accelerated gradient descent iterations are widely used in optimization. It is known that, in the continuous-time limit, these iterations converge to a second-order differential equation which we refer to as the accelerated gradient flow.…
When studying out-of-equilibrium systems, one often excites the dynamics in some degrees of freedom while removing the excitation in others through damping. In order for the system to converge to a statistical steady state, the dynamics…
This is the first in a series of two papers in which we derive a $\Gamma$-expansion for a two-dimensional non-local Ginzburg-Landau energy with Coulomb repulsion, also known as the Ohta-Kawasaki model in connection with diblock copolymer…
We introduce a new model of aggregation of particles where in addition to diffusion and aggregation upon contact, a single unit of mass can dissociate from a conglomerate. This dissociation move conserves the total mass and leads to a…
We prove linear convergence of gradient descent to a global optimum for the training of deep residual networks with constant layer width and smooth activation function. We show that if the trained weights, as a function of the layer index,…
Pair potentials that are bounded at the origin provide an accurate description of the effective interaction for many systems of dissolved soft macromolecules (e.g., flexible dendrimers). Using numerical free-energy calculations, we…
Dissipative phenomena manifest in multiple mechanical systems. In this dissertation, different geometric frameworks for modelling non-conservative dynamics are considered. The objective is to generalize several results from conservative…
The existence of global weak solutions to a parabolic energy-transport system in a bounded domain with no-flux boundary conditions is proved. The model can be derived in the diffusion limit from a kinetic equation with a linear collision…
We formulate power-law holographic dark energy, which is a modified holographic dark energy model based on the extended entropy relation arising from the consideration of state mixing between the ground and the excited ones in the…